A Taylor Series Approach to Correct Localization Errors in Robotic Field Mapping using Gaussian Processes

TL;DR

This paper introduces a second-order correction method using Taylor series expansion to improve Gaussian Process-based field mapping in robots with localization errors, enhancing accuracy and efficiency.

Contribution

It presents a novel second-order correction algorithm leveraging kernel differentiability for real-time GP model updates with localization discrepancies.

Findings

Enhanced prediction accuracy in simulated environments

Reduced computational cost compared to full retraining

Effective correction of localization-induced errors

Abstract

Gaussian Processes (GPs) are powerful non-parametric Bayesian models for regression of scalar fields, formulated under the assumption that measurement locations are perfectly known and the corresponding field measurements have Gaussian noise. However, many real-world scalar field mapping applications rely on sensor-equipped mobile robots to collect field measurements, where imperfect localization introduces state uncertainty. Such discrepancies between the estimated and true measurement locations degrade GP mean and covariance estimates. To address this challenge, we propose a method for updating the GP models when improved estimates become available. Leveraging the differentiability of the kernel function, a second-order correction algorithm is developed using the precomputed Jacobians and Hessians of the GP mean and covariance functions for real-time refinement based on measurement location discrepancy data. Simulation results demonstrate improved prediction accuracy and computational efficiency compared to full model retraining.