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An Analysis of State Vector Propagation Using Differing Flight Dynamics Programs

An Analysis of State Vector Propagation Using Differing Flight Dynamics Programs. David A Vallado Analytical Graphics Inc. Center for Space Standards and Innovation. Paper AAS-05-199, Presented at the AAS/AIAA Space Flight Mechanics Conference, Copper Mountain Colorado, January 23-27, 2005.

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An Analysis of State Vector Propagation Using Differing Flight Dynamics Programs

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  1. An Analysis of State Vector Propagation Using Differing Flight Dynamics Programs David A Vallado Analytical Graphics Inc. Center for Space Standards and Innovation Paper AAS-05-199, Presented at the AAS/AIAA Space Flight Mechanics Conference, Copper Mountain Colorado, January 23-27, 2005

  2. Overview • Introduction • Standards • Objective • Potential Error Sources • Initial State Vectors • Programs • Input Data Sources • Using the Input Data • Interpolation, timing, etc • State vector format • Study Process • Build up the force models

  3. Overview (continued) • Results • Force Model Sensitivity Analysis • Individual Force Model Contributions • Gravity • Atmospheric Drag • Solar Radiation Pressure • Ephemeris Comparison Results • Gravity • Third Body • Solar Radiation Pressure • Atmospheric Drag • Combined Forces • POE Comparison Results • Community Standard Ephemeris Baseline • Conclusions

  4. Introduction • Numerically derived state vectors • Not new to astrodynamics • Navy 1st full numerical catalog in 1997 • Answer fundamental question • What observations and processing are needed to achieve a certain level of accuracy on a particular satellite, now, and at a future time? • Requires • Orbit Determination • Propagation* • Standards • Other

  5. Objectives • Demonstrate the inconsistencies of AFSPC Instructions • 33-105 and 60-102 • Standards are useful when properly applied • Computer code is not a standard • Mathematical theory is a standard • Historically • SGP4 vs. PPT • Mathematical theory differences • Bad example of a need for standards  • WGS-72 vs WGS-84 • Good examples of a need for standards  • 1950 Nutation theory and 1980 IAU nutation theory • Example of need for a recommended practice  • 1980 IAU Nutation sum terms from 1-106 vs. 106 to 1

  6. Potential Error Sources • Inaccurate models • Measurement errors • Truncation error • Round-off • Mathematical simplifications • Human error • Tracking all input parameters* • Treatment of input data* * indicates important outcome from the paper

  7. Tracking All Input Data • Critical to provide adequate information • Proposed format at end of paper and on web • Detail treatment of • Satellite positional information • Forces included • Sizes, coefficients, etc. • Satellite characteristics • BC, mass, area, attitude, etc. • Source and use of data • Solar weather data, EOP, other • Integrator information • Covariance information Current formats simply not adequate

  8. Programs • Legacy Programs • GEODYN • GTDS • Raytheon TRACE • Special-K • STK/HPOP

  9. Input Data • Need correct constants and data • Coordinate system • Mean equator Mean equinox of J2000 • Integrator • Gravitational Model / Constants • EGM-96 Rotational vel 0.0743668531687138 rad/min • EGM-96 Radius earth 6378.137 km • EGM-96 Gravitational param 398600.4418 km3/s2 • EOP Timing coefficients from actual (EOPC04 or USNO) • Solar flux from actual (NGDC) measurements

  10. Test Conditions • Best approach built up force models incrementally • Two-body • Numerical integrators, Coordinate and Time Systems • Gravity Field • Checks mu, re, gravitational coefficients • Two-body plus Atmospheric Drag • Atmospheric density model, solar weather data handling • Two-Body plus Third-body • JPL DE/LE file incorporation, constants • Two-body plus Solar Radiation Pressure • Earth shadow model, solar constants

  11. Sensitivity Results • Force model contributions • Determine which forces contribute the largest effects • 12x12 gravity field is the baseline • Note • Gravity and Drag are largest contributors • 3rd body ~km effect for higher altitudes • Point to take away: • Trying to get the last cm from solid earth tides no good unless all other forces are at least that precise

