The PMHT: Solutions to some of its problems

摘要

Tracking multiple targets in a cluttered environment is a challenging task. Probabilistic Multiple Hypothesis Tracking (PMHT) is an efficient approach for dealing with it. Essentially PMHT is based on the method of Expectation-Maximization for handling with association conflicts. Linearity in the number of targets and measurements is the main motivation for a further development and extension of this methodology. Unfortunately, compared with the Probabilistic Data Association Filter (PDAF), PMHT has not yet shown its superiority in terms of track-lost statistics. Furthermore, the problem of track extraction and deletion is apparently not yet satisfactorily solved within this framework. Four properties of PMHT are responsible for its problems in track maintenance: Non-Adaptivity, Hospitality, Narcissism and Local Maxima. In this work we present a solution for each of them and derive an improved PMHT by integrating the solutions into the PMHT framework. The new PMHT is evaluated by Monte-Carlo simulations. A sequential Likelihood-Ratio (LR) test for track extraction has been developed and already integrated into the framework of traditional Bayesian Multiple Hypothesis Tracking. As a multi-scan approach, also the PMHT methodology has the potential for track extraction. In this paper an analogous integration of a sequential LR test into the PMHT framework is proposed. We present an LR formula for track extraction and deletion using the PMHT update formulae. As PMHT provides all required ingredients for a sequential LR calculation, the LR is thus a by-product of the PMHT iteration process. Therefore the resulting update formula for the sequential LR test affords the development of Track-Before-Detect algorithms for PMHT. The approach is illustrated by a simple example. This manuscript has been accepted for publication in the conference proceedings of SPIE Signal and Data Processing of Small Targets, San Diego Aug 2007. An extended discussion of section 4 Sequential Track Extraction by PMHT (2 pages) has been submitted to EURASIP (24 pages).