remote sensing tools for exploration ||

Chapter 6Processing Information and Data

6.1 The Nature of Remote Sensing Data Processing Tracking and processing information in all forms is essential at every stage of a

remote sensing project. Increasingly sophisticated processing capabilities have been both driven by remote sensing requirements and a driving force behind the development of remote sensing. In fact, due to the large volume of information and the large number and complexity of steps involved in transforming it, sophis-ticated data handling capabilities became an absolute necessity for remote sensing long ago. Thus, computer science and engineering have played major roles in re-mote sensing.

Each step in the remote sensing process has specialized processing software which will be discussed below (Figure 6.1):

1) Mission Planning: Transforming mission goals to measurement objectives and

resource requirements via mission scenario instrument package development, first principles modeling of environment and instrument performance with spreadsheets and other modeling tools, trade study, requirements management, and cost/benefit/risk assessment tools.

2) Entire Life Cycle Flight Support: Communication, Command and Data Han-dling (CC&DH), and assessment of spacecraft/instrument performance and health, all involving signal processing and noise removal tools; Navigation, Guidance, and Tracking (NGT) tools with which spacecraft orientation and pointing are derived.

3) Data Reduction: Transformation from raw to processed (normalized) data com-ponents (such as spectra), including tools for display, calibration, background removal, feature identification and normalization techniques.

4) Data Analysis and Interpretation: Transformation of processed data compo-nents to derived measurement maps and models, with image processing tools for numerical/spatial manipulation including filtering, stretching, and mathe-matical operations; geometric rectification and registration, projection, and mo-saicking; n-dimensional analysis, including principal components analysis, trends surface analysis, supervised and unsupervised classification; statistical assessment and error analysis.

P.E. Clark, M.L. Rilee, Remote Sensing Tools for Exploration,DOI 10.1007/978–1–4419–6830–2_6, © Springer Science+Business Media, LLC 2010

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5) Data Management: data product access and archiving with standard protocols requiring parallel processing techniques and involving database development tools.

6.2 Mission Planning: Roadmaps to Requirements The process of turning high level science goals into missions is time-

consuming. Tools and approaches which facilitate and expedite this process for a new mission concept are thus critical for its timely development.

High level goals are typically articulated through NASA-sponsored decadal surveys soliciting input from the science community on scientific priorities for a particular group of targets, such as small bodies. The Science Mission Directorate appoints the NASA Advisory Committees (NACs), closely tied to the National Academy of Science, to lead such efforts as well as to lead or appoint ongoing working groups for various targets (e.g., MEPAG or LEAG). These groups may use existing decadal surveys or initiate new ones. The final reports incorporate community-wide inputs to at least some extent, but are generated by the appointed committees with the approval of NASA. Recommendations typically come in the form of science goals, with some high level discussion of recommended missions, and little to no discussion of mission requirements (Figure 6.2). Obviously, this

Figure 6.1 Major remote sensing activities, tasks, and mission phases as discussed in the text.

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process tends to favor incremental science, that is anticipated developments, rather than ‘breakthrough’ science. One of the ways breakthroughs may be achieved is with the incorporation of new sensor or subsystem technology in a remote sensing mission. Such components could enable major paradigm shifts through some combination of greater access, sensitivity, and less stringent operational con-straints. However, successful selection of a proposed mission is still largely con-tingent on meeting NAC recommendations.

Mission proposals may originate at any level, depending on the program soli-cited and its scope. Very large scale, long term efforts, programs involving many coordinated missions, may be initiated by Executive Order (e.g., Vision for Space Exploration for the Moon and Mars) and obviously generate new or modify exist-ing requirements. Other efforts, typically focused on a particular target and for longer term, are originated within NASA, run by and associated with institutions (e.g., the Mars exploration programs led by JPL). Shorter term efforts for smaller scale missions are originated by individuals (Principal Investigators) and com-peted for specific programs (e.g., the NEAR mission for the Discovery Program for solar system exploration). Programs become part of the operating plan. NASA directorates maintain mission lines that shepherd missions from the concept stage through implementation and operations. Such institutional support is the start of

Figure 6.2 An example of flowdown from high level science roadmap goals (for lunar science) to tasks and tools from which useful requirements such as those shown can be generated.

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the potentially multi-decade process of developing space missions for program-matic goals.

From a practical standpoint, mission objectives are closely associated with cha-racterizing phenomena and identifying signatures of those phenomena to address underlying problems or questions. What is known, estimated, or guessed at about the nature of these signatures points toward the measurement activities and appro-priate sensor technology. Thus many requirements for science missions resemble signal processing requirements involving sensitivity, duty cycle, sampling rate, stability, noise and interference, dynamic range, saturation level, and so forth.

Generating science requirements which can be translated into an engineering concept is an iterative process which involves the use of practical tools, most of which are readily available, as well as good communication skills, which are not always readily available. First steps reasonably involve brainstorming scenarios to envision how an experiment will be designed and operated, using spreadsheets to record resource requirements (time, bandwidth, maneuvers, human involvement, power) as a function of operational modes.

These scenarios can be the basis for simulations, theoretically with analytical (e.g., Bayesian) or numerical (Monte Carlo) (Amsler et al. 2008) approaches tai-lored to specific sets of measurements (e.g., Monte Carlo based MCNP neutron production and detection code). Spacecraft Tool Kit (STK) and MATLAB both provide packages to simulate spacecraft operations. For especially challenging ac-tivities, such as using Rovers on Mars without real time communication, empirical simulations are provided using special facilities that simulate the real environ-

Figure 6.3 Trade study evaluation criteria and spreadsheet as discussed in the text.


ment. Simulations can help to confirm or identify flaws in the design and train the ground crew. The end-to-end test performed on the instrument package in a simu-lated mission environment and on the integrated spacecraft under simulated deep space conditions are critical.

6.3 Mission Planning: Concept to Implementation Typically trade and feasibility studies consider the impact of using more ad-

vanced but less proven sensor and supporting subsystem technologies. The signa-tures of the phenomena and the environment of the sensor have been quantitative-ly characterized with enough detail to suggest constraints on sensor technologies or mission architectures, to determine what capabilities are required to meet mis-sion goals, and perhaps how close existing technologies or systems are to meeting the task. The trades, or impact on resources, are considered with specially tailored Excel or MATLAB spreadsheets used by systems or discipline engineers (Figure 6.3).

Over the last two decades, NASA policy shifted away from driving the state of the art in technology to support science requirements to the fullest extent and to-ward using existing technology to support baseline science with lower risk and cost. NASA uses a standard against which to measure the readiness of technolo-gies for use in missions called Technological Readiness Levels, and other organi-zations have similar rubrics (Figure 6.4). Despite the greater aversion to risk, re-maining technology development programs are supposed to push technologies up the TRL scale while projects with specific needs tend to identify and pull technol-ogies up to meet those needs. Once an approach has gained flight heritage and an-swers a specific need, it tends to become entrenched and its capabilities are en-hanced over time as experience is iteratively gained over multiple implementations. Unless there is a critical need that is not met by existing me-thods, it is very difficult for a mission manager to justify using new technologies, potentially putting at risk the tremendous resources required for deploying systems in space. That said, as the requirements for many missions are unique, many sen-sors are one-offs or low serial number copies, essentially prototypes whose per-formance on deployment will be a matter of research and analysis.

A trend in the opposite direction is that many commercial technologies can be successfully adapted for use in space or other applications. This includes hard-ware, software, and standards. Adapting commercial-off-the-shelf technologies requires great care and judgment: the behavior of components in the deployed en-vironment must be well understood. Quality control is also a factor as problems that are not fatal in, say, consumer applications, could lead to failures when placed in a system’s critical path. Additionally, in the current environment of growing commercial involvement in space, the production capacity for standard capabili-ties is also growing, leading to the availability of flight certified components. The mission planner has a greater flexibility and choice than ever before: custom in-

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house solutions are no longer the only option. A drawback to this approach is that technology development that is not particularly marketable or necessary for mili-tary use (e.g., ultra low temperature electronics and batteries) will not be available to meet NASA critical needs.

Risk, required redundancy, and acceptable margin for any technological solu-tion must be assessed. This risk could be developmental, i.e. the TRL of the solu-tion may be too low when mission implementation begins. The risk could be for implementation, e.g. the production or test capacity may not meet mission dead-lines. Tests may miss latent problems that show up after the system is deployed. Problems could arise at any step along the way. Components could wear out and break down in unanticipated ways. To mitigate such risks, redundancy and mar-gin are two key tools. Greater redundancy would be required where the risk of failure is greater, perhaps because the mission is longer or new technology has been introduced. Margin is the reserve in various resource budgets (mass, power, cost, volume, bandwidth) held to allow for uncertainty, enabling flexibility when problems occur. These margins are ultimately assigned to fully utilize resources allocated for flight. Tools can be brought to bear at programmatic, technological, system or subsystem levels of the mission.

Planning for scoping, or rather de-scoping, is another way to mitigate risk by splitting goals into sub-goals and then prioritizing them. If de-scoping options

Figure 6.4 Technological Readiness Level (TRL) definition (Courtesy of NASA).


(Figure 6.5) are built into the mission plan and are available at key-decision points, then the changes required can be handled more gracefully, hopefully with-out jeopardizing the entire mission. A baseline mission is established to represent the bottom line capability, below which the mission would not meet the science requirements, and would not be considered successful. Progress towards develop-ing the required capabilities should be continuously monitored during mission de-velopment. Particular attention should be focused on critical path developments, that is, items (hardware or software) that must be delivered at particular times to meet scheduled activities required to go on to the next step.

Resource estimates for the mission are compared with the estimated capabili-ties. Software tools exist to help gauge the agreement or conflict between these two aspects of the mission. Spreadsheet models, analytic and numerical tools can help the individual system or subsystem engineer model and estimate costs and benefits. Database and requirements analysis software can collect information from multi-disciplinary, distributed teams of engineers, check for inconsistencies and gaps, flag potential problems, and generate summaries, reports, and documen-tation.

Risks are identified, and their potential impact and likelihood are recorded us-ing spreadsheet-based packages, often homegrown, and fault tree analysis (Figure 6.6). Value/Cost assessment tools, such as HURON, are used to assess simulations or proposed operational scenarios. Finally, special packages, such IBM Rational DOORS, Siemans Slate, and Vitech Core, keep track of requirements evolving at every level (Figure 6.7), from component to subsystem to system, during the course of mission development. Developing a mission concept and plan is

Figure 6.5 Typical mission descope options and science implications.

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therefore an evolving process in which the entire mission team modifies require-ments to meet evolving goals in the face of growing needs with constant re-sources. Thus, the ability to keep track of risks, priorities, resources, and adjusted requirements is a critical capability. It must be said, that, even with tracking tools, the team will be only as good as their communication skills and discipline.

6.1 Close to home: Unforeseen Consequences. Space missions can spend dec-ades in conceptualization, development, and operations. With mission lifetimes approaching career lifetimes, developing the next generation of engineers and scientists becomes a problem. How can you become a rocket scientist, if you don’t get to work on any rockets? NASA’s Sounding Rocket Program, initiated in 1959, resulted in the development of about 2800 flight missions with a launch success rate of over 95% (NRC 1969; NSRPH 1999; NSRP 2008; Ransone and Gregory 2005). Sounding rockets are smaller, inexpensive, and a mission from concept to flight can fit within a student’s time frames. An average payload is currently about 800 pounds. Altitudes of 1800km can be obtained with over 20 minutes of time in space. The typical 3-year experimental sounding rocket project costs about $3 million and offers training to 3-5 doctoral and master’s student in the complete life cycle of a space mission. Many technological and scientific firsts have been achieved with sounding rockets, and they are the only way to access

Figure 6.6 Risk likelihood and impact as discussed in text.


Earth’s mysterious mesosphere which is too high for balloons and too low for sa-tellites. Even though suborbital rockets are an excellent platform for training space scientists and systems engineers, NASA’s sounding rocket program has only been launching roughly 20 flights a year for the past 25 years. Compare this to ~2300 flights flown in the 25 years before that. The Space Studies Board of the National Research Council has recommended that NASA place a high priority on developing aerospace talent and identified sounding rockets as one way to provide critical experience (NRC 2007). The University Space Research Association (Zurbuchen 2009), concurs, advocating that NASA’s suborbital opportunities be tripled while also pointing out that the aging American aerospace and defense workforce is losing 27,000 skilled and experienced employees a year.

6.4 Flight Support for the Mission Life Cycle The trials which spaceborne remote sensing instruments must undergo are de-

manding and unique. As stated above, mission requirements often drive the dep-loyment of systems that are essentially prototypes. The behavior and performance of the deployed sensor usually differs from expectations, either because there are lessons to be learned about how the system behaves in its target environment, or because of hazards the system encounters during deployment and operations. Be-cause wireless communication is usually the only way to interact with spaceborne systems, an immense burden is placed on information aspects of the mission. As wireless communication is also a physical link, important physical information may be determined from the link itself. Flight operations support is a demanding, resource intensive enterprise designed to address the lack of physical access and demanding environment of deployed flight systems. The primary goal of opera-tions is to execute the mission plan to achieve goals. Though the deployed system generally has some ability to operate without operator intervention for some pe-riod of time, most operations are implemented by loading the deployed control

Figure 6.7 Requirements management schematic.

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computers with sequences of time-tagged commands. These command sequences are carefully constructed and tested in high-fidelity simulators or even flight-quality spares. Errors in command sequences can lead to loss of mission, there-fore great care is taken to determine the current state of the deployed system, in-cluding its configuration, location, attitude, trajectory, as well as a host of other parameters from which system health, safety, and performance can be assessed. In nearly all situations, making these determinations depends on maintaining communications with the deployed system. Many times, the first indication that something has gone wrong with a spacecraft is when it misses a scheduled com-munications opportunity or does not respond to commands. When an operational constraint has been violated, spacecraft are designed to go into safe mode, general-ly a command sequence involving locking onto the sun, charging up batteries, shutting down for 24 hours, and then calling Earth. When a spacecraft signal is not received from the predicted location in 24 hours, a variety of strategies are em-ployed to locate it in the surrounding area. In depth real time error analysis will be performed, and often does offer the insight necessary to locate the craft if it is still alive.

