A Stratified Statistical Filter with Nonlinear Application

This paper introduces a statistical filter (or, more strictly, a filtering algorithm) which has intended application in the area of nonlinear systems. Within this context, the filter enables one to investigate the convergence effects produced by varying the initial estimates associated with the respective state variables, together with the various system parameters. The present algorithm is not intended to replace the more powerful optimal statistical filters used in linear theory, but rather to provide a simulation tool which can readily be applied to a given nonlinear system. The application considered in this paper bears a similarity to a tracking problem which might be encountered by an optical device, where angular information is the primary observable quanity. In this particular application, angular observations are available, and statistical estimates are desired for a position variable, together with an unknown parameter. The application is introduced primarily for the purpose of demonstrating the behavior of the filter when applied to a relatively simple nonlinear system.