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The cardinalized probability hypothesis density (CPHD) filter is a recursive Bayesian algorithm for estimating multiple target states with varying target number in clutter. In particular, the Gaussian mixture variant (GMCPHD) for linear, Gaussian systems is a candidate for real time multi target tracking. The present work addresses the following three issues: (i) we show the equivalence between the GMCPHD filter and the standard Multi Hypothesis Tracker (MHT) in the case of single targets; (ii) using a Gaussian sum approach, we extend the GMCPHD filter by employing digital road maps for road constraint targets. The utilization of such external information leads to more precise tracks and faster and more reliable target number estimates; (iii) we model the effect of Doppler blindness by a target state dependent detection probability, leading to more stable target number estimation in the case of low Doppler targets.

The cardinalized probability hypothesis density (CPHD) filter is a recursive Bayesian algorithm for estimating multiple target states with a varying target number in clutter. In particular the Gaussian mixture variant (GMCPHD), which provides closed-form prediction and update equations for the filter in the case of linear Gaussian systems, is a candidate for real time multi-target tracking. The following three issues are addressed. First we show the equivalence between the GMCPHD filter and the standard multi hypothesis tracker (MHT) in the case of a single target. Second by using a Gaussian sum approach, we extend the GMCPHD filter to incorporate digital road maps for road constrained targets. The use of such external information leads to more precise tracks and faster and more reliable target number estimates. Third we model the effect of Doppler blindness by a target state-dependent detection probability, which leads to a more stable target-number estimation in the case of low-Doppler targets.

Active sonar tracking using measurements from multistatic sensors has shown promise: there are benefits in terms of robustness, complementarity (covariance-ellipse intersection) and of course simply due to the increased probability of detection that naturally accrues from a well-designed data fusion system. It is not always clear what the placement of the sources and receivers that gives the best fused measurement covariance for any target -or at least for any target that is of interest -might be. In this paper, we investigate the problem as one of global optimization, in which the objective is to maximize the information provided to the tracker.We assume that the number of sensors is given, so that the optimization is done in a continuous space. The strong variability of target strength as a function of aspect is integral to the cost function we optimize. Doppler information is not discarded when constant frequency (Doppler-sensitive) waveforms are available. The optimal placements that result are consistent with our intuition, suggesting that our placement strategy may provide a useful tool in more complex scenarios where intuition is challenged. Index TermsMultistatic active sonar, optimization, sensor placement, sensor management, information gain, anti-submarine warfare, ASW.