Novel optimal recursive filter for state and fault estimation of linear stochastic systems with unknown disturbances

Abstract

This paper studies recursive optimal filtering as well as robust fault and state estimation for linear stochastic systems with unknown disturbances. It proposes a new recursive optimal filter structure with transformation of the original system. This transformation is based on the singular value decomposition of the direct feedthrough matrix distribution of the fault which is assumed to be of arbitrary rank. The resulting filter is optimal in the sense of the unbiased minimum-variance criteria. Two numerical examples are given in order to illustrate the proposed method, in particular to solve the estimation of the simultaneous actuator and sensor fault problem and to make a comparison with the existing literature results.

Double fault distinguishability in linear systems

“…Then, the problem of multiple faults can be solved. Khémiri et al (2011) presented a new recursive optimal filter structure. The fault affects both the state and output equations, whereas unknown disturbances only affect the state system equation, without any prior information about their dynamical evolution.…”

Filtering and prediction for discrete systems with unknown input using nonparametric algorithms

“…The optimal Kalman filtering and the H ∞ Kalman filtering for the descriptor systems with an unknown input are studied in [13,14]. Also, in [15][16][17], the problem of robust and optimal fault identification of linear stochastic systems with unknown disturbance is solved. The interesting results are presented in [18], where the smoothing algorithms for discrete-time linear stochastic systems with unknown input are studied.…”

L2Observers for a Class of Nonlinear Systems with Unknown Inputs

“…One way to protect a system against such unknown attacks is by employing unknown input observers (UIOs), as reported in [1] and [2]. Common estimation frameworks for systems in which one assumes stochastic models for the unknown exogeneous input include Kalman filtering [3] and minimum variance filters [4]. For unknown exogeneous inputs where underlying statistics are not available and cannot be guessed, methods that have proven effective include: adaptive estimation [5], sliding mode observers [6,7], and observers that minimize the system's input-output gain such as H ∞ observers [8][9][10][11].…”