Research On State Estimation And Simultaneity Estimation For Multiplicative Noise System

In recent years,the problems of optimal estimation for multiplicative noise system have been paid much attention by scholars.At the same time,the problem of state estimation and simultaneity estimation for the system with unknown input is also the same.The conclusions on these problems obtained by scholars are widely used in the field of industrial applications such as fault detection,image processing,and seabed survey,and the latter can also find its application value in the network control system.Generally,most scholars carry out research on systems with unknown input and multiplicative noise respectively,while there are few literatures are concerned with both unknown input and multiplicative noise.In addition,in the past,scholars usually used scalar to express multiplicative noise,in the context of the continuous development of the industrial level,using multidimensional random diagonal matrix to represent the multiplicative noise in order to simulate multichannel observation models will be more realistic.Therefore,according to the current research status,this paper will solve the following two problems: for discrete time systems with both multiplicative noise and unknown input,two optimal state estimators are given;For the observation time-delay system with unknown input,the simultaneity estimation in the sense of unbiased minimum variance is carried out.The main research work of this paper includes the following points:(1)First,we briefly summarize the theory of multiplicative noise system estimation,the optimal estimation theory of discrete time system with unknown input and the theory of simultaneous estimation for unknown input and state.In addition,some existing methods to solve the delay problem are introduced.(2)For the discrete-time systems with multiplicative noise and unknown input,the optimal estimation algorithm in the sense of unbiased minimum variance is presented in this paper.In the absence of any prior information of unknown input,we give the unbiased estimation algorithm by solving a Riccati equation and a Lyapunov Equation for the system.We derived the optimal estimator we needed by using the Hadamard matrix product(?),then we also derive a suboptimal estimator in the sensor network by using the time stamp technology.(3)Consider the discrete time system,in which both the state equation and the measurement equation has the unknown input,we discuss the situation of time-delay in the system,and give the algorithm of simultaneous unknown input and state estimation based on the linear unbiased minimum variance theory.(4)A large number of simulation studies are carried out by using the drawing function of Matlab software.Under the numerical examples,the above algorithms are proved to be effective respectively.