Maximum Consensus Localization using an Objective Function based on Helmert's Point Error

TL;DR

This paper introduces a novel Helmert's point error-based objective function for maximum consensus localization using LiDAR data, demonstrating improved robustness over traditional methods in ego-localization for autonomous vehicles.

Contribution

The paper proposes a new Helmert's point error objective function for maximum consensus localization, enhancing robustness in LiDAR-based ego-localization tasks.

Findings

Outperforms traditional methods in robustness against outliers

Demonstrates superior accuracy over 3001 measurement epochs

Provides a detailed analysis of maximum consensus localization shortcomings

Abstract

Ego-localization is a crucial task for autonomous vehicles. On the one hand, it needs to be very accurate, and on the other hand, very robust to provide reliable pose (position and orientation) information, even in challenging environments. Finding the best ego-position is usually tied to optimizing an objective function based on the sensor measurements. The most common approach is to maximize the likelihood, which leads under the assumption of normally distributed random variables to the well-known least squares minimization, often used in conjunction with recursive estimation, e. g. using a Kalman filter. However, least squares minimization is inherently sensitive to outliers, and consequently, more robust loss functions, such as L1 norm or Huber loss have been proposed. Arguably the most robust loss function is the outlier count, also known as maximum consensus optimization, where the outcome is independent of the outlier magnitude. In this paper, we investigate in detail the performance of maximum consensus localization based on LiDAR data. We elaborate on its shortcomings and propose a novel objective function based on Helmert's point error. In an experiment using 3001 measurement epochs, we show that the maximum consensus localization based on the introduced objective function provides superior results with respect to robustness.