Research On Anti-interference Filtering Algorithms For Linear Systems With Unknown Inputs And Missing Measurement

State estimation of linear discrete stochastic systems has been widely applied in the fields of integrated navigation,fault detection,signal tracking and industrial control.There is inevitably measurement missing or measurement delay in practical systems,and many unknown inputs often influence these systems.However,these factors are usually not considered when the actual systems are modelled or analyzed.This situation leads to a certain difference between the established system model and the actual system,so that it is difficult to achieve the optimal estimation of the system state.Therefore,considering measurement missing or measurement delay existing at the same time,the optimal estimation of system state and unknown input are studied for linear discrete-time stochastic systems with unknown inputs.The main research work consists of the following parts:(1)For a class of linear discrete stochastic systems with unknown inputs,this paper studies on the optimal estimation of system state and unknown input when the unknown input coefficient matrix is not full rank and there are missing measurements at the same time.Firstly,we construct the model of measurement missing by Bernoulli process with binary variable.Then,for the model with unknown input and missing measurement,an anti-disturbance filter is designed to estimate the system state and unknown input based on the three-step recursive filtering.Using Lagrange multiplier method and diagonal matrix principle,the gain matrix of the filter is determined to ensure the minimum estimation error variance of unknown input and system state.Finally,we provide a numerical example to analyze the estimation effectiveness for different probability of measurement missing,and it shows that the filter performs better in estimating system state and unknown input when the probability of measurement missing is located within a certain range.Subsequently,considering the correlation between the system process noise and the measurement noise,we propose another recursive filter based on the above system.(2)For a class of linear discrete-time uncertain systems with unknown inputs,this paper studies on the optimal estimation of system state and unknown input when measurement is missing at the same time.Firstly,the stochastic uncertainties in the equations of state and measurement are described as multiplicative noises.Then,based on the system model containing multiplicative noise,unknown input and measurement missing,an extended recursive three-step filter is designed,which satisfies unbiased least variance estimation.In addition,the gain matrix of the filter is determined by the methods of weighted least squares and Lagrange multiplier.Finally,numerical simulation is performed to analyze and verify the estimation effectiveness of the proposed filter for steady system and time-varying system respectively,and the effectiveness of the proposed filter is verified again by comparing with the estimation effectiveness of previous filters.(3)For a class of linear discrete-time uncertain systems with measurement delay,an anti-disturbance recursive filtering algorithm is proposed considering the influence of unknown inputs on the system.Firstly,consider the case that there is the unknown input in system state equation and the measurement equation,the system with measurement delay is converted into a standardized model without measurement delay by using the method of new reorganized innovation.Then,a three-step recursive filter based on the standardized mode is proposed to achieve the minimum variance unbiased estimation of system state and unknown input.Finally,the simulation results show that the proposed filter can simultaneously estimate the state and unknown input of the system with measurement delay.