Statistical Orbit Determination:Software Packages and Previous

Research

Brandon A. Jones

University of Colorado / CCAR

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The Orbit Determination Tool Kit (ODTK)

Brandon A. Jones

University of Colorado / CCAR

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Introduction

• Summary of ODTK

• Scenario Setup Process

• Data Processing

• Data Output

• Sample Results

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ODTK Description

• Provides OD and orbit analysis support– Estimates satellite state– Estimates environment parameters– Profile equipment characteristics– Covariance analysis

• Integrated with Satellite Tool Kit (STK)• Primary Tools:

– Tracking Data Simulator– Filter Capabilities

• Least Squares Estimator• Sequential filter

– Filter Smoother– Graph/Report Generator

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ODTK Description

• Residual editing

• Combines multiple observation sources to provide state estimate

• Includes vehicle attitude variations

• Advertises realistic covariance– CCAR studies have shown this varies from

satellite to satellite

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Scenario Setup

• Object Oriented Implementation– Satellites– Sensors: GPS

Receiver/Antenna pair– Filters/Smoother– Etc.

• Object Browser and Properties window provide primary interface

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Satellite Filter Properties

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Data Processing

• Two Primary Data Sources:– Simulation Data– External Data

• Several external data formats recognized:– RINEX– More…

• Data analysis automation through scripting– Monte Carlo Analysis

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Data Processing

• Data simulation tool is capable of generating all data sources processed by ODTK– Used for preliminary analysis and

performance evaluation

• Assists in satellite and ground station design phase

• Helps determine operations requirements

Pg 12 of 35AGI www.agi.com

Characterize filter & smoother

0

400

800

1200

1600

12 16 20 24 28 32 36 40 44 48 52 56 60

Two Sigmas (m)

Intrack Position Uncertainty (0.95P)Intrack Position Uncertainty (0.95P)

Hours

Filter (Current time process)Smoother (Post-fit process)

Filter Processing Direction

Smoother Processing Direction

Data Gap

Prediction ErrorGrowth Filter Correction

at Tracking Data

SmootherPost-FitSolution

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Data Output

• Smoother and Filter output as a STK ephemeris file

• Can output state and covariance information

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Data Output

• Easy import of ODTK output to STK– Allows for analysis utilizing other STK tools– Visual comparisons to another ephemeris

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STK can be used to visualize OD Tool Kit process

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Data Output

• Static/Dynamic Product Builder– Charts for visual

output– Reports for data

output• Multiple data formats:

MS Word, PDF, Text

• Reports allow for post-processing of ODTK results

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Summary

• ODTK provides most OD software required for data analysis

• Includes state estimate and covariance analysis capabilities

• Data export capabilities provide increased flexibility during data analysis process

• Questions?

GIPSY-OASIS (GOA)

Brandon A. Jones

University of Colorado / CCAR

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GOA Overview

• GPS-Inferred Positioning SYstem and Orbit Analysis Simulation Software (GIPSY-OASIS)

• Product of JPL/NASA

• Square-Root Information Filter (SRIF)

• SRIF Smoother

• Advertises 1-2 cm level accuracy: on-orbit and terrestrial scenarios

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GOA Uses

• Primarily processes GPS observations

• Aids in mission design process– Provides capabilities to generate and process

simulated observations

• Aids in operational OD

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GOA vs. STK/ODTK

• Advantages:– Pedigree– Various modules/utilities have uses outside of GOA

data processing– GOA provides increased scenario customization

• Disadvantages– Requires increased understanding of OD process– Unix command line interface reduces user

friendliness• GUI is provided, but reduces user control of OD processing

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GOA Flowchart

Source: GOA Tutorial Course Notes

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GOA Input

• Function inputs provided by FORTRAN namelist files

• Processes simulated and recorded GPS observations– Recorded observation format: RINEX

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GOA Output

• Outputs filter state in FORTRAN binary file– Includes utilities to convert output to text

output in a variety of formats• .sp3, .jpltext, .sp1, etc.

