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 Exact Closed-Form Multitarget Bayes Filters

Sensors ◽  
2019 ◽  
Vol 19 (12) ◽  
pp. 2818 ◽  
Author(s):  
Ronald Mahler
Keyword(s):  
Statistical Theory ◽  
Closed Form ◽  
Information Fusion ◽  
Review Paper ◽  
Measurement Model ◽  
Cutting Edge ◽  
Multitarget Tracking ◽  
Research Groups ◽  
Finite Set

The finite-set statistics (FISST) foundational approach to multitarget tracking and information fusion has inspired work by dozens of research groups in at least 20 nations; and FISST publications have been cited tens of thousands of times. This review paper addresses a recent and cutting-edge aspect of this research: exact closed-form—and, therefore, provably Bayes-optimal—approximations of the multitarget Bayes filter. The five proposed such filters—generalized labeled multi-Bernoulli (GLMB), labeled multi-Bernoulli mixture (LMBM), and three Poisson multi-Bernoulli mixture (PMBM) filter variants—are assessed in depth. This assessment includes a theoretically rigorous, but intuitive, statistical theory of “undetected targets”, and concrete formulas for the posterior undetected-target densities for the “standard” multitarget measurement model.

scholarly journals Finite Set Statistics Based Multitarget Tracking.

2017 ◽  
Author(s):  
Keith LeGrand ◽  
Raymond H. Byrne ◽  
Pavan Datta ◽  
David K. Melgaard ◽  
Johnathan Mulcahy-Stanislawczyk
Keyword(s):  
Multitarget Tracking ◽  
Finite Set

scholarly journals An Elementary Proof of Jin's Theorem with a Bound

10.37236/3846 ◽  
2014 ◽  
Vol 21 (2) ◽  
Author(s):  
Mauro Di Nasso
Keyword(s):  
Ergodic Theory ◽  
Elementary Proof ◽  
Nonstandard Analysis ◽  
Measure Theory ◽  
Difference Sets ◽  
Explicit Bound ◽  
Finite Set

We present a short and self-contained proof of Jin's theorem about the piecewise syndeticity of difference sets which is entirely elementary, in the sense that no use is made of nonstandard analysis, ergodic theory, measure theory, ultrafilters, or other advanced tools. An explicit bound to the number of shifts that are needed to cover a thick set is provided. Precisely, we prove the following: If $A$ and $B$ are sets of integers having positive upper Banach densities $a$ and $b$ respectively, then there exists a finite set $F$ of cardinality at most $1/ab$ such that $(A-B)+F$ covers arbitrarily long intervals.

scholarly journals Distributed Multiagent Control Approach for Multitarget Tracking

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Liang Ma ◽  
Kai Xue ◽  
Ping Wang
Keyword(s):  
Information Fusion ◽  
Multitarget Tracking ◽  
Control Approach ◽  
Numerical Studies ◽  
Utility Optimization ◽  
Partially Observed ◽  
Markov Decision ◽  
Multiagent Control ◽  
Bernoulli Filter ◽  
Effectiveness And Efficiency

In multiagent systems, tracking multiple targets is challenging for two reasons: firstly, it is nontrivial to dynamically deploy networked agents of different types for utility optimization; secondly, information fusion for multitarget tracking is difficult in the presence of uncertainties, such as data association, noise, and clutter. In this paper, we present a novel control approach in distributed manner for multitarget tracking. The control problem is modelled as a partially observed Markov decision process, which is a NP-hard combinatorial optimization problem, by seeking all possible combinations of control commands. To solve this problem efficiently, we assume that the measurement of each agent is independent of other agents’ behavior and provide a suboptimal multiagent control solution by maximizing the local Rényi divergence. In addition, we also provide the SMC implementation of the sequential multi-Bernoulli filter so that each agent can utilize the measurements from neighbouring agents to perform information fusion for accurate multitarget tracking. Numerical studies validate the effectiveness and efficiency of our multiagent control approach for multitarget tracking.

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

2020 ◽  
Author(s):  
Tiancheng Li ◽  
Xiaoxu Wang ◽  
Yan Liang ◽  
Quan Pan
Keyword(s):  
Literature Review ◽  
Information Fusion ◽  
Large Scale ◽  
Gaussian Mixture ◽  
Multitarget Tracking ◽  
Computationally Efficient ◽  
Simple Arithmetic ◽  
Arithmetic Average ◽  
The Core ◽  
Comprehensive Literature Review

<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>

Recent advances in multisensor multitarget tracking using random finite set

2021 ◽  
Vol 22 (1) ◽  
pp. 5-24
Author(s):  
Kai Da ◽  
Tiancheng Li ◽  
Yongfeng Zhu ◽  
Hongqi Fan ◽  
Qiang Fu
Keyword(s):  
Multitarget Tracking ◽  
Random Finite Set ◽  
Recent Advances ◽  
Finite Set

Multi-robot Cardinality Balanced Multi-Bernoulli Filter SLAM Method

2021 ◽  
Author(s):  
Zijing Zhang ◽  
Fei Zhang ◽  
Chuantang Ji
Keyword(s):  
Information Fusion ◽  
Operating Efficiency ◽  
Complex Data ◽  
Indoor Environments ◽  
Probability Hypothesis Density ◽  
Localization And Mapping ◽  
Finite Set ◽  
Bernoulli Filter ◽  
Better Than ◽  
Multi Robot

Abstract In order to improve the Simultaneous Localization and Mapping (SLAM) accuracy of mobile robots in complex indoor environments, the multi-robot cardinality balanced Multi-Bernoulli filter SLAM method (MR-CBMber-SLAM) is proposed. First of all, this method introduces a Multi-Bernoulli filter based on the random finite set (RFS) theory to solve the complex data association problem. Besides, this method aims at the problem that the Multi-Bernoulli filter will overestimate in the aspect of SLAM map features estimation, and combines the strategy of cardinality balanced with the Multi-Bernoulli filter. What’s more, in order to further improve the accuracy and operating efficiency of SLAM, a multi-robot strategy and a multi-robot Gaussian information fusion (MR-GIF) method are proposed. In the experiment, the MR-CBMber-SLAM method is compared with the multi-vehicle Probability Hypothesis Density SLAM (MV-PHD-SLAM) method. The experimental results show that the MR-CBMber-SLAM method is better than MV-PHD-SLAM method. Therefore, it effectively verifies that the MR-CBMber-SLAM method is more adaptable to the complex indoor environment.

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