BLISS Seminar: On sampling and inference of spatial fields from samples taken by a location-unaware mobile sensor
Seminar | December 4 | 3-4 p.m. | 400 Cory Hall
Animesh Kumar, IIT Bombay
We consider the problem of spatial field inference using a location-unaware mobile sensor moving along a known path. The location-unaware sensing/sampling locations are modeled as a renewal process along the path, where the renewal distribution is not known. In this setup, where sampling locations as well as sample-locations distribution is unknown, equispaced approximation of sampling locations is the natural way forward. The effect of this approximation will be shown for the following three applications: (i) reconstruction of a finite parameter smooth field in space which is not changing with time during measurement; (ii) reconstruction of a bandlimited field in space evolving with a time-invariant partial differential equation (such as the diffusion equation); and (iii) distribution learning of a high-bandwidth spatial field at every point on a path. In all of these applications, the statistical risk involved in the inference problem provably improves with the number of samples (or sampling rate along the path).