Spatially Scalable Recursive Estimation of Gaussian Process Terrain Maps Using Local Basis Functions

Abstract

We address the computational challenges of large-scale geospatial mapping with Gaussian process (GP) regression by performing localized computations rather than processing the entire map simultaneously. Traditional approaches to GP regression often involve computational and storage costs that either scale with the number of measurements, or with the spatial extent of the mapped area, limiting their scalability for real-time applications. Our method places a global grid of finite-support basis functions and restricts computations to a local subset of the grid 1) surrounding the measurement when the map is updated, and 2) surrounding the query point when the map is queried. This localized approach ensures that only the relevant area is updated or queried at each timestep, significantly reducing computational complexity while maintaining accuracy. Unlike many existing methods, which suffer from boundary effects or increased computational costs with mapped area, our localized approach avoids discontinuities and ensures that computational costs remain manageable regardless of map size. This approximation to GP mapping provides high accuracy with limited computational budget for the specialized task of performing fast online map updates and fast online queries of large-scale geospatial maps. It is therefore a suitable approximation for use in real-time applications where such properties are desirable, such as real-time simultaneous localization and mapping (SLAM) in large, nonlinear geospatial fields. We show on experimental data with magnetic field measurements that our algorithm is faster and equally accurate compared to existing methods, both for recursive magnetic field mapping and for magnetic field SLAM.