Gaussian mixture filtering for range only tracking problems

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 and unreliable estimates. In this paper, we introduce a new filter specifically designed for range only tracking called the Gaussian mixture range only filter (GMROF). The filter recursively generates Gaussian mixture approximations to the conditional density. The filter equations are derived by analytic techniques based on the specific nonlinearities arising in range only tracking. Simulation results, based on scenarios taken 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.