Nonlinear Filtering With Applications To Communication And Navigation Systems

Most systems are naturally nonlinear in the real physical world and the linear approximation is a powerful method to solve nonlinear problems. The Kalman filter is a classic representative of linear filtering methods and has achieved fruitful results in the past few decades. While as computing power increases, mathematical means enrich and accuracy requires further improvement, the demanding on handling the nonlinear systems directly is urgent and necessary.With the rapid development of computer and control technology, non-linear filtering technique has been widely applied to various fields as signal processing, wireless communication, aerospace, navigation and positioning, computer vision and even financial analysis, etc. This dissertation directs mainly at the researches on the two representative non-linear filtering algorithms:Unscented Kalman filter and particle filter, and their application in carrier frequency offset estimation of OFDM system as well as initial alignment and fault diagnose of Strapdown inertial navigation system. The main contents of the paper are:Firstly, under the unified framework of recursive Bayesian estimation theory, this paper gives in-depth investigation of three classes of non-linear filtering methods as extended Kalman filter, unscented Kalman filter and particle filter. In particular, this dissertation presents in detail the principle of algorithm frame of unscented Kalman filter, the unscented transformation and the sampling strategies, meanwhile the basic structure of particle filter including the sequential importance sampling and resampling together with other key points are also described. The overall comparison of advantages, disadvantages and application conditions of each method is also addressed.Secondly, an adaptive UKF algorithm is proposed to solve the CFO estimation in OFDM system. The study analyzed the carrier frequency offset estimation of OFDM systems, when the frequency offset is large, it will produce inter-carrier interference resulting the performance degradation. To solve this problem, the CFO is modeled as dynamic state space model and UKF is used for the offset estimation. Comparing to other convention methods as SC, MLEE, EKF, UKF enhances the filtering accuracy with better stability and convergence. Further, it derives an adaptive UKF with exponential decay of memory Sage-husa noise estimator based on the maximum posterior probability criteria, which helps to improve the robustness of UKF in unknown or time varying noise conditions.Thirdly, the Stirling formula is described and the central difference Kalman filter (CDKF) is formulated. Based on the weighted statistical linear regression theory, the UKF and CDKF filters are classified into Sigma-point Kalman filter. To reduce the computational complexity, the square root form of Sigma-point Kalman filter is derived and verified, and a brief discuss with a parallel computing framework of UKF is given.Fourthly, this paper addresses an unscented particle filter (UPF) to solve initial alignment problem and presents a adaptive-robust UPF algorithm for fault diagnosis. UPF is obtained by combing UKF into PF algorithm framework, in which UKF is used to acquire more accurate statistical characteristics and help to overcome the drawback in standard PF. UPF is adopted in SINS initial alignment problem and shows better valuation results. When there is no abnormal exists, the residual should meet the white Gaussian noise distribution and the trace conforms Chi-square distribution criteria. Based on this, the algorithm first obtains the residual variance matrix by UPF and then makes a judgment by examining the trace. When a fault is detected, the algorithm further introduces a weighting function to adaptively adjust the Kalman gain factor and suppress the outliers. This method can’t identify the specific cause of malfunction, but still it is a good choice of system-level fault detection and suppression.