Ferromagnetic materials in indoor environments give rise to disturbances in the ambient magnetic field. Maps of these magnetic disturbances can be used for indoor localisation. A Gaussian process can be used to learn the spatially varying magnitude of the magnetic field using magnetometer measurements and information about the position of the magnetometer. The position of the magnetometer, however, is frequently only approximately known. This negatively affects the quality of the magnetic field map. In this paper, we investigate how an array of magnetometers can be used to improve the quality of the magnetic field map. The position of the array is approximately known, but the relative locations of the magnetometers on the array are known. We include this information in a novel method to make a map of the ambient magnetic field. We study the properties of our method in simulation and show that our method improves the map quality. We also demonstrate the efficacy of our method with experimental data for the mapping of the magnetic field using an array of 30 magnetometers.

The count-min sketch (CMS) is a randomized data structure that provides estimates of tokens' frequencies in a large data stream using a compressed representation of the data by random hashing. In this paper, we rely on a recent Bayesian nonparametric (BNP) view on the CMS to develop a novel learning-augmented CMS under power-law data streams. We assume that tokens in the stream are drawn from an unknown discrete distribution, which is endowed with a normalized inverse Gaussian process (NIGP) prior. Then, using distributional properties of the NIGP, we compute the posterior distribution of a token's frequency in the stream, given the hashed data, and in turn corresponding BNP estimates. Applications to synthetic and real data show that our approach achieves a remarkable performance in the estimation of low-frequency tokens. This is known to be a desirable feature in the context of natural language processing, where it is indeed common in the context of the power-law behaviour of the data.