Nonstatistical nonlinear filtering

Abstract

Modern statistical continuous-time nonlinear filtering theory has become so esoteric that its utility for practical applications is frequently questioned. This paper examines whether there may be an alternative rationale for arriving at a plausible nonlinear filter which could be more readily implemented in practice. This rationale dispenses with statistics entirely and approaches the problem as nonlinear least squares curve fitting. In order to do this we consider only a model which contains observation "noise" only, and no state "noise". The object is not so much to come up with a specific filter which solves a specific problem as to gain insight into the nature of the obstacles to computational ease which seem inherent in any formulation.