On Bandlimited Field Estimation from Samples Recorded by a Location-Unaware Location Mobile Sensor
Abstract: Sampling of physical fields with mobile sensor is an emerging area. In this context, this work introduces and addresses some aspects of a fundamental question: can a spatial field be estimated from samples taken at unknown sampling locations? In a field (signal) ignal) sampling setup, unknown sampling locations, sample quantization, unknown bandwidth of the field, and presence of measurementmeasurement noise present difficulties in the process of field estimation. In this work, except for quantization, the other three issues will be tackled together in a mobile-sampling mobile framework. Spatially bandlimited fields are considered. It is assumed that measurement-noise noise affected field samples are collected on spatial locations obtained from an unknown renewal process. That is, the samples samples are obtained on locations obtained from a renewal process, but the sampling locations and the renewal process distribution are unknown. In this challenging unknown sampling location setup, it is shown that the mean-squared mean squared error in field estimation decreases creases as O(1/n) where n is the average number of samples collected by the mobile sensor. The average number of samples collected is determined by the inter-sample sample spacing distribution in the renewal process. An algorithm to ascertain spatial field's band bandwidth width is detailed, which works with high probability as the average number of samples n increases. This algorithm works in the same