Curvature nonlinearity measure and filter divergence detector for nonlinear tracking problems

Several nonlinear filtering techniques are investigated for nonlinear tracking problems. Experimental results show that for a weakly nonlinear tracking problem, the extended Kalman filter and the unscented Kalman filter are good choices, while a particle filter should be used for problems with strong nonlinearity. To quantitatively determine the nonlinearity of a nonlinear tracking problem, we propose two types of measures: one is the differential geometry curvature measure and the other is based on the normalized innovation squared (NIS) of the Kalman filter. Simulation results show that both measures can effectively quantify the nonlinearity of the problem. The NIS is capable of detecting the filter divergence online. The curvature measure is more suitable for quantifying the nonlinearity of a tracking problem as determined via simulations.