Track Initialization for TOMHT Using Auxiliary CPHD Filter Xin Chen, R. Tharmarasa, T. Kirubarajan Department of Electrical and Computer Engineering McMaster University Hamilton, ON, L8S 4L8 905-525-9140 Ext.23151 chenx73@univmail.cis.mcmaster.ca Xavier N. Fernando Department of Electrical and Computer Engineering Ryerson University Toronto, ON, M5B 2K3 416-979-5000 Ext.6077 fernando@ee.ryerson.ca Michel Pelletier FLIR Radar Systems Laval, QC, H7L 5A9 450-663-4554 Ext.315 Michel.Pelletier@ﬂir.com Abstract—In this paper, a new track initialization method for the track–oriented multiple hypothesis tracking (TOMHT) is proposed. An auxiliary cardinalized probability hypothesis density (CPHD) ﬁlter, which is modiﬁed to estimate the distribu- tion of the number of target–originated measurements, is pro- posed. After obtaining the maximum a posteriori (MAP) esti- mate of the number of target–originated measurements, the K– cardinality 2–D assignment technique is used to ﬁnd the optimal measurement–to–track association hypothesis, which is not only subjected to the standard “one–to–one” feasibility constraints, but also the constraint that a given number of measurements are associated to newly initialized tracks. Furthermore, by assuming that the velocities of the initial tracks are independent and identically distributed (i.i.d.) with a probability distribution determined by the output of the auxiliary CPHD ﬁlter, the information about the target state from the auxiliary CPHD ﬁlter is integrated into the track initialization. After the K– cardinality 2–D assignment, the results from the TOMHT are fed back to the CPHD ﬁlter to remove the measurements being associated with the conﬁrmed and the tentative tracks. Then the CPHD will be updated again using the reduced measurement set. Simulation results show that the proposed track initializa- tion method is able to decrease the false track rate by adaptively controlling the track initiation latency, based on the information about the clutter spatial intensity. TABLE OF CONTENTS 1 I NTRODUCTION .................................. 1 2 MODIFIED CPHD FILTER ....................... 2 3 K- CARDINALITY 2–D ASSIGNMENT ............ 4 4 TRACK I NITIALIZATION FOR TOMHT WITH AUXILIARY CPHD FILTER ...................... 5 5 NUMERICAL RESULTS ........................... 6 6 SUMMARY ....................................... 9 REFERENCES .................................... 9 BIOGRAPHY ..................................... 9 1. I NTRODUCTION As an effective Bayesian multitarget tracker, the multiple hy- pothesis tracking (MHT) technique [13], is a data association and target tracking algorithm that aims to evaluate the pos- terior probabilities of multiple sequences of measurements having originated from different targets. In its original form, 978-1-4577-0557-1/12/$26.00 c 2012 IEEE. the probabilities of joint measurement–to–track association hypotheses were directly calculated [13]. Thus, it was also referred to as the “hypothesis–oriented” MHT (HOMHT). However, the MHT technique is typically implemented using the “track–oriented” MHT (TOMHT) [4], because, compared to the HOMHT, the implementation of the TOMHT is sub- stantially simpler. Typically, in the TOMHT, the likelihood ratio is used to update the score for each individual track [4]. After that, the joint measurement–to–track association hypotheses, which must be subjected to “one–to–one” feasibility constraints, are built through multiframe (or multiscan) optimal assignment technique [10]. In a TOMHT with an S–dimensional multi- frame assignment technique, there are S lists, where the ﬁrst list consists of “frozen” tracks, followed by the most recent S − 1 scans of measurements. Besides that, each list also has a “dummy” item to represent the missed detections (for the dummy in the track list) or the extraneous measurements (for the dummy in the measurement list). Except for those dummies, each element from each list should be assigned once and only once and the objective is to form an S–tuple that consists of exactly one element from each of the S lists. Usually, when S =2 (i.e., one track list and only using the most recent scan of measurements), the modiﬁed auction algorithm is used to obtain the most likely assignment. When S> 2, there is no polynomial time algorithm to ﬁnd the most likely assignment. However, by using Lagrangian relaxation, the original S–dimensional multiframe assignment problem can be approximately transformed into several 2–D assign- ment problems and a near–optimal assignment can be found within a quasipolynomial time [10]. To obtain the M most likely joint hypotheses, one can use the M –best multiframe assignment technique [12]. In the above TOMHT implementation via the multiframe assignment technique, two things should be noted: The multi- frame assignment technique itself is a non-Bayesian approach [2]. On the other hand, the MHT technique is Bayesian. Thus, there is a mismatch between theses two techniques. Although estimating the time–varying number of targets is an important objective of multitarget tracking, the total number of targets is not explicitly considered in the TOMHT nor in the multiframe assignment. The number of the tracks is a byproduct of the tracker. In recent years, based on the theory of random ﬁnite sets (RFS) [8], the cardinalized probability hypothesis density (CPHD) ﬁlter has emerged as a powerful tool for the mul- 1