Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Labeled random finite sets vs. trajectory random finite sets

Ronald Mahler

TL;DR

This paper summarizes and augments the main findings of [12], [13]--specifcally, why SoT, PMBM, and TPMBM are physically and mathematically erroneous.

Abstract

The paper [12] discussed two approaches for multitarget tracking (MTT): the generalized labeled multi-Bernoulli (GLMB) filter and three Poisson multi-Bernoulli mixture (PMBM) filters. The paper [13] discussed two frameworks for multitarget trajectory representation--labeled random finite set (LRFS) and set of trajectories (SoT)--and the merging of SoT and PMBM into trajectory PMBM (TPMBM) theory. This paper summarizes and augments the main findings of [12], [13]--specifcally, why SoT, PMBM, and TPMBM are physically and mathematically erroneous.

Labeled random finite sets vs. trajectory random finite sets

TL;DR

This paper summarizes and augments the main findings of [12], [13]--specifcally, why SoT, PMBM, and TPMBM are physically and mathematically erroneous.

Abstract

The paper [12] discussed two approaches for multitarget tracking (MTT): the generalized labeled multi-Bernoulli (GLMB) filter and three Poisson multi-Bernoulli mixture (PMBM) filters. The paper [13] discussed two frameworks for multitarget trajectory representation--labeled random finite set (LRFS) and set of trajectories (SoT)--and the merging of SoT and PMBM into trajectory PMBM (TPMBM) theory. This paper summarizes and augments the main findings of [12], [13]--specifcally, why SoT, PMBM, and TPMBM are physically and mathematically erroneous.
Paper Structure (16 sections, 4 equations)

This paper contains 16 sections, 4 equations.

Table of Contents

  1. 1. Introduction
  2. 2. Labeled Random Finite Sets
  3. 3. Sets of Trajectories
  4. 4. The Mathematical Fundamental SoT Error
  5. 5. SoT Trajectory Modeling Errors
  6. 6. The Physical Fundamental SoT Error
  7. 7. Poisson Random Finite Sets
  8. 8. PMBM, Version 1
  9. 9. PMBM-1 Theoretical Errors
  10. 10. PMBM, Version 2
  11. 11. PMBM-2 Theoretical Errors
  12. 12. PMBM, Version 3
  13. 13. PMBM-3 Theoretical Errors
  14. 14. SoT Contradicts PMBM-2,3
  15. 15. TPMBM Theoretical Errors
  16. ...and 1 more sections