Analytic Combinatorics for Multiple Object Tracking

The book shows that the analytic combinatorics (AC) method encodes the combinatorial problems of multiple object tracking—without information loss—into the derivatives of a generating function (GF). The book lays out an easy-to-follow path from theory to practice and includes salient AC application examples. Since GFs are not widely utilized amongst the tracking community, the book takes the reader from the basics of the subject to applications of theory starting from the simplest problem of single object tracking, and advancing chapter by chapter to more challenging multi-object tracking problems. Many established tracking filters (e.g., Bayes-Markov, PDA, JPDA, IPDA, JIPDA, CPHD, PHD, multi-Bernoulli, MBM, LMBM, and MHT) are derived in this manner with simplicity, economy, and considerable clarity. The AC method gives significant and fresh insights into the modeling assumptions of these filters and, thereby, also shows the potential utility of various approximation methods that are well established techniques in applied mathematics and physics, but are new to tracking. These unexplored possibilities are reviewed in the final chapter of the book. Front Matter ....Pages i-xvi Introduction to Analytic Combinatorics and Tracking (Roy Streit, Robert Blair Angle, Murat Efe)....Pages 1-21 Tracking One Object (Roy Streit, Robert Blair Angle, Murat Efe)....Pages 23-47 Tracking a Specified Number of Objects (Roy Streit, Robert Blair Angle, Murat Efe)....Pages 49-79 Tracking a Variable Number of Objects (Roy Streit, Robert Blair Angle, Murat Efe)....Pages 81-112 Multi-Bernoulli Mixture and Multiple Hypothesis Tracking Filters (Roy Streit, Robert Blair Angle, Murat Efe)....Pages 113-143 Wither Now and Why (Roy Streit, Robert Blair Angle, Murat Efe)....Pages 145-153 Back Matter ....Pages 155-221