Statistical Orbit Determination:Software Packages and Previous
Research
Brandon A. JonesUniversity of Colorado / CCAR
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The Orbit Determination Tool Kit (ODTK)
Brandon A. JonesUniversity 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. JonesUniversity 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 GPSBrandon 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 =
XYZ˙ 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?