EXTENSION OF FRIEDLAND BIAS FILTERING TECHNIQUE TO DISCRETE-TIME-SYSTEMS WITH UNKNOWN INPUTS

The problem of state and bias estimation in the presence of unknown in puts 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 expresse d as x(k/k) = (x) over bar(k/k) + beta(k/k)b(k/k), where (x) over bar( k/k) is the bias-free estimate obtained from a Kalman filter with unkn own inputs and where beta(k/k) depends only on matrices which arise in the computation of the bias-free estimates.