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.

翻译：自主车辆的自我定位是一项关键任务。一方面，它需要具有极高的精度，另一方面，即使在具有挑战性的环境中，也必须具备强鲁棒性以提供可靠的位姿（位置和方向）信息。寻找最佳自我位置通常与基于传感器测量值优化目标函数相关联。最常用的方法是最大化似然，这在高斯随机变量的假设下，导出了广为熟知的最小二乘最小化方法，通常与递归估计（例如，使用卡尔曼滤波器）结合使用。然而，最小二乘最小化本质上对异常值敏感，因此提出了更鲁棒的目标函数，如L1范数或Huber损失。可以说，最鲁棒的目标函数是异常值计数，也称为最大一致性优化，其输出结果与异常值的幅值无关。本文基于激光雷达数据，详细研究了最大一致性定位的性能。我们阐述了其不足之处，并基于赫尔默特点误差提出了一种新颖的目标函数。通过一项涉及3001个测量历元的实验，我们证明，基于所提出的目标函数的最大一致性定位在鲁棒性方面提供了更优越的结果。