PHD filters of higher order in target number

By Ronald P. S. Mahler. IEEE Transactions on Aerospace and Electronic Systems, 2006

1,116 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c9ea770259999ea3a8d93a25bf8e2e534fb4202a

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Citations in the corpus

Adaptive Target Birth Intensity for PHD and CPHD Filters (2012, methodology): “Since the posterior PHD Dkjk(x j Z1:k) is a very crude approximation of fkjk(X j Z1:k), Mahler subsequently proposed [9] to propagate the cardinality distribution 1⁄2(n) = Pr(jXj= n) given by 1⁄2(n j Z1:k) = 1 n! Z fkjk(fx1, : : : ,xng j Z1:k)dx1 : : :xn”
Consensus CPHD Filter for Distributed Multitarget Tracking (2013, methodology): “cluster processes is at the basis of the PHD [16] or, respectively, Cardinalized PHD (CPHD) [17] filtering approaches to MTT.”
A Tutorial on Bernoulli Filters: Theory, Implementation and Applications (2013, background): “…four classes of its simplifications or principled approximations have emerged recently: the Bernoulli filter (also known as JoTT or joint target detection and tracking filter) [10], [15]–[18], the probability hypothesis density (PHD) filter [19]–[22], the cardinalized PHD filter [23], [24] and…”
Marginal multi-bernoulli filters: RFS derivation of MHT, JIPDA, and association-based member (2012, background): “We compare the proposed methods to CPHD [4] [5], CB- MeMBer [6], JITS and linear multi-target ITS (LMITS) [10] [11] (a variant of JITS which replaces the marginal association probabilities with a heuristic approximation).”
Joint Detection and Estimation of Multiple Objects From Image Observations (2010, background): “D. Suter is with the School of Computer Science, University of Adelaide, North Terrace SA 5005, Australia (e-mail: dsuter@cs.adelaide.edu.au).”
Labeled Random Finite Sets and the Bayes Multi-Target Tracking Filter (2013, background): “Each iteration of the δ -GLMB ﬁlter involves multi-target posterior and prediction densities that are weighted sums of multi-target exponentials.”
The Labeled Multi-Bernoulli Filter (2014, methodology): “The PHD and CPHD recursions propagate moments and cardinality distributions while the multi-Bernoulli filter propagates the parameters of a multi-Bernoulli distribution that approximate the posterior multi-target density.”
Analytic Implementations of the Cardinalized Probability Hypothesis Density Filter (2007, background): “Our implementations only have a cubic complexity, but simulations suggest favorable performance compared to the standard Joint Probabilistic Data Association (JPDA) ﬁlter which has a nonpolynomial complexity.”
PHD filters for nonstandard targets, I: Extended targets (2009, neutral): “In 2006 I introduced a generalization called the cardinalized PHD (CPHD) filter [10].”
The Cardinality Balanced Multi-Target Multi-Bernoulli Filter and Its Implementations (2009, background): “Mahler’s finite set statistics (FISST) is an elegant Bayesian formulation of multitarget filtering based on random finite set (RFS) theory, which has generated substantial interest in recent years due to the development of the Probability Hypothesis Density (PHD) filter [4] and the Cardinalized PHD ”
Labeled Random Finite Sets and Multi-Object Conjugate Priors (2013, background): “, Probability Hypothesis Density (PHD) filter [20], Cardinalized PHD filter [21], and multi-Bernoulli filter [1], [22].”
Multisensor data fusion: A review of the state-of-the-art (2013, neutral): “PðUÞ ¼ max x2U fp B ðxÞg 8U # X”
An Efficient Implementation of the Generalized Labeled Multi-Bernoulli Filter (2016, methodology): “The RFS approach has attracted significant attention as a general systematic treatment of multi-object systems and provides the foundation for the development of novel filters such as the Probability Hypothesis Density (PHD) filter [5], Cardinalized PHD (CPHD) filter [6], and multi-Bernoulli filters”
Message Passing Algorithms for Scalable Multitarget Tracking (2018, positive): “This prediction step converting λ k−1 u ( x k−1 , l k−1 ) into λ k|k−1 u (x k , l k ) is equivalent to the prediction step of the PHD filter [111].”