Decentralised possibilistic inference with applications to target tracking

TL;DR

This paper introduces a decentralised possibilistic inference framework for sensor data fusion that preserves source independence and outperforms probabilistic methods in target tracking applications.

Contribution

It develops a principled fusion rule based on possibility theory, proven to asymptotically match the optimal centralised possibilistic approach, and applies it to the Bernoulli filter for improved target tracking.

Findings

The proposed method maintains independence of local posteriors during fusion.

It outperforms probabilistic fusion baselines in cardinality and localisation accuracy.

The approach is effective even with Gaussian mixture approximations.

Abstract

Fusing and sharing information from multiple sensors over a network is a challenging task, partly due to the absence of a foundational rule for fusing probability distributions that preserves the independence of sources. To address this, we propose a decentralised inference framework based on possibility theory. Unlike probabilistic approaches that rely on ad-hoc averaging, we derive a principled fusion rule that is proven to be asymptotically exact, meaning it recovers the posterior of the optimal centralised possibilistic approach. We apply this rule to the possibilistic Bernoulli filter, leveraging its hierarchical nature to jointly infer data association and state estimation, distinct from standard decentralised Kalman filtering. We demonstrate that the proposed approach maintains the independence of local posteriors during fusion and, even under necessary approximations to handle Gaussian mixtures, significantly outperforms probabilistic geometric and arithmetic average fusion baselines in terms of cardinality and localisation error.