a baro-altimeter augmented ins/gps navigation system for...

Presented at SatNav 2003 The 6th International Symposium on

Satellite Navigation Technology Including Mobile Positioning & Location Services

Melbourne, Australia

22–25 July 2003

A baro-altimeter augmented INS/GPS navigation system for an uninhabited aerial vehicle

J.H. Kim Australian Centre for Field Robotics, The University of Sydney, NSW 2006, Australia

Tel: +612 9351 7154, Fax: +612 9351 7474, Email: [email protected]

S. Sukkarieh Australian Centre for Field Robotics, The University of Sydney, NSW 2006, Australia

Tel: +612 9351 8154, Fax: +612 9351 7474, Email: [email protected]

ABSTRACT

This paper presents the results of augmenting an INS/GPS navigation system with a barometric altimeter for an autonomous Uninhabited Aerial Vehicle (UAV). The INS/GPS system was designed using a loosely coupled integration architecture that incorporates the GPS navigation solution. The GPS typically has a poor accuracy in the vertical channel due to satellite geometry and atmospheric effects. Even worse, the vertical channel is vulnerable to faults due to its inappropriate dynamic model coupled with the frequent loss of satellites when the UAV would bank. From the real-time flight tests, huge GPS faults were observed in the vertical axis, causing the INS/GPS navigation system to become unstable. By augmenting the baro-altimeter data, the vertical channel can be stabilized under GPS fault conditions. A ten-state Kalman filter was designed to optimally blend the INS with GPS and baro-altimeter. The results using the flight data show that the baro-altimeter augmented INS/GPS navigation system can provide more reliable and accurate navigation solutions under high maneuvering environments. KEYWORDS: Baro-altimeter, INS/GPS, Kalman filter, UAV.

1. INTRODUCTION Airborne navigation systems can broadly be divided into two categories: inertial (or dead-reckoning) navigation, and reference (or absolute) based navigation. An Inertial Navigation System (INS) makes use of an Inertial Measurement Unit (IMU) to sense the vehicle's angular rotation rate and acceleration. This data is then used to obtain vehicle states such as position,

PAPER 19 (peer-reviewed) 1

velocity and attitude, and it provides these at high data rates that are crucial for guidance and control operation. However, its diverging error nature due to the integration process requires external aiding information in order to constrain the drift. The most common and powerful aiding system can be the Global Positioning System (GPS), which can provide long-term stability with high accuracy, as well as worldwide coverage in any weather conditions. There have been extensive research activities in the fusion of INS and GPS systems, such as in the works of Phillips (1996) and Sukkarieh et al. (1999) and many others. The main drawback of using GPS is its dependency on external satellite signals that can be easily blocked or jammed by intentional/unintentional interference signals and atmospheric errors during signal transmission. An Uninhabited Aerial Vehicle (UAV) typically has limited payload capacity and sometimes requires high manoeuvrability to meet specific missions as well as precise navigation capability for autonomous flight operation. To meet these requirements, the navigation system must incorporate small and light, or equivalently low-quality, inertial sensors with external aiding information. As a result, the system performance becomes more dependent on the aiding quality of GPS. The degraded accuracy of GPS in the vertical axis is a well-known issue due to the effect of GPS satellite geometry. The DOP (Dilution of Precision) value typically has a poorer value in the vertical axis (i.e., VDOP) than in the horizontal. However, the more critical issue is faults in the vertical axis. In a high manoeuvring UAV, the vehicle body itself can easily block the satellite signal. If the number of satellites drops below four, some GPS receivers typically operate in height-fixed mode to provide 2D solution, or it makes use of the last fixed height information. In the integrated navigation system, the INS can provide solution during this height-fixed period and GPS may provide only horizontal position data for aiding. However, this frequent height-fixed operation together with the weakness in the internal GPS dynamic model can results in significant faults in GPS height. Figure 1 depicts this fault from the real-time flight test. Two GPS antennae were installed in both of the wing of UAV. The master antenna is installed in left wing (negative pitch axis). It provides navigation solution to the fusion filter. The slave antenna is installed in right wing (positive pitch axis) for additional attitude determination as well as to provide a redundancy. During flight, the vehicle undergoes successive negative banking for CCW (Counter Clock Wise) direction. This causes more signal shadings to the master antenna, and the number of satellites in the master GPS receiver frequently dropped below four. The slave antenna has a better sky view than master antenna and always see satellites more than six. During the first several rounds, the master receiver recovered the previous height accuracy after height-fixed mode within ten seconds. However, due to successive banking, the height error failed to converge and accumulated as in Figure 1. This is not a surprise because low-cost GPS typically exploits a low-dynamic model and after height-fixed mode, it takes time to converge to the actual height from the last fixed height. In land applications, this delay may not be problem if the terrain undulation is not severe. However, in airborne applications such as UAV, there can be huge difference between the GPS-indicated height and the actual height after height-fixed mode. Around 181050 seconds


