  We study the reconstruction of bandlimited fields from samples taken at
unknown but statistically distributed sampling locations. The setup is
motivated by distributed sampling where precise knowledge of sensor locations
can be difficult.
  Periodic one-dimensional bandlimited fields are considered for sampling.
Perfect samples of the field at independent and identically distributed
locations are obtained. The statistical realization of sampling locations is
not known. First, it is shown that a bandlimited field cannot be uniquely
determined with samples taken at statistically distributed but unknown
locations, even if the number of samples is infinite. Next, it is assumed that
the order of sample locations is known. In this case, using insights from
order-statistics, an estimate for the field with useful asymptotic properties
is designed. Distortion (mean-squared error) and central-limit are established
for this estimate.
