scholarly journals Particle Approximation of the Intensity Measures of a Spatial Branching Point Process Arising in Multitarget Tracking

2011 ◽  
Vol 49 (4) ◽  
pp. 1766-1792 ◽  
Author(s):  
Francois Caron ◽  
Pierre Del Moral ◽  
Arnaud Doucet ◽  
Michele Pace
Keyword(s):  
Point Process ◽  
Multitarget Tracking ◽  
Intensity Measures ◽  
Branching Point ◽  
Particle Approximation

scholarly journals Power spectra of random spike fields and related processes

2005 ◽  
Vol 37 (4) ◽  
pp. 1116-1146 ◽  
Author(s):  
Pierre Brémaud ◽  
Laurent Massoulié ◽  
Andrea Ridolfi
Keyword(s):  
Point Process ◽  
Point Processes ◽  
Power Spectra ◽  
Sampling Point ◽  
Birth And Death Processes ◽  
Large Classes ◽  
Random Samples ◽  
Branching Point ◽  
Random Times ◽  
Random Impulse

In this article, we review known results and present new ones concerning the power spectra of large classes of signals and random fields driven by an underlying point process, such as spatial shot noises (with random impulse response and arbitrary basic stationary point processes described by their Bartlett spectra) and signals or fields sampled at random times or points (where the sampling point process is again quite general). We also obtain the Bartlett spectrum for the general linear Hawkes spatial branching point process (with random fertility rate and general immigrant process described by its Bartlett spectrum). We then obtain the Bochner spectra of general spatial linear birth and death processes. Finally, we address the issues of random sampling and linear reconstruction of a signal from its random samples, reviewing and extending former results.

scholarly journals “Statistics 103” for Multitarget Tracking

Sensors ◽  
2019 ◽  
Vol 19 (1) ◽  
pp. 202 ◽  
Author(s):  
Ronald Mahler
Keyword(s):  
Point Process ◽  
Information Fusion ◽  
Theoretical Foundation ◽  
Measure Theory ◽  
Multitarget Tracking ◽  
Mathematical Abstraction ◽  
Finite Set ◽  
Theoretic Point

The finite-set statistics (FISST) foundational approach to multitarget tracking and information fusion was introduced in the mid-1990s and extended in 2001. FISST was devised to be as “engineering-friendly” as possible by avoiding avoidable mathematical abstraction and complexity—and, especially, by avoiding measure theory and measure-theoretic point process (p.p.) theory. Recently, however, an allegedly more general theoretical foundation for multitarget tracking has been proposed. In it, the constituent components of FISST have been systematically replaced by mathematically more complicated concepts—and, especially, by the very measure theory and measure-theoretic p.p.’s that FISST eschews. It is shown that this proposed alternative is actually a mathematical paraphrase of part of FISST that does not correctly address the technical idiosyncrasies of the multitarget tracking application.

scholarly journals Approximate decomposition of some modulated-Poisson Voronoi tessellations

2003 ◽  
Vol 35 (4) ◽  
pp. 847-862 ◽  
Author(s):  
Bartłomiej Błaszczyszyn ◽  
René Schott
Keyword(s):  
Point Process ◽  
Poisson Point Process ◽  
Voronoi Tessellation ◽  
Distribution Functions ◽  
Voronoi Tessellations ◽  
Intensity Measures ◽  
Voronoi Cells ◽  
True Value ◽  
Homogeneous Models ◽  
Inhomogeneous Poisson Point Process

We consider the Voronoi tessellation of Euclidean space that is generated by an inhomogeneous Poisson point process whose intensity takes different constant values on sets of some finite partition of the space. Considering the Voronoi cells as marks associated with points of the point process, we prove that the intensity measure (mean measure) of the marked Poisson point process admits an approximate decomposition formula. The true value is approximated by a mixture of respective intensity measures for homogeneous models, while the explicit upper bound for the remainder term can be computed numerically for a large class of practical examples. By the Campbell formula, analogous approximate decompositions are deduced for the Palm distributions of individual cells. This approach makes possible the analysis of a wide class of inhomogeneous-Poisson Voronoi tessellations, by means of formulae and estimates already established for homogeneous cases. Our analysis applies also to the Poisson process modulated by an independent stationary random partition, in which case the error of the approximation of the double-stochastic-Poisson Voronoi tessellation depends on some integrated linear contact distribution functions of the boundaries of the partition elements.

scholarly journals Approximate decomposition of some modulated-Poisson Voronoi tessellations

