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17 May 2006 A theory of PHD filters of higher order in target number
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Abstract
The multitarget recursive Bayes nonlinear filter is the theoretically optimal approach to multisensor-multitarget detection, tracking, and identification. For applications in which this filter is appropriate, it is likely to be tractable for only a small number of targets. In earlier papers we derived closed-form equations for an approximation of this filter based on propagation of a first-order multitarget moment called the probability hypothesis density (PHD). In a recent paper, Erdinc, Willett, and Bar-Shalom argued for the need for a PHD-type filter which remains first-order in the states of individual targets, but which is higher-order in target number. In this paper we show that this and much more is possible. We derive a closed-form cardinalized PHD (CPHD), filter, which propagates not only the PHD but also the entire probability distribution on target number.
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Ronald Mahler "A theory of PHD filters of higher order in target number", Proc. SPIE 6235, Signal Processing, Sensor Fusion, and Target Recognition XV, 62350K (17 May 2006); https://doi.org/10.1117/12.667083
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