New Results for Stochastic Prediction and Filtering {w}ith Unknown Correlations

This paper considers state estimation for dynamic systems in the case of nonwhite, mutually correlated noise processes. Here, the problem is complicated by the fact, that only the individual covariances are known; cross covariances between random variables obtained by taking individual noise processes at different time steps and between different noise processes are completely unknown. New estimator equations for solving this problem are derived in feedback form for both the prediction step and for the filtering step based on existing ideas known as covariance intersection. Solutions are given for the most general case of updating an N–dimensional state vector estimate based on M–dimensional observations. Furthermore, computationally efficient solutions for obtaining minimum covariance estimates are derived to avoid numerical optimization otherwise required.