Performance Comparison of Different Forms of Kalman Filter Approaches for a Vector-Based GNSS Signal Tracking Loop

In this paper we discuss several different Kalman filter methods to estimate signal parameters in a GNSS receiver's signal tracking loop with a special emphasis given on how to construct the measurement residuals and the relevant design matrix. There are three variations of error state Kalman filters for a loop filter, and a direct state Kalman filter for the entire signal tracking loop. Based on detailed signal models for a signal tracking loop, four different Kalman filters for signal tracking are compared with the traditional one. Block diagram implementation of the direct state Kalman filter for the entire signal tracking loop is proposed by using the analogy relationship with the traditional method in a scalar tracking mode and a vector tracking mode. Numerical simulation results show that the Kalman filter methods provide 2 to 3 dB carrier-to-noise ratio gain in carrier phase and Doppler tracking compared to the traditional method.