Parameter Estimate And Adaptive Filtering Of Linear Random System

In the classical Kalman filtering theory, estimating state must know all parameters about this system. Furthermore, the noise of this system must be not auto-correlative. But in fact, this is almost impossible in many practical fields. In this paper, some kinds of linear random systems that do not satisfy these conditions are discussed. By the method of mathematical statistics, the corresponding parameter estimate and state filtering are obtained.This paper is made up of five chapters.Chapter one is an introduction of the advance of research of the theory of filtering and some applications. And Kalman filtering is introduced simply.Chapter two discusses a kind of linear random system whose transform-function-matrix is unknown. A corresponding recursive adaptive filtering is obtainea. Aider that, the stability of this algorithm is analyzed.Chapter three discusses a kind of linear random system whose transform-function-matrix is random. A corresponding recursive adaptive filtering is obtained.Chapter four obtained optimal filtering by the methods of innovation for the system contains multiplicative noise. After that, it was proofed that the optimal linear recursive filtering is not existed.The last chapter is a summary of the dissertation and point out some problems that should be researched in the future.