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Statistical Orbit Determination: Software Packages and Previous Research. Brandon A. Jones University of Colorado / CCAR. The Orbit Determination Tool Kit (ODTK) . Brandon A. Jones University of Colorado / CCAR. Introduction. Summary of ODTK Scenario Setup Process Data Processing
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Statistical Orbit Determination:Software Packages and Previous Research Brandon A. Jones University of Colorado / CCAR
The Orbit Determination Tool Kit (ODTK) Brandon A. Jones University of Colorado / CCAR
Introduction • Summary of ODTK • Scenario Setup Process • Data Processing • Data Output • Sample Results Brandon A. Jones
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 Brandon A. Jones
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 Brandon A. Jones
Scenario Setup • Object Oriented Implementation • Satellites • Sensors: GPS Receiver/Antenna pair • Filters/Smoother • Etc. • Object Browser and Properties window provide primary interface Brandon A. Jones
Satellite Filter Properties Brandon A. Jones
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 Brandon A. Jones
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 Brandon A. Jones
Characterize filter & smoother Filter Processing Direction Filter (Current time process) Smoother (Post-fit process) Smoother Processing Direction Prediction Error Growth Filter Correction at Tracking Data Data Gap Smoother Post-Fit Solution
Data Output • Smoother and Filter output as a STK ephemeris file • Can output state and covariance information Brandon A. Jones
Data Output • Easy import of ODTK output to STK • Allows for analysis utilizing other STK tools • Visual comparisons to another ephemeris Brandon A. Jones
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 Brandon A. Jones
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? Brandon A. Jones
GIPSY-OASIS (GOA) Brandon A. Jones University of Colorado / CCAR
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 Brandon A. Jones
GOA Uses • Primarily processes GPS observations • Aids in mission design process • Provides capabilities to generate and process simulated observations • Aids in operational OD Brandon A. Jones
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 Brandon A. Jones
GOA Flowchart Source: GOA Tutorial Course Notes Brandon A. Jones
GOA Input • Function inputs provided by FORTRAN namelist files • Processes simulated and recorded GPS observations • Recorded observation format: RINEX Brandon A. Jones
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 Brandon A. Jones
Expected OD Accuracy for High Altitude, Highly Inclinated Satellites Using GPS Brandon Jones University of Colorado - CCAR
Outline • Simulation development • Summary of previous tests • Results • Future work Brandon A. Jones
Continuous measurement coverage Range (CA and Phase) Range-rate High accuracy (1-2 cm) Reduction in operation costs (Earth based tracking not required) Pedigree GPS and OD (1) Brandon A. Jones
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 Brandon A. Jones
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 Brandon A. Jones
MEO/GEO and GPS • Low elevation satellites provide measurements • Close to limb of Earth • Reduced signal power • Reduced satellite visibility Brandon A. Jones
GPS S/V Inclination • GPS Satellite inclination: 55 deg • Reduced visibility above poles • Low elevation satellites still visible Brandon A. Jones
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 Brandon A. Jones
Simulation Design Other error Sources (ionosphere, relativity, etc.) Antenna Characteristics Multipath Characteristics Gravity Models: GGM, EGM, etc. Atmospheric Drag Models Brandon A. Jones
High fidelity models Gravity - JGM-03 70x70 Ocean Tides Earth Tides Atmo. Drag - DTM94 Relativistic Forces Etc. True State File Measurement generator (qregres) Orbit Integrator(oi) Measurement Selector (C) Add measurement noise (qm_noise) Measurement Generation True GPS S/V File Measurement File Estimated State Files State Estimation Low fidelity models Gravity - JGM-03 70x70 True/Clone Ocean Tides Earth Tides Atmo. Drag - DTM79 Relativistic Forces “Wash Cycle” preprefilter prefilter filter smapper Orbit Integrator(oi) Prepare data for filter (qregres) Estimate GPS S/V File Gipsy-Oasis Simulation Design Brandon A. Jones
Case A: Circular orbit 550 km altitude 96 deg inclination Case C: Eccentric orbit 622 x 20200 km altitude 55 deg inclination Previous Tests • 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 Brandon A. Jones
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) Brandon A. Jones
Results - Case D Brandon A. Jones
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 Brandon A. Jones
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 Brandon A. Jones
Distribution Satellite Inclination Average Number of Satellites Brandon A. Jones
Smoothed Position Brandon A. Jones
Smoothed Position • Increased error with reduced number of satellites. • Inclination changes vs. accuracy Brandon A. Jones
Filter vs. Smoother Filter Smoother RSS 1.159 RSS 1.334 • Small impact for CA and phase processing • Has bigger impact with CA only processing (factor of 2) Brandon A. Jones
RSS = 1.159 RSS = 1.180 Smoothed Position True JGM-3 JGM-3 Gravity Clones • Gravity errors have an impact • Principal error source is measurement noise (~94%) Brandon A. Jones
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 Brandon A. Jones