Distributed Sensor Localization in Random Environments Using Minimal Number of Anchor Nodes

• Published in: IEEE transactions on signal processing Vol. 57; no. 5; pp. 2000 - 2016
• Main Authors: Khan, U.A., Kar, S., Moura, J.M.F.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.05.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Absorbing Markov chain; Absorption; Algorithms; anchor; Anchors; Applied sciences; barycentric coordinates; Cayley-Menger determinant; Computer networks; Convergence; Data processing; Detection, estimation, filtering, equalization, prediction; Determinants; distributed iterative sensor localization; Exact sciences and technology; Global Positioning System; Information theory; Information, signal and communications theory; Iterative algorithms; Mathematical analysis; Mathematical models; Miscellaneous; Robustness; Sensor fusion; sensor networks; Sensor phenomena and characterization; Sensors; Signal and communications theory; Signal processing; Signal, noise; stochastic approximation; Stochastic processes; Studies; Telecommunications and information theory; Working environment noise; Stochastic approximation; Iterative method; Data processing; sensor networks; Distributed system; Cayley-Menger determinant; Markov chain; Absorbing Markov chain; barycentric coordinates; distributed iterative sensor localization; Distributed algorithm; anchor; Signal processing; Data communication; Localization; Sensor array; Deterministic approach; Signal detection
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2009.2014812

The paper introduces DILOC, a distributed, iterative algorithm to locate M sensors (with unknown locations) in R m , m ges 1, with respect to a minimal number of m + 1 anchors with known locations. The sensors and anchors, nodes in the network, exchange data with their neighbors only; no centralized data processing or communication occurs, nor is there a centralized fusion center to compute the sensors' locations. DILOC uses the barycentric coordinates of a node with respect to its neighbors; these coordinates are computed using the Cayley-Menger determinants, i.e., the determinants of matrices of internode distances. We show convergence of DILOC by associating with it an absorbing Markov chain whose absorbing states are the states of the anchors. We introduce a stochastic approximation version extending DILOC to random environments, i.e., when the communications among nodes is noisy, the communication links among neighbors may fail at random times, and the internodes distances are subject to errors. We show a.s. convergence of the modified DILOC and characterize the error between the true values of the sensors' locations and their final estimates given by DILOC. Numerical studies illustrate DILOC under a variety of deterministic and random operating conditions.