On a least squares predictive-transform modeling methodology
A deterministic least squares (LS) predictive-transform (PT) multichannel modeling framework is presented. In a manner analogous to the development of minimum mean square error (MSE) PT, the LS PT signal model is obtained as an inherent byproduct of an optimized predictive-transform signal source "encoder", thereby preserving the direct integration of specific data compression concepts into the basic modeling procedure that have proven very useful in the application of minimum MSE PT to coding, detection, estimation, and control. Fundamental properties of the LS PT signal model are presented, and a recursive least squares (RLS) PT modeling procedure is developed. In addition to subsuming conventional RLS signal modeling as a special case and the presence of an integrated transformation mechanism, RLS PT offers greater flexibility when independent "fading memory" weighting of both the first- and second-order sample moments is desired. Sufficient conditions for the convergence of the RLS PT parameters to their minimum MSE PT counterparts are developed. In addition, the zero mean constraint (either deterministic or stochastic) imposed on the LS PT signal model's innovation sequence is shown to provide a mechanism for mitigating the deleterious effects of a singular or near-singular data correlation matrix.