Study Of Liner Optimal Estimation Methods For Discrete-time Systems With Multi-channel Multiplicative Noises

The optimal estimation theory for systems with multiplicative noises has very important study values and practice applications in many areas such as oil exploration,underwater target detection and so on. However, multiplicative noise is usually assumed to be a scalar in existing literature works.Motivated by recent applications of communication technology, now we consider multi-channel multiplicative noise represented by a diagonal matrix, this form of multiplicative noise means in the true sense of multi-channel. Based on the prior studies,the liner optimal estimation problems for discrete-time systems with multi-channel multiplicative noises are researched in this dissertation and obtain the optimal estimation algorithm. In this dissertation, optimal estimation methods are based on the sense of linear minimum mean squared.The main contents of this dissertation are as follows:(1) In this dissertation, the development and situation of optimal estimation theory are summarized simply. Motivated by the limitations of scalar multiplicative noises, the studies status and values of optimal estimation theory for systems with multi-channel multiplicative noise are further introduced.(2) In this dissertation, the optimal estimation problems for discrete-time systems with multi-channel multiplicative noises are discussed and the optimal estimation algorithm is obtained, where the multiplicative noise appears both in state equation and measurement equation respectively. The Kronecker product and Hadmard product of matrix are introduced and used. Based on the projection theory, the optimal estimator is derived in terms of a difference Riccati equation with Hadamard product and a difference Lyapunov equation.(3) In this dissertation, the estimation problem for multi-channel multiplicative noise systems with time delay is considered and an optimal estimation algorithm is obtained. First of all, we try to use the augmentation approach to transform the systems with time delay to the systems with no time delay, so the estimation problems are constant with the conventional optimal estimation problem for systems with multi-channel multiplicative noises. However, the augmentation approach will bring alarge amount of the computational demands when the delay is very large. Compared with the disadvantage of the augmentation approach, we present the new method, based on the method of innovation analysis, that is to say, the solution to the estimator can be obtained by calculating a partial difference Riccati equation and a Lyapunov equation.The presented new approach lessens the computational demand when the delay is large.(4) Finally, we further validate the efficiency of the proposed method by numerical examples in this paper.