Fusion of Finite-Set Distributions: Pointwise Consistency and Global Cardinality

Üney, Murat; Houssineau, Jérémie; Delande, Emmanuel; Julier, Simon; Clark, D.

doi:10.1109/taes.2019.2893083

Cited by 52 publications

(32 citation statements)

References 34 publications

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“…1. In fact, what has been done with AA-PHD fusion [10]- [14], AA-CPHD fusion [15]- [17], BC-AA fusion [18], MB-AA fusion [9] and RFS-GA fusion [20]- [28] all essentially follow the best-fit-of-mixture principle, aiming to best fit the mixture of unknown-correlated PHDs, CPHDs, BCs and MBs from different sensors, respectively. The key challenge of the fit, however, is from non-closure, for example, the AA of PPPs/MBs is no longer a PPP/MB.…”

Section: B Sub-optimality Of Aa Fusionmentioning

confidence: 99%

“…implementation [10], [11] or particle implementation [12]- [14], cardinalized PHD filters for standard models [15], [16] or for jump Markov system [17], Bernoulli filter [18], multi-Bernoulli (MB) filter [9] and labelled RFS filters [19]. Prior to these, GA-fusion-based RFS filters have been a research focus of the community which are more commonly known as generalized covariance intersection [20]- [26] and geometric/exponential mixture density [27], [28], to name a few. Both AA and GA fusion rules have demonstrated great potential for multi-target information fusion.…”

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confidence: 99%

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Best Fit of Mixture For Distributed Poisson Multi-Bernoulli Mixture Filtering

Li¹,

Da²

2020

Preprint

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<div>The Poisson multi-Bernoulli mixture (PMBM) filter is extended for distributed implementation using a wireless sensor network. At the core of the proposed networking approach, the PMBM posterior is decomposed into two parts corresponding to the undetected and detected targets, respectively. Fusion is motivated to be performed with regard to the latter only which is represented by MBM based on a distributed flooding algorithm for internode communication, which iteratively shares the MBMs between neighbor sensors. Then, a suboptimal “best-fit-ofmixture” principle is followed at each local sensor to find a MBM that best fits the mixture of MBMs aggregated from distinct sensors, leading to an arithmetic average (AA) of these MBMs. We prove the exact closure of the MBM-AA fusion and discuss its sub-optimality and limitations. Simulation demonstrates the effectiveness and limitations of our approach. </div>

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Section: B Sub-optimality Of Aa Fusionmentioning

confidence: 99%

mentioning

confidence: 99%

Best Fit of Mixture For Distributed Poisson Multi-Bernoulli Mixture Filtering

Li¹,

Da²

2020

Preprint

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“…In addition to the posterior PDF, the fusing functions can also be the likelihood functions [32,15,33] or the probability hypothesis density (PHD) functions [14,34,31,35,36,37]. (The PHD [38] differs from the PDF in that its integral over any region gives the expected number of targets in that region which can be any real number.)…”

Section: Introductionmentioning

confidence: 99%

“…In comparison, the AA fusion has also been applied for PHD fusion [39,40,41,42,43,44,45,46] and for raw data fusion in the means of clustering [47,48]. Both averaging approaches to data fusion have demonstrated, either theoretically or experimentally, gains in estimation accuracy and/or robustness, whereas deficiencies have also been identified from different viewpoints [11,12,34,49,50,41,43,44,51,52,36,30].…”

Section: Introductionmentioning

confidence: 99%

Second-order statistics analysis and comparison between arithmetic and geometric average fusion: Application to multi-sensor target tracking

et al. 2019

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Two fundamental approaches to information averaging are based on linear and logarithmic combination, yielding the arithmetic average (AA) and geometric average (GA) of the fusing initials, respectively. In the context of target tracking, the two most common formats of data to be fused are random variables and probability density functions, namely v-fusion and f -fusion, respectively. In this work, we analyze and compare the second order statistics (including variance and mean square error) of AA and GA in terms of both v-fusion and f -fusion. The case of weighted Gaussian mixtures representing multitarget densities in the presence of false alarms and misdetection (whose weight sums are not necessarily unit) is also considered, the result of which appears significantly different from that for a single target. In addition to exact derivation, exemplifying analysis and illustrations are provided.

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“…The combination of the average consensus approach with the RFS filters originates from the log-linear GA fusion, namely generalized covariance intersection [26]- [28] and exponential mixture density [29], [30] approach. However, the GA fusion has been observed suffering from a delay in detecting new targets [31], [32] and cardinality inconsistency [30] (e.g., underestimating the number of targets [33]), prone to missed detections [20], [25], [32], [34], [35] and vulnerable to non-overlapping fields of view [25], [36], [37]. In particular, the GA fusion may degrade [17], [25], [34], [35] with the increase of the number of fusing sensors and then does not suit large number sensor networks (LNSNs).…”

Section: Introductionmentioning

confidence: 99%

On Arithmetic Average Fusion and Its Application for Distributed Multi-Bernoulli Multitarget Tracking

Li¹,

Wang²,

Yan³

2020

Preprint

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<div>Recently, the simple arithmetic averages (AA) fusion has demonstrated promising, even surprising, performance for multitarget information fusion. In this paper, we first analyze the conservativeness and Frechet mean properties of it, presenting new empirical analysis based on a comprehensive literature review. Then, we propose a target-wise fusion principle for tailoring the AA fusion to accommodate the multi-Bernoulli (MB) process, in which only significant Bernoulli components, each represented by an individual Gaussian mixture, are disseminated and fused in a Bernoulli-to-Bernoulli (B2B) manner. For internode communication, both the consensus and flooding schemes are investigated, respectively. At the core of the proposed fusion algorithms, Bernoulli components obtained at different sensors are associated via either clustering or pairwise assignment so that the MB fusion problem is decomposed to parallel B2B fusion subproblems, each resolved via exact Bernoulli-AA fusion. Two communicatively and computationally efficient cardinality consensus approaches are also presented which merely disseminate and fuse target existence probabilities among local MB filters. The accuracy and computing and communication cost of these four approaches are tested in two large scale scenarios with different sensor networks and target trajectories. </div>

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Fusion of Finite-Set Distributions: Pointwise Consistency and Global Cardinality

Cited by 52 publications

References 34 publications

Best Fit of Mixture For Distributed Poisson Multi-Bernoulli Mixture Filtering

Best Fit of Mixture For Distributed Poisson Multi-Bernoulli Mixture Filtering

Second-order statistics analysis and comparison between arithmetic and geometric average fusion: Application to multi-sensor target tracking

On Arithmetic Average Fusion and Its Application for Distributed Multi-Bernoulli Multitarget Tracking

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