Some current directions in nonlinear estimation and filtering theory

Nonlinear estimation and filtering theory began with the pioneering work of Stratonovich and Kushner. After several years of intense activity associated with applying their results (equations) to a great many applied problems of interest via various approximate solution techniques and associated with the development of more rigorous and more general approaches to the problem, several definite and distinct directions in the theory can now be identified. Some of these directions are described and discussed in this paper so as to provide a basis for assessing where the subject stands currently and where it seems to be going.