  Robotic Information Gathering (RIG) relies on the uncertainty of a
probabilistic model to identify critical areas for efficient data collection.
Gaussian processes (GPs) with stationary kernels have been widely adopted for
spatial modeling. However, real-world spatial data typically does not satisfy
the assumption of stationarity, where different locations are assumed to have
the same degree of variability. As a result, the prediction uncertainty does
not accurately capture prediction error, limiting the success of RIG
algorithms. We propose a novel family of nonstationary kernels, named the
Attentive Kernel (AK), which is simple, robust, and can extend any existing
kernel to a nonstationary one. We evaluate the new kernel in elevation mapping
tasks, where AK provides better accuracy and uncertainty quantification over
the commonly used RBF kernel and other popular nonstationary kernels. The
improved uncertainty quantification guides the downstream RIG planner to
collect more valuable data around the high-error area, further increasing
prediction accuracy. A field experiment demonstrates that the proposed method
can guide an Autonomous Surface Vehicle (ASV) to prioritize data collection in
locations with high spatial variations, enabling the model to characterize the
salient environmental features.
