Differential geometry measures of nonlinearity for filtering with nonlinear dynamic and linear measurement models

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.