(GPS time) from Figure 1, the error between two GPS outputs was around 100 m after height-fixed operation. This error in the master GPS was accumulated during successive maneuvering and reached up to 180 m, as shown in Figure 1. The nominal flight height is 110 m above ground, and this kind of error is intolerable for the low-altitude UAV.

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GPS fault in height of master receiver (Flight test on 2/7/2002)

GPS time in seconds (GPS week = 1173)

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)

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2D Mode or Height-fixed Mode

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2

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ber o

f SV

s

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GPS #2

Figure 1. GPS faults in altitude were observed in one of the GPS receivers during real-time flight

tests on July 2, 2002 (top). The GPS antenna installed on left wing side had poorer sky view compared to the other side and its number of satellite frequently dropped to three (bottom).

In INS/GPS navigation systems, this fault in the aiding sensor can be tackled via different methods: by using a statistical fault detection technique as in Sukkarieh (1999), redundant GPS system (if for example a second GPS receiver is placed on the other wing to maximise sky coverage), fusing GPS raw measurement data (which does not requires low-dynamic assumption), or barometric altimeter augmentation. In this paper, the barometric altimeter aiding method is used. It has several advantages compared to the other methods listed above:


A baro-altimeter is a cheap and readily available sensor for most airborne systems. It consists of air pressure sensor and data acquisition system. From the measured air pressure, the altitude above MSL (Mean Sea Level) can be obtained.

It provides an additional redundancy in height and GPS faults in height can be monitored under high manoeuvres.

Reliable altitude can be maintained even in GPS outage condition, which is a safety critical aspect for low-altitude flying UAVs.

The disadvantage is that the pressure-derived altitude is dependent on several factors, such as local temperature variation and wind environment, so proper error modelling is required. It also requires periodic calibration during flight. In this work, the baro-altimeter error is modelled as a first-order Markov process with measurement noise. It is also calibrated whenever the GPS receiver is in 3D mode with a good VDOP value. The developed Baro/INS/GPS system (Figure 2) consists of an IMU, two GPS receivers, and baro altimeter. A light and low-grade IMU is used which has bias repeatability of 0.01 deg/s and 1 mg for the gyros and accelerometers, respectively. The gyros are unable to detect the Earth rotation rate due to their low resolution. Two GPS antennas were installed on the wings of the UAV to provide redundancy as well as attitude information. The master GPS provides a navigation solution to the Baro/INS/GPS filter. Two inclinometers are used to calibrate the accelerometers during the initialisation stage and provide the angle accuracy after the flight test. Due to the highly dynamic nature of the UAV, the sensor instalment offset in vehicle can introduce additional errors with vehicle dynamics. This lever-arm effect was compensated accurately before fusing the data.

IMU

MasterGPS CG

x

yz SlaveGPS

Vision

Radar

Figure 2. The on-board sensor positions in the UAV.

