Multistage estimation of bias states in linear systems†

Abstract

This paper provides an alternative, constructive derivation of Friedland's (1966) method for recursive bias filtering ; and, extends his method to the case where we may wish to increase (or decrease) the number of biases. We show that it is possible to add (or delete) bias states in such a manner that previously computed quantities can be used to obtain new estimates of the dynamical state vector and the now larger bias vector. Adding (or deleting) bias states is important when, for example, the bias states are used to model constant but unknown instrumentation error sources, of which there can be a large number.