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An extensible framework for the probabilistic search of stochastically-moving targets characterized by generalized Gaussian distributions or experimentally-defined regions of interest.

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Název: An extensible framework for the probabilistic search of stochastically-moving targets characterized by generalized Gaussian distributions or experimentally-defined regions of interest.
Autoři: L. Hanson, Benjamin, Zhao, Muhan, Thomas, R. Bewley
Zdroj: Communications in Statistics: Theory & Methods; 2025, Vol. 54 Issue 17, p5480-5505, 26p
Témata: PROBABILITY density function, FOKKER-Planck equation, ADVECTION-diffusion equations, DETECTION algorithms, GAUSSIAN distribution
Abstrakt: This article presents a continuous-time framework for modeling the evolution of a probability density function (PDF) summarizing the region of interest (ROI) during the search for a stochastically-moving, statistically stationary target. This framework utilizes the Fokker-Planck partial differential equation representing the evolution of this PDF subject to: diffusion modeling the spread of the PDF due to the random motion of the target, advection modeling the relaxation of the PDF back to a specified steady profile summarizing the ROI in the absence of observations, and observations substantially reducing the PDF within the vicinity of the search vehicles patrolling the ROI. As a medium for testing the proposed search algorithm, this work defines a new, more general formulation for the multivariate generalized Gaussian distribution (GGD), an extension of the Gaussian distribution described by shaping parameter β. Additionally, we define a formulation with enhanced flexibility, the generalized Gaussian distribution with anisotropic flatness (GGDAF). Two techniques are explored that convert a set of target location observations into a steady-state PDF summarizing the ROI of the target, wherein the steady-state advection is numerically solved for. This work thus provides a novel framework for the probabilistic search of stochastically-moving targets, accommodating both non-evasive and evasive behavior. [ABSTRACT FROM AUTHOR]
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Abstrakt:This article presents a continuous-time framework for modeling the evolution of a probability density function (PDF) summarizing the region of interest (ROI) during the search for a stochastically-moving, statistically stationary target. This framework utilizes the Fokker-Planck partial differential equation representing the evolution of this PDF subject to: diffusion modeling the spread of the PDF due to the random motion of the target, advection modeling the relaxation of the PDF back to a specified steady profile summarizing the ROI in the absence of observations, and observations substantially reducing the PDF within the vicinity of the search vehicles patrolling the ROI. As a medium for testing the proposed search algorithm, this work defines a new, more general formulation for the multivariate generalized Gaussian distribution (GGD), an extension of the Gaussian distribution described by shaping parameter β. Additionally, we define a formulation with enhanced flexibility, the generalized Gaussian distribution with anisotropic flatness (GGDAF). Two techniques are explored that convert a set of target location observations into a steady-state PDF summarizing the ROI of the target, wherein the steady-state advection is numerically solved for. This work thus provides a novel framework for the probabilistic search of stochastically-moving targets, accommodating both non-evasive and evasive behavior. [ABSTRACT FROM AUTHOR]
ISSN:03610926
DOI:10.1080/03610926.2024.2439999