Comparison of measures of nonlinearity for bearing-only and GMTI filtering

Bearing-only and ground moving target indicator (GMTI) filtering are important practical nonlinear filtering problems that have been widely studied. The bearing-only filtering problem is regarded as a challenging nonlinear filtering problem. The degree of nonlinearity (DoN) of these problems were previously studied using differential geometry based parameter-effects and intrinsic curvatures. In this paper we analyze these two problems using a recently proposed measure of nonlinearity (MoN) for state estimation. We compute the conditional MoN (unnormalized and normalized) using an unscented Kalman filter (UKF) and a particle filter (PF). Numerical results from Monte Carlo simulations show that the normalized MoN values for these two problems are quite small, ∼ 10−4 and the normalized MoN values for the GMTI filtering are slightly higher than those for the bearing-only filtering. For each problem, we also compute the root mean square (RMS) position and velocity errors and posterior Cramer-Rao lower bound (PCRLB) to asses the state estimation accuracy.