Multi-model predictive transform estimation

The minimum mean square error (MSE) predictive transform (PT) signal modeling and estimation formalism is extended to the case when the requisite ensemble statistics are not available a priori. This is achieved by the introduction of a comprehensive continuous-update multi-model predictive transform (PT) estimation approach. The system consists of a bank of N, say, PT estimators whose individual conditional estimates are combined into a weighted sum (linear combiner) to produce an overall estimate which is then fed back to each constituent estimator to provide better tracking, of rapid statistical variations, e.g. edges-especially for the filtering case. The determination of the weights is based on an adaptive decisioning algorithm. Unlike the partitioning or multimodel approaches of D.G. Lainiotis (1976) and D.T. Magill (1965), the presence of the overall feedback introduces coupling between the constituent estimators, although the computations can still be performed in parallel. The stability properties of this nonlinear estimation technique are investigated and a set of sufficient conditions is obtained which insures bounded input bounded output stability