用泰勒展开修正机器人定位误差，提升地图建模精度
A Taylor Series Approach to Correct Localization Errors in Robotic Field Mapping using Gaussian Processes
- 基于核函数可微性，用二阶泰勒展开修正定位偏差
- 相比重新训练，预测误差降低18.7%，计算效率提升3.2倍
- 适合高精度移动机器人地图构建场景
高斯过程（GPs）是用于标量场回归的强大非参数贝叶斯模型，其前提是测量位置精确已知且测量值服从高斯噪声。但在实际应用中，传感器搭载的移动机器人采集数据时，定位不准确会引入状态不确定性，导致GP均值和协方差估计退化。为此，本文提出一种在获得更优位置估计后更新GP模型的方法。利用核函数的可微性，基于预计算的GP均值和协方差函数的雅可比与海森矩阵，开发出二阶修正算法，实现基于测量位置偏差数据的实时优化。仿真结果表明，该方法在预测精度上优于全模型重训练，且计算效率提升3.2倍，平均误差降低18.7%。
原文摘要 · Abstract (English)
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.
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