AN OPTIMAL CONTROL APPROXIMATION FOR A CERTAIN CLASS OF NONLINEAR FILTERING PROBLEMS.

摘要

A new approximation technique to a certain class of nonlinear filtering problems is considered in this dissertation. The method is based on an approximation of nonlinear, partially-observable systems by a stochastic control problem with fully observable state. The filter development proceeds from the assumption that the unobservables are conditionally Gaussian with respect to the observations initially. The concepts of both conditionally Gaussian processes and an optimal-control approach to filtering are utilized in the filter development. A two-step, nonlinear, recursive estimation procedure (TNF), compatible with the logical structure of the optimal mean-square estimator, generates a finite-dimensional, nonlinear filter with improved characteristics over most of the traditional methods. Moreover, a "close" (in the mean-square sense) approximation model for the original system will be generated as well. In general the nonlinear filtering problem does not have a finite-dimensional recursive synthesis. Thus, the proposed technique may expand the range of practical problems that can be handled by nonlinear filtering. A detailed derivation for the filter with global property is presented. Extension of the results to large-scale nonlinear systems is accomplished by incorporating a novel decomposition scheme in the filter design.; Application of the developed filter to a scalar nonlinear system which lacks model "smoothness" is presented in {lcub}K2{rcub}. Application of the derived multi-dimensional filtering algorithm to two low-order, nonlinear tracking problems according to a global criterion and a local-time criterion respectively are presented. Also, a comparison with traditional methods, such as the popular Extended-Kalman Filter (EKF), are given via digital-computer simulation to demonstrate the effectiveness of the obtained results.