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

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.

Improving Self-Consistency in Underwater Mapping through Laser-Based Loop Closure (Extended)

“…This application uses a recently developed adaptive robust cost function (RCF) to reject false loop-closure measurements, owing to its ability to handle multivariate, mixedunit error definitions, such as loop-closure errors (35), in a statistically sound manner [57]. The RCF assigns a weight w ( (e )) ∈ (0, 1] to loop-closure error e according to the Mahalanobis distance associated with the error,…”