A Gaussian Mixture Filter for Range-Only Tracking

Range-only tracking problems arise in extended data collection for inverse synthetic radar applications, robotics, navigation and other areas. For such problems, the conditional density of the state variable given the measurement history is multi-modal or exhibits curvature, even in seemingly benign scenarios. For this reason, the use of extended Kalman filter (EKF) and other nonlinear filtering techniques based on Gaussian approximations can result in inaccurate estimates. We introduce a new filter for such tracking problems in two dimensions called the Gaussian mixture range-only filter (GMROF), which generates Gaussian mixture approximations to the conditional densities. The filter equations are derived by analytic techniques based on the specific nonlinearities of range-only tracking. A slight modification of the standard measurement process model, "noise before nonlinearity," is used to simplify the moment calculations. Implementation requires, at each step, the fitting of a low order Gaussian mixture to a simple exponentiated trigonometric function of a scalar variable. Simulations involving scenarios from earlier comparative studies indicate that the GMROF consistently outperformed the EKF, and achieved the accuracy of particle filters while significantly reducing the computational cost.