Abstract
The Kalman filter yields the optimal estimate in the sense of the minimum error variance when all the model parameters are exact. However the model parameters are not always exact in practical cases. The present authors focus on a treatment of Kalman filtering when there are erroneous bias terms in an observation model.
In this case, it is pointed out that the Kalman filter yields neither optimal nor unbiased estimate when it is constructed according to an erroneous observation model. Then, under the existence of errors of the bias terms an estimator is constructed by using a conventional method, where a state vector is augmented with the bias terms. The estimator is proved to be statistically optimal in two different senses. By a simple numerical simulation it is shown to be robust against the errors of the bias terms.
