Kalman filtering with no A-priori information about noise-White noise case: Part I: Identification of covariances

Kalman Filtering in the presence of white process and measurement noises of unknown means and covariances is considered. Only stationary linear discrete stochastic systems are considered. It is shown that noise covariances can be identified without knowledge of noise means. Thus, the identification of noise statistics can be divided into two sub-problems: identification of noise covariances and identification of noise means, and these two subproblems can be solved in that order. The second subproblem is considered in Part II. The procedure for identifying noise covariances is a nontrivial extension of Mehra's results to the case where the process and measurement noises are correlated; it is therefore nonrecursive in nature.