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In this paper a novel distributed algorithm for blind macro-calibration in sensor networks based on consensus 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 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 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 one sensor is selected as a reference. Illustrative simulation examples are provided.

Abstract: In this paper the extremum seeking algorithm with sinusoidal perturbations has been extended and modified in two ways: (a) the output of the system is corrupted with measurement noise; (b) the amplitudes of the perturbation signals, as well as the gain of the integrator block, are time varying and tend to zero at a pre-specified rate. Convergence to the extremal point, with probability one, has been proved. Also, as a consequence of being able to cope with a stochastic environment, it has been shown how the proposed algorithm can be applied to mobile sensors as a tool for achieving the optimal observation positions. The proposed algorithm has been illustrated through several simulations. [ABSTRACT FROM AUTHOR]

Abstract: In this paper a novel distributed algorithm derived from the Generalized Likelihood Ratio is proposed for real time change detection using sensor networks. The algorithm is based on a combination of recursively generated local statistics and a global consensus strategy, and does not require any fusion center. The problem of detection of an unknown change in the mean of an observed random process is discussed and the performance of the algorithm is analyzed in the sense of a measure of the error with respect to the corresponding centralized algorithm. The analysis encompasses asymmetric constant and randomly time varying matrices describing communications in the network, as well as constant and time varying forgetting factors in the underlying recursions. An analogous algorithm for detection of an unknown change in the variance is also proposed. Simulation results illustrate characteristic properties of the algorithms including detection performance in terms of detection delay and false alarm rate. They also show that the theoretical analysis connected to the problem of detecting change in the mean can be extended to the problem of detecting change in the variance. [Copyright &y& Elsevier]

In this paper we propose a novel stochastic consensus seeking algorithm based on the introduction of a nonlinear transformation aimed at robustification with respect to noise influence. The introduced nonlinear transformation is selected according to the methodology of stochastic approximation and robust statistics. The proposed algorithm represents a general nonlinear stochastic consensus seeking scheme, not yet treated in the literature. It provides a significant improvement over the linear algorithms from the point of view of robustness to noise, ensuring better convergence rate and lower sensitivity of the limit state value at consensus. One of the main contributions of the paper is the proof that the algorithm converges almost surely to consensus under general conditions. A detailed analysis of the limit state value at consensus is provided together with an insight into achievable convergence rate. Illustrative simulation results are also provided, demonstrating great advantages of the proposed algorithm compared to the existing consensus schemes. [ABSTRACT FROM AUTHOR]