Linear Least-Squares Estimation of Discrete-Time Stationary Processes by Means of Backward Innovations

Abstract

There has lately been a considerable interest in fast algorithms for recursive linear least squares estimation. This is clearly witnessed by a series of recent papers by Casti, Kalaba and Murthy [1], Rissanen [2], Casti and Tse [3], Kailath [4,5,6], and Lindquist [7,8,9], to just mention some contributions related to the work presented in this paper. Among these [1,3,4,5,8,9] concern stochastic processes in continuous time, while [2,6,7,9] deal with discrete-time processes. For an account on the relation between these papers, among which [4,5,6,7,8] and to a certain extent [3] are concerned with Kalman-Bucy filtering,we refer the reader to [9] where we also try to clarify the connections between these recent results and some classical results in filtering [10,11,12], the theory of polynomials orthogonal on the unit circle [13,14,15] and the theory of Fredholm integral equations [16,17,18,19].