An Analysis of State Vector Propagation Using Differing Flight Dynamics Programs

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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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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

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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

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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

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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

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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

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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

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Programs

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

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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

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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

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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

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Force Model Contributions
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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

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Gravitational Modeling

• Satellite JERS (21867)
• Note the dynamic variability over time

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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 kp and converting between these
  values
• Use of F10.7 vs E10.7 in the atmospheric models
  (not well characterized yet)

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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

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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

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Sensitivity Results

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

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Ephemeris Comparisons

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

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Ephemeris Comparisons

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

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Ephemeris Comparisons

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

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Ephemeris Comparisons

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

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Ephemeris Comparisons

• Combined forces
• Several runs made without detailed build-up of
  forces
• Included drag

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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

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Ephemeris Comparisons

• GEODYN (cont)
• TDRS comparison (4 days and 1 month)

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Ephemeris Comparisons

• Special-K Comparisons

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POE Ephemeris Comparisons

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

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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

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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

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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