  Sampling of physical fields with mobile sensor is an emerging area. In this
context, this work introduces and proposes solutions to a fundamental question:
can a spatial field be estimated from samples taken at unknown sampling
locations?
  Unknown sampling location, sample quantization, unknown bandwidth of the
field, and presence of measurement-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 framework. Spatially bandlimited
fields are considered. It is assumed that measurement-noise affected field
samples are collected on spatial locations obtained from an unknown renewal
process. That is, the samples are obtained on locations obtained from a renewal
process, but the sampling locations and the renewal process distribution are
unknown. In this unknown sampling location setup, it is shown that the
mean-squared error in field estimation decreases 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 spacing distribution in the
renewal process. An algorithm to ascertain spatial field's bandwidth is
detailed, which works with high probability as the average number of samples
$n$ increases. This algorithm works in the same setup, i.e., in the presence of
measurement-noise and unknown sampling locations.
