Study Of Optimal Estimation Algorithm For Singular Systems With Multiplicative Noise Based On Jordan Transformation

In the field of signal processing theory, it is a significant matter to study the signal estimation for stochastic systems with multiplicative noise. In this dissertation, algorithms of signal optimal estimation for stochastic singular systems with multiplicative noise have been studied.In the past, the research productions with regard to the systems with multiplicative noise are almost aimed at normal stochastic linear systems. However, in practice, most of the mathematical models depicting the large and complex systems which are multidimensional, multilevel and multi-target are singular systems, especially some coupling systems, because singular systems are more natural, convenient and accurate. Although the research productions with regard to singular systems are abundant, the research literature about singular systems with multiplicative noise is few. In the instance of one-channel and complicated multi-channel singular systems with multiplicative noise, the dissertation discusses the optimal estimation of state filtering and smoothing and the stochastic input signal with the technique of innovation and projection theorem of Hilbert space, based on Jordan transformation. All the proposed algorithms in this dissertation are optimal in the linear minimum variance.The main study of the dissertation is introduced as follows:1. Using Jordan transformation, stochastic discrete singular systems with multiplicative noise can be transformed into normal systems with multiplicative noise, then an optimal filtering algorithm is developed under the condition that the multiplicative noise is one-dimension stochastic serial. According to the practical requirement, a filtering algorithm for singular systems with multiplicative noise is developed under the condition that the multiplicative noise is in the form of a general stochastic matrix.2. Based on the optimal filtering algorithm, the direct algorithm of the optimal fixed-interval smoothing is deduced for the one-channel and complicated multi-channel singular systems with multiplicative noise. With the introduction of the auxiliary variables, the fixed-interval state optimal indirect smoothing algorithm is obtained, which makes the algorithm more practical.3. Based on the filtering and smoothing algorithm, the optimal fixed-interval deconvolution estimation algorithm is developed.4. The algorithms are tested through simulation, and satisfactory simulation results are obtained, which validate the algorithms.