  In this paper a novel distributed algorithm for blind macro calibration in
sensor networks based on output synchronization is proposed. The algorithm is
formulated as a set of gradient-type recursions for estimating parameters of
sensor calibration functions, starting from local criteria defined as weighted
sums of mean square differences between the outputs of neighboring sensors. It
is proved, on the basis of an originally developed methodology for treating
higher-order consensus (or output synchronization) schemes, that the algorithm
achieves asymptotic agreement for sensor gains and offsets, in the mean square
sense and with probability one. In the case of additive measurement noise,
additive inter-agent communication noise, and communication outages, a
modification of the original algorithm based on instrumental variables is
proposed. It is proved using stochastic approximation arguments that the
modified algorithm achieves asymptotic consensus for sensor gains and offsets,
in the mean square sense and with probability one. Special attention is paid to
the situation when a subset of sensors in the network remains with fixed
characteristics. Illustrative simulation examples are provided.
