An Optimal Approximation for a Certain Class of Nonlinear Filtering Problems.
OREGON STATE UNIV CORVALLIS DEPT OF ELECTRICAL AND COMPUTER ENGINEERING
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A new approximation technique to a certain class of nonlinear filtering problems is considered. 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 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. 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.
- Statistics and Probability