Optimisation and sensitivity analysis of GPS receiver tracking loops in dynamic environments

For a GPS receiver, decreasing the receiver tracking loop bandwidth reduces the probability of loss of lock if there are no vehicle dynamics. However, reduced bandwidth increases tracking errors due to dynamics. Beyond a certain limit it causes a serious degradation in the dynamic tracking performance. Therefore, there is involvement of a tradeoff between two opposing considerations: narrow tracking loop bandwidths are desired for filtering noise due to thermal effects, but wide tracking loop bandwidths are desired to permit tracking of vehicle dynamics. Optimal tracking loop bandwidths, which yield the minimum errors in a certain dynamics environment, are first investigated. The linear Kalman filter is employed as the optimal estimator. The covariance for the arbitrary gain model is solved and applied to the sensitivity analysis for investigating error growth due to incorrect noise level estimate. Theoretical results are verified by numerical simulation, and results from both approaches are in very good agreement.