Modified Observation Model and Design Computations for Positioning with GPS and Pseudolites

Sandra Verhagen

Abstract:	Numerous applications where pseudolites can be used have been suggested in the past. They may involve using both GPS and pseudolites in an integrated system, or pseudolites on a stand-alone basis. It is well known that the inclusion of pseudolite observations implies that the functional model as well as the stochastic model may need to be modified compared to the standard GPS observation model. In this contribution it is shown how the observation model can be constructed for different measurement scenarios. Special attention is given to the impact of biases in the positions of the reference receiver and the pseudolites. Experimental results are used to investigate their impact and how they can be dealt with. For that purpose, the positioning results obtained with three different approaches are compared. First, the impact of the biases is simply ignored. Second, the functional model is modified by introducing an additional unknown. In other words, it is assumed that a constant bias is introduced by the inclusion of the pseudolite observations in the linearized model. In the last approach the stochastic model is modified instead of the functional model. This gives essentially the same results as the second approach, which are clearly better than in case the impact of the errors is ignored. However, the advantage of modifying the stochastic model is that it is still possible to obtain a high probability that the integer ambiguities are fixed to their correct values, i.e. a high success rate. The knowledge of the observation model allows you to compute design parameters in order to study the performance of your positioning system. For example, the internal and external reliability and the success rates can be computed without the need for actual observations. However, the closed-form expressions that can be used for the computation of the design parameters for GPS measurements cannot always be used when pseudolite observations are included. Therefore, it is studied how these expressions have to be modified if pseudolite observations are added to the model with the goal to arrive at expressions which are easy to implement. The resulting expressions are used to study the performance of an integrated GPS -pseudolite system. The results for some scenarios will be shown and discussed here.
Published in:	Proceedings of the 15th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2002) September 24 - 27, 2002 Oregon Convention Center Portland, OR
Pages:	2745 - 2755
Cite this article:	Verhagen, Sandra, "Modified Observation Model and Design Computations for Positioning with GPS and Pseudolites," Proceedings of the 15th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2002), Portland, OR, September 2002, pp. 2745-2755.
Full Paper:	ION Members/Non-Members: 1 Download Credit Sign In