• Outputs covariance in similar binary file• Includes some graphical output

capabilities– CCAR studies utilize MATLAB to customize

graphical output

Expected OD Accuracy for High Altitude, Highly Inclinated

Satellites Using GPS

Brandon Jones

University of Colorado - CCAR

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Outline

• Simulation development

• Summary of previous tests

• Results

• Future work

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GPS and OD (1)

• Continuous measurement coverage– Range (CA and Phase)– Range-rate

• High accuracy (1-2 cm)• Reduction in operation

costs (Earth based tracking not required)

• Pedigree

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GPS and OD (2)

• Satellite positions are known, thus range measurements are used to triangulate the satellite position

• For real-time position estimation, four satellites must be visible for position estimation– Requires at least four equations for the four

unknown values• X, Y, and Z• Time

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GPS Visibility

• GPS satellites orbit at ~20,200 km altitude

• Primary signals broadcast in 27.8 deg cone– Side lobes provide

weakened signal

• Limits satellite altitudes for optimal visibility– Acceptable for most LEO

satellites

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MEO/GEO and GPS

• Low elevation satellites provide measurements– Close to limb of Earth

• Reduced signal power

• Reduced satellite visibility

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GPS S/V Inclination

• GPS Satellite inclination: 55 deg

• Reduced visibility above poles

• Low elevation satellites still visible

How do we determine accuracy and visibility?

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Gipsy-Oasis

• Software package developed by NASA-JPL for POD studies– Specialized in GPS data processing

• Implements a Sequential Square Root Information Filter (SRIF) with data smoothing

• Provides capabilities for data simulation

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Other errorSources (ionosphere, relativity, etc.)

Simulation Design

€

Xo =

X

Y

Z˙ X ˙ Y ˙ Z

M

⎡

⎣

⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥

Gravity Models:GGM, EGM, etc.

Atmospheric Drag Models

Antenna Characteristics

Multipath Characteristics

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Gipsy-Oasis Simulation Design

OrbitIntegrator(oi)

OrbitIntegrator(oi)

High fidelity modelsGravity - JGM-03 70x70Ocean TidesEarth TidesAtmo. Drag - DTM94Relativistic ForcesEtc.

Low fidelity modelsGravity - JGM-03 70x70 True/CloneOcean TidesEarth TidesAtmo. Drag - DTM79Relativistic Forces

True State File

Measurement generator (qregres)

Measurement Selector (C)

Add measurement noise (qm_noise)

Prepare data for filter (qregres)

Measurement File

“Wash Cycle”preprefilterprefilterfiltersmapper

Estimated State Files

Measurement Generation

State Estimation

True GPS S/V File

Estimate GPS S/V File

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Previous Tests

• Case A:– Circular orbit– 550 km altitude– 96 deg inclination

• Case C:– Eccentric orbit– 622 x 20200 km

altitude– 55 deg inclination

• Case B:– Eccentric orbit– 520 x 7800 km altitude– 116.57 deg inclination

• Case D:– Molniya orbit– 1600 x 38900 km

altitude– 63.4 deg inclination

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Simulation Details

• Run for 3 orbital periods• GPS transmission EIRP: 28.2 dBW• Signal power strengths of at least 35 dB-Hz• 12 Channel receiver modeled• Measurement types: DF M-code (Range and

Phase)• Measurement noise: = 1.72 m (Logan, 2005)• Filter noise (simulation dependent)

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Results - Case D

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Test Expansion

• Expand tests for many sun-synchronous orbits– Used software batch processing and Python to

automate processing– Eccentricity between 0.0 and 0.5, increments of 0.2– Altitude of periapsis between 800 and 6300 km,

increments of 250 km– Processed CA and Phase (DF, Single differenced

measurements)– Filter and smoother– Gravity clones

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Gravity Clone?

• When gravity models determined, there is a corresponding covariance matrix– A gravity clone is a similar model that satisfies

the covariance matrix

• Used 6, 1- gravity clones of the JGM-3 model for reference trajectory

• Allows for processing with gravity errors– Characterize impact on gravity error on state

estimation

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Distribution

Satellite Inclination Average Number of Satellites

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Smoothed Position

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Smoothed Position

• Increased error with reduced number of satellites.

• Inclination changes vs. accuracy

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Filter vs. Smoother

• Small impact for CA and phase processing• Has bigger impact with CA only processing (factor of 2)

RSS 1.334 RSS 1.159

Filter Smoother

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Smoothed Position

• Gravity errors have an impact• Principal error source is measurement noise (~94%)

RSS = 1.159

RSS = 1.180

True JGM-3 JGM-3 Gravity Clones

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Other Tests

• Critically inclined orbits– Both prograde and retrograde– Eccentricities between 0.0 and 0.7, increments of

0.02– Altitude of periapsis between 800 and 20,200 km,

increments of 500 km– Maximum altitude at apoapsis of 20,200 km (semi-

synchronous orbit)

• Recommended future tests include major transfer orbits

• Increase model fidelity

Questions?