Enhanced Approximation of Labeled Multi-object Density based on Correlation Analysis

TL;DR

This paper introduces an improved method for approximating labeled multi-object densities by adaptively analyzing and preserving correlations between objects, leading to more accurate and computationally feasible models in point process theory.

Contribution

It proposes an adaptive correlation-based factorization of LMO density, considering object correlations while simplifying the complex structure of multi-object densities.

Findings

Enhanced approximation preserves essential correlations.

Derivation of set marginal density for subsets of labeled RFS.

Improved computational efficiency with accurate correlation modeling.

Abstract

Multi-object density is a fundamental descriptor of a point process and has ability to describe the randomness of number and values of objects, as well as the statistical correlation between objects. Due to its comprehensive nature, it usually has a complicate mathematical structure making the set integral suffering from the curse of dimension and the combinatorial nature of the problem. Hence, the approximation of multi-object density is a key research theme in point process theory or finite set statistics (FISST). Conventional approaches usually discard part or all of statistical correlation mechanically in return for computational efficiency, without considering the real situation of correlation between objects. In this paper, we propose an enhanced approximation of labeled multi-object (LMO) density which evaluates the correlation between objects adaptively and factorizes the LMO density into densities of several independent subsets according to the correlation analysis. Besides, to get a tractable factorization of LMO density, we derive the set marginal density of any subset of the universal labeled RFS, the generalized labeled multi-Bernoulli (GLMB) RFS family and its subclasses. The proposed method takes into account the simplification of the complicate structure of LMO density and the reservation of necessary correlation at the same time.