## Fundamentals of Object TrackingKalman filter, particle filter, IMM, PDA, ITS, random sets... The number of useful object-tracking methods is exploding. But how are they related? How do they help track everything from aircraft, missiles and extra-terrestrial objects to people and lymphocyte cells? How can they be adapted to novel applications? Fundamentals of Object Tracking tells you how. Starting with the generic object-tracking problem, it outlines the generic Bayesian solution. It then shows systematically how to formulate the major tracking problems - maneuvering, multiobject, clutter, out-of-sequence sensors - within this Bayesian framework and how to derive the standard tracking solutions. This structured approach makes very complex object-tracking algorithms accessible to the growing number of users working on real-world tracking problems and supports them in designing their own tracking filters under their unique application constraints. The book concludes with a chapter on issues critical to successful implementation of tracking algorithms, such as track initialization and merging. |

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### Contents

1 Introduction to object tracking | 1 |

2 Filtering theory and nonmaneuvering object tracking | 22 |

3 Maneuvering object tracking | 62 |

4 Singleobject tracking in clutter | 103 |

objectexistencebased approach | 133 |

randomsetbased approach | 223 |

7 Bayesian smoothing algorithms for object tracking | 265 |

8 Object tracking with timedelayed outofsequence measurements | 289 |

9 Practical object tracking | 312 |

Mathematical and statistical preliminaries | 344 |

Finite set statistics FISST | 354 |

Pseudofunctions in object tracking | 358 |

361 | |

370 | |

### Common terms and phrases

ˆxk|k approximation AS-PDA assumed augmented Bar-Shalom Bayes Bayesian filter chapter clutter measurement density Compute conditional density covariance matrix denotes density estimation derived distribution false track discrimination feasible joint events ﬁlter Gaussian mixture given IMM-JITS IMM-PDA IPDA JIPDA Kalman filter likelihood function linear maneuvering object tracking Markov chain mean and covariance measurement equation measurement likelihood measurement yk model probability multi-object tracking Mušicki non-parametric normalization factor number of objects object dynamics object existence object tracking algorithms object tracking problem object trajectory model OOSM p(xk|yk p(yk particle filter Pk|k posterior density prediction density prior probabilistic data association probability density function probability of object propagation random variable recursion RMS error sample scan selected measurements selection gate simulation single-object tracking single-scan surement target tentative track components theorem total probability theorem trackers tracking in clutter trajectory state pdf transition density update vector Yk_1