Theoretical Performance Analysis of GNSS Tracking Loops

This paper aims to characterize the estimation precision at the output of the GNSS receiver tracking stage. We define an original statistical modelling of the GNSS tracking loop, which can then be exploited by an optimal linear Kalman Filter (KF) in order to obtain an analytical expression of the steady-state regime. The latter is designed to encompass dynamic information of the GNSS receiver. Two observation models are of interest: the first one considers the propagation delay and Doppler parameters, and the second one also including the Doppler rate, i.e., the acceleration, which is known to be relevant for high dynamics scenarios and can easily be included into the acquisition step. Within this context, the steady-state asymptotic performance of the tracking stage is obtained by solving an algebraic discrete Riccati equation. In both cases, simulation results are provided to show the validity of the proposed approach and the resulting steady-state performance.