  Sampling of a spatiotemporal field for environmental sensing is of interest.
Traditionally, a few fixed stations or sampling locations aid in the
reconstruction of the spatial field. Recently, there has been an interest in
mobile sensing and location-unaware sensing of spatial fields. In this work,
the general class of fields governed by a constant coefficient linear partial
differential equations is considered. This class models many physical fields
including temperature, pollution, and diffusion fields. The analysis is
presented in one dimension for a first exposition. It is assumed that a mobile
sensing unit is available to sample the spatiotemporal field of interest at
unknown locations and unknown times -- both generated by independent and
unknown renewal processes. Based on measurement-noise affected samples, a
spatial field reconstruction algorithm is proposed. It is shown that if the
initial condition on the field is bandlimited, then the mean squared error
between the original and the estimated field decreases as $O(1/n)$, where $n$
is the average sampling density of the mobile sensor. The field reconstruction
algorithm is universal, that is, it does not require the knowledge of unknown
sampling locations' or unknown time instants' statistical distributions.
