A Kalman Filter Approach to Precision GPS Geodesy

The high stability of the GPS signals makes it possible to determine differential position over short baselines with an accuracy of the order of centimeters. This has been demonstrated using very long baseline interferometry (VLBI) methods of radio astronomy. This paper presents an alternative approach using Kalman filter methods. It is based on an adaptive filter concept developed by D. T. Magill in 1965. The scheme employs parallel Kalman filters with each filter being modeled for a different integer wavelength assumption. As the phase measurement sequence progresses, the adaptive scheme “learns” which Kalman filter corresponds to the correct hypothesis, and thus it both resolves the wavelength ambiguity and estimates differential position simultaneously. Simulated results are presented which indicate convergence in about 10 minutes of satellite observation time.