Filters for Spatial Point Processes
TL;DR: The posterior distribution of $\mathbf{X}$ under marginal Poisson and Gauss-Poisson priors is characterized and the results are applied in a filtering context when the hidden process evolves in discrete time in a Markovian fashion.
read more
Abstract: We study the general problem of estimating a “hidden” point process $\mathbf{X}$, given the realization of an “observed” point process $\mathbf{Y}$ (possibly defined in different spaces) with known joint distribution We characterize the posterior distribution of $\mathbf{X}$ under marginal Poisson and Gauss-Poisson priors and when the transformation from $\mathbf{X}$ to $\mathbf{Y}$ includes thinning, displacement, and augmentation with extra points These results are then applied in a filtering context when the hidden process evolves in discrete time in a Markovian fashion The dynamics of $\mathbf{X}$ considered are general enough for many target tracking applications
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
The Cauchy-Schwarz divergence for poisson point processes
Hung Gia Hoang,Ba-Ngu Vo,Ba-Tuong Vo,Ronald P. S. Mahler +3 more
- 28 Aug 2014
TL;DR: It is shown that the Cauchy-Schwarz divergence between two Poisson point processes is the half the squared L2-distance between their respective intensity functions.
120
The Cauchy-Schwarz divergence for Poisson point processes
TL;DR: In this paper, the authors extend the notion of Cauchy-Schwarz divergence to point processes and establish that the divergence between the probability densities of two Poisson point processes is half the squared L 2 -distance between their intensity functions.
108
CPHD-DOA Tracking of Multiple Extended Sonar Targets in Impulsive Environments
TL;DR: A Cardinalized Probability Hypothesis Density (CPHD) filter for tracking multiple targets with non-deterministic contributions, more specifically, Spherically Invariant Random Vector processes is developed by analytically integrating the SIRV and angularly distributed target signals in the update step.
99
The Cauchy–Schwarz Divergence for Poisson Point Processes
TL;DR: It is established that the Cauchy-Schwarz divergence between the probability densities of two Poisson point processes is half the squared L2-distance between their intensity functions.
97
Second Order Statistics Analysis and Comparison between Arithmetic and Geometric Average Fusion.
TL;DR: In this article, the second order statistics (including variance and mean square error) of the arithmetic average and geometric average are compared in terms of both $v$-and $f$-fusion.
73
References
•Book
An introduction to the bootstrap
Bradley Efron,Robert Tibshirani +1 more
- 01 Jan 1993
TL;DR: This article presents bootstrap methods for estimation, using simple arguments, with Minitab macros for implementing these methods, as well as some examples of how these methods could be used for estimation purposes.
•Book
Stochastic Processes and Filtering Theory
Andrew H. Jazwinski
- 14 Mar 1970
TL;DR: In this paper, a unified treatment of linear and nonlinear filtering theory for engineers is presented, with sufficient emphasis on applications to enable the reader to use the theory for engineering problems.
7.9K
Sequential Monte Carlo methods in practice
Arnaud Doucet,Nando de Freitas,Neil Gordon,Adrian F. M. Smith +3 more
- 01 Jan 2001
TL;DR: This book presents the first comprehensive treatment of Monte Carlo techniques, including convergence results and applications to tracking, guidance, automated target recognition, aircraft navigation, robot navigation, econometrics, financial modeling, neural networks, optimal control, optimal filtering, communications, reinforcement learning, signal enhancement, model averaging and selection.
•Book
Stochastic Geometry and Its Applications
Sung Nok Chiu,Dietrich Stoyan,Wilfrid S. Kendall,Joseph Mecke +3 more
- 18 Jul 1996
TL;DR: Random Closed Sets I--The Boolean Model. Random Closed Sets II--The General Case.
4.7K
An introduction to the theory of point processes
Daryl J. Daley,David Vere-Jones +1 more
TL;DR: An introduction to the theory of point processes can be found in this article, where the authors introduce the concept of point process and point process theory and introduce point processes as a theory for point processes.
4.2K