Study Of Estimation Algorithm For A Class Of Nonlinear Systems With Multiplicative Noise

In the field of modern control theory, it is a significant matter to study the signal estimation for stochastic systems with multiplicative noise, which is to obtain useful information from signals polluted by noises, for example, the state estimation of the dynamic system, the signal deconvolution estimation and the parameter recognition estimation, etc. It has important values of application in many fields, such as rocket control and guidance system, oil exploration, underwater object tracking, speech signal processing, communication engineering etc. In this dissertation, algorithms of signal estimation for a class of nonlinear discrete stochastic systems with multiplicative noise have been studied, which have important background of application.In the past, the research productions with regard to the systems with multiplicative noise, such as various filtering and smoothing algorithms, controlling algorithms, adaptive algorithms, various deconvolution algorithms and stability of filtering algorithm, stability of numerical values, controllability, observability etc. are almost aimed at linear systems. However, in the engineering practices, most of the mathematical models depicting the practical systems are nonlinear and the linear systems are approximately depiction of nonlinear systems. At the same time, as far as the state estimation for nonlinear systems is concerned, most previous observation systems depicting nonlinear systems were only involved in addictive noise, actually, many observation systems include not only addictive noise, but also multiplicative noise. All the facts make it necessary to study the estimation theory for nonlinear systems with multiplicative noise. On the basis of these two research directions, algorithms of signal estimation for nonlinear stochastic systems with multiplicative noise have been studied in this dissertation.Based on the kind of nonlinear discrete stochastic systems with multiplicative noise, which is more complex than linear systems with multiplicative noise and nonlinear systems without multiplicative noise, studies of state filtering,smoothing and deconvolution estimation of stochastic input signals are made with the technique of innovation and projection theorem of Hilbert space. The followings have been finished:1. For a class of nonlinear systems with multiplicative noise, when dynamic noise, observation noise and multiplicative noise are all white noise, a suboptimal state filtering algorithm with strong tracking factor and a suboptimal state iterative filtering algorithm are derived for systems with multiplicative noise of 1-D stochastic serial, and a suboptimal state iterative filtering algorithm for systems with multiplicative noise of diagonal matrix serial; under the non-white noise of observation noise condition, a suboptimal state filtering algorithm is proposed.2. On the basis of state filtering algorithms, under the condition of white noise, a...