Principled Random Finite Set Approximations of Labeled Multi-Object Densities

TL;DR

This paper develops principled approximation methods for labeled multi-object densities in Bayesian inference, addressing computational challenges and analyzing their errors and complexities, with practical guidance and numerical validation.

Contribution

It introduces several novel approximation techniques for labeled multi-object densities, including labeled multi-Bernoulli, Poisson, and IID clustering, with detailed analysis and practical insights.

Findings

Proposed principled approximations reduce computational complexity.

Analyzed approximation errors and computational costs.

Numerical example validates the effectiveness of the methods.

Abstract

As a fundamental piece of multi-object Bayesian inference, multi-object density has the ability to describe the uncertainty of the number and values of objects, as well as the statistical correlation between objects, thus perfectly matches the behavior of multi-object system. However, it also makes the set integral suffer from the curse of dimensionality and the inherently combinatorial nature of the problem. In this paper, we study the approximations for the universal labeled multi-object (LMO) density and derive several principled approximations including labeled multi-Bernoulli, labeled Poisson and labeled independent identically clustering process based approximations. Also, a detailed analysis on the characteristics (e.g., approximation error and computational complexity) of the proposed approximations is provided. Then some practical suggestions are made for the applications of these approximations based on the preceding analysis and discussion. Finally, an numerical example is given to support our study.