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. MORE Relativity Meeting, Rome February 2009

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 MORE Relativity Meeting, Rome February 2009

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 MORE Relativity Meeting, Rome February 2009

5. The Algorithms • The algorithms of our software are based to a very large extent on Moyer’s 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 MORE Relativity Meeting, Rome February 2009

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. MORE Relativity Meeting, Rome February 2009

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. MORE Relativity Meeting, Rome February 2009

8. Modeling Radiometric Tracking Data (1/2) • Station location corrected for plate motion and solid Earth tides • Transformation ITRF <-> 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) MORE Relativity Meeting, Rome February 2009

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 MORE Relativity Meeting, Rome February 2009

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. MORE Relativity Meeting, Rome February 2009