Distributed Localization of a RF Target in NLOS Environments

We propose a novel distributed expectation maximization (EM) method for non-cooperative RF target localization using a wireless sensor network. We consider the scenario where few or no sensors receive line-of-sight signals from the target. In the case of non-line-of-sight signals, the signal path consists of a single reflection between the transmitter and receiver. Each sensor is able to measure the time difference of arrival of the target's signal with respect to a reference sensor, as well as the angle of arrival of the target's signal. We derive a distributed EM algorithm where each node makes use of its local information to compute summary statistics, and then shares these statistics with its neighbors to improve its estimate of the target localization. We show that our distributed algorithm converges, and simulation results suggest that our method achieves an accuracy close to the centralized EM algorithm. We apply the distributed EM algorithm to a set of experimental measurements with a network of four nodes, which confirm that the algorithm is able to localize a RF target in a realistic non-line-of-sight scenario.

[1]  Fredrik Gustafsson,et al.  TOA-Based Robust Wireless Geolocation and Cramér-Rao Lower Bound Analysis in Harsh LOS/NLOS Environments , 2013, IEEE Transactions on Signal Processing.

[2]  Markku J. Juntti,et al.  Positioning for NLOS Propagation: Algorithm Derivations and Cramer–Rao Bounds , 2006, IEEE Transactions on Vehicular Technology.

[3]  Jaehyung Kim,et al.  The Design Method and Performance Analysis of RF Subsampling Frontend for SDR/CR Receivers , 2010, IEEE Transactions on Industrial Electronics.

[4]  D. Penenberg Mathematical Statistics: Basic Ideas and Selected Topics, 2nd edn, vols I and II P. J. Bickel and K. A. Doksum, 2015 Boca Raton, Chapman and Hall–CRC xxii + 548 pp., $99.95 (vol. I); 438 pp., $99.95 (vol. II) ISBN 978-1-498-72380-0 , 2016 .

[5]  Soon Yim Tan,et al.  Non-Line-of-Sight Localization in Multipath Environments , 2008, IEEE Transactions on Mobile Computing.

[6]  Stephen P. Boyd,et al.  Randomized gossip algorithms , 2006, IEEE Transactions on Information Theory.

[7]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[8]  O. Cappé,et al.  On‐line expectation–maximization algorithm for latent data models , 2009 .

[9]  Pascal Bianchi,et al.  Convergence of a Multi-Agent Projected Stochastic Gradient Algorithm for Non-Convex Optimization , 2011, IEEE Transactions on Automatic Control.

[10]  Tony Q. S. Quek,et al.  Cooperative and distributed localization for wireless sensor networks in multipath environments , 2011, 2011 8th International Conference on Information, Communications & Signal Processing.

[11]  Markku J. Juntti,et al.  Positioning for NLOS Propagation: Algorithm Derivations and Cramer-Rao Bounds , 2007, IEEE Trans. Veh. Technol..

[12]  Hongyang Chen,et al.  An Importance Sampling Method for TDOA-Based Source Localization , 2011, IEEE Transactions on Wireless Communications.

[13]  Zhiping Lin,et al.  Individual aoameasurement detection algorithm for target tracking in mixed LOS/NLOS environments , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

[14]  Brian D. O. Anderson,et al.  Wireless sensor network localization techniques , 2007, Comput. Networks.

[15]  Pascal Bianchi,et al.  On-line gossip-based distributed expectation maximization algorithm , 2012, 2012 IEEE Statistical Signal Processing Workshop (SSP).

[16]  Tae Sung Yoon,et al.  Compensated robust least-squares estimator for target localisation in sensor network using time difference of arrival measurements , 2013, IET Signal Process..

[17]  Reiner S. Thomä,et al.  State Space Initiation for Blind Mobile Terminal Position Tracking , 2008, EURASIP J. Adv. Signal Process..

[18]  P. Bickel,et al.  Mathematical Statistics: Basic Ideas and Selected Topics , 1977 .

[19]  Alfred O. Hero,et al.  Space-alternating generalized expectation-maximization algorithm , 1994, IEEE Trans. Signal Process..

[20]  Dinesh K. Pai,et al.  Bayesian estimation of distance and surface normal with a time-of-flight laser rangefinder , 1999, Second International Conference on 3-D Digital Imaging and Modeling (Cat. No.PR00062).

[21]  Vincent Creuze Distance and orientation measurement of a flat surface by a single underwater acoustic transducer , 2011, 2011 19th European Signal Processing Conference.

[22]  Robert D. Nowak,et al.  Distributed EM algorithms for density estimation and clustering in sensor networks , 2003, IEEE Trans. Signal Process..

[23]  G. Carter,et al.  The generalized correlation method for estimation of time delay , 1976 .

[24]  R. O. Schmidt,et al.  Multiple emitter location and signal Parameter estimation , 1986 .

[25]  Fredrik Gustafsson,et al.  EM- and JMAP-ML Based Joint Estimation Algorithms for Robust Wireless Geolocation in Mixed LOS/NLOS Environments , 2014, IEEE Transactions on Signal Processing.

[26]  Gaetano Scarano,et al.  Discrete time techniques for time delay estimation , 1993, IEEE Trans. Signal Process..

[27]  K. C. Ho,et al.  A simple and efficient estimator for hyperbolic location , 1994, IEEE Trans. Signal Process..

[28]  J. Conan,et al.  Mobile Terminal Location for MIMO Communication Systems , 2007, IEEE Transactions on Antennas and Propagation.

[29]  La-or Kovavisaruch,et al.  Source Localization Using TDOA and FDOA Measurements in the Presence of Receiver Location Errors: Analysis and Solution , 2007, IEEE Transactions on Signal Processing.

[30]  W. Marsden I and J , 2012 .

[31]  Kannan Ramchandran,et al.  Collaborative High-Accuracy Localization in Mobile Multipath Environments , 2016, IEEE Transactions on Vehicular Technology.

[32]  Weihua Zhuang,et al.  Non-line-of-sight error mitigation in TDOA mobile location , 2001, GLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No.01CH37270).

[33]  T. Kirubarajan,et al.  Passive geolocation and tracking of an unknown number of emitters , 2006, IEEE Transactions on Aerospace and Electronic Systems.

[34]  Upamanyu Madhow,et al.  Cooperative localization using angle of arrival measurements in non-line-of-sight environments , 2008, MELT '08.

[35]  Maya R. Gupta,et al.  EM Demystified: An Expectation-Maximization Tutorial , 2010 .