Orbit Determination Software at ESOC Flight Dynamics

1
Orbit Determination Software at ESOC Flight
Dynamics

• Frank Budnik
• Ruaraidh Mackenzie

2
Overview of OD software

• MSSS Multi-Satellite Support System
• NAPEOS Navigation Package for Earth Orbiting
  Satellites
• PEPSOC Portable ESOC Package for Synchronous
  Orbit Control
• IPSF Interplanetary Software Facility
• AMFIN Advanced Modular Facility for
  Interplanetary Navigation
• Main purpose of all is to support spacecraft
• operations and to ensure a safe navigation of the
  spacecraft.

3
Interplanetary Software Facility

• Spacecraft orbit determination program
• "Default" OD program to determine the spacecraft
  orbit relative to the SSB, Sun or any of the
  planets using radiometric tracking data
• Comet and asteroid orbit determination program
• OD program to determine the orbit of minor solar
  system bodies relative to the SSB using
  ground-based astrometric observations
• Relative orbit determination program
• Improvement of the estimates of the state of a
  solar system body relative to the state of the
  spacecraft by using optical data including
  background stars
• Orbit determination program for a spacecraft
  orbit around the comet
• Simultaneous determination of the spacecraft
  orbit relative to the comet, the orbit of the
  comet relative to the Sun, the attitude and the
  body rates of the comet using optical data
  providing measurements of cometary landmarks

4
Measurements

• Radiometric tracking data
• 2-way Doppler and range from DSN and ESA tracking
  systems
• Delta-DOR from DSN and ESA
• Angular measurements from ESA stations
• Camera observations
• Images of a solar system body in front of the
  stellar background obtained from a camera onboard
  a spacecraft
• Images of landmarks on a solar system body
  obtained from a camera onboard a spacecraft
• Astrometric Data
• Ground-based astrometric observations mainly
  supplied by the Minor Planet Centre

5
The Algorithms

• The algorithms of our software are based to a
  very large extent on Moyers books
• Moyer, T.D., Mathematical Formulation of the
  Double-Precision Orbit Determination Program
  (DPODP), Technical Report 32-1527, JPL, 1971
• Moyer, T.D, Formulation for Observed and Computed
  Values of Deep Space Network Data Types for
  Navigation, Deep Space Communications and
  Navigation Series, Monograph 2, JPL, 2000.
• The implementation of the algorithms has been
  validated extensively against the ODP

6
Integrating the Equation of Motion (1/2)

• The equation of motion and variational equations
  are integrated using an 8th order numerical
  integration scheme attributed to Nordsieck.
• Nordsieck's method is a multi-value, variable
  step size algorithm for integrating first order
  differential equations which is known to be
  numerically very stable.
• Variable step size control determined by the
  Newtonian forces only.
• Treatment of discontinuities (e.g. manoeuvres,
  slews, etc.) in the right-hand side of the
  equation of motion is included.
• Disadvantage of multi-value method requirement
  of re-initialisation at force function
  discontinuities.

7
Integrating the Equation of Motion (2/2)

• Point mass and relativistic perturbative
  accelerations in the solar-system barycentric
  frame of reference according to Moyer 1971,
  2000.
• Coordinate time is expressed in TDB time scale.
• Considered Bodies Sun, Planets, Pluto, the Moon,
  Phobos Deimos and the big three asteroids
• DE405 planetary ephemerides are used so far
  update to DE421 and INPOP will happen this year
• Centre of integration can be the SSB, the Sun,
  the Earth, the Moon or one of the planets, it can
  be automatically switched when entering or
  leaving the sphere of influence of a body.
• Other perturbative forces that can be taken into
  account
• solar radiation pressure
• spherical harmonic gravity field expansion of a
  planet
• air drag
• manoeuvres.

8
Modeling Radiometric Tracking Data (1/2)

• Station location corrected for plate motion and
  solid Earth tides
• Transformation ITRF lt-gt ICRF according to 1984
  theory of precession and nutation
• EOP parameters updated daily from IERS
• Modified Lorentz correction when transforming
  from the local geocentric to the barycentric
  space-time frame of reference
• Time transformation from UTC to TDB at the
  tracking station on Earth is computed using the
  algorithm described in Moyer 1971, 2000 taking
  into account station location dependent terms
  with amplitudes of 0.1 ps.
• Light time solution computed according to Moyer
  2000 taking into account the Shapiro effect due
  to all planets and the Sun and the bending of the
  light path due to the Sun only
• Range is derived directly from the light-time
  equation
• Range-rate is modeled as differenced range
  (alternatively but rarely used by us as Taylor
  series expansion)

9
Modeling Radiometric Tracking Data (2/2)

• Tropospheric corrections
• derived from weather data acquired at the
  tracking station
• Saastamoinen Model Niell elevation mapping
  function
• Ionospheric corrections
• provided by TSAC group at JPL for current
  interplanetary probes
• interface for TEC values derived from GPS
  measurement is being established
• Klobuchar iononspheric model
• Solar plasma corrections
• simple plasma model included
• predictive capabilities are limited
• Ground station and transponder group delay
  calibration

10
Parameter Estimation

• Parameter estimation performed by a batch square
  root information filter (SRIF)
• SRIF is mathematically equivalent to weighted
  least squares but numerically superior
• On a basic level colored noise can be included in
  form of Exponentially Correlated Random Variables
  (ECRVs)
• A flexible parameter-book keeping system allows
  to treat parameters as fixed, consider,
  solve-for, or as ECRV.