A hybrid global minimization scheme for accurate source localization in sensor networks

We consider the localization problem of multiple wideband sources in a multi-path environment by coherently taking into account the attenuation characteristics and the time delays in the reception of the signal. Our proposed method leaves the space for unavailability of an accurate signal attenuation model in the environment by considering the model as an unknown function with reasonable prior assumptions about its functional space. Such approach is capable of enhancing the localization performance compared with only utilizing the signal attenuation information or the time delays. In this article, the localization problem is modeled as a cost function in terms of the source locations, attenuation model parameters, and the multi-path parameters. To globally perform the minimization, we propose a hybrid algorithm combining the differential evolution algorithm with the Levenberg-Marquardt algorithm. Besides the proposed combination of optimization schemes, supporting the technical details such as closed forms of cost function sensitivity matrices are provided. Finally, the validity of the proposed method is examined in several localization scenarios, taking into account the noise in the environment, the multi-path phenomenon and considering the sensors being not synchronized.

[1]  Julius O. Smith,et al.  Closed-form least-squares source location estimation from range-difference measurements , 1987, IEEE Trans. Acoust. Speech Signal Process..

[2]  L. Coelho,et al.  Combining of chaotic differential evolution and quadratic programming for economic dispatch optimization with valve-point effect , 2006, IEEE Transactions on Power Systems.

[3]  Kirk Martinez,et al.  Environmental Sensor Networks: A revolution in the earth system science? , 2006 .

[4]  Ian F. Akyildiz,et al.  Wireless sensor networks: a survey , 2002, Comput. Networks.

[5]  YaoKung.  Maximum-likelihood source localization and unknown sensor location estimation for wideband signals in the near-field , 2002 .

[6]  Ilan Ziskind,et al.  Maximum likelihood localization of multiple sources by alternating projection , 1988, IEEE Trans. Acoust. Speech Signal Process..

[7]  K. Bube,et al.  Hybrid l 1 /l 2 minimization with applications to tomography , 1997 .

[8]  S. Kay.  Fundamentals of statistical signal processing: estimation theory , 1993 .

[9]  Tim Hesterberg,et al.  Introduction to Stochastic Search and Optimization: Estimation, Simulation, and Control , 2004, Technometrics.

[10]  King Lun Yiu.  Ad-hoc positioning system , 2008 .

[11]  Janez Brest,et al.  Self-Adapting Control Parameters in Differential Evolution: A Comparative Study on Numerical Benchmark Problems , 2006, IEEE Transactions on Evolutionary Computation.

[12]  Viii Supervisor.  Sonar-Based Real-World Mapping and Navigation , 2001 .

[13]  Yu Hen Hu,et al.  Maximum likelihood multiple-source localization using acoustic energy measurements with wireless sensor networks , 2005, IEEE Trans. Signal Process..

[14]  John E. Dennis,et al.  Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

[15]  G. Clifford Carter.  Coherence and time delay estimation : an applied tutorial for research, development, test, and evaluation engineers , 1993 .

[16]  R. Horst,et al.  Global Optimization: Deterministic Approaches , 1992 .

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

[18]  P. Preux,et al.  Towards hybrid evolutionary algorithms , 1999 .

[19]  Jan M. Rabaey,et al.  Location in distributed ad-hoc wireless sensor networks , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[20]  Alfred O. Hero,et al.  Energy-based sensor network source localization via projection onto convex sets , 2005, IEEE Transactions on Signal Processing.

[21]  Kikuo Fujita,et al.  Hybrid Approach for Optimal Nesting Using a Genetic Algorithm and a Local Minimization Algorithm , 1998 .

[22]  Kung Yao,et al.  Array Processing for Target DOA, Localization, and Classification Based on AML and SVM Algorithms in Sensor Networks , 2003, IPSN.

[23]  B. R. Badrinath,et al.  Ad hoc positioning system (APS) , 2001, GLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No.01CH37270).

[24]  Kaj Madsen,et al.  Methods for Non-Linear Least Squares Problems , 1999 .

[25]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[26]  Michael S. Brandstein,et al.  A closed-form location estimator for use with room environment microphone arrays , 1997, IEEE Trans. Speech Audio Process..

[27]  James C. Spall,et al.  Introduction to Stochastic Search and Optimization. Estimation, Simulation, and Control (Spall, J.C. , 2007 .

[28]  D. D. Morrison.  Methods for nonlinear least squares problems and convergence proofs , 1960 .

[29]  Kung Yao,et al.  Maximum-likelihood source localization and unknown sensor location estimation for wideband signals in the near-field , 2002, IEEE Trans. Signal Process..

[30]  F. Glover,et al.  Handbook of Metaheuristics , 2019, International Series in Operations Research & Management Science.

[31]  C. N Bouza,et al.  Spall, J.C. Introduction to stochastic search and optimization. Estimation, simulation and control. Wiley Interscience Series in Discrete Mathematics and Optimization, 2003 , 2004 .

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

[33]  Yu Hen Hu,et al.  Energy-Based Collaborative Source Localization Using Acoustic Microsensor Array , 2003, EURASIP J. Adv. Signal Process..

[34]  Alberto Elfes,et al.  Sonar-based real-world mapping and navigation , 1987, IEEE J. Robotics Autom..

[35]  G. Lambert-Torres,et al.  A hybrid particle swarm optimization applied to loss power minimization , 2005, IEEE Transactions on Power Systems.

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

[37]  Morteza Hashemi,et al.  A Source Localization Based on Signal Attenuation and Time Delay Estimation in Sensor Networks , 2012 .