Modified Kalman filtering with an optimal target function

Abstract

A general criterion is given to improve the accuracy of the predicted state x(k/k-1) in Kalman filter processing. The criterion is based on the orthogonal relation between the innovations process and past observations. Though this relation is basic to the operation of the Kalman filter, it is often not satisfied in the course of computation because of many target factors. The authors use this relation to construct a target function for minimizing the error. A nonlinear optimal algorithm, combining the standard Kalman filter and the target function equation, is formulated to process the target tracking problem. This algorithm is effective in decreasing the estimation error.<>