6.2 Close to home: Desperately Seeking SOHO. In 1998, the Solar and Heli-

ospheric Observatory (SOHO) spacecraft, which points an array of telescopes and spectrometers at the Sun, was commanded to perform a routine calibration of the three roll gyroscopes used to measure the spacecraft’s (roll) rotation rate (Trella and Greenfield 1998). Reaction wheels are used on the SOHO spacecraft to store angular momentum acquired over the course of mission maneuvers and pointing changes. In a process called momentum management, this angular momentum is then periodically dumped into space via attitude control thrusters, allowing the reaction wheels to be spun down. Approximately every two months, the error or drift bias of the rotation rate sensors are measured by placing the spacecraft into a calibration mode. Then, mission operators analyze the telemetry, determine the new bias parameters, and upload these to the spacecraft, so that the onboard flight software correctly interprets the rotation rate sensor readings. The routine calibration was performed and afterward one of the gyros was de-spun to extend its life. Unfortunately, in an effort to maximize the availability of the spacecraft for science operations, a procedure that had been broken out into multiple 12-hour segments had been compressed to a single continuous sequence. In the mod-ified sequence, a command that allowed SOHO on-board flight software to spin-up the de-spun gyro was omitted. Also, a second gyro was left in a high resolution calibration mode in which its rotation rate measurements were multiplied by a factor of 20. When the angular momentum was dumped during the momentum management maneuver, fault detection software interpreted the magnified rotation rate as an error. Flagging an emergency, the spacecraft then tried to enter a safe mode and point itself at the Sun. The faulty mode in the gyro was corrected and the spacecraft used measurements from the third gyro to control its rotation to-ward the Sun. The spacecraft did not, however, know that the first gyro had not


been reactivated and interpreted its despun null as a rotation to be corrected. One minute of thrusting had the spacecraft spinning fast enough to trigger another roll rate fault. Not realizing the first gyro was not currently spinning, operators concluded that the second gyro had failed since it disagreed with the first. The second gyro was commanded off, and the spacecraft was commanded to stop its spinning using measurements from the inactive first gyro! The pointing error in-stead increased. In three minutes, the spacecraft attempted to safe itself again, and five minutes after that all communications with SOHO was lost. “At any time during the over five hour emergency situation, the verification of the spinning sta-tus of Gyro A would have precluded the mishap”(SOHO Mission Interruption Joint NASA/ESA Investigation Board Final Report).

6.5 Flight Support: Communication, Command, and Data Handling

The role of communications is to provide access to the deployed sensors and its

platform, so that commands and data may be exchanged between the remote sys-tem and its operators. Early spacecraft were not programmable, often using timed sequencers to operate spacecraft subsystems and transmitting telemetry data as it was collected. Thus, the communication was one-way, downlink to ground. As mission requirements became more demanding, more complex approaches were implemented and spacecraft became commandable and programmable with an on-going trend toward automated operations, and eventually autonomous, operations (Griffin and French 2004, Ellwood et al. 2008, Leary 2008). Currently, command and data handling computers manage and execute commands and interact with the other subsystems of the deployed system. Such interaction can include copying

Figure 6.8 Command and Data Handling functions (from Brown 2002, Table 8.12, reprinted with permission of American Institute of Aeronautics and Astronautics, Inc.

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data or programs to and from subsystems, higher level communications such as status requests or other commands, or even electrical power control in which C&DH literally toggles the power to a device or subsystem (Figure 6.8). A criti-cal parameter is the communications data rate available between the mission oper-ations and the deployed system. Uplink and downlink each have their own band-width (data rate), latency (lag time), and availability.

Communication is divided between different functional roles of the system with engineering and science being the main division for remote sensing missions. Engineering data focuses on health, safety, operational status, and various control parameters and measurements. Science data is generated from onboard instru-ments. Where science data are stored and processed depends on the mission archi-tecture (Figure 6.9). Obviously, science data is strongly payload and mission phase dependent. Contextual or reference data gathered from the spacecraft (mis-sion elapsed time, system or subsystem status, navigational parameters, thermal conditions) as well as the instrument (component status, data status), sometimes

Figure 6.9 Current communications architecture (Lesh 2006), Figure 1.1, in Deep Space OpticalCommunications, Copyright 2006 Wiley, reproduced by permission of Wiley.


called ancillary or housekeeping data, is required to render the science data intel-ligible (Figure 6.10).

On current deep space missions, essential ancillary navigational and positional data are provided through SPICE kernels and NAIF software made available to investigators as the data is being collected (Acton 1996). The kernels are files con-taining inputs on the Spacecraft (position and velocity of spacecraft and target bo-dies as a function of time), Planet or target (selected target physical and carto-graphic constants), Instrument (pointing, field of view, timing, command dictionary), C-matrix (inertially referenced spacecraft attitude, pointing as a func-tion of time), Events (science plan, command logs and mission operations note-books), and Timing (spacecraft clock inputs and coefficients needed for timing conversions). The NAIF software toolkit allows access to the data in these nodes and calculations requiring knowledge of spacecraft/instrument/ target/source geo-metries, such as target footprint and its aspects in latitude and longitude.

Spacecraft communications are now subjected to world-wide standardization. As spacecraft and their functions become more sophisticated, so do the require-ments on the data structure (e.g., CCSDS 2006). Mark-up languages, command and data schema, and modeling technologies such as UML or ontologies (OWL)

Figure 6.10 Types and sources of ancillary data as discussed in text.

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have been brought into play to manage the complexity of communicating with re-mote modern spacecraft systems. Data object design (i.e., schema specification) is an important part of the information architecture of a modern spacecraft (Brown 2002) (Figure 6.11).

Subsystems or sensors are often allocated communication bandwidth according to mission phase, priorities, or operating mode. For the most part, spacecraft communications are packet-based, much as most computer network information traffic is contained in standards-conforming packets or frames. Different subsys-tems may be allocated their own packetized virtual communications channels. The packets of information contained in these virtual channels may be distributed across one or more frames and then reconstructed during a decommutation step af-ter being received. Note that the packetization or framing used in the communica-tions system is independent of the packetization of data sent over the communica-tions channel. This allows the communications subsystem to choose a transmission scheme appropriate to its conditions and resource allotment, for ex-ample, a deep space mission may resort to more robust communication methods as the mission progresses and the deployed components are further from the Earth. Payload information/packets are normally returned sequentially, as gathered along an orbital or flyby trajectory. In general, each observation has a unique identifier and an accurate time stamp. Sensor information contained in the packet depends on the sensor operating mode and the C&DH logic. In general, each packet covers only a fraction of the target phenomena. Higher order information must be recon-structed later from the ancillary information on orientation and position of the dep-loyed sensor. Temporal variation can be assessed later as part of higher order data analysis by creating a time lapse movie from a selected perspective.

Figure 6.11 Spacecraft command and communications schema as discussed in text.


A good fraction of the flight software is devoted to operating system-like tasks with subsystem control and is built on a real-time operating system such as VxWorks (Wind River). Onboard logic is included to verify commands sent to the spacecraft, and the commands are typically loaded into table-driven executive controllers. In addition to command management and execution, health and safety (H&S) functions are generally a critical part of the onboard operating logic, in-cluding Fault Detection, Isolation, and Recovery (FDIR). H&S logic monitors da-ta being generated by the spacecraft for anomalous values. These data may origi-nate in the science instruments, but the primary focus is on data from engineering sensors (Figure 6.12).

Attitude Control is also a critical function for most missions. Its control logic can be one of the more computationally expensive modules of the software be-cause the spacecraft regularly checks its attitude data and then calculates, plans, and executes corrections as necessary. These functions are generally more math-intensive than much of the operating logic of the spacecraft, though some signal processing and data encoding/decoding for communications can also be demand-ing. For standardized tasks such as communications, specialized and efficient electronics allow the transfer of the computational load from a central control computer and into the subsystem. Communication latency between operator and spacecraft introduces an offline period which must be minimized to decrease the response time in case of spacecraft failure. To handle contingencies, the AC logic must have a certain amount of autonomy with closed-loop control, to provide a

Figure 6.12 Schematic of control loop for onboard rendezvous and docking (Fehse 2003), Figure 6.1 in Automated Rendezvous and Docking of Spacecraft ©Cambridge University Press.

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limited command of the spacecraft over short timescales in nominal circumstances described as fail safe mode above (Brown 2002).

6.6 Flight Support: Use of Signal Processing Spacecraft communications require the transmitting and receiving of a variety

of signals, from measurements of natural processes to system status data, signals must travel over great distance on radio or microwave carrier waves at given fre-quencies or bands, including X-band (3.5 cm), S-band (12.5 cm), and Ka band

Figure 6.13 Schematic of carrier wave modulation (From Brown 2002, Figures 9.10 and 9.11,reprinted with permission of American Institute of Aeronautics and Astronautics, Inc.)


(1.5 cm). A monochromatic carrier wave of fixed amplitude carries no informa-tion. In order to transmit information, we impose artificial temporal structure on the wave, called modulation, analogous to the cyclical temporal structures ob-served at different scales or frequencies in signals from natural processes, such as planetary rotation, or ocean waves.

Modulation can be performed in two principal ways. Phase modulation mani-pulates the phase of the signal, while frequency modulation works with small shifts of frequency (Figure 6.13). Changing the phase or shifting the frequency broadens the carrier wave by an amount proportional to the rate at which the shifts occur. All of the information contained in the carrier can be obtained at the re-ceiver by sampling an incoming signal at twice the frequency of the carrier wave. This sampling rate is called the Nyquist frequency, and in general the incoming signal must be sampled more often to generate higher quality data (Bose 2004, Boulet 2006). Extracting all of the information from the carrier is the basis of software defined radios, which allow full access to the radio spectrum for a maxi-mum of flexibility and dynamic reconfigurability (Mitola 2000). This rate is ex-cessive for most spacecraft applications (greatly increasing need for bandwidth and power), so a more traditional and specialized approach is taken. Instead of sampling the incoming signal directly, a receiver mixes the incoming signal with a locally generated reference signal producing signals at the sum and difference of the local signal frequency (constructive and destructive interference) and the in-coming carrier wave frequency. A low pass filter keeps the frequency-difference component, which is at a much lower frequency than the carrier and can be more easily sampled. Thus, sampling can occur at a rate based on the modulation band-width that carried the information, perhaps measured in MHz or less, instead of at more than twice the full rate of the carrier wave, which may be many GHz. This description is a simplification because multiple mixing stages may be involved and the modulation bandwidth may itself contain several subcarriers.

A carrier wave is modulated by encoding the information to be communicated (Figure 6.13). The modulation schemes can be quite flexible, for example, in bandwidth division the modulation itself is composed of multiple frequency bands (as in natural processes). Different encoding schemes may be used in each of these bands, for example, encryption, digital, or even analog techniques may be used. The modulating signal may be digitized and extra bits added for error cor-rection and message formatting. Convolutional encoding spreads the information associated with each bit in the signal across several bits by algorithmically map-ping numbers to numbers that must obey certain rules or constraints to be valid. The loss of one or more bits during communications can often be detected and corrected by checking these rules. Reed-Solomon is a standard algorithm so com-monly used that flight qualified application specific integrated circuits (ASICs) are readily available. When an algorithm is not so common, or greater flexibility is required, algorithms may be implemented on programmable electronics, such as digital signal processors (DSPs), field programmable gate arrays (FPGAs), or gen-eral purpose computers if a project cannot afford the time and expense of con-

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structing and verifying its own special purpose ASICs. Beam forming is a special purpose application, in which multiple signal phases are synthetically adjusted to point a multi-antenna array for reception or transmission. A carrier waveform can be used or modified for applications other than communication, including ranging, navigation, trajectory determination, and other radio science applications. These are discussed in Chapter 5.

Other modes of wireless communication are or potentially could affect mission design. Some commercial software-defined radio technology is enhancing our ability to specialize communications subsystems to specific purpose while using a common hardware base. Cell phone use is driving low-power technologies and protocols. GSM (Global System for Mobile Communications) protocols, the most popular standard for mobile phones, promise to enhance the data rate per watt ra-tio (Sessler et al. 2007), and may have a higher level of operational automation based on existing standards. Other modes for telecommunications have already been used on remote sensing missions. The first is a beacon mode which makes use of a lower frequency signal, typically omnidirectional, that may be used to convey a limited amount of information (Sherwood et al. 2000). This mode has been used to monitor spacecraft health in deep space missions (Kletzing et al. 2005, Park et al 2002). It can be useful for remote sensing missions that require the coordination of multiple sensor platforms , such as the IRAS system onboard the MMS mission. An alert of a sensor event detected on one spacecraft could be broadcast via the beacon to the other spacecraft. This would require some event detection logic, as well as alert-response logic. However, such communications strategies can be very expensive, particularly for omnidirectional transmission. Another interesting special-purpose communications strategy developed for ex-tremely high data rates modulated an RF carrier with the output of a wide band re-ceiver (Barrington and Belrose 1963, Rönnmark 1990). This experiment was de-signed to study radio wave fluctuations of the plasma about the spacecraft, and instead of digitizing the receiver’s output, that output was transmitted to Earth on the spacecraft’s main carrier signal. This experiment only produced data when the sensor was operating and the spacecraft was transmitting to a terrestrial ground station with the appropriate receiver electronics. This was a special-purpose solu-tion with a special set of operating requirements, but it does remind us that packet-based solutions are not the only answer.

6.3 Close to home: Ultimate Confirmation. The former GSFC director was of-

ten seen visiting mission control during critical phases of deep space missions. He has said that during missions that enter the atmosphere, he watches a display of the frequency of the carrier wave. If the carrier wave frequency doesn’t start to change when the spacecraft is scheduled to enter the atmosphere of the target planet, adjusted for communication lag times, then the spacecraft missed the pla-net. We don’t have to wait for the spacecraft to phone home.


6.7 Signal Processing: The Relationship between Signal and Noise

Noise, anything which obscures or distorts the meaning of a message or signa-

ture of a process being conveyed in a signal, is such a pervasive issue that it is given its own section here. Noise is a crucial concern for telecommunication sys-tems. Instrument data can be received and analyzed after collection, whether good or poor in quality. In practice, if the signal level falls below the noise level in a telecommunication system receiver, data can no longer be decoded and is effec-tively lost.

Why is noise so pervasive? Noise is experienced as an anticipated or even an unintended consequence of operating in an uncontrolled environment with many degrees of freedom affecting a sensor’s output. The data obtained from the sensor may vary greatly in quality. Conditions that compromise data quality are dealt with through data processing. Though we intend our sensors to produce the most clearly intelligible data given our resources and technology, we usually do not re-ally know how any given system will perform until it is deployed. We may fore-see some aspects of its operation, but others we may not, making data processing, post-processing, and analysis critical for generating usable results.

