Measurement outliers are unavoidable when solving real-world robot state estimation problems. A large family of robust loss functions (RLFs) exists to mitigate the effects of outliers, including newly developed adaptive methods that do not require parameter tuning. All of these methods assume that residuals follow a zero-mean Gaussian-like distribution. However, in multivariate problems the residual is often defined as a norm, and norms follow a Chi-like distribution with a non-zero mode value. This produces a "mode gap" that impacts the convergence rate and accuracy of existing RLFs. The proposed approach, "Adaptive MB," accounts for this gap by first estimating the mode of the residuals using an adaptive Chi-like distribution. Applying an existing adaptive weighting scheme only to residuals greater than the mode leads to more robust performance and faster convergence times in two fundamental state estimation problems, point cloud alignment and pose averaging.

翻译：在解决实际机器人状态估计问题时，测量异常值不可避免。现有大量鲁棒损失函数可用于减轻异常值的影响，包括无需参数调优的新开发自适应方法。所有此类方法均假设残差服从零均值类高斯分布。然而，在多变量问题中，残差通常定义为范数，而范数服从具有非零众数值的类卡方分布。这会产生"众数差距"，影响现有鲁棒损失函数的收敛速度与精度。本文提出的"自适应MB"方法通过首先使用自适应类卡方分布估计残差众数来弥补这一差距，仅对大于众数的残差应用现有自适应加权方案，从而在点云配准和位姿平均这两个基础状态估计问题中实现更鲁棒的性能与更快的收敛速度。