ABSTRACT
Multitarget Calculus .......................................................................... 394 16.4.7 Basic Differentiation Rules ................................................................................ 394
16.5 Multitarget Likelihood Functions .................................................................................. 395 16.5.1 Multitarget Measurement Models .................................................................... 395
16.5.1.1 Case I: No Missed Detections, No False Alarms ........................... 395 16.5.1.2 Case II: Missed Detections ................................................................ 395 16.5.1.3 Case III: Missed Detections and False Alarms .............................. 396 16.5.1.4 Case IV: Multiple Sensors .................................................................. 396
16.5.2 Belief-Mass Functions of Multitarget Sensor Models ................................... 396 16.5.3 Constructing True Multitarget Likelihood Functions .................................. 397
16.6 Multitarget Markov Densities ........................................................................................ 397 16.6.1 Multitarget Motion Models ............................................................................... 398
16.6.1.1 Case I: Target Number Is Constant .................................................. 398 16.6.1.2 Case II: Target Number Can Decrease ............................................ 398 16.6.1.3 Case III: Target Number Can Increase and Decrease ................... 399
16.6.2 Belief-Mass Functions of Multitarget Motion Models .................................. 399 16.6.3 Constructing True Multitarget Markov Densities ......................................... 399
16.7 Multisource-Multitarget Bayes Filter .............................................................................400 16.7.1 Multisensor-Multitarget Filter Equations ........................................................400 16.7.2 Initialization .........................................................................................................400 16.7.3 Multitarget Distributions and Units of Measurement ................................... 401 16.7.4 Failure of the Classical State Estimators .......................................................... 401 16.7.5 Optimal Multitarget State Estimators ..............................................................402 16.7.6 Multitarget Miss Distance ..................................................................................402 16.7.7 Uni ed Multitarget Multisource Integration ..................................................403
16.8 PHD and CPHD Filters ....................................................................................................403 16.8.1 Probability Hypothesis Density ......................................................................404 16.8.2 PHD Filter ............................................................................................................404 16.8.3 Cardinalized PHD Filter ...................................................................................405 16.8.4 Survey of PHD/CPHD Filter Research ............................................................405
16.9 Summary and Conclusions .............................................................................................406 Acknowledgments ......................................................................................................................407 References ....................................................................................................................................407
This chapter deals with nite-set statistics (FISST),1-3,80 which is also described in practitioner-level detail in the new textbook Statistical Multisource-Multitarget Information Fusion.4 FISST provides a uni ed, scienti cally defensible, probabilistic foundation for the following aspects of multisource, multitarget, and multiplatform data fusion: (1) multisource integration (i.e., detection, identi cation, and tracking) based on Bayesian ltering and estimation;5-9 (2) sensor management using control theory;7,10 (3) performance evaluation using information theory;11-14 (4) expert systems theory (e.g., fuzzy logic, the
