Optimal Estimation of Measurement Bias

A method is described for the optimal estimation of measurement biases in a Kalman filtering application. The method, which was originally developed by B. Friedland, is based on the decoupling of a large Kalman filter into two smaller filters. One of the smaller filters produces a state estimate which assumes that all measurement biases are zero and the other called the bias filter estimates the measurement biases. The outputs of the two smaller filters are recombined to form the optimal state estimates. Restrictions on the form of the filters which are imposed by the decoupling are discussed. Several extensions of Friedland's original method are presented. Finally, the implementation of the filters via square root filtering techniques is developed.