An Importance Sampling Method for TDOA-Based Source Localization

We consider the source localization problem using time-difference-of-arrival (TDOA) measurements in sensor networks. The maximum likelihood (ML) estimation of the source location can be cast as a nonlinear/nonconvex optimization problem, and its global solution is hardly obtained. In this paper, we resort to the Monte Carlo importance sampling (MCIS) technique to find an approximate global solution to this problem. To obtain an efficient importance function that is used in the technique, we construct a Gaussian distribution and choose its probability density function (pdf) as the importance function. In this process, an initial estimate of the source location is required. We reformulate the problem as a nonlinear robust least squares (LS) problem, and relax it as a second-order cone programming (SOCP), the solution of which is used as the initial estimate. Simulation results show that the proposed method can achieve the Cramer-Rao bound (CRB) accuracy and outperforms several existing methods.

[1]  Don J. Torrieri,et al.  Statistical Theory of Passive Location Systems , 1984, IEEE Transactions on Aerospace and Electronic Systems.

[2]  Frankie K. W. Chan,et al.  Semidefinite Programming Approach for Range-Difference Based Source Localization , 2009, IEEE Transactions on Signal Processing.

[3]  Jian Li,et al.  Exact and Approximate Solutions of Source Localization Problems , 2008, IEEE Transactions on Signal Processing.

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

[5]  Masakazu Kojima,et al.  Exploiting sparsity in primal-dual interior-point methods for semidefinite programming , 1997, Math. Program..

[6]  John F. Raquet,et al.  Positioning for Range-Based Land Navigation Systems Using Surface Topography , 2006 .

[7]  Frankie K. W. Chan,et al.  Accurate time delay estimation based passive localization , 2009, Signal Process..

[8]  B.D.O. Anderson,et al.  Optimal Range-Difference-Based Localization Considering Geometrical Constraints , 2008, IEEE Journal of Oceanic Engineering.

[9]  K. C. Ho,et al.  An Approximately Efficient TDOA Localization Algorithm in Closed-Form for Locating Multiple Disjoint Sources With Erroneous Sensor Positions , 2009, IEEE Transactions on Signal Processing.

[10]  Martin Pincus,et al.  Letter to the Editor - -A Closed Form Solution of Certain Programming Problems , 1968, Oper. Res..

[11]  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.

[12]  Alfred O. Hero,et al.  Relative location estimation in wireless sensor networks , 2003, IEEE Trans. Signal Process..

[13]  Steven M. Kay,et al.  An Importance Sampling Maximum Likelihood Direction of Arrival Estimator , 2008, IEEE Transactions on Signal Processing.

[14]  Gang Wang,et al.  Efficient Convex Relaxation Methods for Robust Target Localization by a Sensor Network Using Time Differences of Arrivals , 2009, IEEE Transactions on Signal Processing.

[15]  Steven M. Kay,et al.  Maximum likelihood parameter estimation of superimposed chirps using Monte Carlo importance sampling , 2002, IEEE Trans. Signal Process..

[16]  Nando de Freitas,et al.  Sequential Monte Carlo Methods in Practice , 2001, Statistics for Engineering and Information Science.

[17]  K. C. Ho,et al.  An accurate algebraic solution for moving source location using TDOA and FDOA measurements , 2004, IEEE Transactions on Signal Processing.

[18]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[19]  Jacob Benesty,et al.  Real-time passive source localization: a practical linear-correction least-squares approach , 2001, IEEE Trans. Speech Audio Process..

[20]  Julius O. Smith,et al.  Source range and depth estimation from multipath range difference measurements , 1989, IEEE Trans. Acoust. Speech Signal Process..

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

[22]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

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

[24]  Yiu-Tong Chan,et al.  Exact and approximate maximum likelihood localization algorithms , 2006, IEEE Trans. Veh. Technol..