Study Of State Estimation Algorithms And Deconvolution Algorithms For Multi-channel Nonlinear Systems With Multiplicative Noise

Systems with multiplicative noise universally exist in many application fields, such as oil seismic exploration, underwater remote targets detection, communication engineering and speech signal processing. The state estimation and the random input signal deconvolution for such systems are important to theory research and engineering application. In this dissertation, state estimation algorithms and deconvolution algorithms of random input signals for a class of multi-channel nonlinear systems with multiplicative noise have been studied.In the engineering practices, most mathematical models are usually nonlinear. In this dissertation, approximate linearizations of the nonlinear systems have been done based on extended Kalman filter. And considering the system noise and observation noise of the complex multi-channel systems with multiplicative noise are correlated at the same time, state filtering estimation, smoothing estimations and random input signals deconvolution estimations have been studied for the systems. The following have been finished:1. According to the practical requirement of complex multi-channel systems with multiplicative noise, the dissertation deduced a filtering algorithm for multi-channel nonlinear systems with multiplicative noise under the condition that system noise and observation noise are correlated at the same time based on the projection theorem. The application ranges of this algorithm are more extensive.2. Based on the filtering algorithms, a direct smoothing algorithm and an indirect smoothing algorithm were deduced by using innovation method and the projection theorem. Because the indirect algorithm used an indirect variable, so the algorithm is more applied than direct algorithm. And then an indirect smoothing algorithm has further been given for the system which dynamic noise and observation noise are correlated at the same time.3.With the results of filtering and smoothing algorithms, a fixed-field deconvolution algorithm and a fixed-points deconvolution algorithm for random input signals of the nonlinear systems with multiplicative noise have been conducted under the condition that system noise and observation noise are uncorrelated.4. The computer simulation results show that the algorithms are available.