  12. Force Model Contributions

  13. Sensitivity Results • Gravitational modeling • Typically square gravity field truncations • Appears the zonals contribute more • Point to take away: • Use “complete” field • Any truncations should include additional, if not all, zonals

  14. Gravitational Modeling • Satellite JERS (21867) • Note the dynamic variability over time

  15. Sensitivity Results • Atmospheric Drag • Large variations • Several sources • Using predicted values of F10.7, kp, ap for real-time operations • Not using the actual measurement time for the values (particularly F10.7 at 2000 UTC) • Using step functions for the atmospheric parameters vs interpolation • Using the last 81-day average F10.7 vs. the central 81-day average • Using undocumented differences from the original atmospheric model definition • Not accounting for [possibly] known dynamic effects – changing attitude, molecular interaction with the satellite materials, etc. • Inherent limitations of the atmospheric models • Use of differing interpolation techniques for the atmospheric parameters • Using approximations for the satellite altitude, solar position, etc. • Using ap or kpand converting between these values • Use of F10.7 vs E10.7 in the atmospheric models (not well characterized yet)

  16. Sensitivity Results • Plot • Note Dap almost as large as ap values • Note Last - Ctrd 81 day, 30-50 SFU • Factors examined • Daily • 3-Hourly • 3-Hourly interp • Last 81 day • Last 81 day, 2000 • F10.7 Day Con • F10.7 Avg Con • F10.7 All Con • All Con

  17. Atmospheric Drag • Differing models (left) • Note grouping of similar models • “transient” effects only for first day or so • Options for processing data (right) • Note 10-100km effect

  18. Sensitivity Results • Solar Radiation Pressure • Several variations shown • Notice maximum is only about 100m • Point to take away • Relatively small effect • Some variations

  19. Ephemeris Comparisons • Gravitational • GTDS (left) and Ray TRACE (right) examples • Generally cm and mm-level comparisons • Regularized time not explored

  20. Ephemeris Comparisons • Third-Body • GTDS (left) and Ray TRACE (right) examples • Generally a few cm

  21. Ephemeris Comparisons • Solar Radiation Pressure • GTDS (left) and Ray TRACE (right) examples • Generally a few m

  22. Ephemeris Comparisons • Atmospheric Drag • GTDS (left) and Ray TRACE (right) examples • A few km to many km • Recall sensitivity results which were even higher

  23. Ephemeris Comparisons • Combined forces • Several runs made without detailed build-up of forces • Included drag

  24. Ephemeris Comparisons • GEODYN tests • Starlette (7646) • Note plot on right • Difference of 2 GEODYN runs with different models • Nearly identical to sensitivity tests run for 7646

  25. Ephemeris Comparisons • GEODYN (cont) • TDRS comparison (4 days and 1 month)

  26. Ephemeris Comparisons • Special-K Comparisons

  27. POE Ephemeris Comparisons • POE Comparisons • Initial state taken and propagated • No coordination, estimate of drag and solar radiation pressure • Perturbed initial state results

  28. Community Ephemeris Baseline • Need to provide standard ephemeris comparison data • Provide community baseline on the web • Interactive forum for cooperative comparisons • Initial release designed to stimulate community involvement • NOT intended to force compliance • CSSI clearinghouse for this innovation • Data hosted under CenterForSpace website • www.centerforspace.com/EphemerisBaseline • Scenarios available for use in STK • CSSI available for consultation, analysis, inputs, questions

  29. Conclusions • Numerous conclusions in topical areas • Standards, Code, Instructions • Recommended Practice needed • Data Formats • Proposed format of additional information • Force model contributions • Summary for a particular satellite • Identify which are important • Results for comparisons • Conservative, cm-level • Non Conservative, km-level • Tremendous variability just with input data • Sensitivity studies • Tremendous variation • POE “analyses” • No propagation perfectly matches “truth”

  30. Conclusions • Bottom line • With variability on treatment of input data, • What does exact agreement mean? • Nothing • Right and wrong are indistinguishable! • Identical code is not needed to align programs • Attention to detail is • Adequate data formats is • Standardized approach for treating input data is • Cooperation is • Organizations involved in this study were tremendously helpful and cordial

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