Analysis of Scale-Variant Robust Kernel Optimization for Non-linear Least Squares Problems

TL;DR

This paper introduces an adaptive robust estimation method that learns residual distribution parameters to improve non-linear least squares optimization, especially under varying noise conditions.

Contribution

It proposes a novel parameter learning approach for robust kernel optimization that eliminates manual tuning and enhances performance in non-linear least squares problems.

Findings

Outperforms existing methods with manual residual scale tuning.

Effectively adapts to varying noise levels in data.

Decoupling scale and shape parameters improves robustness.

Abstract

In this article, we present a method for increasing adaptivity of an existing robust estimation algorithm by learning two parameters to better fit the residual distribution. The analyzed method uses these two parameters to calculate weights for Iterative Re-weighted Least Squares. This adaptive nature of the weights can be helpful in situations where the noise level varies in the measurements. We test our algorithm first on the point cloud registration problem with synthetic data sets and LiDAR odometry with open source real-world data sets. We show that the existing approach needs an additional manual tuning of a residual scale parameter which our method directly learns from data and has similar or better performance. We further present the idea of decoupling scale and shape parameters to improve performance of the algorithm. We give detailed analysis of our algorithm along with its comparison with similar well-known algorithms from literature to show the benefits of the proposed approach.