GPS High Precision Orbit Determination Software Tools (GHOST)

Overview

GHOST is a powerful software package for GPS based orbit determination of satellites low Earth orbit (LEO). GHOST comprises different modules for data preprocessing, kinematic positioning and reduced dynamic orbit determination using spaceborne GPS measurements. Satellite laser ranging data can, furthermore, be processed for orbit validaton purposes.

All programs build up on a common library of C++ modules for GNSS data processing, spacecraft trajectory modeling, and estimation. The GHOST library and application programs have been developed by DLR's German Space Operations Center (DLR/GSOC) in close cooperation with the Delft Institute of Earth Observation and Space Systems (DEOS) at TU Delft.

GHOST Processing Chain

The GHOST suite is made up of individual tools that can freely be combined by the user to implement a mission specific processing scheme. All programs operate in a non-interactive mode which facilitates their use in script based procedures and the setup of automated processing chains.

Fig. 1 Core GHOST processing scheme

Typically, the following steps are performed in sequence:

Initially, the coarse position and clock offset at each epoch are determined from the observed pseudoranges using the SPPLEO (Single-Point POsitioning for LEO Satellites) program. Depending on the available receiver, the results have a typical accuracy between 3 m (dual-frequency) and 10 m (single-frequency). Optionally, the SPPLEO can also determine the velocity and clock drift at each from Doppler measurements.
The coarse position fixes are subsequently smoothed by the PosFit program, which adjusts a reduced-dynamics trajectory using the positions as pseudo-measurements. The resulting trajectory can already achieve an accuracy of 0.2-2 m but serves primarily as a reference for the data in the following processing steps.
The actual precise orbit determination is carried out in the RDOD (Reduced Dynamics Orbit Determination) program. Using the a priori orbit as a reference, the code and carrier phase measurements are initially screened for outliers and bad data. The spacecraft trajectory is modelled using a concise dynamically model with supplementary empirical acceleration parameters that are adjusted along with epoch wise clock offsets and pass-by-pass biases in a large least-squares process. Typically, a total of 4000 parameters is adjusted in a 24 hours arc, but the size of the normal equations can conveniently be reduced by factorization and pre-elimination. Through the use of low-noise carrier phase measurements, the position accuracies down to the level of a few centimeters can be achieved in this orbit determination process.
As an alternative to the reduced dynamics processing, purely kinematic solutions can be obtained in the KIPP (Kinematic Point Positioning) program. Similar to RDOD, this program benefits from the processing of highly accurate carrier phase measurements and can thus achieve accuracies of 10 cm or better. However, no dynamical model is employed and individual positions are adjusted at each epoch along with the associated receiver clock offsets. Kinematic orbits are generally more sensitive to modeling errors and the comparison with reduced dynamic solutions can provide valuable insight into the achieved orbit dtermimation quality. In addition, kinematic orbit determination results are of interest for gravity field studies since they do not involve any a a priori assumptions on the spacecraft dynamics.
Satellite laser ranging provides high accuracy measurements that can be used for an external validation of GPS based orbit determimation results. To this end residuals of the SLR measurements with respect to the GPS based reduced dynamic orbit solutions are computed and statistically anyalzed in the SLRRES program.

The entire processing chain requires some 5-10 min on a standard desktop computer for representative LEO data sets with 24-30h arcs, 10-30 s step size, and 8-12 receiver channels. Single-orbit arcs in a near-real-time orbit determination system can be processed within less than one minute.

Models

GHOST employs state of the art dynamical and measurement models for the processing of GPS and SLR observations and the modeling of spacecraft trajectories.

Item Description

GPS measurement model Undifferenced ionospheric-free code and phase observations;
IGS GPS orbits and 30s clock solutions in IGS05 reference system;
GPS and receiver antenna phase center offsets and variations;
phase wind-up.

SLR measurement model SLRF2005 station coordinates;
Solid Earth and pole tides (IERS2005),
GOT00.2 ocean loading,
Marini & Murray tropospheric delay model (IERS2005).

Gravitational forces Earth gravity field (UT/CSR GGM01 100x100, or other)
relativity
solid-earth tides, pole tide (IERS2003)
ocean tides (UT/CSR TOPEX_3.0 or other)
luni-solar third body acceleration using low-accuracy analytical ephemerides

Non-gravitational forces Jacchia-Gill atmospheric density model with daily F10.7 and 3-hourly Kp values
Cannon ball solar radiation pressure model with conical Earth shadow model (umbra, penumbra)
Empirical accelerations in radial, along-track and cross-track direction at 10 min (default) interval

Reference frames EME2000
IAU 1976 precession (Lieske model)
IAU 1980 nutation (Wahr model)
Earth orientation from IERS igs96p02 solution
Spacecraft body frame orientation modelled based on attitude quaternions or default attitude modes

Item	Description
GPS measurement model	Undifferenced ionospheric-free code and phase observations; IGS GPS orbits and 30s clock solutions in IGS05 reference system; GPS and receiver antenna phase center offsets and variations; phase wind-up.
SLR measurement model	SLRF2005 station coordinates; Solid Earth and pole tides (IERS2005), GOT00.2 ocean loading, Marini & Murray tropospheric delay model (IERS2005).
Gravitational forces	Earth gravity field (UT/CSR GGM01 100x100, or other) relativity solid-earth tides, pole tide (IERS2003) ocean tides (UT/CSR TOPEX_3.0 or other) luni-solar third body acceleration using low-accuracy analytical ephemerides
Non-gravitational forces	Jacchia-Gill atmospheric density model with daily F10.7 and 3-hourly Kp values Cannon ball solar radiation pressure model with conical Earth shadow model (umbra, penumbra) Empirical accelerations in radial, along-track and cross-track direction at 10 min (default) interval
Reference frames	EME2000 IAU 1976 precession (Lieske model) IAU 1980 nutation (Wahr model) Earth orientation from IERS igs96p02 solution Spacecraft body frame orientation modelled based on attitude quaternions or default attitude modes

GPS High Precision Orbit Determination Software Tools (GHOST)

Overview

GHOST Processing Chain

Models

Further Reading