Modelling and performance analysis of constrained GNSS vector tracking using moving horizon estimation

Abstract

Vector tracking of GNSS signals has attracted much attention in recent years because of its superiority in dealing with weak signals and signals with high dynamics. In vector tracking loops, the parameters of the locally generated signals are determined by the estimated navigation solutions and satellite ephemeris, thus the channels are aided by each other. However, as it was highlighted in many previous studies, vector tracking is sensitive to faults because a fault occurs in one channel could propagate to other channels, thus the robustness of vector tracking is severely reduced. In this work, a novel method is proposed to enhance the vector tracking robustness by incorporating constraints, through a moving horizon estimation (MHE) approach. Previous work on vector tracking are mostly based on an extended Kalman filter (EKF). In this work, we propose a MHE technique, which is designed based on the dynamics model of the vector tracking loop. The basic idea of MHE is to reformulate the estimation problem as a quadratic programming (QP) problem within a moving, fix-size estimation window. The main advantage of MHE is that it naturally allows the incorporation of inequality constraints on the state vector and disturbances. When applied to vector tracking, MHE can constrain the effect from each channel within a priori defined range, thus to mitigate the effect from the channel where fault presents. Another advantage of MHE is that it is less sensitive to tuning parameters than the commonly used EKF, which makes it more robust to environment change. The constrained vector tracking loop is implemented in MATLAB, and its performance is tested with several simulation datasets from a Spirent G8000 Simulator and real GPS L1 signal. The simulation is based on a high dynamic flight profile, and includes two challenging scenarios: one channel’s outage and ionosphere scintillation; the experiment is conducted using a period of real signal collected on Ascension Island containing an ionosphere scintillation event. The results confirm the improved robustness performance of vector tracking by using MHE.