Minimum-Variance State and Fault Estimation for Multi-Rate Systems with Dynamical Bias

This paper presents a new robust filter structure to solve the simultaneous state and fault estimation problem of linear stochastic discrete-time systems with unknown disturbance. The method is based on the assumption that the fault and the unknown disturbance affect both the system state and the output, and no prior knowledge about their dynamical evolution is available. By making use of an optimal three-stage Kalman filtering method, an augmented fault and unknown disturbance models, an augmented robust three-stage Kalman filter (ARThSKF) is developed. The unbiasedness conditions and minimum-variance property of the proposed filter are provided. An illustrative example is given to apply this filter and to compare it with the existing literature results.

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Recursive Five-Step Filter for State and Fault Estimation of Linear Descriptor Stochastic Systems with Unknown Disturbances

Journal of Circuits System and Computers ◽

10.1142/s0218126618500834 ◽

2018 ◽

Vol 27 (06) ◽

pp. 1850083 ◽

Cited By ~ 3

Author(s):

Talel Bessaoudi ◽

Fayçal Ben Hmida

Keyword(s):

Stochastic Systems ◽

Filter Design ◽

Design Method ◽

Minimum Variance ◽

Descriptor Systems ◽

Fault Estimation ◽

Recursive Filter ◽

Unknown Disturbances ◽

State Space System ◽

The Relationship

This study deals with state and fault estimation for linear descriptor systems. The main contribution lies in the synthesis of a novel filter to estimate both state and fault for linear discrete-time descriptor stochastic systems in an unbiased minimum variance sense and without making any assumption on the direct feedthrough matrix. In this study, an equivalent standard state-space system (ESSS) with fault and unknown disturbances is firstly obtained for the considered descriptor stochastic system, and then a recursive filter is designed based on the ESSS representation. Moreover, this study proposes a recursive filter design method to deal with the effect of the unknown disturbances. The relationship between the proposed filter and the existing results in the literature is addressed. Finally, an illustrative example is given to illustrate the effectiveness of the recursive five-step state and fault estimator.

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

Mathematical Problems in Engineering ◽

10.1155/2010/343586 ◽

2010 ◽

Vol 2010 ◽

pp. 1-17 ◽

Cited By ~ 5

Author(s):

Fayçal Ben Hmida ◽

Karim Khémiri ◽

José Ragot ◽

Moncef Gossa

Keyword(s):

Linear Time ◽

Dynamical Evolution ◽

Full Rank ◽

Discrete Systems ◽

Minimum Variance ◽

The State ◽

Fault Estimation ◽

Time Varying ◽

Time Varying Systems ◽

Unknown Disturbances

This paper presents a new recursive filter to joint fault and state estimation of a linear time-varying discrete systems in the presence of unknown disturbances. The method is based on the assumption that no prior knowledge about the dynamical evolution of the fault and the disturbance is available. As the fault affects both the state and the output, but the disturbance affects only the state system. Initially, we study the particular case when the direct feedthrough matrix of the fault has full rank. In the second case, we propose an extension of the previous case by considering the direct feedthrough matrix of the fault with an arbitrary rank. The resulting filter is optimal in the sense of the unbiased minimum-variance (UMV) criteria. A numerical example is given in order to illustrate the proposed method.

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

International Journal of Applied Mathematics and Computer Science ◽

10.2478/v10006-011-0049-3 ◽

2011 ◽

Vol 21 (4) ◽

pp. 629-637 ◽

Cited By ~ 19

Author(s):

Karim Khémiri ◽

Fayçal Hmida ◽

José Ragot ◽

Moncef Gossa

Keyword(s):

Stochastic Systems ◽

Original System ◽

Minimum Variance ◽

Fault Estimation ◽

Sensor Fault ◽

Recursive Filter ◽

Filter Structure ◽

Linear Stochastic Systems ◽

Unknown Disturbances ◽

Value Decomposition

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

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