Adaptive Graduated Nonconvexity Loss

by   Kyungmin Jung, et al.

Many problems in robotics, such as estimating the state from noisy sensor data or aligning two LiDAR point clouds, can be posed and solved as least-squares problems. Unfortunately, vanilla nonminimal solvers for least-squares problems are notoriously sensitive to outliers. As such, various robust loss functions have been proposed to reduce the sensitivity to outliers. Examples of loss functions include pseudo-Huber, Cauchy, and Geman-McClure. Recently, these loss functions have been generalized into a single loss function that enables the best loss function to be found adaptively based on the distribution of the residuals. However, even with the generalized robust loss function, most nonminimal solvers can only be solved locally given a prior state estimate due to the nonconvexity of the problem. The first contribution of this paper is to combine graduated nonconvexity (GNC) with the generalized robust loss function to solve least-squares problems without a prior state estimate and without the need to specify a loss function. Moreover, existing loss functions, including the generalized loss function, are based on Gaussian-like distribution. However, residuals are often defined as the squared norm of a multivariate error and distributed in a Chi-like fashion. The second contribution of this paper is to apply a norm-aware adaptive robust loss function within a GNC framework. This leads to additional robustness when compared with state-of-the-art methods. Simulations and experiments demonstrate that the proposed approach is more robust and yields faster convergence times compared to other GNC formulations.


page 1

page 7


A More General Robust Loss Function

We present a two-parameter loss function which can be viewed as a genera...

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

Measurement outliers are unavoidable when solving real-world robot state...

Changepoint Detection in the Presence of Outliers

Many traditional methods for identifying changepoints can struggle in th...

Maximum Consensus Localization using an Objective Function based on Helmert's Point Error

Ego-localization is a crucial task for autonomous vehicles. On the one h...

Nonlinear Least Squares for Large-Scale Machine Learning using Stochastic Jacobian Estimates

For large nonlinear least squares loss functions in machine learning we ...

CIRA Guide to Custom Loss Functions for Neural Networks in Environmental Sciences – Version 1

Neural networks are increasingly used in environmental science applicati...

Consistency of Ranking Estimators

The ranking problem is to order a collection of units by some unobserved...

Please sign up or login with your details

Forgot password? Click here to reset