Generically, Signal noise, defined as fluctuations and additions of extraneous inputs to the information on the target received at a detector, are experienced as random or patterned interference to the signal. There are several sources and kinds of noise that may impede interpretation of sensor data. We can model an additive noise (Equation 6.1): s = s0 + n (6.1)

n is a noise term representing fluctuations that may create difficulty in deter-mining the ideal response, s0, given the signal, s. Often, the noise level is ex-pressed as signal to noise ratio (SNR), the power ratio between a typical signal and the background noise, a way of seeing how far the signal stands out (Figure 6.14).

In applications, including image processing, SNR has come to be defined as the ratio of the mean pixel value to the standard deviation in pixel values. If we sup-pose that the noise in the additive noise model above, has zero-mean, and that its variation is uncorrelated with the signal, then we can write for example (Equation 6.2), SNR 2> – <s>2)-0.5 : s0/(<n2>)-0.5 (6.2)

‹ › denotes a calculated expectation value (e.g., Gray and Davisson 2004). The denominator can be identified as the root mean square (RMS) noise.

Dynamic range, the ratio of the greatest undistorted signal to the noise, is also a measure of the noise environment. In decibels (DB), the SNR is by definition 10

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times the logarithm of the power ratio and 20 times the logarithm of the amplitude ratio which is squared (Equation 6.3). SNR = 10 log10 (Psignal/Pnoise)dB = 20 log10 (Asignal/Anoise)dB (6.3)

When the signal is linearly related to the power, as it is for most optical sen-sors, the SNR is 10 times the log of the ratio. When dealing directly with the wave amplitudes, e.g. as in interferometric systems like synthetic aperture radars, the amplitude of the electromagnetic wave is proportional to the voltage, so that the SNR is 20 times the log of the ratio.

Analog to digital conversion involved in digital data storage or compression in-troduces noise, here loss of information, due to the uncertainty of where the conti-nuous (analog) measurement falls within values associated with the least signifi-cant bit. This is called quantization error (Schreir and Temes 2005, Christiansen et al. 2005). The number of values an integer (n bits in size) may take on is 2n, and the range of values is called the data or dynamic range. For example, a linear mapping from an integer value to signal measurement follows (Equation 6.4). scontinuous = smin + I (smax – smin)/(2n – 1) = smin + Q sint (6.4)

The extrema (smin and smax) of the data range selected will depend on which values of the sensor output need to be resolved to meet mission requirements. The mapping need not be linear. For example, if knowledge of the detailed statistical

Figure 6.14 Signal to noise ratios based on power of (top to bottom) 0, 1, 3, 10, and infinity (linein bottom row) represented by sinusoids.


fluctuations measurements are not required, then the data values, sint, may map to intervals or bins with a size associated with the size of those fluctuations. Loga-rithmic scaling is one way to extend the dynamic range, though at the expense of a loss of detail when neighboring data values are treated as virtually the same. At the low end of the data range, the number of available bits and thus the amount of detail with which the noise floor of a system can be measured is limited. Setting the value of smax too high will cause a paucity of data, while setting the value too low will cause saturation.

When n is larger, the number of values 2n represented by an integer is larger. In that case, the integer is a more sensitive indicator of variation in the data. One way to measure this effect is to construct the ratio of the extrema of the data range described above, setting the minimum of the data range to an internal noise or er-ror. This ratio (the Dynamic Range) of maximum to minimum signal can be ex-pressed in dB. If we consider the quantization noise, we note that as dynamic range increases the number of bits the measurement can support increases (Equa-tion 6.5): DR = 20 log10 (smax/smin) dB = 20 log10 2n db (6.5)

This is also the best signal-to-noise ratio achievable with a linear quantization scheme. With floating point numbers of n bits, with n-m bits in the mantissa and m bits in the exponent, greater dynamic range can be achieved at the expense of the signal to noise ratio (Equation 6.6): DR = 2m SNR -m) dB (6.6)

Here we see a mixing of the linear and logarithmic scaling mentioned before, with the bits of a data value apportioned between them.

6.8 Signal Processing: Noise Sources and Types Noise comes in many forms affecting all aspects of a mission: mechanical vi-

brations and acoustic noise, electronic noise originating from all onboard electron-ics, variations at the source or in the environment, originating from fluctuations or interference by natural processes in the source/target/detector system and the sig-nal processing intrinsic to the sensor and its own electronics.

External variations from the source or environment include temperature, at-mosphere, wind, gravity, energetic particles, which induce changes in the hard-ware performance. Control over these variations is achieved by recognizing the pattern of the noise, possibly using Fourier transform analysis and filtering or processing the signal to remove it. Lengthening the integration time will generally reduce the impact of such noise.

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Electronic components are a fundamental part of nearly all sensor and mea-surement systems. Electronic signal fluctuations, inducing electronic noise, are fundamental and necessary to their operation. Understanding how electronics be-have and interact with their environment is important. This noise comes in many forms, including thermal (Johnson) or shot noise, burst noise, avalanche noise, or ambient electromagnetic interference.

Thermal noise is induced by random movement of the electron carrying the current and resulting in random variations in current or voltage, regardless of ap-plied voltage. A key to dealing with this kind of noise is lowering the temperature to reduce the activity and energy level of interactions of electrons. Active or pas-sive cooling are used to decrease the noise, and thus increase sensitivity and signal to noise ratio, for many remote sensing detection systems.

Shot noise results from random fluctuations of the current through an electrical conductor because electrons have discrete charges. Although it is correlated with current, it doesn’t increase at the same rate as the signal and is thus a particular problem only at relatively small currents.

Burst noise involves sudden large transitions in voltage for periods of millise-conds. These events that occur at random and unpredictable intervals arise in semi-conductors and are worse at low temperatures. The standard theory for burst noise predicts that as transistor size decreases the frequency of the fluctuations should increase. However, according to a recent discovery, this frequency be-comes constant. Furthermore, the fluctuations become more pronounced as device power decreases, indicating a serious problem with the standard theory. (Campbell et al. 2009a,b).

Avalanche noise occurs when an electronic component, say a diode or a semi-conductor junction, nears its breakdown voltage. In this regime, current carriers accelerate rapidly and can create new current carriers by collision, leading to a cascade or avalanche of current. We take advantage of this effect in photo-multipliers and other sensor technologies to construct detectors. Calibration sources have been made from semiconductor junctions driven at breakdown. Building an adaptive gain to limit electrical current will help protect the health and safety of detectors vulnerable to this effect.

Fluctuations may affect observations in a number of ways, depending on the physical couplings involved. For example, flicker noise results from fluctuations in direct current due to impurities or boundary effects at interfaces in conductors, resistors, and semiconductors. This is a source of noise in photo-detectors (Sze and Ng 2007) affecting measurements of light intensity. In a wide range of signal processing applications flicker, as well as other processes, can affect the temporal characteristics of the sensors.

Time or Frequency Noise, including phase noise, is induced by instability in signal-generating mixers, oscillators, samplers, and logic circuits, and results in rapid, short-term, random fluctuations in wave phase caused by jitter (time do-main instabilities). Such signal generating components do not produce perfect waves at a single frequency, but spread the power to adjacent frequencies resulting


in sidebands around a central frequency peak. Such noise power is expressed as offset from the carrier (or ideal) frequency in dB. As previously mentioned, flick-er, also called 1/f or pink noise, features a noise power spectrum fall off at higher frequencies resulting from fluctuations in direct current. Typically, a low frequen-cy phenomenon correlated with DC level, flicker can be overshadowed by white noise at higher frequencies. A strategy for minimizing the effects of flicker, such as non-linear carrier frequency modulation, minimizes current (Figure 6.15) (McClaning and Vito 2000, Schiek et al. 2006, Sze and Ng 2007).

Mechanical or structural systems are susceptible to vibrations, particularly dur-ing launch (Figure 6.16). Even at equilibrium, each mode or degree-of-freedom of the system will have at least ½ kT of energy associated with it, where k is Boltzmann’s constant and T is the temperature. Through the normal course of op-eration, energy will be deposited in a structure exciting the various modes of vi-bration which in turn couple with the sensor and appear in measurements. A va-riety of physical couplings could be at work. Mechanical flexing of mirrors, swaying of booms, or vibration of electrical components could give rise to an elec-tromagnetically induced signal. Vibration could be acoustic, like a high-frequency sound, a low-frequency flexing, or impulsive and shock-like. Depending on the structure, the spectrum of the vibrations will change as some modes will dampen more rapidly than others, changing the signature of the noise. Shocks and vibra-tions result from interaction with introduced energy sources, occurring, for exam-ple, when a spacecraft emerges from eclipse or shadow into sunlight. Once the

Figure 6.15 Flicker (pink noise) and brown noise signals in time (top) and their frequency spec-tra (bottom) (e.g., Timmer and Konig 1995).

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signatures of these effects are established, they can be removed from the data. On the other hand, vibrations and noise may also require more careful analyses and modeling, particularly in cases where greater sensitivity requires the elimination of false detections.

Errors, fluctuations, or noise in components in one system can affect the per-formance of not only that system, but others, in random or systematic ways. For example, radiometric (intensity and energy) errors can be induced by electronic noise within the instrument or spacecraft, or spatial (pointing) errors induced by spacecraft mechanical systems or even attitude control. Errors in ancillary data, for example, in attitude determination, may affect the usefulness of a data set, even if a science sensor is working properly. The loss of a Sun sensor may mean that the data can no longer be registered in any reference frame other than the spacecraft’s (Boardsen and Kessel 2002).

We have only touched on some noise phenomena that may affect sensor mea-surements. Changes in the environment, the sensor, or its platform can lead to changes in sensor response. Temperature changes may cause frequencies to shift. Plasma density may inhibit wave propagation. Amplifier gains may drift over time. Sensor nulls may drift leading to zero-offset changes. Keeping careful track of sensor response through periodic calibration over the course of a mission is crit-ical.

Figure 6.16 Variations caused by Delta II 7920 and 7925 (with 9.5 ft fairing) during launch. The threshold for ear pain is 130 (Griffin and French 2004, Figure 4.21, Courtesy of United Launch Alliance.


6.9 Signal Processing: Types of Error Generally, measurements are subject to two types of errors: those of accuracy

and those of precision. Accuracy is the measure of absolute error, how well a measurement or set of measurements represent a true value, either calculated or previously measured. Precision is the indication of relative error, the degree of spread or reproducibility in given set of measurements, or the magnitude of devia-tions from the average value. A given set of measurements may have high preci-sion, showing relatively little variation and small relative error, and yet be highly inaccurate, offset considerably relative to the calculated or previously measured correct value, with a large absolute error. This is known as a systematic error. On the other hand, the average of a given set of measurements may represent the true value accurately, but be highly imprecise, with large variations among measure-ments.

For a well designed experiment in the laboratory, good accuracy and precision normally go hand in hand. Despite the availability of precision instruments, be-cause the remote sensing environment is not subject to the kind of control achiev-able in a laboratory, precision is more difficult to achieve, and the relative error bars are larger. Pre-flight and in-flight calibration with known sources should preclude obvious systematic errors or problems with accuracy. Still, calculation of absolute values from remote sensing measurements is extremely challenging, because of the many uncertainties and the need to make assumptions about the processes in the relatively large measurement footprint. As a result, various error-minimizing strategies are used when designing remote experiments or deriving useful information from individual instrument or combined instrument datasets.

Comparison of data from different instruments is best done when the measure-ments are taken simultaneously from the same platform viewing the same target, the basic concept of a remote sensing mission. Depending on the circumstances, for a given set of measurements, differences or ratios may be more accurate than the measured values themselves. A good practice is to estimate the variation or uncertainty from the data itself. The variation in the observed data may be larger or smaller than predicted using statistical arguments. Differences between empiri-cal and a priori statistics should be understood in order to distinguish statistically significant trends and patterns from normal fluctuations.

In order to develop a successful error-mitigation strategy in hardware design, the nature of potential errors in the environment and in instrument performance must be known. An engineer can build extra margin or tolerance into a system or procedure if the quantitative extent of an error source is uncertain. However, if the engineer misapprehends the qualitative nature of an error, then perhaps no amount of design margin or operational adjustment can correct the effects.

Stochastic error, affecting precision, is perhaps the simplest type encountered. It is seen as random fluctuations whose precise values are unpredictable but may be statistically distributed. It can arise from noise described elsewhere. From the viewpoint of statistical mechanics, we can never completely characterize the posi-

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tion and motion of all the parts, e.g. the atoms, of the sensor system. This lack of knowledge leads to unavoidable fluctuations whose properties are based on the statistical physical properties of the system. In these days of nano-technology and quantum effect devices, quantum uncertainty can also appear as a stochastic error in a sensor’s measurements. The variation of the fluctuations associated with sto-chastic error can recommend an appropriate level of precision.

Systematic errors, affecting accuracy, can be more troublesome than stochastic errors, because systematic errors do not cause measurements to fluctuate in the vi-cinity of correct values. Systematic errors lead to some shift or offset in the values obtained. The answers are simply wrong and may lead to incorrect inferences. The scale of the systematic error may not be apparent, and in some circumstances may greatly exceed the precision and variability of the data set. On the other hand, accounting for and correcting systematic errors may be quite easy with a suitable guide, standard, or calibration.

Secular error is a special kind of systematic error affecting accuracy that changes over time. Secular errors accumulate over time, generally growing. If we follow dynamical systems terminology, we might find the rate of growth of the er-ror is constant leading to a linear increase in error. However, the usage is not strict. In general, if the error is changing over time without a periodic pattern, we can identify the trends as secular. The existence of secular error may point to a failing instrument or sensor.

Periodic errors are systematic errors affecting both accuracy and precision that resemble secular errors except that the error increases and decreases in a periodic fashion. Mechanical vibration and orbital dynamics are two sources for such er-rors. Many times, a periodic error will be identified when an unexpected cycle or period appears as a periodic anomaly in the measurements. When such a signal appears, scientists and engineers search for an explanation. If a physical mechan-ism can be worked out to explain the anomaly, then the source of error is noted and can become part of the data analysis process.

6.10 Signal Processing: Noise Removal Strategies As much as possible must be done to reduce the obscuring effect of noise be-

fore measurements are obtained. After measurements are obtained, the analyst must make do with the information that was obtained, whatever its quality. Here we discuss a few broad strategies for minimizing noise.

