Study Of Estimation Problem For Measurement-Delay Systems With Multiplicative Noise

Recently,the problems of estimation for discrete-time systems with measurement-delay and multiplicative noise have been paid much attention by scholars due to the fact that these problems are used in many practical application fields,such as oil exploration,communication systems,image processing and so on.Scholars use scalar to represent multiplicative noise usually.However,we represent the multiplicative noise with a stochastic diagonal matrix in this paper and provide two algorithms,which are optimal estimation and limited memory optimal filter algorithm,respectively.The main contributions of this paper are following:(1)For measurement-delay systems with multiplicative noise,we put forward optimal state estimator for finite horizon based on Kalman filter theory.Firstly,we transform system with measurement-delay to system without measurement-delay according to the reorganized innovation analysis approach.Then,based on the orthogonal projection theorem and Kalman filter theory,the state estimator is derived in terms of two Riccati difference equations of the same dimension as that of the original system and one Lyapunov difference equation.We introduce and use the Hadmard product(?)of matrix during the calculative process.(2)Then,stable estimator is designed under the condition that system matrix is stable.For measurement-delay systems with multiplicative noise,we have studied optimal deconvolution estimation,the process of which is based on Kalman filter and orthogonal projection theorem.(3)With the accumulation of the estimate error,old measurements may could not reflect the real situation of systems accurately.Compared with optimal estimation algorithm,the advantage of the limited memory optimal filter algorithm is that we only utilize a fixed number of measurements before the current moment,therefore using this algorithm could reduce computation.For system with measurement-delay,we provide effective method to calculate the initial value of the limited memory optimal filter algorithm,and gain the limited memory optimal filter according to the Kalman filter and orthogonal projection theorem.(4)Finally,we give some emulational researches and numerical examples gained by using Matlab to show that the optimal estimator and the limited memory optimal filter are effective,respectively.