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 Novel Carrier Loop Algorithm Based on Maximum Likelihood Estimation (MLE) and Kalman Filter (KF) for Weak TC-OFDM Signals

Digital broadcasting signals represent a promising positioning signal for indoors applications. A novel positioning technology named Time & Code Division-Orthogonal Frequency Division Multiplexing (TC-OFDM) is mainly discussed in this paper, which is based on China mobile multimedia broadcasting (CMMB). Signal strength is an important factor that affects the carrier loop performance of the TC-OFDM receiver. In the case of weak TC-OFDM signals, the current carrier loop algorithm has large residual carrier errors, which limit the tracking sensitivity of the existing carrier loop in complex indoor environments. This paper proposes a novel carrier loop algorithm based on Maximum Likelihood Estimation (MLE) and Kalman Filter (KF) to solve the above problem. The discriminator of the current carrier loop is replaced by the MLE discriminator function in the proposed algorithm. The Levenberg-Marquardt (LM) algorithm is utilized to obtain the MLE cost function consisting of signal amplitude, residual carrier frequency and carrier phase, and the MLE discriminator function is derived from the corresponding MLE cost function. The KF is used to smooth the MLE discriminator function results, which takes the carrier phase estimation, the angular frequency estimation and the angular frequency rate as the state vector. Theoretical analysis and simulation results show that the proposed algorithm can improve the tracking sensitivity of the TC-OFDM receiver by taking full advantage of the characteristics of the carrier loop parameters. Compared with the current carrier loop algorithms, the tracking sensitivity is effectively improved by 2–4 dB, and the better performance of the proposed algorithm is verified in the real environment