Section 2 will describe the INS/GPS system with the error model of the baro-altimeter. It also presents the integrated Kalman filter. Section 3 will describe the physical flight system. Section 4 will present the results and Section 5 will finish with a conclusion.


2. BARO-AUGMENTED INS/GPS SYSTEM The UAV navigation system consists of a strapdown inertial navigation system, and fusion filter with aiding sensor as shown in Figure 3. The fusion filter plays a key role in navigation system. The main purpose of the fusion filter is to estimate the error of the inertial navigation solution as well as the baro-altimeter error from the external aiding information. The fusion filter is configured as multi-rate, multi-sensor aiding structure with an indirect complementary form as shown in Figure 3. The INS provides high-frequency vehicle states as a main navigation loop and the filter estimates and corrects the navigation error whenever the aiding information is available. The error in baro-altimeter typically has its own dynamics, so this error should be modelled and augmented into the fusion filter.

IMU StrapdownINS

GPS

FusionKalman

Filter

1z

2z

+-

+-

Angular RatesAccelerations Position, Velocity, and Attitude

MeasuredPosition and Velocity

PredictedPosition and

Velocity

Measured Altitude

PredictedAltitude

Estimated Errors inPosition, Velocity,

and Attitude

Baro-Altimeter

Figure 3. The structure of baro-altimeter augmented INS/GPS navigation system. 2.1 Strapdown Inertial Navigation The inertial navigation system provides vehicle states with high output rates to the guidance, flight controller and other mission sensor nodes such as target registration and picture compilation unit. It also has to provide precise timing synchronisation to other sensor nodes. Figure 4 describes the mechanization of strapdown INS in an Earth-fixed tangent frame where the navigation frame is local-level or tangent to local gravity vector and is fixed on a ground reference point, which can be either the pilot position or the ground station. The Earth is considered as a flat surface in the local vicinity of the flight test. As the mission profile has short flight duration and only covers several kilometres, the Coriolis effect due to the rotation of Earth and navigation frame are negligible. The change of gravity vector direction can also be ignored. The attitudes can be parameterised as Euler angles, quaternion, or as a direction cosine matrix. In this work the quaternion parameter was used to update the attitude as in Ignagni (1996) and Savage (1998). The INS initial alignment and calibration was performed using on-board tilt sensors before take-off. The low-resolution gyros cannot detect the Earth rotation rate, so the initial self-alignment technique for the heading cannot be exploited. The heading is transferred to UAV from dual GPS antennae.


ComputeEuler Angle

Accels

Gyros

bf nf na nv

ng

∫∫-

Position

Velocity

Attitude

+

(0)nv (0)np

1q q2

= ⊗ω&

nbC (q)

nbC (q)

0q

nibω

+

Figure 4. The strapdown INS is mechanised in an Earth-fixed tangent frame

where the reference frame is considered as an inertial frame. 2.2 Error Model for the Inertial Navigation The INS error model is required to estimate the error from the fusion filter. It is fairly well developed and can be found in many inertial navigation literatures as in the works of Chatfield (1997) and Meskin (1992). The model used in this work is for the INS mechanised in Earth-fixed frame as in the work of Sukkarieh et al (1999). The discrete time error equation can be summarized

n n

n

(k 1) (k) t (k)(k 1) (k) t( (k) (k) (k))(k 1) (k) t (k)

δ + = δ + ∆ δ

δ + = δ + ∆ ×δ + δ

δ + = δ −∆ δ

P P VV V f Ψ fΨ Ψ ω

(1)

where, δ , (δ and is the position error, velocity error, and misalignment error respectively, is the navigation update time interval, δ is the accelerometer noise transformed in NED frame and δ is the gyro noise transformed in NED frame.

