Kalman Filter for Discrete-Time Stochastic Linear Systems Subject to Intermittent Unknown Inputs

Abstract

State estimation of stochastic discrete-time linear systems subject to persistent unknown inputs has been widely studied but only few works have been dedicated to the case where unknown inputs may be simultaneously or sequentially active or inactive. In this paper, a Kalman filter approach is proposed for state estimation of systems with unknown intermittent inputs. The design is based on the minimisation of the trace of the state estimation error covariance matrix under the constraint that the state estimation error is decoupled from the unknown inputs corrupting the system at the current time. The necessary and sufficient stability conditions are established considering the upper bound of the prediction error covariance matrix.Index Terms-Kalman filter, intermittent unknown inputs, linear system, covariance matrices.

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

“…wherex k+1∕k is the state prediction of covariance 23 to left invertible systems of structural delays α = 0, α = 1 or α > 1. If α = 0, the unbiased minimum-variance (UMV) state prediction so that E {x k+1∕k } = x k+1 ∀{ρ j } k 0 will depend on the binary sequence from a combinational logic.…”

“…For each subsystem, a solution to the autonomous distributed state filtering problem consists in solving online the state filtering problem of the discrete-time linear stochastic systems subject to data-driven unknown inputs triggered by data losses. The intermittent unknown input Kalman filter (IIKF) in the work of Keller and Sauter 23 solves this state filtering problem when data losses are described as known binary sequences by parameterizing the solution to the intermittent unknown input decoupling constraint from 2 constant-size matrices. These matrices are called the free and the constrained part of the filter gain that are used to minimize the trace of the state and the unknown input estimation error covariance matrix from a 2-stage optimization strategy.…”

“…When the number of intermittent unknown inputs is equal to the number of measurements, Keller et al 24 showed the duality between Kalman filters with intermittent observations in the work of Sinopoli et al 22 and with intermittent unknown inputs in the work of Keller and Sauter. 23 The problem of inverting linear time-invariant systems has been of interest to control engineers for many years. The existence conditions under which a linear discrete-time system with permanent unknown inputs is left invertible with zero, one or more structural delays has been discussed in previous works [25][26][27][28] or in Appendix A.…”

Input reconstruction for networked control systems subject to deception attacks and data losses on control signals

“…As shown by Keller and Sauter (2013), the ASIIKF's RDE (3.15) can take the form of a switching standard RDE…”

“…Even if the augmented state Kalman filter (ASKF) (Alouani, Rice, & Blair, 1992;Friedland, 1969;Hsieh & Chen, 1999;Ignagni, 2000;Kim, Lee, & Park, 2006) should be used to estimate the constant bias, no work has been dedicated to estimate a disturbance that switches between unknown input and constant bias at the occurrence times of packet This paper avoids the use of a variable dimensional state model by forcing the intermittent unknown input to be the complementary state of the intermittent bias. The resulting fixed dimensional augmented state model of the plant is used to estimate the switching disturbance from an augmented state version of the intermittent unknown input Kalman filter (IIKF) (Keller & Sauter, 2013). Necessary and sufficient stochastic stability conditions are established when the arrival sequence of data losses follows a Bernoulli random process.…”