Isolation of sensors from sources of noise or interference is one technique to improve data quality. This isolation can arise from configuration, i.e. a magneto-meter may be placed on a boom to keep it far from the electric currents of a space-craft. As an observing platform, JWST will be a free-flyer in deep space at the Earth-Sun L2 point beyond the Moon, isolated from thermal cycles and many sources of mechanical vibration. Shielding is another form of isolation and has different forms based on the application. A Faraday Cage, essentially a conduct-


ing box, will protect its interior from external electromagnetic disturbances. Shielding from energetic neutral radiations requires more extreme measures, for example, thick walls of high-Z materials or underground installations.

Cooling, or more generally thermal control, can be used to reduce the noise generated by the system itself. As discussed previously, thermal fluctuations drive many kinds of noise, and cooling the system will reduce many of these. An infra-red sensor will pick up a background from its own structure and the optics that steer light to it, because they will emit blackbody radiation. And in the vicinity of the Earth, most things will acquire a temperature at which they glow copiously in the infrared. Thermal control involves a variety of technologies ranging from the use of sun shades, heat pipes, radiators, refrigerators, to refrigerants, and others. Many approaches involve the use of consumables such as liquid helium (LHe). Once the consumables are gone, the performance of the system may degrade or vanish. Isolation and cooling are ways to remove or reduce the effect of noise sources.

On-Off Measurement, or in some applications bore sighting, is the practice of pointing the sensor at the target, obtaining an on-target measurement, and then pointing the sensor slightly off target, obtaining a background sample. These mea-surements are then fused to infer properties of the target and the background. In many cases, it may be possible to simply subtract the off-target signal from the on-target signal to obtain a reasonable on-target result. The measurement protocol or strategy must balance system limitations and resource use against the need to ob-tain compelling data. For example, a long exposure may be needed to acquire data on a dim target, during which time the background may change. Therefore, mul-tiple alternating on-target/off-target measurements are obtained. The target and areas nearby are sampled to determine any spatial or temporal variations in the background contribution to the target signal. Many sensors actually scan their field of view across their targets, naturally obtaining on-off measurements. Some instruments are designed to simultaneously obtain on-off measurements from two fields of view and then combine the signals forming a differential sensor. Some of the most sensitive sensors are nulling instruments that electronically balance si-multaneous on-off signals against each other and measure the current or voltage required to maintain this balance.

Chopping generally refers to a more sophisticated approach to on-off measure-ment. In chopping, the field of view of a sensor is periodically truncated or switched, so that the target is only visible for a portion of the time. The time-resolved response of the sensor is measured, and the signal from the target has the chopping frequency. Putting this signal through a bandpass filter based on the chopping frequency will allow the target signal to pass and reject the background. Spinning reticles placed in the optical path of the sensor are one means to truncate the field of view and can be seen as a way to convert spatial information to tem-poral (Figure 6.17). Acting as a spatial filter, large scale structure will provide a more constant signal when viewed through the reticle, whereas scales smaller than the size of the reticle’s sectors will pick up the chopping frequency (Hudson

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2006). Spinning or rocking mirrors are other means to switch between fields of view. For sensors that have a significant internally generated background, switch-ing between a view of the target and a calibration source may be helpful.

Noise originating in the vicinity of the sensor may be counteracted using active suppression. Mechanically stabilized platforms have found wide use in remote sensing systems, for example to point telescopes and compensate for vibrations and other motions (Kaercher 2003). Acoustic noise suppression has found its way into commercial applications such as consumer headphones (Tokhi et al. 2002). A more esoteric example occurs in the measurement of plasma properties in the vi-cinity of a spacecraft. A spacecraft bathed in ultraviolet light from the Sun emits electrons and becomes positively charged, which in turn leads to a local increase in the electron plasma density in the vicinity of the spacecraft (Whipple 1981, Lai and Tautz 2006). This disturbance of the space plasma introduces errors in the de-termination of plasma parameters, particularly for lower frequency phenomena (Ashour-Abdalla et al. 1993). To counteract this disturbance, some spacecraft have sprayed positively charged ions into nearby plasma to reduce spacecraft charge effects (Torkar et al. 2005). This is not a completely satisfactory solution because beams of ions moving out into the plasma will generate noisy waves that may obscure signatures of the target phenomena.

Waveform manipulation consists of constructing a signal with structure to en-hance its detectability or other measure of usefulness. It is particularly important for radar applications which have conflicting goals in time and frequency domains

Figure 6.17 Schematic of optical modulation, or chopping technique, to remove environmental background (Hudson 2006, Figure 6.1, in Infrared System Engineering, Copyright 2006 Wiley,reproduced by permission of Wiley.


for determining range and Doppler shift (speed) respectively. The general idea is that the waveform is designed to have a (relatively) long duration to enhance the overall signal power put onto the target. At the same time, the waveform contains significant short timescale structure which enhances the frequency resolution maintaining Doppler precision. For radar, the return signal is compared with the transmitted waveform using a matched filter which compresses the signal, hence the name waveform compression (Jankiraman 2007).

Auto-calibration, an overloaded term, can be used to eliminate errors resulting from physical constraints, usually involving multiple measurements and sensors. Data fusion strategies are designed to make measurements insensitive to important error sources. Interferometric systems coherently combine signals from multiple wave sensors producing measurements of the phase differences between different points in the sensor array. The closure phase is the sum of the phase differences around a closed loop of sensors (Figure 6.18). Phase errors arising individually at each sensor both add and subtract for adjacent legs in the loop, eliminating them from the closure phase. Thus, closure phase is insensitive to individual sensor er-rors and can be used as a constraint for calibrating sensor phases. Least squares fitting can be used to determine a set of phase corrections for the sensor signals and remove closure-errors. This is the basis for the auto- or self-calibration me-thods developed for synthetic aperture radio techniques (Imbriale and Jones 2007).

These are just a few general strategies for dealing with noise in remote sensing. Noise removal in post-processing is discussed in the section on Data Analysis, and other strategies are discussed throughout this work in a variety of observational contexts and sensing technologies.

Figure 6.18 Phase differences in a closed loop. Schematic self–calibration with a train of wave fronts passing over an array of antennas (1, 2, and 3). Adding the phase measurements around the closed loop (longer arrows) causes single–telescope errors (shorter arrows) to cancel. Onlyone component of the waves is shown (Modified from Imbriale and Jones 2007).

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6.4 Close to home: All in the Attitude. One of the problems the Hubble Space Telescope faced early in its life was motion induced blurring (Polidan 1991, Wie 1998). HST is in low Earth orbit which means that it moves from sunlight to dark and vice versa on every orbit. This sets up a thermal shock as the spacecraft structures adjust to the thermal inputs. Mornings were difficult for HST’s twin lightweight solar power arrays. HST’s original 20-foot long solar power arrays would flap about as much as 3 feet on entering sunlight after an eclipse. This flex-ing, called thermal flutter, was seen in sensor signals as jitter, an enormous prob-lem for what was the most precisely pointable telescope ever made. The wiggling may not have looked like much, but it was more than enough to wiggle the stars around on the imaging detectors, hampering operations (Benedict et al. 1994). On-board attitude control did provide a significant improvement (Benedict et al. 1994, Wie 1998), as did the replacement of the solar power arrays (Maly 2003).

6.11 Data Reduction: Assessment Steps Data reduction is the process of creating normalized and standardized data,

such as spectra, broadband data strings, or even images, from raw measurements obtained from spacecraft and instrument systems. Such standardized data can be compared and thus used to initiate quantitative analysis. At the end of the data re-

Figure 6.19 Processing steps in data reduction, analysis, and interpretation.


duction steps (Figure 6.19), data should be presented in forms and units generally understandable to a broad potential user community. The data reduction steps in-volve obtaining, monitoring, and calibrating data which illustrate variations not only in instrument performance but the surrounding environment, and the space-craft components themselves.

At any level of the processing discussed above, all involved, from the develop-ers, to the operators, to the broader user community, pose basic questions which reduction efforts are designed to address. For example, are the data valid and are they within our expectations are two questions asked early and continuously from the time the data are collected. An analyst takes on such questions in a step-by-step manner, recasting the data if necessary, into a form that communicates the an-swer to the questions posed. This is an iterative process as we may update our re-duction methods, questions, and interpretive models as we learn more or the con-text of the data acquisition changes. Multi-faceted, specialized, interactive tools built onboard software libraries place a great deal of functionality in the hands of the analyst to perform data visualization, quality assessment, systematic noise and background removal, calibration, and feature identification. Relaying the nature of data variations by clearly showing relationships without overloading the end-user with too much information is an art as well as a science. The analyst is an es-sential third component, along with the deployed system and the analysis soft-ware, for intelligent data interpretation.

Initial Translation. Data arrives from the DSN, having been demodulated and decoded in an agreed upon standard packing protocol, and is unpacked. A data packet consists of output, such as spectra, from an instrument or instrument for an agreed upon integration interval. Science data is accompanied by essential ancil-lary information labels, sometimes known as housekeeping data. Recorded infor-mation could include the performance of instrument and relevant spacecraft com-ponents, environmental conditions, operational modes, flags indicating conditions or performance, viewing geometry, spacecraft orientation, instrument pointing in-formation, data summary parameters, and any other monitored parameters.

Visualization for Quality Assessment. Summarizing the raw data in a timely fa-shion as it is delivered follows the unpacking step. If the recorded performance and environmental indicators (housekeeping data) are chosen carefully and the displays are created thoughtfully, sequential plots of data values, flags, and status bits allow quick look data visualization as well as assessment of data quality. This visualization should allow bad data to be readily recognized. Flags are carefully selected to indicate out of specification conditions or performance for the instru-ment or spacecraft. These conditions (such as changes in temperature, turning on of components, such as microphonics-generating momentum wheels, affecting in-strument performance, or instrument gain shift) should be readily apparent in the display as well. However, the display should also indicate when unplanned com-munication drop outs cause zero bits, not a flagged condition. For spectral data, 2D Histograms can provide a good way to quickly spot characteristic features and classes as well as outliers that may indicate problems requiring further attention.

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Figure 6.20 is an example of such an approach applied to the NEAR XRS data (McClanahan et al. 1999). Such visualization tools can be extended of course, to display data step by step during the process of background removal and calibra-tion.

6.12 Data Reduction: Calibration Steps Background Removal. External sources may generate noise which must be

measured to be removed from measurements. One example is the pronounced high energy particle background induced in ray region detectors in deep space. Spectra of background typical of a given timeframe can be generated by taking a mea-surement from a non-illuminated target or from deep space without the target in the field of view. This may be done as frequently as every orbit.

Instrument Calibration. Noise may also be generated internally by instability within spacecraft hardware, as described above. The instrument gain, voltage re-sponse to energy, may shift, change in slope, a condition known as gain shift. The DC relationship, the zero channel, may change, a condition known as zero drift. Such noise is removed in two ways. Pre-flight calibration with standard sources of known composition establishes a baseline for instrument performance, including gain and zero. Regular in-flight calibration with standard sources allows normali-zation of measurements. Such calibration, when combined with housekeeping da-

Figure 6.20 Example of quick–look spectrogram (total counts above, sequential counts by chan-nel below) used for initial evaluation of NEAR X–ray Solar Monitor data, showing enhance-ments in brighter tones. Note 6 minor solar flares (Courtesy of NASA).


ta, should enable precise measurements. The degree of accuracy established in the energy domain depends on the inherent spectral resolution and spacing of energy features. For instruments acquiring images, such as those using CCD arrays, radi-ometric corrections to reestablish a uniform response across the field of view may be necessary. CCD array elements may not all have the same sensitivity, or the sensitivity across the entire array may shift, requiring the data to be flat fielded. Many semiconductor-based sensors are more or less linear in their response, i.e. doubling the stimulus leads to doubling the sensor response. However, in some cases, array elements may saturate at some level or the sensitivity may change during their operation, possibly due to radiation damage. Sensitivity may be effec-tively zero for a short time after a stimulus, a phenomenon known as dead time. The duration of dead time is likely to increase as damage caused by prolonged radiation exposure increases.

Source Normalization: If the source is a natural one, it is intrinsically variable and must be monitored in some way. Measurements made as a result of monitor-ing provide the basis for normalizing target measurements to account for source variations as a function of energy (for spectral observations) or overall intensity (in broadband region of interest).

Feature Identification. Once the spectrum is calibrated, identification and comparison of spectral and spatial features can occur. Laboratory work or theoret-ical models have established the characteristic energies or temperatures for com-ponents of interest in this part of the spectrum, including elements, functional groups, minerals, or grains. Complicated spectra use least squares library fit ap-proaches to identify individual lines. In principle, calibration and feature identifi-cation techniques establish accuracy in the energy domain. Relative abundances of components can be established relatively easily by ratioing features to each other, or ratioing features to surrounding adjacent background in the spectral domain. Much harder is the establishment of accurate quantitative estimates of individual components. The use of ground truth, either from samples collected from remotely observed areas or used to generate in-flight calibration sources, can, in principle, improve the accuracy with which spectral or spatial components are determined. The lack of control and need for assumptions about conditions within the field of view translate into larger errorbars than those used to working with laboratory data find acceptable.

6.13 Analysis: Statistics of Individual Datasets The next steps in data treatment involve analysis of calibrated and normalized

data (Figure 6.19). The analysis process may begin with a look at data distribution using statistical analysis methods (Amsler et al. 2008) to check the assumption that the data sampling strategy has generated a truly representative dataset (Figure 6.21). Generally, routine statistical analysis tools assuming normal Gaussian dis-tributions are used first. If these prove inadequate in revealing the relationships

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and structures within the data, non-standard treatments may be required. Various statistical parameters illustrate the distribution of a dataset. Normally the mean (x) and standard deviation (s) are calculated as shown in Equations 6.7 and 6.8: x = i/N (6.7) s = [{ i – x)2}/(N-1)]0.5 (6.8)

The mean and standard deviation determine the normal distribution, but may be misleading for data with non-normal distribution.

