Analysis of a federal Kalman filter-based tracking loop for GPS signals

Kalman filter is widely used in modern GPS receivers. A traditional receiver based on Kalman filter (KF) tracks the GPS signals from each satellite separately, and so its tracking performance could be inferior in challenging situations. The vector delay frequency-locked loop (VDFLL) combines all tracking channels into one Kalman filter and so has a better tracking performance. But VDFLL has two primary drawbacks: high computational cost and low robustness. To solve this problem, the federal tracking loop is proposed. The single Kalman filter of the traditional federal loop is separated into a least-squares block and a master filter in consideration of reducing the computational complexity at the cost of a slight performance reduction. In this tracking loop, the GPS signal from each satellite is tracked independently in the subfilters. The master filter works as a navigation processor, which estimates the acceleration of the receiver and feeds it back to the subfilters. The thermal jitter and dynamic stress error of the federal tracking loop are analyzed theoretically and demonstrated with simulation data. The dynamic performance, robustness and computational complexity of the traditional KF loop, the proposed federal tracking loop and the VDFLL are compared. Analysis and simulation results show that the dynamic tracking performance of the federal loop is much better than that of the KF loop and is almost close to that of the VDFLL. Also, the federal loop has advantages over the VDFLL in terms of robustness and the computational complexity. Therefore, the federal tracking loop can be implemented as a new method in the practical implementation for high-performance applications in the future.