Nonlinear filtering for systems with actively changing parameters: Algorithms and their performance analysis in application to target tracking

The problem of signal detection and tracking is referred to as one of the most actively explored subjects in applied mathematical sciences. The filtering problem considered in the dissertation is complicated by two major factors. Non-linearity of both state process and observed process is assumed. And we also consider a possible change of parameters for both processes in time. The newly developed method of Interacting Bayesian Matched Filters (BIBMF) suggests a framework, in which we are able to estimate the state process with low signal-to-noise ratio even in such a difficult situation. Bayesian recursion, constructing the basis of BIBMF algorithm, is computationally efficient and can be used for data filtering in real time. BIBMF is capable of handling discrete and continuous state processes and shows a superior performance in comparison to well-known methods. We provide an experimental analysis for its performance compared to those of 3-dimensional matched filter suggested by I. Reed et al., Dynamic Programming (Viterbi) algorithm by J. Arnold et al. and Y. Barniv, Interacting Multiple Models suggested by Y. Bar-Shalom. BIBMF also proved itself to be a universal method solving the nonlinear filtering problems in the setups, for which neither of the mentioned alternative methods provide meaningful solution.; Experimental part of the dissertation is based on simulations for target tracking. The general framework of a target detection and tracking problem is discussed, and application of nonlinear filtering to track-before-detect is formulated.