Recursive algorithm for state space spectrum estimation

A new method is proposed for implementing an adaptive state space filter. This method is based upon the matrix minimum principle of optimal control theory. The adaptive state space filter is a two part algorithm. The first part is a recursive algorithm for optimizing a predictor matrix which describes the transformation from past data to future data. A matrix steepest descent algorithm is developed for use as the update equation in optimizing the predictor matrix. The second part determines the system parameters from the optimized predictor matrix by the decomposition of the predictor matrix and the use of projection techniques. The result is the estimation of the innovations realization which can further describe the spectral characteristics of the model.<>