A unified filter for simultaneous input and state estimation of linear discrete-time stochastic systems

Abstract

In this paper, we present a unified optimal and exponentially stable filter for linear discrete-time stochastic systems that simultaneously estimates the states and unknown inputs in an unbiased minimum-variance sense, without making any assumptions on the direct feedthrough matrix. We also provide the connection between the stability of the estimator and a system property known as strong detectability, and discuss the global optimality of the proposed filter. Finally, an illustrative example is given to demonstrate the performance of the unified unbiased minimum-variance filter.

Optimal state filter from sequential unknown input reconstruction: Application to distributed state filtering

“…Under permanent unknown inputs, the filter of Theorem 3 reconstructs the unknown input sequence {d is avoided, which is the main difference with the joint unknown inputs and the state filtering problem presented in the work of Yong et al, 16 where d k is estimated from measurements y k and y k+1 .…”

“…In the work of Kitanidis, 4 an optimal linear state filter is obtained by minimizing the trace of the state estimation error covariance matrix under the constraint that the state estimation error is decoupled from unknown inputs or obtained from the state filtering of singular systems as in the work of Darouach et al 5 Other optimal filters having a structure closer to that of the standard Kalman filter are designed in previous works. [6][7][8][9][10][11][12] The problem studied in previous works, [13][14][15][16] which is the most closely related to joint input and state estimation, is of great importance to fault-tolerant control when each component of the unknown input vector may represent actuator, sensor, or transmission faults as explained in the works of Blanke et al 17 and Patton et al…”

Optimal Position and Velocity Estimation for Multi‐USV Positioning Systems with Range Measurements

“…Floquet and Barbot designed an input and state delayed estimator for discrete-time linear systems even if some wellknown matching condition does not hold [33]. Yong et al presented an exponentially stable filter for linear discretetime stochastic systems that simultaneously estimates the state and unknown input [34]. Su et al investigate the properties of the Kalman filter for linear stochastic time-varying systems with partially observed inputs [35].…”

Structural and Strongly Structural Input and State Observability of Linear Network Systems

“…[9], [8]). Both tests require exact knowledge of entries in the matrices of interest and are computationally heavy as the dimension of the system grows, while the latter is not suitable for LTV systems.…”

“…The concept of uniform δ-step ISO (i.e., ISO over every time window of length δ) gets rid of this drawback. The notion of ISO is of particular importance in designing unbiased minimum-variance filters that simultaneously estimate both state and unknown input [6]- [8]. It is well-known…”