Generalized canonical variate analysis of nonlinear systems

The canonical variate analysis (CVA) is extended to general nonlinear systems. Nonlinear canonical variables are shown to determine the optimum nonlinear transformation of the past maximizing the mutual information between the true and an approximating normal distribution. A sequential procedure for selection of the canonical variables is described. Nonlinear CVA is applied to nonlinear controlled Markov processes to obtain approximating nonlinear filters. A recursive innovations representation is given for the nonlinear filter that also yields an innovations representation for the Markov process model