(k)P kVt∆

) (k)δΨn (k)f

n (k)ω 2.3 Error Model for the Barometric-Altimeter As the Kalman filter set-up operates on system errors, the error behaviour of the barometric altimeter is also required. Figure 5 shows the block diagram for the error model of the barometric altimeter. It is modelled as the first order Markov process where the baro error is considered as the output of a first order system with the input of white Gaussian noise: w (Brown and Hwang, 1997). The time constant (

(t)β ) and standard deviation ( ) can be

determined by analysing the real baro-altimeter data. The resulting baro-altitude also contains measurement noise in addition to the Markov noise, so a measurement noise process v is added. The baro-altitude error becomes exponentially correlated in time (or has negative pole in frequency domain as shown in Figure 5) and it is a stable and bounded noise process.

σ

(t)


22sσ β+ β

w(t)

v(t)

zBaroP (t)δ z

BaroP (t) v(t)δ ++

Figure 5. The error of the baro-altimeter can be modelled as the sum of

Markov process, , with additional measurement noise, . zBaroP (tδ ) v(t)

The state dynamic equation can be directly obtained from Figure 3 in continuous time,

z zBARO BAROP (t) P (t) 2 w(tδ = −β⋅δ + σ β& 2 )

)

(2) Finally, the discrete time model can be obtained by integrating the above equation during the sampling time ( ), t∆

z t zBARO BARO dP (k 1) e P (k) w (k−β∆δ + = ⋅δ + (3)

where is a discrete noise process. This baro-altimeter error model together with the INS error model forms the state dynamic model in fusion filter.

dw (k)

2.4 State Dynamic Model for Fusion Kalman Filter The fusion filter state consists of 10 error states for the position, velocity, Euler angle of the INS and baro-altitude:

TBaro(k) [ (k) (k) (k) P (k)]δ = δ δ δ δx P V Ψ (4)

The discrete state dynamic model of filter in state-space form can be expressed as,

(k 1) (k) (k) (k) (k)δ + = δ +x F x G w (5) where is the noise input vector defined as [ ( with noise variance, Q . The state transition matrix F and process noise transfer matrix G is defined from Equation (1) and (3),

(k)w(

n ndk), (k), w (k)]δ δ δf ω T

k) (k) (k)


D E

D N

E N

t

1 0 0 t 0 0 0 0 0 00 1 0 0 t 0 0 0 0 00 0 1 0 0 t 0 0 0 00 0 0 1 0 0 0 f t f t 00 0 0 0 1 0 f t 0 f t 0

(k)0 0 0 0 0 1 f t f t 0 00 0 0 0 0 0 1 0 0 00 0 0 0 0 0 0 1 0 00 0 0 0 0 0 0 0 1 00 0 0 0 0 0 0 0 0 e−β∆

∆ ∆ ∆ − ∆ ∆ ∆ − ∆

= − ∆ ∆

F (6)

nb

nb

0 0 0 00 (k) 0

(k)0 0 (k) 00 0 0 1

0 = −

CG

C (7)

where C is the direction cosine matrix constructed from current quaternion, q . n

b (k) (k) 2.5 Observation Model The integrated navigation system makes use of two types of observation: GPS data and baro-altitude. The GPS receiver provides position and velocity in MGA (Map Grid Australia) format in 1Hz output rates. The baro-altimeter provides height measurement in 50Hz sample rates. These aiding data typically contain high-frequency measurement noise while the INS solution has low-frequency drifting error. The discrete observation model of filter in state-space form can be expressed by

(k) (k) (k) (k)= δ +z H x v (8) where is the observation noise vector with noise variance, . (k)v (k)R Whenever aiding information is available, the observation residual z is generated which contains an error of the inertial navigation as well as the aiding sensor. As the filter fuses two types of observation with different aiding rates, the observation model has two different forms according to the aiding data. When the GPS provides position and velocity data then the observation, , to the filter input can be obtained,

(k)

1(k)z

INS GPS INS P1

INS GPS INS V

(k) (k) (k) (k)(k)

