Extension of Friedland's bias filtering technique to discrete-time systems with unknown inputs

Abstract

Abstract The problem of state and bias estimation in the presence of unknown inputs is addressed. The proposed approach is an extension of Friedland's method. It is shown that the optimum estimate xk/k of the state xk in the presence of constant bias and unknown inputs can be expressed as xk/k = x¯k/k + βk/k bk/k, where x¯k/k is the bias-free estimate obtained from a Kalman filter with unknown inputs and where βk/k depends only on matrices which arise in the computation of the bias-free estimates