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Statistical Orbit Determination: Software Packages and Previous Research

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

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  1. Statistical Orbit Determination:Software Packages and Previous Research Brandon A. Jones University of Colorado / CCAR

  2. Brandon A. Jones

  3. Brandon A. Jones

  4. The Orbit Determination Tool Kit (ODTK) Brandon A. Jones University of Colorado / CCAR

  5. Introduction • Summary of ODTK • Scenario Setup Process • Data Processing • Data Output • Sample Results Brandon A. Jones

  6. 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

  7. 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

  8. 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

  9. Satellite Filter Properties Brandon A. Jones

  10. 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

  11. 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

  12. 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

  13. Data Output • Smoother and Filter output as a STK ephemeris file • Can output state and covariance information Brandon A. Jones

  14. Data Output • Easy import of ODTK output to STK • Allows for analysis utilizing other STK tools • Visual comparisons to another ephemeris Brandon A. Jones

  15. STK can be used to visualize OD Tool Kit process

  16. 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

  17. 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

  18. GIPSY-OASIS (GOA) Brandon A. Jones University of Colorado / CCAR

  19. 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

  20. 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

  21. 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

  22. GOA Flowchart Source: GOA Tutorial Course Notes Brandon A. Jones

  23. GOA Input • Function inputs provided by FORTRAN namelist files • Processes simulated and recorded GPS observations • Recorded observation format: RINEX Brandon A. Jones

  24. 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

  25. Expected OD Accuracy for High Altitude, Highly Inclinated Satellites Using GPS Brandon Jones University of Colorado - CCAR

  26. Outline • Simulation development • Summary of previous tests • Results • Future work Brandon A. Jones

  27. 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

  28. 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

  29. 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

  30. MEO/GEO and GPS • Low elevation satellites provide measurements • Close to limb of Earth • Reduced signal power • Reduced satellite visibility Brandon A. Jones

  31. GPS S/V Inclination • GPS Satellite inclination: 55 deg • Reduced visibility above poles • Low elevation satellites still visible Brandon A. Jones

  32. How do we determine accuracy and visibility?

  33. 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

  34. Simulation Design Other error Sources (ionosphere, relativity, etc.) Antenna Characteristics Multipath Characteristics Gravity Models: GGM, EGM, etc. Atmospheric Drag Models Brandon A. Jones

  35. 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

  36. 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

  37. 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

  38. Results - Case D Brandon A. Jones

  39. 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

  40. 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

  41. Distribution Satellite Inclination Average Number of Satellites Brandon A. Jones

  42. Smoothed Position Brandon A. Jones

  43. Smoothed Position • Increased error with reduced number of satellites. • Inclination changes vs. accuracy Brandon A. Jones

  44. 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

  45. 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

  46. 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

  47. Questions?

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