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

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 maximum-likelihood 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.Peer reviewe

A Carrier Estimation Method Based on MLE and KF for Weak GNSS Signals

Maximum likelihood estimation (MLE) has been researched for some acquisition and tracking applications of global navigation satellite system (GNSS) receivers and shows high performance. However, all current methods are derived and operated based on the sampling data, which results in a large computation burden. This paper proposes a low-complexity MLE carrier tracking loop for weak GNSS signals which processes the coherent integration results instead of the sampling data. First, the cost function of the MLE of signal parameters such as signal amplitude, carrier phase, and Doppler frequency are used to derive a MLE discriminator function. The optimal value of the cost function is searched by an efficient Levenberg–Marquardt (LM) method iteratively. Its performance including Cramér–Rao bound (CRB), dynamic characteristics and computation burden are analyzed by numerical techniques. Second, an adaptive Kalman filter is designed for the MLE discriminator to obtain smooth estimates of carrier phase and frequency. The performance of the proposed loop, in terms of sensitivity, accuracy and bit error rate, is compared with conventional methods by Monte Carlo (MC) simulations both in pedestrian-level and vehicle-level dynamic circumstances. Finally, an optimal loop which combines the proposed method and conventional method is designed to achieve the optimal performance both in weak and strong signal circumstances