A variable geometric state filtering for stochastic linear systems subject to intermittent unknown inputs

In this paper, a new approach for state filtering of dynamic stochastic discrete-time systems affected by unknown inputs is presented. The proposed state filtering scheme includes a restricted diagonal detection filter generating a set of minimum variance white detection signals, each of them sensitive to a particular component of the unknown input vector. After having tested the statistical effect of each unknown input in order to update online the unknown inputs decoupling constraint, the variable geometric state filtering is obtained by minimizing the state estimation errors covariance matrix. Compared to the standard unknown input Kalman filter, a new degree of freedom appears in the covariance optimisation problem at the detection time of a non significant unknown input. A comparative study with the standard unknown input Kalman filter shows the efficiency of the proposed approach, particularly when the unknown inputs are intermittent.