Polytopes, a novel approach to tracking

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Abstract
Standard target tracking techniques such as Kalman filters or maximum liklihood estimators approach nonlinearities from an essentially local point of view; that is, they determine a single solution even though the problem may admit more than one. This lack of uniqueness may be due to the absence of global observability as in Doppler tracking where several isolated solutions can occur, or a result of imperfect measurements producing multiple minima in a cost function. The latter is particulary significant since noisy data often produce situations in which local minima abound, trapping a maximum liklihood steepest descent search or causing an extended Kalman filter to diverge. This paper introduces a novel tracking algorithm based on a global approach utilizing containment regions approximated by four-dimensional polytopes. The algorithm is presented in the context of bearings-only tracking, the various tradeoffs with conventional techniques are examined, and potential applications discussed.

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