A Novel Carrier Loop Based on Adaptive LM-QN Method in GNSS Receivers

Abstract

A well-designed carrier tracking loop in a receiver of the Global Navigation Satellite System (GNSS) is the premise of accurate positioning and navigation in an aircraft-based surveying and mapping system. To deal with the problems of Doppler estimation in high-dynamic maneuvers, the interest on maximumlikelihood estimation (MLE) is increasing among the academic community. Levenberg-Marquardt (LM) method is usually regarded as an effective and promising approach to obtain the solution of MLE, but the computation of Hessian matrix loads a great burden on the algorithm. Besides, a poor performance on convergency in final iterations is the common failing of LM implementations. To solve these problems, an LM method based on Gauss-Newton and a Quasi-Newton (QN) method based on Hessian approximation are derived, making the computation cost of Hessian decline from O(N) to O(1). Then, on the basis of these two methods, a closed carrier loop with adaptive LM-QN algorithm is further proposed which can switch between LM and QN adaptively according to a damping parameter. Besides, an ideal LM with super-linear convergence (SLM) is constructed and proved as a reference of the convergence analysis. Finally, through the analyses and experiments using aircraft data, the improvements on computation cost and convergence are verified. Compared with scalar tracking and vector tracking, results indicate a magnitude increase in the precision of LM-QN loop, even though more computation counts are needed by LM-QN.

A Multi-Correlation Peak Phase Deblurring Algorithm for BeiDou B1C Signals in Urban Environments

“…These algorithms primarily focus on two aspects: loop bandwidth and loop order. Dynamic loop bandwidth adjustment is commonly based on the consideration of system signal-tonoise ratio and correlation accumulation time, aiming to reduce the noise error in the loop by changing the bandwidth to thereby achieve carrier tracking [29][30][31][32][33]. On the other hand, variations in the loop order do not alter the noise characteristics of the loop, but instead affect the steady-state tracking error.…”