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：在解决真实世界机器人状态估算问题时,测量外差是不可避免的。 有大量强大的损失函数( RLF ), 以缓解外差效应, 包括不需要参数调整的新开发适应方法。 所有这些方法都假设剩余值遵循零位高斯式分布法。 然而, 在多变问题中, 剩余值通常被定义为一种规范, 规范则遵循一种非零模式值的类似Chi的分布法。 这产生了“ 模式差距 ”, 影响现有RLF的趋同率和准确性。 提议的方法, “ 适应性 MB, ” 将这一差距的计算方法首先使用适应性的Chi类分布法来估计剩余值的模式。 将现有的适应性加权办法只适用于比模式更大的剩余值, 导致两种基本状态估算问题, 点云的趋同和形成平均度, 更强劲的性能和更快的趋同时间。