Fundamentals of Object Tracking

Abstract

Kalman 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.

Bayesian environment representation, prediction, and criticality assessment for driver assistance systems

“…The transition density is induced by the system dynamic equation (3.9a), while the measurement likelihood is generated from the measurement equation (3.9b) according to [53,166] …”

“…if the initial conditions are chosen wrongly [17,113]. The UKF presented in the following does not suffer from the first drawback and often performs better with regard to false initial conditions [53].…”

“…This filtering distribution can be derived from (3.6) by marginalization over all states of all previous time steps [53], therefore…”

“…Since p(x 0:k−1 |z 1:k−1 ) = p(x k−1 , x 0:k−2 |z 1:k−1 ), the inner integrals over x 0 through x k−2 simplify to p(x k−1 |z 1:k−1 ) via marginalization and the recursive Bayesian filtering solution, the posterior state pdf or filtering distribution, is finally given by [18,53,208] …”

“…Various approaches to cope with this problem can be found in the literature, which are summarized under the term multiple model methods, see for example [18,53,153]. In the Bayesian framework, this general inference task is equal to estimate the joint pdf…”