More robust versions of these statistics attempt to reduce the role of outlying data (Thompson 1989). Numerical methods are used to identify outliers, determine the proportion of outliers (c), and derive functions (B) used to weight statistical calculations, where X is the normal standard deviation (Equations 6.9 and 6.10):

Figure 6.21 Role of sampling in statistical inference (Ang and Tang 2007), Figure 6.2, in Proba-bility Concepts in Engineering, 2nd Edition, Copyright 2007 Wiley, reproduced with permissionof Wiley.


s2 = var(x)/B (6.9) B = p(|X| < c) + c2p(|X| < c) – 2c exp(-c2/2)/( (6.10)

Basic techniques are used to illustrate data distribution on a horizontal axis, highlighting extrema, identifying modes/antimodes (peaks & valleys), tails, and the nature of the distribution for one dataset. Data could be grouped by windows of various spatial temporal widths, lags (for running or sliding windows), or by any other relevant criteria in the same manner as an ongoing search or query.

Skewness (Equations 6.11) is an indication of the asymmetry of a distribution. Positive skewness indicates a tail at the upper end, negative skewness a tail at the lower end of the distribution. Kurtosis (Equation 6.12) is an indication of the rela-tive flatness (smaller dy/dx) or relief (greater dy/dx) of the distribution. xi-x 3/N (6.11) 4

4 where 4 4 2 2 4 (6.12)

Various tests are used to compare populations. The F Test is used to compare the variance of two populations in terms of F (Equation 6.13). The t test is used to determine if new samples are centered on a given mean (x1), or if two populations (x2 and x1) have the same (normal) distribution (Equations 6.14 and 6.15). F = s1

2/s22 (6.13)

t = (x1 – xi)/(s/ (6.14) t = (x1 – x2)/sx1 – x2) where sx1 – x2 = 1

2/n1 + s22/n2) (6.15)

N is the number of bins and n the number of data points. Probability plots show relationships between observed and theoretical data dis-

tributions. Typically, observations are initially compared to the normal distribu-tion (Figure 6.22). Observations, ordered by measurable quantity, are plotted on the y axis, versus the probability for each observations based on a normal distribu-tion. A non-linear plot indicates a non-normal distribution, with observable tails and deviations from normality. The steeper slope at higher values indicates the relatively greater incidence of higher rather than lower values. Cumulative distri-butions can be compared quantitatively using the K-S test (Press et al. 2007).

Typical probability distributions are associated with observable parameters for physical processes or instrument performance. Some are illustrated in Figure 6.22, and include Normal (Gaussian), Poisson, exponential, and logarithmic distri-butions (e.g., Balakrishnan and Nevzorov 2003). Random statistical distributions are generally assumed to be a bell shaped curve, or Gaussian, as described by Eq-

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uation 6.16, where x is the mean, x-xi processes are also assumed to be Gaussian. -[(x- (6.16)

The binomial probability distribution describes a series of events with two (e.g., yes or no) possible outcomes. Each event is independent and has a probabili-ty of the outcome illustrated in Equation 6.17 where n is the number of events, and p is the probability of one of the two outcomes: p(x,n,p) = n!/[x!(n-x)!] px (1-p)-x (1-p)n (6.17)

Poisson probability describes a stochastic process, where relatively rare events occur continuously and independently of one another, as in the response of a par-ticle detector, as described by Equation 6.18, where t is time, is increment in time, N(t) is the number of events, is the rate parameters, and k is the interval number (0,1…). The Poisson distribution could be approximated by the binomial distribution when the total number of events observed is small:

Figure 6.22 Gallery of distributions. From top counter–clockwise, simple Gaussian with varyingstandard deviation and height; binomial with varying definitions of upper and lower bounds; ex-ponential distributions; logarithmic distributions; and Poisson at various rates.


– N(t)] = k = e- k (6.18)

An exponential distribution, associated with, for example, atmospheric attenua-tion, is described in Equation 6.19: - (6.19)

A logarithmic distribution is described in Equation 6.20: -1/[ln(1-p)]} = k/pk (6.20)

The extent to which two populations are related is also useful to establish. A li-near relationship, associated with, for example, Beer’s Principle for the relation-ship between component visible absorptivity and abundance is described in Equa-tion 6.21: y = mx + b (6.21)

A more general polynomial relationship is associated with physical processes involving momentum transfer or velocity (Equation 6.22): y = a + bx + cx2 + dx3 + … (6.22)

Power Law relationships (Clauset et al. 2009) are associated with, for example, the solar flux in the X-ray region (Equations 6.23 and 6.24): y = bxm (6.23) ln(y) = m ln(x) = ln(b) (6.24)

Least squares is a method that determines the relationships between two popu-lations by iteratively minimizing deviations. The equations used here assume a normal distribution. Equation 6.25 2, an estimate for the degree of fit for a linear relationship. Equations 6.26 through 6.27 are the two simultaneous equations that solve for a and b (Cheney and Kincaid 2004, Chapra et al. 2005, Keller 2005). Non-linear versions of these equations exist as well. 2 = yi/ i)2 = i

2)(yi – a – bxi)2] (6.25) a = 1/c [(n+1) i yi) – ( i)) ( i))] (6.26) b = 1/c [( i)2) ( i)) – ( i)) ( i yi))] (6.27)

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To show distribution of individual components, histograms (Figure 6.23) are created by dividing the data range into bins and associating a value with each bin proportional to the frequency with which data is found within the bin’s range. His-tograms provide a visual representation of the modal distribution of the data as well as the degree of normality of skew in the population (Equation 6.28). Modes represent population types or classes, e.g. a bimodal distribution is showing signa-tures of 2 populations. The size of the bin depends on the range of data. Too few bins hide features while too many will show a continuum as a noisy sea of spikes. Equation 6.29 expresses minimum the deviation between histogram and point dis-tribution function (PDF): c = (n+1) ( i)2) – ( i))2 (6.28) N = range/1.35 s [(log n)/n]1/3 (6.29)

6.14 Analysis: Image Generation and Enhancement These processing steps involve either generating a continuous image from point

measurements (e.g., elemental or mineralogical abundances derived from spectra, or radiance or brightness temperature derived from broadband data) or enhancing existing images created either directly from, for example, scanned CCD arrays, or through extensive prior signal processing of interferometric data. In each case, in-dividual elements in column x and row y of the digital array, correspond to a sur-face location of longitude x’ and latitude y’, and have assigned digital values, or DN. Typically, the initial analog range of real values is transformed to an n-bit in-teger range, corresponding to values from 0 to 2n, where n is typically 8. Raw pix-

Figure 6.23 Histograms. From left to right, unimodal distribution, skewed unimodal distribution,and bimodal distribution (Courtesy of NIST).

i l f i h i d l di ib i k d i d l di ib i


el values may also use a nonlinear encoding of the original detector data to extend the dynamic range of the measurement. The digital array format may be either a mission or planetary database specific standard. A continuous image is generated by smoothing or applying a low pass filter representing the field of view of the in-strument that generated the measurements, as described below.

6.15 Analysis: Image Mathematical Operations Images may be subjected to simple mathematical operations, including division

by images at other bands to create simple band ratios, multiplication by normaliza-tion factors to remove systematic errors or source variations, subtraction to re-move background. Simple algebraic expressions may be applied, calibrating the relationship between measurement intensity and component abundance based on ground truth. (This is effectively the same operation as stretching, described be-low.) In addition, the variance or standard deviation of each pixel may be dis-played, in order to indicate reliability of component map. The first or second de-rivative of an image can also be calculated, acting like a high pass filter to emphasize smaller scale or higher frequency features, whether undesirable, such as speckle noise, in order to remove it, or desirable, such as edges, in order to identify them.

Any time such operations are performed on digital data, either the original real data must be used (ideal) or data must be converted to real numbers before the op-eration is performed. After the operation is performed, the range can be renorma-lized to the original range (e.g., 0 to 255 for 28, or 8 bit, data). Care must be taken in interpreting the results, as aliasing (truncation caused by the use of integers and the limited number of energy bins) and degradation of resolution may occur.

6.16 Analysis: Stretching Stretching is a form of mathematical manipulation which alters the range and

can alter the distribution of DN values in order to preferentially enhance all or part of an image (Figure 6.24). If you have modified the color tables using an image manipulation program, then this process may be familiar to you. Altering the dis-tribution of DN values is the equivalent of changing imaging properties such as the development rate, exposure time, or the type of paper, and the resulting densi-ty, of film. A linear stretch is used to change the contrast by expanding or con-tracting the range between minimum and maximum values. In a piecewise linear stretch, the distribution of DN values themselves can be changed by enhancing one part of range but not another. Typically, the user refers to the nature of the population and its modalities as indicated on a histogram. The population will have one or more modes or peaks, which may have a normal (Gaussian) or skewed distribution. A lookup table (from old DN to new DN) is used to selectively

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expend or compress parts of the original range. Only a certain part of the range may be emphasized, by stretching it from 0 to 255. When a distribution of DN values is modified so that the more populous parts of a range represent a greater number of DN values, a histogram-equalization stretch may be performed. Each mode, tail, or shoulder, may be stretched differently. The lowest and highest por-tions of the histogram may be saturated, or forced to the ends.

Systematic non-linear stretches may be performed. A power or logarithmic stretch will expand and enhance contrast in light or dark areas respectively. Co-sine/sine stretch increases contrast at ends, and Gaussian and ramp stretches in-creases contrast in the middle, with Gaussian saturating ends. Many of these mappings are implemented in image processing or manipulation packages.

6.17 Analysis: Density Slicing and Trend Surface Analysis The assigning of DNs in each stretch to the same value is technique called den-

sity slicing (Figure 6.24). The resulting map allows classes to be distinguished in a primitive way. A component contour map, analogous to a topography map, is generated.

Another technique, known as trend surface analysis (Krumein and Graybill 1965), can also be used to generate a data contour map. A trend surface is a least squares best fit of an n degree polynomial equation to data points in three dimen-sions where two dimensions represent map coordinates of a sample location and the third dimension is the component being contoured (Podwysocki et al. 1974). This technique is useful for extracting larger scale regional models when the data are noisy. Analysis of variance is applied to progressively higher order surfaces to determine when the rate of improvement plateaus. When this technique was

Figure 6.24 Stretching (to expand brightness range) and density slicing (to identify four bright-ness classes) of one of the first LRO LROC images acquired of the Moon (Courtesy of NASA).

hi ( d b i h ) d d i li i ( id if f b i h


applied to Apollo X-ray fluorescence intensity ratios, little improvement occurred after the fourth order surface. In addition to showing trends, the maps also indicate local anomalies to the trends, expressed as maxima or minima. Typically, these were associated with impact craters exposing underlying stratigraphy of different composition. Kriging is a similar least squares fitting technique used to generate smooth surfaces from scattered data (Cressie 1993, Press et al. 2007).

6.18 Analysis: Filtering Images are generated or enhanced using an image processing technique called

filtering (Figure 6.25). Low pass filters remove small random spatial variations, typically noise, also known as high frequency variations, through averaging or smoothing. This approach effectively sacrifices resolution for better statistics. Noise will be removed, but some real high frequency signal as well. For example, filtering noise from an image of the ocean surface will certainly affect wave spec-tra calculations at the shorter wavelengths and introduce uncertainty into that part of the spectrum. The simplest such filtering technique is simply a sliding boxcar, replacing the value of each pixel with the average of a box of n columns by m rows around it. Such a filter is generically known as a mask. A more sophisticated version can be generated by weighting different pixels within the box to apply a radiometric correction (flat fielding) or to simulate the spatial response function within the instrument field of view (Equations 6.31 and 6.32): y+m x+n pxy0 = { [ xy0]}/((2m)(2n)) (6.31) y-m x-n

Figure 6.25 Filtering of lunar orbiter data. From left to right, original; low pass filter applied to emphasize real low frequency variations and eliminate striping; high pass filter to emphasize real high frequency variations; summation of low and high pass filters with striping eliminated (Courtesy of USGS, Lunar Digitization Project).

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pxy12… = w1 pxy1 + w2 pxy2 + … (6.32)

High pass filters can be generated in the spatial domain by subtracting the orig-inal image from one that has been subjected to a low pass filter, or by generating derivatives. The subtraction image is sometimes known as a variable threshold fil-ter. The threshold, or scale of detected features, depends on the scale of the low pass filter. Threshold filters ring at sharp edges. In addition, they exaggerate fea-tures on the diagonal when the low pass filter is a sliding boxcar filter. As a low pass filter window gets larger, and the resulting image gets smoother, the comple-mentary high pass filter becomes more sharply edged. Low pass filters are typical-ly used to remove random noise, or speckle. However, a series of high pass filters with carefully selected thresholds, applied from one or from several directions, can be used to detect edges (in a particular direction) or shapes (by combining fil-ters favoring different directions).

Noise is normally random and uncorrelated with surrounding pixels, causing recognizable high frequency speckle; on the other hand, correlation from pixel to pixel in an image is high for real features. These tendencies are the basis for any enhancement scheme. A value derived from interpolation between surrounding pixels can replace the uncorrelated pixels. This suggests an enhancement or filter-ing scheme in which an interpolation is used to replace pixels varying from its nearest neighbors by more than some threshold value. Speckle pixel outliers can be removed with a high pass filter. Using Fourier analysis, a noise filter can also be applied to cutoff features with the higher frequencies associated with noise in the frequency domain. Indeed, any periodic structure, e.g., recurrent spikes, can be removed in either the image (spatial) or wave (frequency) domains, but, if they are larger than single pixels, removal in the frequency domain is easier.

6.19 Analysis: The Relationship Between Spatial and Frequency Domains

Filtering may be implemented either in the image (spatial) space, or in a trans-

formed (frequency, spatial periodicity, wave or wave number, basis function or mode) space. A low pass filter, for example, replaces pixel values by an average of nearby pixels which can be implemented by convolution with a convolution kernel, or mask (e.g., Jähne 2005). Instead of an arbitrary averaging kernel, a function that represents the imaging sensor’s footprint or field of view, such as a point spread function (PSF) can be used to simulate the detector spatial response function, or, in other words, what the detector actually sees. In the case of the X-ray spectrometer on the Apollo missions, for example, most of the signal comes from the center of the field of view, which would generate a PSF with a strong peak in the center decaying away toward the edges. Such non-uniform filters are not very efficient, but can be made more efficient if front ends are added and backends subtracted as the box slides across the image data. The operation of con-


volving a mask or kernel with an image, i.e. linear filtering, becomes a point-by-point multiplication in the Fourier domain. Linear filters can be represented by li-near transformations of the data. Filters may be designed by considering properties in both the image and Fourier domains.

