Optimal estimation of nonlinear state nonlinear observation systems

The concept of this work is that research on nonlinear modeling and estimation in a stochastic framework brings with it the study of the orthogonality structure of the probability densities involved. The connection is made by means of a probabilistic quantity, called the theta function, which under fairly broad integrability conditions defines the class of factorable random processes. These processes play a central role in the derivation of a recursive estimation scheme which is mathematically optimal and computationally attractive. The theory of factorable processes is simpler and its relevance to estimation practice is more direct than that of other sophisticated nonlinear approaches, such as martingales and Lie algebras.The author is indebted to Prof. D. R. Smith, University of California, San Diego, for helpful suggestions.