Polynomial estimators

Minimal mean square error polynomial estimators are developed for time discrete systems. The estimation problem is formulated in Hilbert space with the optimal as the projection on the linear manifold generated by finite polynomials of the observer. The estimate is partitioned into a predictor and corrector where the corrector is expressed as the product of a weighting vector and residual. Methods of determing the residuals and the weighting vectors are developed. An example applying the techniques is included.