The spatial dimension of the digital picture element, or pixel, should not be larger than the effective spatial resolution as defined by the footprint convolved with the integration interval. According to the Nyquist sampling definition (signal processing section above), the resolution, as defined by the ability to detect change, would then be defined as the width of 2 pixels. The integration interval is typically derived from the modeling of the minimum acceptable accumulated sig-nal to noise ratio for anticipated features, and thus also connected to the spectral resolution constraints of the detector. The narrower the spectral line is, the better the spectral resolution, the intrinsically greater the signal to noise ratio, the smaller the required integration interval, and the inherently better the spatial resolution can be.

Image processing in the frequency domain is commonly done with discrete Fourier transform (DFT) involving linear transformations in the frequency do-main. With the DFT approach, real structures or features in an image are viewed as a series features with spatial frequencies, or periodicities. Equation 6.33 de-scribes the discrete Fourier transform, Fn, where fk is the image feature at interval k out of N intervals, and e –(2 i n k)/N is the Nth root of unity (Bose 2004): Fn = k e – (6.33)

Each such set of related structures could be expressed by a fundamental basis function, or mode in the frequency domain. In other words, an image could be de-composed into its periodic components, contributions of these spatial components could be enhanced or reduced, and then the image could be rendered again with the modified set of components. For spatial structure, Fourier components (sine and cosine functions) provide a useful set of basis modes with a variety of spatial frequencies or wavelengths that span the entire image. For more localized struc-ture, Wavelets, basis functions of finite size, provide another useful set of features at a variety of size scales and positions. For example, an image might exhibit small-scale variation, or texture, associated with a particular ground-cover or ter-rain, and larger-scale variation associated with fault patterns. Surfaces vary in complexity, depending on the number and type of modification processes ex-pressed and the nature of the underlying terrain (Figure 6.26). More complex sur-faces, expressing processes on a variety of scales, would require a greater number of fundamental modes. Examples of such surfaces might be young lava flows, with great variation in slope and brightness texture on a variety of scales over small areas. Karst topography would show great relief on relatively small scale. Some systematic noise should also have an associated fundamental mode and thus recognizable and removable.

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Fourier analysis can thus be used to identify patterns in feature distribution, as well as gradients in properties such as brightness, color, and feature distribution.

Operations in the frequency domain are potentially more efficient and accurate than local finite-difference operations in the spatial domain. However, the peri-odicity in features assumed in the frequency domain can be problematic. How does the implied periodicity affect analysis? As a mathematical representation that conserves the intensity, DFT techniques will spread the energy to the basis func-tions, i.e., frequencies, that the transform is built on, whether or not they have any real connection with the data. An aliasing problem occurs if two or more modes combine to give an apparent mode that doesn’t represent a real process. On the other hand, a brute force approach can attempt to identify modes anticipated with terrain or features of particular types, to get around the aliasing problem. Unitary transformations, such as Fourier transformations, must conserve the total intensity of the image data. If these combined functions don’t match the input image or the analysis well, the basis functions don’t describe anything real and the process may mislead or fail. One problem with applying signal processing techniques to image data is that while for many signals, the data can be reasonably considered periodic, many images are far from periodic. Temporal periodicity, such as seasonal or diurnal variation, may be represented in the frequency domain. A time series of images is decomposed to show trends, long (climatic) to short term (diurnal), using frequency domain filtering algo-rithms. Data stream analysis involves the review of data sequences to make infe-rences, often with requirements for online processing or real-time results.

Figure 6.26 Variable complexity surface illustrated by large lunar crater Tsiolkovsky, with its features diverse in shape, brightness, texture, and scale, including circular features (craters), li-near features (faults, rilles, slumping terraces parallel to surrounding crater walls), irregular rough large central peak with surrounding small kipukas, and smooth dark mare (Courtesy of


6.20 Interpretation: Multivariate Classification and Correlation In the preceding sections, we have illustrated how contour mapping of one component can be used as a primitive classification technique. The combining of multi-component or multi-spectral images allows even greater capability to identi-fy classes with distinctive signatures, or population clusters, in n-dimensions. Recognition of patterns in the distribution of classes is an important outcome of remote sensing studies. Ratioing of two bands, as mentioned above, is a simple way to begin this process. As the number of variables increases, classification based on statistical cluster-ing becomes more attractive. In the Bayesian classification approach, clusters are identified in hyper-ellipsoids with surfaces a specified number of standard devia-tions from the center. The delimiting and defining selection criteria appropriate for all classes is most challenging. These methods correlate populations from data-sets based strictly on statistics (unsupervised) or on the basis of a priori indepen-dently determined signatures provided as ground truth for supervised classifica-tion using training sites on images, using numerical discriminators. Classes identified are clearly recognizable on the basis of statistical significance, beyond the intrinsic scatter or spread within a given class. Results are also reported as on the basis of typical DN values and number of pixels in each class. A pixel is classified either on the basis of proximity to class population centers (minimum distances) or a Bayesian probability function (maximum likelihood) us-ing variance/covariance matrices. The former can be visualized (Figure 6.27) by identifying the shortest parallelepiped that can be drawn from an unclassified

Figure 6.27 Maximum Like 1 2) is plotted relative to cen-troids of the three classes A, B, and C already identified from relationships of data to the two

1 2). x is classified on the basis of the shortest distance to a band center, in this case A (Courtesy of NASA).

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point to surrounding population centers. In the latter, each population can be visu-alized as a series of ellipsoidal contours, decreasing in distance from the center as the probability increases. Each pixel has associated probability likelihoods for the surrounding populations. It is classified on the basis of the most probable associa-tion. In contrast, a fuzzy classifier would maintain a list of these associations inter-preted as simultaneous membership in different populations. In unsupervised classification, population clusters are identified, and pixels as-signed to the closest cluster in n-dimensional space. Each class is assigned a color, and the classification map must then be interpreted in terms of what each class means. The user influences the process by determining the criteria for including pixels in a class. In a preliminary run, the program determines the maximum num-ber of potential classes, often a confusingly large number. Then, the investigator typically broadens the class acceptance criteria, thereby reducing the number of classes to a reasonable number, based on field observations, or available ground truth. The investigator must be very familiar with the terrain to make a meaning-ful interpretation of such a map, and, even so, the result can be somewhat subjec-tive. AutoClass is an example of this approach (Cheeseman and Stutz 1999). Supervised classification depends on the investigator’s a priori knowledge. Features selected must be relatively homogenous and exhibit clear differences in signatures of terrains for the spectral regions used. For example, rocks, vegeta-tion, water, and soil respond differently in different spectral regions, and their sig-natures can be identified at locations where they have been confirmed to occur in

Figure 6.28 Scatter plot showing the relationship between Apollo XRF Mg/Si and Al/Si intensi-ty ratios. The two distinct clusters represent two major rock suites, mare basalts (left) and high-land anorthosite/norite/troctolite (ANT) Suite (right).


a digital image. The same signatures can be used to train discriminator functions to find occurrences where there is no ground truth. Unassigned pixels are assigned to a class on the basis of the class discriminants it most closely matches. This is more difficult when signatures (e.g., types of forest of vegetation cover) are statis-tically difficult to distinguish. Generally, pre-flight versions of instruments are tested in the field to determine discriminating spectral features. The results of classification can vary depending on training sites and their number and on classification methodology. While image processing techniques may do well in determining the proportion of major terrains, they do not necessari-ly do well at determining the exact spatial distribution of terrains, substantiating the need for ground truth (Landgrebe 2003). One cause for this failure may be that features controlling the signatures are smaller than the effective resolution of the data. Use of the highest resolution bands increases accuracy, and facilitates inter-pretation, providing the training features are large compared to the resolution. The relationship between two components can be described in a two dimen-sional histogram, or correlation diagram, otherwise known as a scatter plot (Fig-ure 6.28). Population clusters can be assigned values or colors, unsupervised clas-sification, or the 2D space can be divided into an n x m matrix with color used as an indicator of the degree of correlation, parallelepiped supervised classification (Clark et al. 1978; Clark and Hawke, 1981, 1987, 1991). The correlation coeffi-cient, r, for pixels for the two datasets, x and y at location i, where x and y are the

ation, is described by Equation 6.34: r xi – x)(yi – y xi – x)2 yi – y)2]0.5 (6.34) Principal Components Analysis is another classification technique (Figure 6.29). The number of relationships that can be used to describe a group of related datasets, typically three spectral bands, is reduced based on the assumption that the data are not entirely independent and have varying degrees of correlation. If two datasets are well correlated, only one relationship, the axis of correlation, is needed to optimally describe them. Multi-spectral image data are generally strong-

FFigure 6.299 Principal components analysis. As discussed in the text, from left to right, initial in-formation plotted in three dimensions (three components); plotted with third component set at 0, to create “scatter plot” rotated to be parallel with one axis with a constant value on the other, and then plotted again on three axes, with principal variations emphasized.

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ly correlated; thus, their axes are not orthogonal. The statistical test of correlation is covariance. The smallest covariance indicates the most independence, the high-est covariance indicates the most dependence. The primary component axis is de-rived from the strongest covariance relationship. The secondary component axis is derived from the second strongest covariance relationship. The tertiary component axis represents the weakest covariance relationships for the case of three datasets. Each axis is created by linear transformation-rotation and translation. Typically, each covariance axis is assigned a color; typically red, green, and blue are used to represent each axis, and the resulting color for a pixel depends on the degree to which each axis represents it. 6.21 Interpretation: Modeling Modeling source/target/detector interactions from first principles, sometimes known as simulation, is not only an iterative step used to interpret measurements but often an early step used to design instruments for optimal operation by consi-dering the spectral and spatial response for potential detector configurations. In-strument response may be linear or non-linear. Non-linear responses are some-times amenable to linear analysis, capable of being approximated by a power law transformation. Historically, models have been chosen for their analytic properties and conve-niences. Probability distribution models for outcomes of energy/particle interac-tions are useful starting points, and in some cases the theoretical underpinnings are compelling. Models may be either theoretically based or strictly empirical, arising from distributions functions which best fit the observations. Modeling may be numerical or analytical. Analytical models are based on algebraic parametric eq-uations, with constants and parameters represented by functions which depend on the nature of the physical processes, including power laws and exponentials (Clau-set et al. 2009). Numerical modeling is computationally intensive and based on iterative numerical approximations of the relevant physics, as with Maxwell’s eq-uations or with Monte Carlo or other stochastic simulation techniques that are based on the probabilities that a series of energy/particle interactions will occur (Amsler et al. 2008).

6.22 Interpretation: Pattern Recognition and Learning Models Classification, the process of identifying target classes and determining the membership of targets within those classes, is closely related to learning. Generally, two phases are associated with learning algorithms. The first is a training phase during which distinguishing characteristics of targets within a data set are learned, and an execution or application phase during which new observa-tions may be classified. A wide variety of algorithms have been developed. Un-


supervised learning, the basis for data cluster analysis, generates classes from data and starts with limited a priori input (Jain et al. 1999). High-dimensional data sets are particularly challenging, as discussed below (Kriegel et al. 2009, Kogan 2007). Supervised algorithms rely on the a priori identification of class exemplars, usual-ly communicated through the use of training sets (subsets of the data identified with target classes). At present, many learning algorithms require a complete pass through the training data sets before they can be used (batch processing). For real-time applications or those with large data sets, we may turn to online or incremen-tal learning algorithms that learn as data is presented, continuously updating them-selves (e.g., Zhong 2005). The analyst should be careful assessing the significance of classes and the infe-rence of properties such as class membership and trends. Each channel, i.e. every pixel and each of its spectral channels, adds another dimension or degree of free-dom to the space of possible observations, or from another viewpoint, interpreta-tions. As the number of dimensions grows, the relative contribution from edges of data distributions grows to dominate the interior of typical data values (Landgrebe 2003, Gershenfield 1999). A great many more observations are required in high-dimensional situations (e.g., hyperspectral observations) to constrain models or identify classes. One way to pose the question is to ask how complicated a distri-bution, e.g., how many classes, can be justified by the data (Landgrebe 2003). There are various ways to parameterize the classes or patterns, to define objec-tive functions or metrics, and to determine which classes or patterns score best on the objectives or metrics. Patterns or distributions may be parameterized in a variety of ways. Piecewise products and sums of elementary functions and more can be cobbled together to provide functional forms for target signatures or distributions within data or para-meter space. Artificial neural nets (NN) are an important class of functions in that any function can be approximated by a NN with two hidden layers (Komolgorov 1957, Cybenko 1989). Because of this generality, NN can be used for recogniz-ing, classifying, and defining patterns or distributions. Classes may be defined in a variety of ways. These can include explicit parti-tioning of the data space by surfaces or hyper-planes through the space (e.g., Fi-lippone 2008). Because of their convenience and applicability, Gaussian or other statistically motivated distributions of observed signatures are often used to model target classes. Artificial neural nets may be used to implicitly specify classes. Approaches using Fuzzy Logic approach allow membership in multiple classes simultaneously. A great many objective functions and metrics have been examined, but perhaps the most widely used is the sum of squares of the differences between the signal predicted by the pattern and the sensor, also known as the mean square residual (MSR). For Gaussian-distributed signals, the MSR is proportional to the loga-rithm of the probability of that the observation would occur given the parameters defining the pattern. The MSR is the logarithm of the likelihood. A Bayesian ap-proach posits a prior probability distribution that accounts for information known

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prior to obtaining the data (Gregory 2005). Some controversy is associated with the choice of the prior probability, which the maximum entropy approach ad-dresses by choosing a prior probability distribution that constrains the results as little as possible. Likelihood functions need not be based on Gaussian distribu-tions, but can be constructed using distributions appropriate for the task, sensor physics, and so forth. Objective functions need not be based on a statistical argu-ment, though semantics useful in the formulation of odds, confidence limits, or statistical tests, may be lost. Once the formal relationship between the classes, the data, and the objective function has been chosen, determining the classes resembles a search or functional fit. Parameters are selected to describe classes that optimize the objective func-tion. A number of search algorithms are available. Essentially all methods begin with some initial guess and then iterate through a series of guesses until some stopping criteria is met, e.g. number of iterations or residual error. Press and co-workers (2007) provide a general overview of optimization methods. Iterative Learning methods use different approaches, including grid, gradient, stochastic, and genetic (Figure 6.30). Grid searches evaluate the objective func-tion at points on a grid of parameters, making a map of relative merit. Gradient searches use the gradient of the objective function or its estimate. An Artificial Neural Net (ANN) is generally trained with a gradient search, though interesting techniques have been invented to speed convergence (Lary and Mussa 2004). Sto-chastic searches randomly perturb, discard, and retain sets of guesses according to some protocol. In stochastic annealing the perturbations start large and gradually shrink. In genetic or evolutionary search methods, the perturbation and update of the guesses bears some resemblance to biological genetic evolution. For genetic methods, a set of alternative models operate interactively and compete to be re-tained in future iterations. An interesting aspect of the genetic approach is that if genetic programming techniques are used, then potentially unforeseen and quite sophisticated solutions may be built up as the algorithm progresses (Koza 1992).

