Distribution Learning of a Random Spatial Field with a Location-Unaware Mobile Sensor

Measurement of spatial fields is of interest in environment monitoring. Recently mobile sensing has been proposed for spatial field reconstruction, which requires a smaller number of sensors when compared to the traditional paradigm of sensing with static sensors. A challenge in mobile sensing is to overcome the location uncertainty of its sensors. While GPS or other localization methods can reduce this uncertainty, we address a more fundamental question: can a location-unaware mobile sensor, recording samples on a directed non-uniform random walk, learn the statistical distribution (as a function of space) of an underlying random process (spatial field)? The answer is in the affirmative for Lipschitz continuous fields, where the accuracy of our distribution-learning method increases with the number of observed field samples (sampling rate). To validate our distribution-learning method, we have created a dataset with 43 experimental trials by measuring sound-level along a fixed path using a location-unaware mobile sound-level meter.