Proper Treatment of the Delta-Range Measurement in an Integrated GPS/Inertial System

R. Grover Brown, Paul W. McBurney

Abstract: Pseudorange and delta-range are the basic measurements that a GPS receiver provides in an integrated GPS/inertial system. Usually the delta-range measurement is treated as an instantaneous velocity measurement in the Kalman filter integration of the two systems. This is an approximation since the actual measurement is proportional to the integral of the Doppler shift over the delta-range integration interval. The Kalman filter model can be modified to accommodate the true measurement situation, and the results of the true model can be compared with those obtained with the approximate instantaneous velocity model. Error covariance analysis was performed to compare the relative accuracy between the two measurement models for an eight-state Kalman filter and an integration interval of one second. The main difference between the two models occurs in the velocity estimates (in contrast to the position estimates), where the approximate model predicts RMS velocity errors which are much less than those determined with the true measurement model. This is to say that the approximate velocity model often used in error analysis yields overly optimistic results for the velocity estimates.
Published in: Proceedings of the 1987 National Technical Meeting of The Institute of Navigation
January 20 - 23, 1987
Anaheim, CA
Pages: 32 - 39
Cite this article: Brown, R. Grover, McBurney, Paul W., "Proper Treatment of the Delta-Range Measurement in an Integrated GPS/Inertial System," Proceedings of the 1987 National Technical Meeting of The Institute of Navigation, Anaheim, CA, January 1987, pp. 32-39.
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