Convergence results for the particle PHD filter

Clark, Dan E.; Bell, Judith

doi:10.1109/tsp.2006.874845

Cited by 90 publications

(54 citation statements)

References 12 publications

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“…This article demonstrates the uniform convergence of the errors for each of the stages of the Gaussian Mixture PHD Filter [1], [2] using results already established for the particle implementation of the PHD filter [3] and Wiener's Theory of Approximation [4]. Error bounds are provided in L 1 for the pruning and merging stages of the algorithm, based on those established for the Gaussian Sum filter [5].…”

Section: Introductionmentioning

confidence: 95%

“…This is achieved through the successive application of triangle inequalities and Hölder's inequality. Finally the observation update is shown to converge using an adaptation of the previous result on particle PHD convergence [3].…”

Section: Measurement Updatementioning

confidence: 99%

“…This is a reasonable assumption as there would be no intensity to update when the measurements are received if it were zero. Proof: Using the convergence result for the particle PHD filter (Lemma 2, Clark [3]), we have the inequality…”

Section: Measurement Equationmentioning

confidence: 99%

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Convergence Analysis of the Gaussian Mixture PHD Filter

Clark

2007

IEEE Trans. Signal Process.

106

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Abstract-The Gaussian mixture Probability Hypothesis Density (PHD) filter was proposed recently for jointly estimating the time-varying number of targets and their states from a sequence of sets of observations without the need for measurement-totrack data association. It was shown that, under linear-Gaussian assumptions, the posterior intensity at any point in time is a Gaussian mixture. This article proves uniform convergence of the errors in the algorithm and provides error bounds for the pruning and merging stages. In addition, uniform convergence results for the extended Kalman PHD Filter are given, and the unscented Kalman PHD Filter implementation is discussed.

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Section: Introductionmentioning

confidence: 95%

Section: Measurement Updatementioning

confidence: 99%

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Convergence Analysis of the Gaussian Mixture PHD Filter

Clark

2007

IEEE Trans. Signal Process.

106

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“…In [123], a flexible modularized structure for SMC-PHD filter is introduced, and the particles with the same class label and their corresponding weights represent the estimated class-conditioned PHD distribution. The mathematical proofs of convergence for the SMC algorithm and gives bounds for the mean-square error is presented in [124].…”

Section: Implementation Of Fisst Based Filtersmentioning

confidence: 99%

A Survey of Motion-Based Multitarget Tracking Methods

Qiu¹,

Zhang²,

Lü³

et al. 2015

PIER B

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Abstract-Multitarget tracking (MTT) in surveillance system is extremely challenging, due to uncertain data association, maneuverable target motion, dense clutter disturbance, and real-time processing requirements. A good many methods have been proposed to cope with these challenges. However, no up-to-date survey is available in the literature that can help to select suitable tracking algorithm for practical problem. This paper provides a comprehensive review of the state-of-the-art motion-based MTT techniques, classifies existing methods into two groups, i.e., the detect-beforetrack (DBT) scheme and the track-before-detect (TBD) scheme. The DBT scheme is employed to achieve robust and tractable tracking performance when the signal-noise-ratio (SNR) is strong. The TBD scheme is used in the scenarios of low SNR, and it aims to cumulate target energy by multiple sensor frames. Furthermore, depending on the data association mechanism, the DBT methods can be classified into two categories, data association based approaches and finite set statistics (FISST) based approaches. And the TBD methods can be classified into non-Bayesian approaches and Bayesian approaches depending on the basis theory used for tracking. For each category, this paper provides the detailed descriptions of the representative algorithms, and examines their pros and cons. Finally, new trends for future research directions are offered.

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“…So from now on we assume that the targets and their associated measurements follow a PMC model and we extend the PHD filter (14)- (15) to these new conditions.…”

Section: B a Pmc Approachmentioning

confidence: 99%

Bayesian Multi-Object Filtering for Pairwise Markov Chains

Petetin

Desbouvries

2013

IEEE Trans. Signal Process.

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Abstract-Random Finite Sets (RFS) are recent tools for addressing the multi-object filtering problem. The Probability Hypothesis Density (PHD) Filter is an approximation of the multiobject Bayesian filter which results from the RFS formulation of the problem and has been used in many applications. In the RFS framework, it is assumed that each target and associated observation follow a Hidden Markov Chain (HMC) model. HMCs conveniently describe some physical properties of practical interest for practitioners, but they also implicitly imply restrictive independence properties which, in practice, may not be satisfied by data. In this paper, we show that these structural limitations of HMC models can somehow be relaxed by embedding them into the more general class of Pairwise Markov Chain (PMC) models. We thus focus on the computation of the PHD filter in a PMC framework, and we propose a practical implementation of the PHD filter for a particular class of PMC models.

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Convergence results for the particle PHD filter

Cited by 90 publications

References 12 publications

Convergence Analysis of the Gaussian Mixture PHD Filter

Convergence Analysis of the Gaussian Mixture PHD Filter

A Survey of Motion-Based Multitarget Tracking Methods

Bayesian Multi-Object Filtering for Pairwise Markov Chains

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