Extensions of Discrete‐Time Linear Estimation

The major assumptions of the optimal linear estimator for dynamic systems (the Kalman filter) are that the process noise sequence is white, the measurement noise sequence is white, and the two noise sequences are uncorrelated. This chapter discusses the procedures to reduce the problems where the above assumptions are not satisfied, to the standard case. The prewhitening and state augmentation technique needed in the case of autocorrelated process noise is presented. The case of correlated noise sequences and how this correlation can be eliminated are shown. The situation of autocorrelated measurement noise, which is solved with the help of the techniques from the previous chapters, is also shown. Estimation of the state at times other than the current time is discussed. Prediction and smoothing—estimation of the state at an earlier time than the last data point—is also presented. A problem solving section appears at the end of the chapter.