2003 ◽  
Vol 35 (04) ◽  
pp. 847-862
Author(s):  
Bartłomiej Błaszczyszyn ◽  
René Schott
Keyword(s):  
Point Process ◽  
Poisson Point Process ◽  
Voronoi Tessellation ◽  
Distribution Functions ◽  
Voronoi Tessellations ◽  
Intensity Measures ◽  
Voronoi Cells ◽  
True Value ◽  
Homogeneous Models ◽  
Inhomogeneous Poisson Point Process

We consider the Voronoi tessellation of Euclidean space that is generated by an inhomogeneous Poisson point process whose intensity takes different constant values on sets of some finite partition of the space. Considering the Voronoi cells as marks associated with points of the point process, we prove that the intensity measure (mean measure) of the marked Poisson point process admits an approximate decomposition formula. The true value is approximated by a mixture of respective intensity measures for homogeneous models, while the explicit upper bound for the remainder term can be computed numerically for a large class of practical examples. By the Campbell formula, analogous approximate decompositions are deduced for the Palm distributions of individual cells. This approach makes possible the analysis of a wide class of inhomogeneous-Poisson Voronoi tessellations, by means of formulae and estimates already established for homogeneous cases. Our analysis applies also to the Poisson process modulated by an independent stationary random partition, in which case the error of the approximation of the double-stochastic-Poisson Voronoi tessellation depends on some integrated linear contact distribution functions of the boundaries of the partition elements.

scholarly journals Power spectra of random spike fields and related processes

2005 ◽  
Vol 37 (04) ◽  
pp. 1116-1146 ◽  
Author(s):  
Pierre Brémaud ◽  
Laurent Massoulié ◽  
Andrea Ridolfi
Keyword(s):  
Point Process ◽  
Point Processes ◽  
Power Spectra ◽  
Sampling Point ◽  
Birth And Death Processes ◽  
Large Classes ◽  
Random Samples ◽  
Branching Point ◽  
Random Times ◽  
Random Impulse

In this article, we review known results and present new ones concerning the power spectra of large classes of signals and random fields driven by an underlying point process, such as spatial shot noises (with random impulse response and arbitrary basic stationary point processes described by their Bartlett spectra) and signals or fields sampled at random times or points (where the sampling point process is again quite general). We also obtain the Bartlett spectrum for the general linear Hawkes spatial branching point process (with random fertility rate and general immigrant process described by its Bartlett spectrum). We then obtain the Bochner spectra of general spatial linear birth and death processes. Finally, we address the issues of random sampling and linear reconstruction of a signal from its random samples, reviewing and extending former results.

Habitat use of toothed whales in a marine protected area based on point process models

2019 ◽  
Vol 609 ◽  
pp. 239-256 ◽  
Author(s):  
TL Silva ◽  
G Fay ◽  
TA Mooney ◽  
J Robbins ◽  
MT Weinrich ◽  
...  
Keyword(s):  
Habitat Use ◽  
Point Process ◽  
Protected Area ◽  
Marine Protected Area ◽  
Process Models ◽  
Point Process Models

On the generation and origin of I/f noise

1999 ◽  
Vol 4 ◽  
pp. 87-96 ◽  
Author(s):  
B. Kaulakys ◽  
T. Meškauskas
Keyword(s):  
Point Process ◽  
Solvable Model ◽  
Autoregressive Process ◽  
Wide Range ◽  
Occurrence Times

Simple analytically solvable model exhibiting 1/f spectrum in any desirably wide range of frequency is analysed. The model consists of pulses (point process) whose interevent times obey an autoregressive process with small damping. Analysis and generalizations of the model indicate to the possible origin of 1/f noise, i.e. random increments between the occurrence times of particles or pulses resulting in the clustering of the pulses.

Connected-Tube MPP Model for Unsupervised 3D Fiber Detection

2020 ◽  
Vol 2020 (14) ◽  
pp. 305-1-305-6
Author(s):  
Tianyu Li ◽  
Camilo G. Aguilar ◽  
Ronald F. Agyei ◽  
Imad A. Hanhan ◽  
Michael D. Sangid ◽  
...  
Keyword(s):  
Composite Material ◽  
Point Process ◽  
Marked Point ◽  
Experimental Results ◽  
Marked Point Process ◽  
Fiber Reinforced Composite ◽  
Reinforced Composite ◽  
Proposed Model ◽  
Cylinder Model ◽  
Reinforced Composite Material

In this paper, we extend our previous 2D connected-tube marked point process (MPP) model to a 3D connected-tube MPP model for fiber detection. In the 3D case, a tube is represented by a cylinder model with two spherical areas at its ends. The spherical area is used to define connection priors that encourage connection of tubes that belong to the same fiber. Since each long fiber can be fitted by a series of connected short tubes, the proposed model is capable of detecting curved long tubes. We present experimental results on fiber-reinforced composite material images to show the performance of our method.

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