Target tracking in the framework of possibility theory: The possibilistic Bernoulli filter

TL;DR

This paper introduces a possibilistic Bernoulli filter for target tracking that operates effectively with incomplete or imprecise measurement and dynamic models by using possibility theory instead of probability.

Contribution

It formulates a new possibilistic Bernoulli filter that handles uncertainty without requiring precise models, extending target tracking capabilities.

Findings

Operates with incomplete measurement data

Handles imprecise dynamic models

Demonstrates effectiveness with multi-static Doppler measurements

Abstract

The Bernoulli filter is a Bayes filter for joint detection and tracking of a target in the presence of false and miss detections. This paper presents a mathematical formulation of the Bernoulli filter in the framework of possibility theory, where uncertainty is represented using {\em possibility} functions, rather than {\em probability} distributions. Possibility functions model the uncertainty in a non-additive manner, and have the capacity to deal with partial (incomplete) problem specification. Thus, the main advantage of the possibilistic Bernoulli filter, derived in this paper, is that it can operate even in the absence of precise measurement and/or dynamic model parameters. This feature of the proposed filter is demonstrated in the context of target tracking using multi-static Doppler shifts as measurements.