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Information Filter Occupancy Mapping using Decomposable Radial Kernels

Building occupancy maps of the environment is a fundamental problem for robot autonomy. A common assumption in early work was that the occupancy states of different map elements are independent. Recently, Gaussian Process (GP) techniques were proposed to capture correlation, which is important not only for improved accuracy but also for uncertainty quantification and autonomous exploration based on the predicted occupancy of nearby unexplored areas. Despite these desirable properties, current GP mapping techniques are limited to small maps and slow inference speeds. This paper proposes an information space formulation of the GP mapping problem. If a decomposable radial kernel is evaluated over a latent grid of pseudo-input points, the resulting kernel matrix has a Kronecker-product-of-Toeplitz-matrices structure that allows very efficient representation of the occupancy distribution. We utilize this structure to design an information filter occupancy mapping algorithm with linear time and memory complexity that still permits continuous space observations and predictions.