On the choice of reference in offset calibration

Sensor calibration is an indispensable task 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 first show that the \emph{average} reference yields an efficient minimum variance unbiased estimator. If the underlying noise is homoscedastic in nature, then we prove the \emph{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 discuss directions for future work.