Nonadditive probability, finite-set statistics, and information fusion

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.

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Exact Closed-Form Multitarget Bayes Filters

Sensors ◽

10.3390/s19122818 ◽

2019 ◽

Vol 19 (12) ◽

pp. 2818 ◽

Cited By ~ 9

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.

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Multi-robot Cardinality Balanced Multi-Bernoulli Filter SLAM Method

Measurement Science and Technology ◽

10.1088/1361-6501/ac3784 ◽

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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