Robust State and fault Estimation of Linear Discrete Time Systems with Unknown Disturbances

TL;DR

This paper introduces a robust recursive least squares filter for linear stochastic systems that accurately estimates states and faults despite unknown disturbances, improving numerical stability and implementation simplicity.

Contribution

It proposes a novel, easily implementable square root method combined with an iterative framework for simultaneous state and fault estimation in linear systems.

Findings

Enhanced numerical stability over existing filters

Effective simultaneous estimation of states and faults

Validated performance through numerical example

Abstract

This paper presents a new robust fault and state estimation based on recursive least square filter for linear stochastic systems with unknown disturbances. The novel elements of the algorithm are : a simple, easily implementable, square root method which is shown to solve the numerical problems affecting the unknown input filter algorithm and related information filter and smoothing algorithms; an iterative framework, where information and covariance filters and smoothing are sequentially run in order to estimate the state and fault. This method provides a direct estimate of the state and fault in a single block with a simple formulation. A numerical example is given in order to illustrate the performance of the proposed filter.