Unbiased Minimum-Variance Filter for State and Fault Estimation of Linear Time-Varying Systems with Unknown Disturbances (original) (raw)

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

2011

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.

Three-stage Kalman filter for state and fault estimation of linear stochastic systems with unknown inputs

Journal of the Franklin Institute, 2012

The paper studies the problem of simultaneously estimating the state and the fault of linear stochastic discrete-time varying systems with unknown inputs. The fault and the unknown inputs affect both the system state and output. However, if the dynamical evolution models of the fault and the unknown inputs are available the filtering problem is solved by the Optimal Three-Stage Kalman Filter (OThSKF). The OThSKF is obtained after decoupling the covariance matrices of the Augmented state Kalman Filter (ASKF) using a Three-Stage U-V transformation. Nevertheless, if the fault and the unknown inputs models are not perfectly known the Robust Three-Stage Kalman Filter (RThSKF) is applied to give an unbiased minimum-variance estimation. Finally, a numerical example is given in order to illustrate the proposed filters.

Robust fault and state estimation for discrete time-varying uncertain systems

2009

Abstract In this paper, we consider the robust Kalman filtering for uncertain discrete time-varying systems, to solve the problem of simultaneously state and fault estimation. The system under consideration is subjected to time-varying norm-bounded parameter uncertainty in both the state and measurement matrices. The approach suggested rests on the use of the Augmented State Robust Kalman Filter (ASRKF) based on the optimization of an upper bound on the variance error of the state estimation.

Joint Estimation of States and Parameters of Linear Systems with Parameter Faults Under Non-Gaussian Noises

Facta Universitatis, 2020

Joint estimation of states and time-varying parameters of linear state space models is of practical importance for the fault diagnosis and fault tolerant control. Previous works on this topic consider the joint estimation in the Gaussian noise environment, but not in the presence of outliers. The known fact is that the measurements have inconsistent observations with the largest part of the observation population (outliers). They can significantly make worse the properties of linearly recursive algorithms which are designed to work in the presence of Gaussian noises. This paper proposes the strategy of the joint parameter-state robust estimation of linear state space models in the presence of non-Gaussian noises. The case of parameterdependent matrices is considered. Because of its good features in robust filtering, the extended Masreliez-Martin filter represents a cornerstone for realization of the robust algorithms for joint state-parameter estimation of linear time-varying stochastic systems in the presence of non-Gaussian noises. The good features of the proposed robust algorithm for joint estimation of linear time-varying stochastic systems are illustrated by intensive simulations.

Fault isolation filter design for linear stochastic systems

Automatica, 1999

This paper is concerned with the problem of detecting and isolating multiple faults by a special structure of the full-order Kalman "lter. A new state "ltering strategy is developed to detect and isolate multiple faults appearing simultaneously or sequentially in discrete time stochastic systems. Under a fault isolation condition, the proposed method can isolate q simultaneous faults with at least q output measurements. The fault isolation "lter generates a reduced output residual vector of dimension q so that its ith component is decoupled from all but the ith fault and so that the e!ect of plant and state noises is minimized. Necessary and su$cient conditions for stability and convergence of the proposed "lter are established.

A fault detection and isolation filter for discrete linear systems

Isa Transactions, 2003

The problem of fault and/or abrupt disturbances detection and isolation for discrete linear systems is analyzed in this work. A strategy for detecting and isolating faults and/or abrupt disturbances is presented. The strategy is an extension of an already existing result in the continuous time domain to the discrete domain. The resulting detection algorithm is a Kalman filter with a special structure. The filter generates a residuals vector in such a way that each element of this vector is related with one fault or disturbance. Therefore the effects of the other faults, disturbances, and measurement noises in this element are minimized. The necessary stability and convergence conditions are briefly exposed. A numerical example is also presented.

Design of unknown input observers for non-linear stochastic systems and their application to robust fault diagnosis

The paper deals with the problem of designing filters for non-linear discrete-time stochastic systems. In particular, it is shown how to design an unknown input filter for a single (constant) unknown input distribution matrix, which guarantees that the effect of a fault will not be decoupled from the residual. Subsequently, the problem of using one, fixed disturbance distribution matrix is eliminated by using the interacting multiple models algorithm to select an appropriate unknown input distribution matrix from a predefined set of matrices. The final part of the paper shows an illustrative example, which confirms the effectiveness of the proposed approach.

Novel recursive optimal filter for the joint input-state estimation in linear discrete-time systems

2013 International Conference on Control, Decision and Information Technologies (CoDIT), 2013

This paper presents a new recursive optimal filter structure for joint input and state estimation of linear timevarying discrete systems in the presence of unknown inputs. The method is concerned with the direct feedthrough matrix which has an arbitrary rank. The resulting filter is optimal in the sense of the unbiased minimum-variance (UMV) criteria. The paper extends the existing results, in particular the ones of Hsieh in 2009. A numerical example is given in order to make a comparison between the proposed filter and the Hsieh filter developed by .