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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


Overview
Overview Flight Dynamics Programs

  • 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) Flight Dynamics Programs

  • 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


Introduction
Introduction Flight Dynamics Programs

  • 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


Objectives
Objectives Flight Dynamics Programs

  • 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 Flight Dynamics Programs

  • 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 Flight Dynamics Programs

  • 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


Programs
Programs Flight Dynamics Programs

  • Legacy Programs

    • GEODYN

    • GTDS

    • Raytheon TRACE

    • Special-K

    • STK/HPOP


Input data
Input Data Flight Dynamics Programs

  • 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 Flight Dynamics Programs

  • 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 Flight Dynamics Programs

  • 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


Force model contributions
Force Model Contributions Flight Dynamics Programs


Sensitivity results1
Sensitivity Results Flight Dynamics Programs

  • 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 Flight Dynamics Programs

  • Satellite JERS (21867)

    • Note the dynamic variability over time


Sensitivity results2
Sensitivity Results Flight Dynamics Programs

  • 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 Flight Dynamics Programs

  • 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 Flight Dynamics Programs

  • 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 Flight Dynamics Programs

  • 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 Flight Dynamics Programs

  • Gravitational

    • GTDS (left) and Ray TRACE (right) examples

    • Generally cm and mm-level comparisons

    • Regularized time not explored


Ephemeris comparisons1
Ephemeris Comparisons Flight Dynamics Programs

  • Third-Body

    • GTDS (left) and Ray TRACE (right) examples

    • Generally a few cm


Ephemeris comparisons2
Ephemeris Comparisons Flight Dynamics Programs

  • Solar Radiation Pressure

    • GTDS (left) and Ray TRACE (right) examples

    • Generally a few m


Ephemeris comparisons3
Ephemeris Comparisons Flight Dynamics Programs

  • 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 Flight Dynamics Programs

  • Combined forces

    • Several runs made without detailed build-up of forces

    • Included drag


Ephemeris comparisons5
Ephemeris Comparisons Flight Dynamics Programs

  • 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 Flight Dynamics Programs

  • GEODYN (cont)

    • TDRS comparison (4 days and 1 month)


Ephemeris comparisons7
Ephemeris Comparisons Flight Dynamics Programs

  • Special-K Comparisons


Poe ephemeris comparisons
POE Ephemeris Comparisons Flight Dynamics Programs

  • 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 Flight Dynamics Programs

  • 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


Conclusions
Conclusions Flight Dynamics Programs

  • 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”


Conclusions1
Conclusions Flight Dynamics Programs

  • 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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