(k) (k) (k) (k)− δ

= = − δ

P P P vz

V V V v

+

(9)

where the GPS position/velocity errors are assumed as white Gaussian noise processes. The observation residual contains the error in INS as well as the observation noise that can be


filtered out due to the low-pass filtering property. When the barometric altimeter data is available, the observation residual from baro-altimeter to the filter, z , is formed by subtracting the baro-measured altitude from the INS-indicated altitude:

2 (k)

z z

2 INS BARO

z z z zTURE INS TURE BARO 2

z zINS BARO 2

(k) P (k) P (k)

(P (k) P (k)) (P (k) P (k) v (k))

P (k) P (k) v (k)

= − = + δ − −δ − = δ + δ +

z

(10)

The resulting observation residual, z , contains INS altitude error, baro-altimeter error and observation noise. The INS altitude error mainly stems from the integration process and becomes an integrated random walk process that grows without bounds. While the baro-altitude error comes from local temperature variation, wind gust, and vehicle dynamics.

2 (k)

The observation model for GPS can be expressed in state-space form from Equation (9) by

3 11

3 1

(k) (k) (k)

δ

×

×

I 0 0 0z = x + v

0 I 0 0 1 (11)

and observation model for baro-altimeter can also be obtained from Equation (10) by

[ ]2 2(k) 0 0 1 0 0 0 0 0 0 1 (k) v (k= δz xM )+ (12) In Equation (11), the Figure Of Merit (FOM) information from GPS receiver is used as observation noise strength in . 1(k)v From these filter parameters, ,G , , and with the initial condition , the Kalman filter can complete its estimation cycle.

(k)F (k) (k)H (k)R (0)P

3. PHYSICAL SYSTEM The physical system can be divided into four categories; the flight vehicle, on-board systems, communication links, and ground station. The flight platforms are Brumby-MK3 as shown in Figure 5, which has a 20 kg payload capacity, 45 min flight duration, and 100 knots maximum speed. The on-board system consists of flight control computer, Baro/INS/GPS fusion filter, vision system, radar/laser system with gimballed scanner, and flight electronics. The vision and radar system perform target-tracking, target registration and decentralized data fusion. The air-to-air communication links are established for the decentralized fusion network and the air-to-ground link is used for pilot control, differential GPS correction, and monitoring vehicle status. The ground station consists of a DGPS receiver with antenna at a pre-surveyed position and monitoring systems. For details, refer to the work of Kim (2002). The onboard sensor configuration is shown in Figure 6. The IMU, two GPS receivers and tilt sensor are connected to the Flight Control System (FCS). The IMU from Inertial Science is


very light and small, which makes it suitable for UAV applications. Two AllstarTM GPS receivers from BAE Systems are stacked on the FCS with two antennae installed on each of the wings. The master GPS receiver provides navigation solution to the filter and the slave receiver operates as a complementary sensor. The barometer’s pressure sensors are installed in the right wing tip and fuselage. The absolute and differential pressures are sampled in a FlexIOTM system, which was developed at the University of Sydney. The sampled pressure data is sent to the FCS via serial connection.

Figure 6. A fleet of four UAVs: MK3-Brumby. Four sets of identical navigation and guidance systems are installed with different mission payloads.

