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.

Measurement of spatial fields is of interest in environment monitoring.

As the title suggests, this paper uses learning-theoretic tools to study a problem of estimating a (Lipschitz) spatial field using sensors which are location-unaware. The main contributions are the formulation of the sensing problem, a proposed algorithm, an analysis of its sample complexity, and some proof-of concept experiments. While in the future this may involve new "contributions to statistical learning theory," the present study does not really develop new techniques. Overall, the problem is interesting but the paper could be strengthened significantly in several directions as noted by the reviewers. In particular some more specific motivating examples would help ground the paper -- the authors mention "spatial sensing... in smart cities or IoT or climatology" but do not elaborate.

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).

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).