Distributed Change Detection Based on a Consensus Algorithm

• Published in: IEEE transactions on signal processing Vol. 59; no. 12; pp. 5686 - 5697
• Main Authors: Stankovic, S. S., Ilic, N., Stankovic, M. S., Johansson, K. H.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-12-2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithm design and analysis; Algorithms; Applied sciences; Asymmetry; Change detection; Change detection algorithms; Consensus; Control charts; Detection, estimation, filtering, equalization, prediction; distributed detection; Exact sciences and technology; geometric moving average control charts; Heuristic algorithms; Information, signal and communications theory; Mathematical analysis; Matrices; Matrix methods; Mean square error methods; Mean square errors; Networks; real time change detection; Real time systems; sensor networks; Signal and communications theory; Signal, noise; Statistics; Studies; Telecommunications and information theory; Space time correlation; Statistical process control; Control chart; geometric moving average control charts; Deflection; Forgetting factor; real time change detection; Change detection; Moving average; Lossy medium; sensor networks; Recursive algorithm; Time variation; Consensus; Mean square error; distributed detection; Simulation; Distributed algorithm; Signal processing; Real time processing; Sensor array; Signal detection
• ISSN: 1053-587X; 1941-0476; 1941-0476
• DOI: 10.1109/TSP.2011.2168219

In this paper a novel distributed recursive algorithm is proposed for real time change detection using sensor networks. The algorithm is based on a combination of geometric moving average control charts generating local statistics and a global consensus strategy; it does not require any fusion center, so that the final decision is made by testing the state of any node in the network with respect to a given common threshold. The mean-square error with respect to the centralized solution defined by a weighted sum of the local statistics is analyzed in the case of constant asymmetric consensus matrices with constant and time varying forgetting factors in the underlying recursions, assuming spatially and temporally correlated data. These results are consistently extended to the case of time varying random consensus matrices, encompassing asymmetric gossip schemes, lossy networks and intermittent measurements, proving that the algorithm can be an efficient tool for practice. The given simulation results illustrate the main characteristics of the proposed algorithm, including the consensus matrix design, the mean square error with respect to the centralized solution as a function of the forgetting factor, the obtained detection quality expressed using deflection and estimation of the instant of parameter change.