4. RESULTS A flight test was performed on April 17, 2003. The main purpose of this test was to demonstrate the real-time autonomous navigation as well as the corporation between multiple-vehicles. The total flight time was around 15 minutes and the nominal flight height was 330 ft above ground. The maximum ground speed was 80 knots. Figure 7 shows the estimated flight trajectory with GPS output. The navigation output was plotted from the real-time INS/GPS filter and the baro-altimeter data was logged for the Baro/INS/GPS filter. The visibility of GPS Satellite Vehicle (SV) was normal condition where the number of SV varied from 4 to 8 during flight. The maximum bank angle was limited to 60 deg, which was required to meet the mission profile. This steep banking typically caused the number of SV to drop to 4 as shown in Figure 8. After take-off the baro-altimeter is calibrated from the GPS height with good VDOP value. Then the baro-altitude is used for vertical aiding while the GPS data is used for horizontal aiding. The GPS height information is ignored inside the filter by allocating large measurement noise in height. Figure 9 compares the estimated height between Baro/INS/GPS filter with INS/GPS filter. From this plot, it can be shown that the baro-integrated filter can suppress the high-frequency noise in baro-altitude as well as estimate the drifting INS errors in height. As the number of SV was more than four at all time, the height fixed mode was not occurred and no significant faults were observed. As a result, both of the Baro/INS/GPS and INS/GPS filter showed similar performance in altitude. However, the Baro/INS/GPS filter showed smoother and reliable results compared to that of the INS/GPS, as the GPS height still degraded from poor satellite geometry and iono/atmospheric effects.


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MGA North (m)

Hei

ght (

ft)

NAVGPS

Drive-way Runway

Take-off

LandingApproach

Figure 7. The fight trajectory from test on April 17, 2003.

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ber o

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ellit

e V

ehic

les

Time from start navigation (sec)

Figure 8. The 2D position using the GPS horizontal aiding (left) and satellite visibility during flight test (right).

600 650 700 750 800 850 900 950725

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Figure 9. Comparison of height results from INS/GPS/Baro filter and INS/GPS filter (left) and its enhanced view (right).



5. CONCLUSIONS This paper presented the results of augmenting an INS/GPS navigation system with a baro-altimeter data. The GPS typically shows a poor accuracy in vertical channel due to poor vertical dilution of precision. In high-manoeuvring UAV platform, vertical channel is also vulnerable to faults due to its inappropriate dynamic model coupled with the frequent loss of satellites when the UAV would bank. In this paper, the vertical channel was stabilized by augmenting the baro-altimeter. The fusion filter was designed as ten states complementary filter with nine INS error states and one baro-altimeter error state, which was modelled as a first-order Markov process. By processing the real-flight data, the Baro/INS/GPS filter shows that it can suppress the high-frequency baro-altimeter noise as well as estimate the drifting INS vertical error properly. Compared to the GPS only aided INS system, it also shows smoother and more reliable solution even in high manoeuvring environments. ACKNOWLEDGEMENTS: The authors wish to thank BAE Systems (UK and Australia) for their support in providing funding and systems engineering towards this project. REFERENCES Brown RG, Hwang PYC (1997) Introduction to Random Signals and Applied Kalman Filtering, John

Wiley and Sons, Inc, USA, 407-410. Chatfield A (1997) Fundamentals of High Accuracy Inertial Navigation, American Institute of

Aeronautics and Astronautics, Inc, USA, 211-237. Ignagni MB (1996) Efficient Class of Optimized Coning Compensation Algorithm, Journal of

Dynamic Systems, Measurement and Control 19(2): 424–429. Meskin DG, Bar-Itzhack IY (1992) Unified Approach to Inertial Navigation System Error Modeling,

Journal of Guidance, Control, and Dynamics 15(3): 648–653. Kim J, Sukkarieh S (2002) Flight Test Results of GPS/INS Navigation Loop for an Autonomous

Unmanned Aerial Vehicle (UAV), in Proceedings of the 15th International Technical Meeting of the Satellite Division of the Institute of Navigation, Portland, USA, Sep., 510–517.

Phillips R, Schmidt G (1996) GPS/INS Integration, Advisory Group for Aerospace Research and

Development (AGARD), Lecture series 207, 9.1–9.10. Savage PG (1998) Strapdown Inertial Navigation Integration Algorithm Design Part I: Attitude

Algorithms, in Journal of Dynamic Systems, Measurement and Control 21(1): 19–28. Sukkarieh S, Nebot E, Durrant-Whyte H (1999) A High Integrity IMU/GPS Navigation Loop for

Autonomous Land Vehicle Applications, IEEE Transactions on Automatic Control 15: 572–578.

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