Direct Estimation of Noise Covariances

A direct technique for estimating unknown covariances of the stationary noise processes disturbing a linear time-invariant system is discussed and analyzed in this paper. The technique which is referred to as the stationary preprocessed measurement correlation (SPMC) technique is direct in the sense that the unknown noise covariances can be estimated without requiring the estimate of the state and the stationarity of the measurements. Under certain conditions on the fourth moments of the noise processes, it is shown that the estimate of the noise covariances converges in quadratic mean to their actual value.