Bandlimited Spatiotemporal Field Sampling with Location and Time Unaware Mobile Sensors

Sampling of smooth spatiotemporally varying fields is a well-studied topic in the literature. Classical approach assumes that the field is observed at known sampling locations and known timestamps ensuring field reconstruction. In a first, in this work the sampling and reconstruction of a spatiotemporal bandlimited field is addressed, where the samples are obtained by a location-unaware, time-unaware mobile sensor. The spatial and temporal order of samples is assumed to be known. It is assumed that the field samples are affected by measurement-noise. The spatial field's evolution is modeled by a linear constant coefficient partial differential equation. A regression style estimate is developed for reconstruction of the spatial field. The intersample spacings and the intersample timestamp differences are assumed to be from independent unknown renewal processes. If n is the average number of samples of the field obtained by the mobile sensor, then it is shown that the mean-squared error decreases as O(1/n).