<title>Differential geometry measures of nonlinearity for filtering with nonlinear dynamic and linear measurement models</title>

Abstract

In our previous work, we presented an algorithm to quantify the degree of nonlinearity of nonlinear filtering problems with linear dynamic models and nonlinear measurement models. A quantitative measure of the degree of nonlinearity was formulated using differential geometry measures of nonlinearity, the parameter-effects curvature and intrinsic curvature. We presented numerical results for a number of practical nonlinear filtering problems of interest such as the bearing-only filtering, ground moving target indicator filtering, and video filtering problems. In this paper, we present an algorithm to compute the degree of nonlinearity of a nonlinear filtering problem with a nonlinear dynamic model and a linear measurement model. This situation arises for the bearing-only filtering problem with modified polar coordinates and log polar coordinates. We present numerical results using simulated data.