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Sensor calibration is an indispensable feature in any networked cyberphysical
system. In this paper, we consider a sensor network plagued with offset errors,
measuring a rank-1 signal subspace, where each sensor collects measurements
under a linear model with additive zero-mean Gaussian noise. Under varying
assumptions on the underlying noise covariance, we investigate the effect of
using an arbitrary reference for estimating the sensor offsets, in contrast to
the `average of all the unknown offsets' as a reference. We show that the
average reference yields an efficient minimum variance unbiased estimator. If
the underlying noise is homoscedastic in nature, then the average reference
yields a factor 2 improvement on the variance, as compared to any arbitrarily
chosen reference within the network. Furthermore, when the underlying noise is
independent but not identical, we derive an expression for the improvement
offered by the \emph{average} reference. We demonstrate our results using the
problem of clock synchronization in sensor networks, and present directions for
future work.