On predictive least squares filtering

In this paper, a class of filters based on the Predictive Least Squares principle recently suggested by Rissanen are proposed and studied. The proposed filtering technique provides a consistent estimate of the number of parameters for a Gaussian regression model while still minimizing the accumulated least squares error. Thus, the proposed filters combine model estimation and parameter estimation to provide optimal prediction and estimation. The proposed Predictive Least Squares filtering has potential application for adaptive coding, spectrum estimation, harmonic retrieval and many other digital signal processing areas.