Mind the Gap: Norm-Aware Adaptive Robust Loss for Multivariate Least-Squares Problems

TL;DR

This paper introduces an adaptive robust loss function that accounts for the mode gap in multivariate residuals, improving robustness and convergence in robot state estimation tasks.

Contribution

It proposes the Adaptive MB method that estimates residual modes and applies adaptive weighting, addressing the mode gap issue in multivariate robust loss functions.

Findings

Enhanced robustness in point cloud alignment and pose averaging.

Faster convergence compared to traditional methods.

Better handling of residual distributions with non-zero modes.

Abstract

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.