Characteristics of Kalman Filters for GNSS Signal Tracking Loop

Characteristics of signal tracking Kalman filter (KF) approaches for a Global Navigation Satellite System (GNSS) receiver are presented. In particular the direct-state KF is designed by using a state vector for signal parameters not for signal parameter errors, so as to directly utilize the discriminator output as a measurement residual. This enables the reuse of the existing signal tracking loop structure by simply adjusting the filter coefficients based on a time-varying optimal Kalman gain. The characteristics of the direct-state KF together with the error-state KF are analyzed by comparing their noise bandwidth and open- and closed-loop transfer functions with those of a traditional method. These KF approaches are mathematically equivalent to the traditional method except for the use of time-varying gains. This fact provides an insight how to tune the designed KFs based on their expected performances.