Figure 6.30 Iterative Learning Schemes for data as described in the text, including A grid, Bgradient, C stochastic, and D genetic.


6.5 Close to home. Learning lessons. Learning algorithms are meant to con-nect, or at least help connect, the dots. They can sometimes uncover surprising structure within data sets. Sometimes, the surprises involve more than just the da-ta. The Infrared Astronomical Satellite (IRAS) Low Resolution Spectral Atlas, a collection of 5425 infrared (7-24 μm) stellar spectra, was the first real-world test of the AutoClass unsupervised classifier (Cheeseman and Stutz 1999). After ob-taining poor initial results, the analysts found that the spectra provided by the IRAS team had been artificially normalized so that all of the spectra had the same peak intensity and noise dominated their classification. Renormalizing the data helped. Another problem discovered was that data was provided from only the brightest stars in just ¼ of the sky. The IRAS team was trying to help by providing a presumably manageable data set with good quality data. Unfortunately, most stars are not bright and with data from only one direction, distinguishing between stars from the local neighborhood, galactic disk, or galactic core is impossible! After obtaining more data, the analysts discovered that many spectra had chan-nels with negative intensities, a physical impossibility, because an estimated back-ground contribution had been removed from the spectra before they were pro-vided to the AutoClass team. In general, corrections should be applied as part of the statistical analysis itself. Otherwise, as these circumstances indicate, the analysis may have more to do with the biases of the corrections than the popula-tion of targets. In this case, AutoClass discovered 77 classes including previously known classes, subtly different classes, and previously unknown classes. It tripled the number of stars suspected of having carbon atmospheres and identified a blue anomaly in many spectra that proved to be an important calibration error. In fact, AutoClass was able to identify other calibration errors and artifacts of data processing steps including a cosmic ray removal step that sometimes eliminated valid target signatures while passing noise-corrupted data. One interesting by-product of the AutoClass classes was that after combining the spectra from all of the members of a class, an apples-and-apples summation, weak signatures in the class spectra were discovered that could not have been otherwise detected (Goe-bel et al. 1989). Caution should be used when combining signals from different targets, to avoid conflation of their signatures. As AutoClass analysts brought newly discovered structure in the data to the attention of IRAS experts, many times the experts would bring up previously undisclosed data or data processing steps. A similar process occurred when AutoClass was turned to LandSat data (Cheese-man and Stutz 1996, Kanefsky et al. 1994). In the end, AutoClass analysts had to become mini-experts with a grasp of the data and the end-to-end process in order to understand the structure their algorithm was discovering within the data. Access to the raw data, documentation of all known biases, data transformations and processing, and the use of reversible transformations that do not destroy in-formation were all key to maintaining the statistical integrity of the data.

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6.23 Dealing with Geometry: Footprint Determination The first step in dealing with target/detector geometry is footprint determina-tion. This involves processing SPICE data, as described in the Flight Project Sup-port section, a relatively straightforward step for a regular planetary body, but far more challenging for an object irregular on the scale of the observations, such as an asteroid. Spacecraft orientation and instrument pointing relative to the target are used to determine the physical footprint for each integration interval. Data from successive footprints can then be rectified to form a continuous mosaic. 3D analysis using successive image, or stereogrammetry, is described in Chapter 3. Data can be reprojected to match the selected cartographic projection.

Figure 6.31 Geographic projections. Typical cylindrical projections, where cylindrical circumfe-rence is equivalent to a great circle such as the equator, include simple cylindrical (the relation-ship between spatial positi a-

mercator (cylinder rotated 90 degrees)). A typical conic projection drawn relative to a cone withpolar apex is Lambert conformal conic, and a typical azimuthal projection drawn relative to a circle with polar center is Lambert azimuthal equal-area (Smith 2009) (Courtesy of MicroImag-es, Inc.)


6.24 Dealing with Geometry: Geographic Projection

One of several standard geographic projections are typically selected for dis-playing and storing data (Figure 6.31). Simple cylindrical projection with constant longitude and latitude scales makes for easy data manipulation, but distances at the poles are greatly distorted. Lines of longitude and latitude are perpendicular all across the Mercator projection, which makes it useful for marine navigation, but also leads to a latitudinal increase in area toward the poles (Dana 1999, Furuti 1997, Anderson 2009).

An orthographic (simple perspective) plane of Cartesian coordinates can be re-lated to geographic/Cartesian coordinates (Equations 6.35 through 6.37) x = r cos( ) sin( ) (6.35) y = r cos( ) cos( ) (6.36) (6.37)

longitude. The image data, which doesn’t start with any intrinsic geometry, must be mapped into a reference geometry based on a standard cartographic projection. Standard geographic projections, simple cylin-drical, mercator, and Lambert azimuthal (preserves directions from a point) (Weisstein 2009) used for polar projections, are described in Equations 6.38 through 6.41), respectively, where longitude is x = – 0, y = - 0 (6.38) x = – 0, y = ln(tan( ) + sec( )) (6.39) x = k’ [cos( ) sin( – 0)], y = k’{[cos( 1) sin( )] – [sin( 1) cos( ) cos( – 0)]} (6.40) k’ = 1) sin( )) + (cos( 1) cos( ) cos( – 0))]} (6.41)

1 is the standard parallel, and 0 the central longitude. Typically, resampling and interpolation between pixels are used to create a new

pixel grid. A net of control points, associated with well defined features, is estab-lished, usually starting with the assignment of a small, well defined feature to es-tablish a longitude reference or point of origin.

6.25 Dealing with Geometry: Rectification and Registration

Uncertainties in viewing geometry (source incident angle relative to normal, instrument viewing angle relative to nadir) lead to distortion. Geometries and dis-

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tortions also vary for images taken at different times with overlapping coverage of the same area. Two approaches, nearest neighbor and interpolation algorithms are used to rectify data.

With a nearest neighbor approach to rectification, a pixel takes the DN value of the closest data point. Such a scheme is fast, but the local geometry may be inac-curate, and comparisons with other data may suggest that the location or target properties have suddenly shifted. Such mismatches can trend or vary across an image, so while the registration between two images or pixel grids may be good in some places, it may be quite bad in others. Still, no new data values (DNs) are generated, merely remapped in location; thus, no artificial data is created and all results can be traced back to a measurement. The detail and statistics available in the image are not necessarily degraded as they are in interpolation techniques.

Interpolation algorithms assign pixel values based on some function of nearby image data. Bilinear interpolation averages the DNs of the 4 surrounding pixels, whereas cubic convolution involves averaging the DNs of the 16 closest data-points. Bilinear interpolation, the 2D equivalent of linear interpolation, is geometr-ically more accurate than nearest neighbor but as stated before, the accuracy of the statistics decreases. Ideally, all of the pixels would be used to generate new val-ues, but in practice a limited number of pixels are used. For example, interpola-tion or transformation schemes based on Fourier transforms (DFTs) can be fully invertible with no loss of information. But when less than 4 pixels around any point are used, techniques yield results comparable to bilinear interpolation.

In fact, convolving a continuous positive function of finite support, i.e. a smoothing or averaging kernel, with a discrete image, acts as a moving average (See the filtering section above). Transforming the image using the Fourier mod-es, in effect reconstructs the natural continuous input from which the original im-age was formed, albeit with the unresolved information aliased across the Fourier basis. The convolution kernel collects data from neighboring samples by resam-pling the continuum at desired points. When dealing with irregular image geome-tries, performing a FT-based interpolation may be too time consuming to be used at each pixel. The distortion may be sampled at least every 50 pixels or so and cor-rected by a cheaper interpolation in between, assuming distortion changes slowly and fairly uniformly across the image (e.g., El-Sheimy et al. 2005).

Registration, where two or more images are aligned with each other or a geo-metry standard, may lead to conflicting data even after projection. Disagreement between the exact locations within two overlapping images can result from a va-riety of sources. Errors can come from imprecise space craft data, timing, ranging, telemetry, or ephemerides uncertainties or errors. Differences can be introduced by data modification from resampling or interpolation. To ameliorate these ef-fects, the location of features in each image is measured and used to create a dis-placement map. A transformation (rotation and translation) that best fits the dis-placements can be calculated. Local modeling or local kernel convolution can be used for transformations that are non-uniform across the image. Windowed cross- correlations of the images are often used to determine the transformations. The


transformations are applied, and the remapped data are passed to the resampling program, a tedious process best accomplished interactively. The analyst examines the image overlays and the cross- correlation, which will be dominated by a strong central symmetric peak. This process works best with high quality images with the minimal random or coherent noise.

Rectification of images with a 3D (topographic) component, such as topogra-phy, is discussed in Chapter 5.

6.26 Data Management: Planning

A data management plan is required for every mission. This means that an end-to-end data system and instrument team data distribution networks must be de-signed, and a schedule for delivery of data products into a publicly accessible space data archive must be developed (Figure 6.32). A number of such archives

Figure 6.32 Data management scheme for NEAR XGRS data (Courtesy of NASA).

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exist, including NASA’s Planetary Data System (PDS) for solar system data. For NASA missions, raw data are immediately in the public domain, and higher level data products are usually due within 6 months to a year from the start of the active mission. Archived data is stored in a standardized format, frequently time-consuming for the investigators to create from their original data, but usually ac-cessible with standardized query and processing tools available in the archive. La-bel formats are standardized, and the data are systematically tabulated according to pre-established protocols. Access is critical, because relatively little of the anal-ysis that could potentially be done with mission data is achieved by the higher lev-el product deadline.

A spacecraft’s sensors, the way we use them, and our understanding of them, change over time. These are some reasons to maintain a disciplined and structured approach to the collection, archival, reduction, and provision of data from these missions. Version control is an important fact of life for mission data, as entire datasets may require recalibration as other analyses become available. At the same time, though, some users of the data may require older methods and data be maintained for the continuity of their own work, at least until they are ready to up-grade to the new data. Uncertainty about the validity of upgraded versions of ca-libration software will lead to reasonable arguments over data interpretation. The data processing architecture implemented should allow for such disagreements. These concerns drive the design of the mission database and the data flow into and through it. The data and derived products are an important part of the legacy of the mission.

The archive must have an interface that can support a range of queries from a variety of users with varying degrees of sophistication, including the science user community, educators and students, the public, and policymakers. Queries could thus range from target, to mission, to instrument within a given mission. In the PDS archive, data from individual instruments is delivered in ASCII format, as tables, with each line representing a sequential data packet, and labels, describing each column in the table. Separate files describe the contents and format of labels and text files. Metadata, including mission ancillary data, describing the mission become part of the archive. These metadata could contain reports, histories, and include software and models for working with the mission data.

6.27 Data Management: Processing

Typically, data processing is modularized in a way reminiscent of some soft-ware systems architectures. Processing is divided into stages associated with le-vels of data with lower levels of data being more closely related to the data in the state as received from the spacecraft. The nature of the division and the tasks per-formed at each stage depend on the mission architecture.

Data generation actually begins with mission planning. Typically, these docu-ments are not captured in data archives, although instrument schematics, theoreti-


cal models, and analytical tools may be captured as metadata, as described below. Flight project support materials generated by instrument teams, such as logs of da-ta planning requests to make certain kinds of observations are generally not main-tained, except as recorded indirectly in ancillary instrument data.

Onboard a spacecraft, data in the accumulating buffer are coded and packed as sequential frames by the command and data handling subsystem for transmission to the Earth on regularly scheduled intervals (Figure 6.33). Such frames include inputs from all spacecraft systems generated during that interval. When these data are received at the DSN, they are decoded, unpacked, and repacked in packets for individual instrument teams. The mission data system architecture determines where the primary site of unpacking occurs, where the permanent and temporary data storage facilities are located, and how the instrument data packets will be dis-tributed to the instrument teams. A schematic data format protocol for a telemetry data stream is indicated in Figure 6.34. The data management plan assigns roles and responsibilities, in terms of individuals and facilities, and creates a plan for delivering data products (above Level-Zero).

Level-Zero data is typically rather compact and not really intelligible except to a few thoroughly familiar with the mission implementation and engineering. Ba-sic organizing and archiving of the data is typically the goal of Level-0, so that the data can be searched and retrieved both for real-time operations and for the pro-duction of higher-level data products. From a science viewpoint, ensuring that re-levant engineering and science data are properly associated in the database is a critical Level-0 function. For example, placing science sensor observations in context may require star-tracker data for onboard attitude determination and range data from the terrestrial receiving station, so these critical data are ingested by the database and become part of the Level-0 data product. With the Level-0 product,

Figure 6.33 Transfer and data format protocols as described in the text (CCSDS Report, Courte-sy of NASA).

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basic questions about instrumental response and status and engineering data such as the location and attitude and operational mode can be answered. This is also usually the most automated of the data processing steps, and can usually be well determined before spacecraft launch and deployment.

Level-1 data generally represent data reduction efforts. A data production pipe-line is used to generate Level-1 from Level-0 data products. Instrument calibra-tions would be applied at Level-1, and these will likely be semi-automated, requir-ing human interaction and review until the instrument performance is fully understood. Furthermore, calibration may require understanding longer-term trends or patterns in the data. Conditions may change rapidly. A trend or pattern may not be apparent right away, perhaps not until well after the mission ends. Da-ta processing is thus an ongoing activity, involving update of analysis methods and revision of data products. Level-1 data represent the first step toward placing the data in a mission scientific context. Conversions to physical units are made and assessed. Data is uncompressed, and perhaps normalized. Flagging and cha-racterization of data occur; data dropouts or instrumental idiosyncrasies should be identified and labeled, instrumental marks or data artifacts labeled or removed.

Level-2 products, representing the data analysis process, are typically high sig-nal, low noise, well-calibrated data from a known observational context. Uncer-tainties in input data should be understood. The relative amount of emission or absorption in a number of spectral bands might be a product at this stage. Data were calibrated in Level-1, thus in Level-2 we can start to compare signatures in related data.

Figure 6.34 Science data format for NEAR XGRS Data (Courtesy of NASA).


