Title :
A Gaussian Mixture Filter for Range-Only Tracking
Author :
Clark, J.M.C. ; Kountouriotis, P.A. ; Vinter, R.B.
Author_Institution :
Dept. of Electr. & Electron. Eng., Imperial Coll. London, London, UK
fDate :
3/1/2011 12:00:00 AM
Abstract :
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.
Keywords :
Gaussian processes; Kalman filters; nonlinear filters; particle filtering (numerical methods); synthetic aperture radar; target tracking; Gaussian mixture approximations; Gaussian mixture range-only filter; exponentiated trigonometric function; extended Kalman filter; filter equations; inverse synthetic radar applications; measurement process model; navigation; nonlinear filtering techniques; particle filters; range-only tracking problem; robotics; Bayesian methods; Gaussian mixtures; range-only tracking; target tracking;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2010.2072590