An Algorithm for Instantaneous Position Estimation of GPS Satellites in SBAS Applications

Rajneesh Gupta, and A. S. Ganeshan

Abstract:	The precise estimation of GPS satellite position or orbit, is a classical problem wherein the orbit is estimated using a set of range measurements over a time span of typically two days or more. The orbit estimation process generally involves the usage of a high fidelity orbit model for state propagation and a least square scheme for state estimation. The approach presented in this paper brings out an algorithm design for the instantaneous estimation of 2 GPS satellite position vectors, using simultaneous range measurements from 8 stations, analytically. The sets of 8 stations provide 16 measurements for 2 GPS satellites, to estimate accurately the 6 parameters (3 components of position x, y, and z) for each GPS satellite. Measurement source for the demonstration of the capability have been (1) using IGS data and, (2) simulated measurement data. The algorithm has been designed and tested using a simulated model with uncertainties associated with the GPS clocks and station clocks. For measurement simulation, the GPS almanac containing orbital information of the GPS satellites and a set of 8 ground stations were employed. At each step of time, the true ranges were computed by propagating the GPS state vector at the desired time and using the known station positions. The measurement errors for GPS clocks and station clocks were added, to compute the realistic noisy measurements. The estimated positions through the algorithm were compared with the assumed true positions of the GPS satellites. It is to be noted that the station position errors are assumed to be negligible for the simulation, since these are generally known very accurately. It is a pre-requisite for the algorithm that the pseudo range measurements are corrected for ionosphere, troposphere and multi path errors etc. The computation of ionosphere error through dual frequency measurements and troposphere error through a model can be performed easily. The formulation design is based on the concept of double differencing, wherein an instantaneous least square technique is applied to derive accurate GPS positions. The final measurements contain only the GPS clock errors and the station clock errors. Further, in the course of formulation, these range measurements become free from GPS clock errors and station clock errors. These measurements are processed through an instantaneous batch least square estimation scheme for the GPS satellite position vector estimation. The scheme will be particularly useful in SBAS applications, for the estimation of GPS position through safety processor, wherein the computational time requirements and accuracy are very stringent. This algorithm considers all the instantaneous measurements from station to GPS line of sight and provides an accurate estimate of GPS positions.
Published in:	Proceedings of the 2004 National Technical Meeting of The Institute of Navigation January 26 - 28, 2004 The Catamaran Resort Hotel San Diego, CA
Pages:	994 - 1004
Cite this article:	Gupta, Rajneesh, Ganeshan, A. S., "An Algorithm for Instantaneous Position Estimation of GPS Satellites in SBAS Applications," Proceedings of the 2004 National Technical Meeting of The Institute of Navigation, San Diego, CA, January 2004, pp. 994-1004.
Full Paper:	ION Members/Non-Members: 1 Download Credit Sign In