  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.

Robotics