Simultaneous Unknown Input and State Estimation for the Linear System with a Rank-Deficient Distribution Matrix

Keyou Zhao,Jinyan Song,Yu Hua,Na Wang

doi:10.1155/2021/6693690

Abstract

The classical recursive three-step filter can be used to estimate the state and unknown input when the system is affected by unknown input, but the recursive three-step filter cannot be applied when the unknown input distribution matrix is not of full column rank. In order to solve the above problem, this paper proposes two novel filters according to the linear minimum-variance unbiased estimation criterion. Firstly, while the unknown input distribution matrix in the output equation is not of full column rank, a novel recursive three-step filter with direct feedthrough was proposed. Then, a novel recursive three-step filter was developed when the unknown input distribution matrix in the system equation is not of full column rank. Finally, the specific recursive steps of the corresponding filters are summarized. And the simulation results show that the proposed filters can effectively estimate the system state and unknown input.

Highlights

Introduction e traditionalKalman filter [1] and its extension can recursively estimate the state of the linear system with process noise and measurement noise. e time-domain recursive filter brings greater convenience for continuously processing input data, so it can play a more important role in control theory and engineering. e Kalman filter requires the noise to be stationary white noise, but this supposition is sometimes not feasible because unknown input may not be white noise and cannot be measured.In the fields of environmental monitoring [2] and disturbance suppression [3, 4], the system equation or output equation contains unknown input owing to environmental impacts and improper selection of model parameters
Using (8) and (12), we find that x􏽥k|k I − LkCk􏼁x􏽥k|k−1 − LkHkdk − Lkvk
[15] can solve the state estimation problem when Hk 0, but the application conditions to use this filter are that the unknown input distribution matrix Gk−1 in the system equation must meet rank(Gk−1) m, k 1, 2

Summary

Introduction

Introduction e traditionalKalman filter [1] and its extension can recursively estimate the state of the linear system with process noise and measurement noise. e time-domain recursive filter brings greater convenience for continuously processing input data, so it can play a more important role in control theory and engineering. e Kalman filter requires the noise to be stationary white noise, but this supposition is sometimes not feasible because unknown input may not be white noise and cannot be measured.In the fields of environmental monitoring [2] and disturbance suppression [3, 4], the system equation or output equation contains unknown input owing to environmental impacts and improper selection of model parameters. For systems with direct feedthrough, if the distribution matrix of unknown input in output equation is not of full column rank, Cheng et al [17] presented an unbiased minimum-variance state estimation (UMVSE). E RTSF proposed by Steven Gilljins in [16] can solve the state and unknown input estimation problem of linear system (1)-(2) while rank(Hk) m, k 0, 1, .

Results

Conclusion