# Adaptive Robust Kernels for Non-Linear Least Squares Problems

arXiv: https://arxiv.org/abs/2004.14938 · HTML: https://mlsanity.com/paper/2004.14938/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Apr 2020.

## Built on by (most cited first, 13 of 13)

- [MULLS: Versatile LiDAR SLAM via Multi-metric Linear Least Square](https://mlsanity.com/paper/2102.03771/) (2021)
- [Beyond Robustness: A Taxonomy of Approaches towards Resilient Multi-Robot Systems](https://mlsanity.com/paper/2109.12343/) (2021)
- [Estimation Contracts for Outlier-Robust Geometric Perception](https://mlsanity.com/paper/2208.10521/) (2022)
- [Efficient LiDAR Odometry for Autonomous Driving](https://mlsanity.com/paper/2104.10879/) (2021)
- [Adaptive Robust Estimator for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2603.21574/) (2026)
- [From Variance to Veracity: Unbundling and Mitigating Gradient Variance in Differentiable Bundle Adjustment Layers](https://mlsanity.com/paper/2406.07785/) (2024)
- [KM-ViPE: Online Tightly Coupled Vision-Language-Geometry Fusion for Open-Vocabulary Semantic SLAM](https://mlsanity.com/paper/2512.01889/) (2025)
- [RADIO-ViPE: Online Tightly Coupled Multi-Modal Fusion for Open-Vocabulary Semantic SLAM in Dynamic Environments](https://mlsanity.com/paper/2604.26067/) (2026)
- [Joint Spatial-Temporal Calibration for Camera and Global Pose Sensor](https://mlsanity.com/paper/2403.00976/) (2024)
- [Unleashing the Power of Discrete-Time State Representation: Ultrafast Target-based IMU-Camera Spatial-Temporal Calibration](https://mlsanity.com/paper/2509.12846/) (2025)
- [Quality-controlled registration of urban MLS point clouds reducing drift effects by adaptive fragmentation](https://mlsanity.com/paper/2510.23416/) (2025)
- [Triangulation-Free Bundle Adjustment with Graduated Non-Convexity for Camera Pose Refinement from Coarse Priors](https://mlsanity.com/paper/2608.21008/) (2026)
- [PARTE: Plane-Assisted Robust Transformation Estimation for Point Cloud Registration](https://mlsanity.com/paper/2609.25375/) (2026)

## Abstract (arXiv)

State estimation is a key ingredient in most robotic systems. Often, state estimation is performed using some form of least squares minimization. Basically, all error minimization procedures that work on real-world data use robust kernels as the standard way for dealing with outliers in the data. These kernels, however, are often hand-picked, sometimes in different combinations, and their parameters need to be tuned manually for a particular problem. In this paper, we propose the use of a generalized robust kernel family, which is automatically tuned based on the distribution of the residuals and includes the common m-estimators. We tested our adaptive kernel with two popular estimation problems in robotics, namely ICP and bundle adjustment. The experiments presented in this paper suggest that our approach provides higher robustness while avoiding a manual tuning of the kernel parameters.