Tropospheric Model Error Reduction in Pseudolite-Based Positioning Systems

T.J. Bouska, J.F. Raquet

Abstract:	The tropospheric delay encountered with GPS measurements can be significantly reduced with the application of differential techniques. Due to geometries associated with pseudolite applications, however, differential techniques are not as successful at reducing tropospheric error. After applying a tropospheric model, uncancelled residual errors remain and can be significant enough to warrant further reduction. This paper describes two methods for reducing the effects of this residual tropospheric error on a navigation Kalman filter that exclusively uses pseudolites for positioning. The results are tested on a simulated pseudolite network. The first method applies a weighted measurement covariance matrix, using the the tropospheric model values to weight the phase measurement covariances. This method is based on the premise that the errors in the tropospheric model will be generally proportional to the modeled tropospheric delay (i.e., there are small modeling errors for short ranges and larger errors for long ranges). Since tropospheric model error is one of the key errors for precise (cm-level) pseudolite-only positioning, it is important for the Kalman filter to account for the varying statistics of the measurement errors. Even though this method is very simple, the results are surprisingly good, yielding a significant improvement in carrier-phase ambiguity resolution capability. The second method explicitly estimated the tropospheric model error as an additional state in the filter. The error, when expressed as a scale factor error, was modeled as a first order Gauss-Markov process. Initally, the scale factor errors of the mobile receiver and refernce receiver were modeled separately. The filter could successfully estimate the percentage of tropopspheric model error in the absence of measurement noise, multipath, and pseudolite position errors. When these errors were included in the measurement-corrupted ranges, the filter correctly estimated the mobile error percentage, but not the reference receiver error percentage. The lack of motion between the reference receiver and the pseudolites caused the pseudolite position errors to be bias-like, and the filter was apparently unable to distinguish the tropospheric model error from the biased multipath and pseudolite position errors in the received signal at the reference receiver. This problem suggested use of a single tropospheric model error state that lumped together the scale factor error of both the mobile and reference pseudolites. This implementation improved position accuracy by over 30 percent, and improved ambiguity resolution ability. This paper describes both methods, and then presents results for a simulated pseudolite network. Suggestions for future development are also given. The primary purpose of this research was to determine design tradeoffs for a pseudolite navigation system, not to predict absolute performance.
Published in:	Proceedings of the 16th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS/GNSS 2003) September 9 - 12, 2003 Oregon Convention Center Portland, OR
Pages:	390 - 398
Cite this article:	Bouska, T.J., Raquet, J.F., "Tropospheric Model Error Reduction in Pseudolite-Based Positioning Systems," Proceedings of the 16th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS/GNSS 2003), Portland, OR, September 2003, pp. 390-398.
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