New Kalman Filter Formulation for GPS Delta Pseudo Range Processing

David F. Hartman, Douglas B. Tyler

Abstract:	Algorithms commonly used in Kalman Filter processing of GPS measurements do not properly account for process noise effecting the delta pseudo range measurements. The delta pseudo range measurement is formed by integrating carrier phase information over a finite interval. The error in predicting the value of the measurement can be related to the pseudo range errors at the beginning and end of that integration interval. To be exactly correct, the conventional Kalman Filter must carry additional states to "remember" certain state errors at the beginning of the integration interval since the filter relates measurements to states at the current time only. Most algorithms in use essentially contain a backward prediction of the current states to the beginning of the integration interval in formulating the measurement matrix. This "backward prediction" is exact in the absence of process noise, but cannot be made exactly if such noise is present. The error in conventional algorithms can be substantial if process noise is large. New generalized filter formulas are developed which are optimal and do not require any additional states over the conventional formulation. New formulas are presented for the Kalman Gain and covariance update applied with delta pseudo range measurements. These formulas apply to the case where the measurements are processed in a batch. A validation methodology for the algorithm is also discussed.
Published in:	Proceedings of the 11th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1998) September 15 - 18, 1998 Nashville, TN
Pages:	1395 - 1400
Cite this article:	Hartman, David F., Tyler, Douglas B., "New Kalman Filter Formulation for GPS Delta Pseudo Range Processing," Proceedings of the 11th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1998), Nashville, TN, September 1998, pp. 1395-1400.
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