Differential Geometry Measures of Nonlinearity with Applications to Ground Target Tracking

Most ground target tracking problems involve nonlinear filtering due to nonlinearity in the measurement model. At present, a quantitative measure of nonlinearity and its relationship with the performance of the filtering algorithms are lacking. We quantify the degree of nonlinearity of a filtering problem using the differential geometry based measures of nonlinearity such as the parameter-effects curvature and intrinsic curvature. The algorithm for calculating these two measures of nonlinearity was first presented for a static least squares estimation problem. In this paper, we extend the approach to calculate these two measures of nonlinearity for a problem involving a linear system dynamic model and nonlinear measurement model using the maximum likelihood estimator. We present numerical results using simulated data for the constant velocity motion of a target with range and azimuth measurements.