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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

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

  • 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
overview continued
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
  • 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
  • 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
potential error sources
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

tracking all input data
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

  • Legacy Programs
    • GEODYN
    • GTDS
    • Raytheon TRACE
    • Special-K
    • STK/HPOP
input data
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
test conditions
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
sensitivity results
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
sensitivity results1
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
gravitational modeling
Gravitational Modeling
  • Satellite JERS (21867)
    • Note the dynamic variability over time
sensitivity results2
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)
sensitivity results3
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
atmospheric drag
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
sensitivity results4
Sensitivity Results
  • Solar Radiation Pressure
    • Several variations shown
    • Notice maximum is only about 100m
    • Point to take away
      • Relatively small effect
      • Some variations
ephemeris comparisons
Ephemeris Comparisons
  • Gravitational
    • GTDS (left) and Ray TRACE (right) examples
    • Generally cm and mm-level comparisons
    • Regularized time not explored
ephemeris comparisons1
Ephemeris Comparisons
  • Third-Body
    • GTDS (left) and Ray TRACE (right) examples
    • Generally a few cm
ephemeris comparisons2
Ephemeris Comparisons
  • Solar Radiation Pressure
    • GTDS (left) and Ray TRACE (right) examples
    • Generally a few m
ephemeris comparisons3
Ephemeris Comparisons
  • Atmospheric Drag
    • GTDS (left) and Ray TRACE (right) examples
    • A few km to many km
      • Recall sensitivity results which were even higher
ephemeris comparisons4
Ephemeris Comparisons
  • Combined forces
    • Several runs made without detailed build-up of forces
    • Included drag
ephemeris comparisons5
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
ephemeris comparisons6
Ephemeris Comparisons
  • GEODYN (cont)
    • TDRS comparison (4 days and 1 month)
ephemeris comparisons7
Ephemeris Comparisons
  • Special-K Comparisons
poe ephemeris comparisons
POE Ephemeris Comparisons
  • POE Comparisons
    • Initial state taken and propagated
    • No coordination, estimate of drag and solar radiation pressure
    • Perturbed initial state results
community ephemeris baseline
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
      • Scenarios available for use in STK
    • CSSI available for consultation, analysis, inputs, questions
  • 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”
  • 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