Asynchronous Distributed Blind Calibration of Sensor Networks Under Noisy Measurements

In this paper, a novel distributed algorithm for asynchronous blind macro-calibration in sensor networks with noisy measurements is proposed. The algorithm is formulated as a set of instrumental variable type recursions for estimating parameters of sensor calibration functions. It is proved using asynchronous stochastic approximation arguments and properties of block-diagonally dominant matrices that the algorithm achieves asymptotic consensus for sensor gains and offsets in the mean square sense and with probability one. Recommendations for system design in terms of the choice of a priori tunable weights are provided. Special attention is paid to the situation when a subset of sensors in the network (reference sensors) remains with fixed characteristics. In the case of only one reference sensor, convergence of the remaining sensors to its characteristics is proved. In the case of more than one reference sensor, it is proved that the calibration parameters converge to points that depend only on the characteristics of the reference sensors and the network properties.