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

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 x_k/k of the state x_k in the presence of constant bias and unknown inputs can be expressed as x_k/k = x¯_k/k + β_k/k b_k/k, where x¯_k/k is the bias-free estimate obtained from a Kalman filter with unknown inputs and where β_k/k depends only on matrices which arise in the computation of the bias-free estimates