Control For Energy and Sustainability

EPSRC Programme Grant

[CKV10] J. M. C. Clark, P. A. Kountouriotis and R. B. Vinter, A Gaussian mixture filter for range-only tracking, IEEE Transactions on Automatic Control, vol.56, no.3, pp.602-613, March 2011


Range only tracing 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 the extended Kalman filter (EKF) and other nonlinear filtering techniques based on Gaussian approximations can result in inaccurate estimates and unreliable confidence region information. 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 approximations to the conditional density. The filter equations are derived by analytic techniques based on the specific nonlinearities arising in range only tracking. A slight modification of the standard measurement process model, to place the noise before the measurement nonlinearity, is introduced to simplify the moment calculations involved. Implementation of the filter requires, at each step, the fitting of a low order Gaussian mixture to a simple exponentiated trigonometric function of a scalar variable. Simulation results, based on scenarios taken form earlier comparative studies, indicate that the GMROF consistently outperformed the EKF, and achieved the accuracy of particle filters while significantly reducing the computational burden.