Fusion of finite set distributions: Pointwise consistency and global cardinality

TL;DR

This paper analyzes the limitations of exponential mixture densities in multi-sensor finite set fusion, revealing potential inconsistencies in cardinality estimation and proposing a new framework for consistent fusion.

Contribution

It demonstrates that existing EMD-based fusion may be inconsistent for cardinality and introduces a new variational framework ensuring cardinality consistent fusion.

Findings

EMDs can lead to inconsistent cardinality fusion in practice.

Pointwise consistency does not guarantee global cardinality consistency.

A new iterative framework guarantees cardinality consistent fusion.

Abstract

A recent trend in distributed multi-sensor fusion is to use random finite set filters at the sensor nodes and fuse the filtered distributions algorithmically using their exponential mixture densities (EMDs). Fusion algorithms which extend the celebrated covariance intersection and consensus based approaches are such examples. In this article, we analyse the variational principle underlying EMDs and show that the EMDs of finite set distributions do not necessarily lead to consistent fusion of cardinality distributions. Indeed, we demonstrate that these inconsistencies may occur with overwhelming probability in practice, through examples with Bernoulli, Poisson and independent identically distributed (IID) cluster processes. We prove that pointwise consistency of EMDs does not imply consistency in global cardinality and vice versa. Then, we redefine the variational problems underlying fusion and provide iterative solutions thereby establishing a framework that guarantees cardinality consistent fusion.