Level-3 represents data interpretation efforts to produce high level products in the scientific context. Level-3 data products include maps of compositional com-ponent abundances derived from spectral bands or lines. Such maps have been geometrically rectified by the incorporation of spacecraft radio science data (to account for spacecraft perturbations) derived in Level-2. The higher level data are of greatest interest to the broader scientific community. More efforts are required to develop products that integrate data from multiple sensors or satellites, particu-larly in preparation for simulations of complex systems such as weather or cli-mate.

Each stage of data processing requires particular software, as described above, which may be developed separately or as part of an integrated whole, depending on mission architecture and implementation. The software tools can be very spe-cialized, reflecting the understanding and work of the mission engineers and scien-tists. Although documentation of these tools is required, a great deal is carried around in the heads and hands of those who worked on the mission. For the most part, the instrumentalists, expert in their own sensors, focus on supporting their own sequence of data products, though they may rely on data from other sensors for certain critical items, e.g. spacecraft attitude or position. The data are general-ly stove-piped, or pipelined with comparisons or integration of observations from different instruments occurring in late stages of data processing or waiting for post-mission scientific analysis and synthesis.

After an embargo period, higher level data products with some degree of do-cumentation will be documented and made available to the scientific community as a resource for future research in many disciplines. Much of the analysis will go on after the mission, so both the maintenance of the archive and access tools are critical. For example, features in the data that are unusable for higher-level data products, might be available for statistical analyses of solar events.

What will the future hold for data archives, especially when the data volume generated by successive missions increases dramatically? Database technology is evolving and advances in the commercial world affect space data systems. Yet an important question is how to use new technologies to make the most of NASA’s legacy data. Today, a wide variety of data formats in use, including JPEG, TIFF, GIF, IMG, ASCII tables, among others. For scientific or other technical uses, these familiar formats are supplemented with metadata stored in file headers, data definition files, or perhaps even in printed documents. The Flexible Image Trans-port System (FITS) is used in NASA PDS and other projects with astronomical heritage. Net CDF, CDF, and HDF have wide penetration in the Earth Science community. Scientific file formats are getting to be quite sophisticated providing file-system-like features. Project-specific formats abound, e.g. the XDR data files of ITT’s Interactive Data Language have been used in a number of NASA mis-sions. The XML revolution for structuring and providing data is making its mark to structure data and transactions (Hodgson et al. 2006). Commercial relational da-tabases have been used, as well as project specific data access tools. Web-based querying and data product retrieval is generally based on keywords, menus, or

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rarely SQL. Next generation archives, such as the NSF-sponsored National Vir-tual Observatory, use ontologies for semantic information to aid data ingest, search, and retrieval and enable federated databases to synthesize data products. (NVO 2009, Moore et al. 2004). The use of semantics in answering queries al-lows more intelligent results to be generated (Allemang and Hendler 2008).

6.6 Close to Home: Too Good to be True. Not only was the Apollo orbiting X-

ray fluorescence experiment a success in producing the first elemental abundance maps for the Moon. The aluminum map showed a simple bimodal distribution for that element, low in one major terrane (younger maria volcanic flood plains), and high in the other (older crater saturated highlands). This was such a dramatic re-sult, that the more complex distributions of the other elemental datasets were largely ignored for years. This led to the construction of simple paradigm for the origin of the lunar crust. Eventually, as a growing body of evidence illustrating the heterogeneity of the highland crust accumulated, the inadequacy of the origi-nal paradigm became evident, along with the realization that we were misled by our desire for elegant simplicity.

6.28 New Tools

Projects generating remote sensing data require tools to construct data products for their own operations and for their user communities. The Planetary Data Sys-tem (PDS) and its various nodes provide a convenient gateway into these commu-nity tools (McMahon 1996). Over the years, a significant investment has been made to develop software that provides cross-cutting functions, including mathe-matical and geometric functions, image manipulation and display, interactive user interfaces, data formatting and transformation, database, querying, web-based access, and so forth. Standards and protocols provide some portability for planeta-

Figure 6.35 Example of ontology for a spectral band (Ashish 2004) (Courtesy of NASA).


ry data, but the user base for extra-terrestrial data is comparatively small. These communities of experts have evolved software for processing and analyzing soft-ware over decades, supporting multiple projects and space missions, spearheading or infusing new technologies as resources permit (PDSTools 2009). The USGS provides an online capability to display and download maps and higher order mis-sion data products for planetary targets via their Integrated Software for Imagers and Spectrometers (ISIS) website. The market for terrestrial remote sensing data is vastly larger and standards-based software is providing ever increasing capabili-ties. In fact, remote sensing is just one facet of the large and dynamic field of geospatial information. The Open Geospatial Consortium (OGC) develops con-sensus-based standards that enable developers to make geospatial (or geographic) information systems (GIS) and tools that work together, including integration with the web and mobile devices (ESRI 1999, OGC 2009). At this writing, OGC membership lists 384 companies, government agencies, and universities. There is an effort within the planetary science community to take advantage of GIS tech-nologies and tools to develop a planetary GIS (Frigeri et al. 2007, Tanaka 2006, Hare et al. 2008). One interesting extension of this effort involves the develop-ment of web-publishable data models called ontologies that associate data with semantic networks of specifications, concepts, and terms that enable applications to reason about the data (Figure 6.35) (Hughes et al. 2009, Raskin 2008, Sinha et al. 2005). NASA is turning to this technology to organize its systems engineering for the decades-spanning Constellation effort (Hodgson et al. 2006, Shishko 2006, Dutra and Smith 2006, Fayez et al. 2006). Ontologies provide a framework for or-

Figure 6.36 Example of ontology schematic for Earth environmental applications (Ashish 2004) (Courtesy of NASA).

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ganizing data that is more flexible than spreadsheets or more conventional data-base technologies (Allemang and Hendler 2008). For example, executable ontol-ogies could specify a data processing pipeline which could also be run as a pro-gram or chain of services (e.g., Di et al. 2006) (Figure 6.36). By including semantic information, search engines gain a rudimentary ability to avoid nonsen-sical responses. They can even fill in some gaps in data or metadata through logi-cal inference, perhaps even constructing a data processing pipeline as a query re-sult. Semantic web technologies being developed for interoperability, discovery, and verification of data and services will likely recast the way we obtain and work with all kinds of data, not just remote sensing data (Berners-Lee 2001, Jackson et al. 2009).

6.29 Summary

The primary goal of flight operations is to execute the mission plan to achieve mission goals. Tracking and processing information in all forms is essential at every stage of a remote sensing project, involving mission planning, life cycle flight support, data reduction, data analysis and interpretation, and data manage-ment.

Proposals for remote sensing missions may originate at any level, but must ad-dress high level science goals as established through organizational, e.g. NASA, protocols. The process of turning such goals into science requirements and thence into an engineering concept is facilitated by the development of scenarios allow-ing a vision of how experiments will be operated and thus operational require-ments. The development of a mission concept and its implementation involves modeling via tools such as Excel or MatLab to assess the relationship between re-quirements, costs, and risks tailored for use by systems or discipline engineers. In some cases, especially powerful specialized tools, such as DOORS for tracking requirements at every level, and HURON for evaluating the relationship between operations, activity value, and costs, have come to be widely used.

Signal processing based tools are used to support guidance, navigation, and tracking, as well as communication, command, and data handling. Navigation and tracking involve processing of delay and Doppler shifts of the radio signal, as dis-cussed in the section on radar. The role of communications is to provide access to the deployed sensors and its platform, so that commands and data may be ex-changed between the remote system and its operators. Spacecraft communications generally involve wireless telecommunications. For wireless communications a carrier wave is modulated by a signal encoding the information to be communi-cated. The modulation schemes can be quite flexible, for example, in bandwidth division, the modulation itself is composed of multiple frequency bands. Some bands may contain digital information, while others may even contain analog in-formation. Other modes for telecommunications with spacecraft communications


on remote sensing missions include the beacon omnidirectional lower frequency lower power mode for conveying a limited amount of information.

Noise is anything which obscures or distorts the meaning of a message or sig-nature of a process being conveyed in a signal and is to be anticipated in an uncon-trolled environment. Important noise parameters are the signal to noise ratio and signal dynamic range. Types of electronic noise affecting instrument systems are thermal (random variations in current or voltage), shot (electrical conductor), burst (semiconductor), avalanche noise (electronic component near breakdown voltage) or ambient EM interference. Vibrations can also create mechanical offsets in, for example, pointing, reducing signal. Errors may result from systematic offsets from an absolute reference values, resulting in inaccuracy, or from fluctuations relative to a given value, resulting in imprecision, or from both. Periodicities in er-rors creates both inaccuracy and imprecision. In-flight noise removal strategies include cooling, active suppression, wave-forming and phase-locking, and instru-ment calibration procedures.

Data reduction is the process of creating normalized and standardized data, such as spectra, broadband data strings, or even images, from raw measurements obtained from spacecraft and instrument systems. Steps involve the initial unpack-ing and translation of downlinked data and rapid quality assessment of raw data in terms of flagged conditions, variations in instrument performance, and data cali-bration. Data calibration consists of background removal, pre- and in-flight in-strument calibration, source monitoring and normalization, and feature identifica-tion.

Next steps in data treatment involve the analysis of calibrated and normalized data, starting with statistical analysis of data to determine the nature of its distribu-tion (normal, Poisson, exponential or logarithmic), and modality, range, mean and variance. Histograms are a good visual representation. Continuous images can be created through low pass filtering or smoothing, using a weighted filter that represents the window spatial response function. Floating point data are converted to n-bit integers, where n is typically 8. Ideally, pixel size should represent the ef-fective spatial resolution. High pass filtering techniques are used to identify high-er frequency components of the image, such as edges, or random noise, or speckle. Images may be subjected to simple mathematical operations, including division by images at other bands to create simple band ratios, multiplication by normalization factors to remove systematic errors or source variations, subtraction to remove background. Images may be stretched, or density sliced, to show data value con-tours, with contour intervals assigned colors. Processing may be performed in the spatial or the frequency domains. An image could be decomposed into its periodic components, contributions of these spatial components could be enhanced or re-duced, and then the image could be rendered again with the modified set of com-ponents. More complex surfaces, expressing processes on a variety of scales, would require a greater number of fundamental modes. Although operation in the frequency domain is potentially more efficient and accurate than local finite-difference operations in the frequency domain, such operations imply a periodicity

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which may not be present in the spatial domain and modes may be artificially gen-erated.

Correlation and classification techniques establish the relationship between two or more datasets. Ratios or two datasets are a primitive form of classification. Two components can be classified on the basis of supervised or unsupervised clas-sification using a scatter plot. Principal Components Analysis relies on the fact that the number of relationships that can be used to describe a group of datasets is reduced based on fact that datasets have varying degrees of correlation. Cova-riance relationships are derived from axes of correlation of dataset pairs, with the most influential primary component axis have the strongest covariance relation-ship or dependence, and each covariance axis is represented by a color, the result-ing color of a pixel depending on the degree to which each it is correlated along each axis.

Bayesian classification scores clusters using hyper-ellipsoids whose surfaces mark standard deviations from the class center. These methods correlate popula-tions from datasets based strictly on statistics (unsupervised) or, for supervised classification, on the basis of a priori independently determined numerical discri-minators of signatures provided as ground truth using training sites on images. Classes identified are clearly recognizable on the basis of statistical significance, which can be assessed by the scatter or normally distributed spread, within a given class.

Modeling, or simulations of energy production from first principles, may be performed early to assist in the design of an instrument, or later to assist in the in-terpretation of the results. Modeling may be analytical, numerical, or empirical. Learning models, varying from Bayesian to neural network to genetic algorithm based, are used to perform pattern recognition.

Learning is a natural follow-on to data classification. Two phases are asso-ciated with learning algorithms. First, a training phase involves learning to distin-guish characteristics of targets. This is followed by an execution or application phase during which new observations are classified. A wide variety of algorithms have been developed. Unsupervised learning, the basis for data cluster analysis, generates classes from data and starts with limited a priori input. Supervised algo-rithms rely on the a priori identification of class exemplars, usually communicated through the use of training sets, subsets of the data identified with target classes. At present, many learning algorithms require a complete pass through the training data sets before they can be used (batch processing). For real-time applications or those with large data sets, we may turn to online or incremental learning algo-rithms that learn as data is presented, continuously updating themselves.

Geometric rectification or registration may be performed using nearest neigh-bor or interpolation algorithms. Images are transformed into the geographic pro-jection offering convenience (for purposes of comparison with other datasets) and the least distortion for the latitudes and longitudes of interest. Typically simple cy-lindrical (orthogonal), mercator, or polar conical projections are used for regular objects.


Essential data management means designing and operating an end-to-end data system during the course of a mission, a data distribution network responsive to the needs of the team, and delivering data products in an agreed upon schedule to temporary and permanent archives. The data management process begins with da-ta generation during mission planning. Data are accumulated, coded, packed ac-cording to protocols, and the process is reversed and data made available in an agreed upon format. Instrument and essential ancillary science or housekeeping data arrive as level zero, intelligible to those familiar with the mission. Level 1 da-ta represent the data reduction efforts, and level 2 data the analysis process. Level 3 data are high level interpretive products derived from measurements, for exam-ple. Each level has its own documented software products.

New tools for the data processing pipeline will enable greater automation and autonomy for onboard data processing and selection for download at one end, and smarter, more interactive archives on the other.

6.30 Some Questions for Discussions 1. What information processing steps should be accomplished before an instru-

ment is flown and why? 2. What is the role of signal processing in flight support? 3. What are the primary sources of noise for a typical spacecraft instrument and

how would an investigator best deal with them? 4. Describe the role of simulation and statistical analysis throughout the stages of a

remote sensing mission. 5. How can long integration time non-imaging spectral data be compared with

high resolution thermal imaging data acquired for the same target? Consider all the processing steps you would need to perform to correlate the two sets of measurements without producing processing artifacts.

6. An orbital lunar mission has just acquired visual imaging, moderate resolution

X-ray spectrometer data from which surficial iron abundances can be derived, and low resolution Gamma-ray spectrometer data from which iron abundances to greater depth can be derived, over the course of a year. Data reduction steps have already been performed. What types of processing would you now per-form to establish 1) relationship between iron derived from X-ray and Gamma-ray spectrometers, 2) relationship between iron abundance and visual features, and 3) an interpretation for your results in terms of iron distribution?

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