Equivalence and Divergence of Bayesian Log-Odds and Dempster's Combination Rule for 2D Occupancy Grids

TL;DR

This paper compares Bayesian log-odds and Dempster's rule for occupancy grid mapping using a pignistic-transform-based method, revealing that Bayesian fusion generally performs better under certain matching criteria, with results dependent on the matching method used.

Contribution

Introduces a pignistic-transform-based methodology for fair comparison of Bayesian and Dempster's fusion rules in occupancy grids, isolating the fusion rule effects from sensor parameters.

Findings

Bayesian fusion outperforms Dempster's rule under BetP matching (15/15 cases).

Results depend on the matching criterion used, reversing under plausibility matching.

Methodology is reusable for future comparisons of Bayesian and belief function methods.

Abstract

We introduce a pignistic-transform-based methodology for fair comparison of Bayesian log-odds and Dempster's combination rule in occupancy grid mapping, matching per-observation decision probabilities to isolate the fusion rule from sensor parameterization. Under BetP matching across simulation, two real lidar datasets, and downstream path planning, Bayesian fusion is consistently favored (15/15 directional consistency, p = 3.1e-5) with small absolute differences (0.001-0.022). Under normalized plausibility matching, the direction reverses, confirming the result is matching-criterion-specific. The methodology is reusable for any future Bayesian/belief function comparison.