Regional variance in target number: Analysis and application for multi-Bernoulli point processes

Delande, Emmanuel; Houssineau, Jérémie; Clark, Dan E.

doi:10.1049/cp.2014.0531

Cited by 7 publications

(4 citation statements)

References 61 publications

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“…In [7] and [8], Delande et al showed that the regional variance of the number of targets quantifies the certainty of the filter estimates of the number of the targets that evolve in surveillance region. Following [8], we chose the variance of the cardinality as a meaningful measure for its uncertainty or estimation error. In terms of the updated probabilities of existence this variance is given by:…”

Section: Methodsmentioning

confidence: 99%

Multi-Bernoulli Sensor-Control via Minimization of Expected Estimation Errors

Gostar¹,

Hoseinnezhad²,

Bab-Hadiashar³

2015

Preprint

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This paper presents a sensor-control method for choosing the best next state of the sensor(s), that provide(s) accurate estimation results in a multi-target tracking application. The proposed solution is formulated for a multi-Bernoulli filter and works via minimization of a new estimation error-based cost function. Simulation results demonstrate that the proposed method can outperform the state-of-the-art methods in terms of computation time and robustness to clutter while delivering similar accuracy.

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Section: Methodsmentioning

confidence: 99%

Multi-Bernoulli Sensor-Control via Minimization of Expected Estimation Errors

Gostar¹,

Hoseinnezhad²,

Bab-Hadiashar³

2015

Preprint

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“…Previous work derived expressions for the first and second moments of FoV cardinality distributions given Poisson, independently and identically distributed cluster (i.i.d.c.) [41], and multi-Bernoulli (MB) [42] workspace densities. This section instead develops full pmfs expressions, from which first, second, or any higher-order moments can be easily obtained.…”

Section: Fov Cardinality Distributionmentioning

confidence: 99%

Split Happens! Imprecise and Negative Information in Gaussian Mixture Random Finite Set Filtering

LeGrand¹,

Ferrari²

2022

Preprint

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In object tracking and state estimation problems, ambiguous evidence such as imprecise measurements and the absence of detections can contain valuable information and thus be leveraged to further refine the probabilistic belief state. In particular, knowledge of a sensor's bounded field-of-view can be exploited to incorporate evidence of where an object was not observed. This paper presents a systematic approach for incorporating knowledge of the field-of-view geometry and position and object inclusion/exclusion evidence into object state densities and random finite set multi-object cardinality distributions. The resulting state estimation problem is nonlinear and solved using a new Gaussian mixture approximation based on recursive component splitting. Based on this approximation, a novel Gaussian mixture Bernoulli filter for imprecise measurements is derived and demonstrated in a tracking problem using only natural language statements as inputs. This paper also considers the relationship between bounded fields-of-view and cardinality distributions for a representative selection of multiobject distributions, which can be used for sensor planning, as is demonstrated through a problem involving a multi-Bernoulli process with up to one-hundred potential objects.

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“…which describes the variance in the number of targets localised to a userspecified subset of the surveillance region. This has been used to compare different filters, and has been proposed to analyse the performance of filters [13].…”

Section: A Cramér Rao Bounds For Multi-target Tracking Applicationsmentioning

confidence: 99%

Kullback’s inequality and Cramer Rao bounds for point process models

Clark¹

2022

Preprint

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<p>A lower bound on the Kullback-Leibler divergence known as Kullback’s inequality can be determined with the Legendre transform of the cumulant generating function. The Cramer Rao bound can be derived from Kullback’s inequality as the inverse of the second order term in a Taylor expansion. Analogous forms for Kullback’s inequality and the Cram er</p><p>Rao bound for point processes were recently derived using functional methods from quantum field theory. This article develops Kullback’s inequality and the Cramer Rao bound for point process parametrisations as performance bounds for models used in multi-object filtering.</p>

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Regional variance in target number: Analysis and application for multi-Bernoulli point processes

Cited by 7 publications

References 61 publications

Multi-Bernoulli Sensor-Control via Minimization of Expected Estimation Errors

Multi-Bernoulli Sensor-Control via Minimization of Expected Estimation Errors

Split Happens! Imprecise and Negative Information in Gaussian Mixture Random Finite Set Filtering

Kullback’s inequality and Cramer Rao bounds for point process models

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