IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING, VOL. 7, NO. 3, JUNE 2013 461 A Multiple-Detection Joint Probabilistic Data Association Filter B. Habtemariam, R. Tharmarasa, T. Thayaparan, M. Mallick, and T. Kirubarajan Abstract—Most conventional target tracking algorithms assume that a target can generate at most one measurement per scan. How- ever, there are tracking problems where this assumption is not valid. For example, multiple detections from a target in a scan can arise due to multipath propagation effects as in the over-the- horizon radar (OTHR). A conventional multitarget tracking algo- rithm will fail in these scenarios, since it cannot handle multiple target-originated measurements per scan. The Joint Probabilistic Data Association Filter (JPDAF) uses multiple measurements from a single target per scan through a weighted measurement-to-track association. However, its fundamental assumption is still one-to- one. In order to rectify this shortcoming, this paper proposes a new algorithm, called the Multiple-Detection Joint Probabilistic Data Association Filter (MD-JPDAF) for multitarget tracking, which is capable of handling multiple detections from targets per scan in the presence of clutter and missed detection. The multiple-de- tection pattern, which can account for many-to-one measurement set-to-track association rather than one-to-one measurement-to- track association, is used to generate multiple detection associa- tion events. The proposed algorithm exploits all the available infor- mation from measurements by combinatorial association of events that are formed to handle the possibility of multiple measurements per scan originating from a target. The MD-JPDAF is applied to a multitarget tracking scenario with an OTHR, where multiple detections occur due to different propagation paths as a result of scattering from different ionospheric layers. Experimental results show that multiple-detection pattern based probabilistic data asso- ciation improves the state estimation accuracy. Furthermore, the tracking performance of the proposed filter is compared against the Posterior Cramér-Rao Lower Bound (PCRLB), which is ex- plicitly derived for the multiple-detection scenario with a single target. Index Terms—Multitarget tracking in clutter, data association, probabilistic data association, multiple-detection per target per scan, over-the-horizon radar (OTHR), multiple-detection JPDAF (MD-JPDAF). I. INTRODUCTION M OST detection-based target tracking algorithms assume that a target generates at most one detection per scan with probability of detection less than unity. In this case, the data association uncertainty is only the measurement origin uncer- Manuscript received September 14, 2012; revised December 18, 2012 and March 20, 2013; accepted March 28, 2013. Date of publication April 03, 2013; date of current version May 13, 2013. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Ba-Ngu Vo. B. Habtemariam, R. Tharmarasa, and T. Kirubarajan are with the De- partment of Electrical and Computer Engineering, McMaster Univer- sity, Hamilton, ON L8S 4K1, Canada (e-mail: habtembk@mcmaster.ca; tharman@grads.ece.mcmaster.ca; kiruba@mcmaster.ca). T. Thayaparan is with Defence Research and Development Canada, Ottawa, ON, Canada (e-mail: thayananthan.thayaparan@drdc-rddc.gc.ca). M. Mallick is an an independent consultant, Anacortes, WA 982212 USA (e-mail: mahendra.mallick@gmail.com). Digital Object Identifier 10.1109/JSTSP.2013.2256772 tainty [2]. Thus, given a set of measurements in a scan, at most one of them can originate from the target and the rest have to be false alarms. This basic assumption results in the formulation of one-to-one measurement-to-track association as an optimiza- tion or enumeration problem. For example, in the Probabilistic Data Association Filter (PDAF) [2], [5], [15] and its multitarget version, the Joint Probabilistic Data Association Filter (JPDAF) [7], [20], weights are assigned to measurements based on the Bayesian assumption that at most one of the measurements is from the target and the rest are false alarms. In the Multiple Hy- pothesis Tracker (MHT) [18], [6], [16] using the multiframe as- signment (MFA) algorithm [4], the measurement-to-track asso- ciation is evaluated as one-to-one combinatorial optimization in the best global hypothesis. In all these cases, the one-to-one as- sumption is fundamental for measurement-to-track association and target state estimation. However, a target can generate multiple detections in a scan due to, for example, multipath propagation or extended nature of the target with a high resolution radar. In this paper, we address multiple detections due to multipath propagation only. When multiple detections from the same target fall within the asso- ciation gate, the PDAF and its multitarget version, the JPDAF, tend to apportion the association probabilities, but still with the fundamental assumption that only one of them is correct. When the measurements are not close to one other, as in the case of multipath detections, the PDAF and JPDAF initialize multiple tracks for the same target. The MHT algorithm tends to generate multiple tracks to handle the additional measurements from the same target due to the basic assumption that at most one mea- surement originated from each target. Such ad hoc handling of multiple detections has undesirable side effects. Thus, an algorithm that explicitly considers multiple detec- tions from the same target in a scan needs to be developed so that all useful information in the received measurements about the target is processed with the correct assumption. Presence of multiple detections per target per scan increases the com- plexity of a tracking algorithm due to uncertainty in the number of target-originated measurements, which can vary from time to time, in addition to the measurement origin uncertainty. How- ever, estimation accuracy can be improved and the number of false tracks can be reduced using the correct assumption with multiple-detection. Multiple-detection is a common phenomenon in over-the- horizon radars (OTHRs) [8], [11], which provides the motiva- tion for this work. This is due to the OTHR’s reliance on the ionospheric layers for signal transmission and reception. The signal transmitted from an OTHR will be scattered by one of the ionospheric layers, then scattered from the target, and fi- nally scattered by another or the same ionospheric layer be- 1932-4553/$31.00 © 2013 IEEE