An efficient algorithm for estimating noise covariances in distributed systems

We present an efficient computational algorithm for estimating the noise covariance matrices of large linear discrete stochasticdynamic systems. Such systems arise typically by discretizing distributed-parameter systems, and their size renders computational efficiency a major consideration. Our adaptive filtering algorithm is based on the ideas of Bélanger, and is algebraically equivalent to his algorithm. The earlier algorithm, however, has computational complexity proportional to p⁶, where is the number of observations of the system state, while the new algorithm has complexity proportional to only p³. Furthermore, our formulation of noise covariance estimation as a secondary filter, analogous to state estimation as a primary filter, suggests several generalizations of the earlier algorithm. The performance of the proposed algorithm is demonstrated for a distributed system arising in numerical weather prediction.