Sensor-Model Matching for Controlled Comparison of Bayesian and Belief-Function Occupancy Grid Fusion

Comparisons of Bayesian log-odds and Dempster's combination rule for occupancy grid mapping typically parameterize the two sensor models independently, so that observed performance differences confound the fusion rule with the sensor parameterization. We develop a pignistic-transform-based matching methodology that derives belief function masses producing identical per-observation decision probabilities, isolating the accumulation rule as the sole variable. We show that the confound is large: in multi-robot experiments under two noise conditions, applying the match reversed boundary sharpness from a +6% to +14% advantage for belief functions to a -17% to -22% deficit favoring Bayesian log-odds-a 23 to 36 percentage-point reversal, consistent across both conditions-motivating per-observation matching as the basis for controlled comparison. Under BetP-matched comparison in single-agent simulation (15 independent runs) and on two real indoor lidar datasets (Intel Research Lab, Freiburg Building 079), the two frameworks produce practically equivalent maps on the reported point-probability metrics (cell accuracy, boundary sharpness, Brier score), with a small directional advantage for Bayesian log-odds (absolute differences 0.001-0.022 on [0, 1] scales). Under normalized plausibility (PPl) matching, the direction reverses for boundary sharpness and Brier score, indicating that the ranking depends on the probability transform used for matching, not solely on the fusion rule. All evaluation is restricted to point-probability metrics on 2D binary grids with Dempster's and Yager's rules. The interval-valued representation [Bel(A),Pl(A)] unique to belief functions is not assessed. The matching methodology is applicable to other Bayesian/belief function comparisons.