The Integrated Probabilistic Data Association Filter Adapted to Lie Groups

TL;DR

This paper extends the Integrated Probabilistic Data Association Filter to operate on Lie groups, enabling more accurate tracking of targets like ground vehicles in complex geometric spaces such as SE(2).

Contribution

It introduces a novel adaptation of IPDAF for target models and measurements on connected, unimodular Lie groups, including SE(2).

Findings

Successfully applied to ground vehicle tracking on SE(2).

Demonstrates improved tracking accuracy on Lie group models.

Abstract

The Integrated Probabilistic Data Association Filter (IPDAF) is a target tracking algorithm based on the Probabilistic Data Association Filter that calculates a statistical measure that indicates if an estimated representation of the target properly represents the target or is generated from non-target-originated measurements. The main contribution of this paper is to adapt the IPDAF to constant velocity target models that evolve on connected, unimodular Lie groups, and where the measurements are also defined on a Lie group. We present an example where the methods developed in the paper are applied to the problem of tracking a ground vehicle on the special Euclidean group SE(2).