Distributed calibration for sensor networks under communication errors and measurement noise

In this paper a new distributed calibration algorithm based on consensus is proposed for sensor networks. The algorithm is basically formulated as a set of stochastic gradient type recursions for estimating parameters of local sensor calibration functions, starting from local criteria defined as weighted sums of mean square errors between the outputs of neighboring sensors. It is proved that the proposed algorithm provides asymptotic consensus in the space of the sensor gains and offsets. In the case of communication dropouts and additive communication and measurement noise, a modification of the instrumental variable type of the original calibration scheme is proposed. It is proved using stochastic approximation arguments that in this case the proposed algorithm achieves asymptotic consensus in the mean square sense and with probability one. Some illustrative simulation examples are provided.