Cramer-Rao bounds for acoustic emission events localization in a flat plate

by Alain Le Duff, Seif Eddine Hamdi, Guy Plantier, Anthony Sourice, Romain Feron
Abstract:
This article addresses the problem of 2D localization of acoustics source in a plate. This localization is based on Time Difference of Arrival (TDOA) measurements thanks to an array of three sensors arbitrary distributed on the 2D plane. Some previous works proposed approximated solutions or maximum likelihood methods. In order to obtain a fast, but robust and accuracy, algorithm, allowing an online estimation of the location of hits or Acoustic Emission (AE) events in a composite plate for example, the authors propose an exact solution of the TDOA problem by solving a nonlinear system of coupled equations. The exact analytical Cramer-Rao Bounds (CRBs) on the variance of the estimations is then presented. Moreover, the statistical performances of the method are illustrated by means of Monte-Carlo simulations and are compared to the CRBs. These last expressions can be very useful in order to justify the accuracy of TDOA measurements and for guiding the choice of the sensors position.
Reference:
Alain Le Duff, Seif Eddine Hamdi, Guy Plantier, Anthony Sourice, Romain Feron, « Cramer-Rao bounds for acoustic emission events localization in a flat plate », In Acoustics 2012, Nantes, France, 2012.
Bibtex Entry:
@INPROCEEDINGS{Acoustics2012Hamdi3,
  author = {Le Duff, Alain and Hamdi, Seif Eddine and Guy Plantier and Anthony
	Sourice and Romain Feron},
  title = {Cramer-Rao bounds for acoustic emission events localization in a
	flat plate},
  booktitle = {Acoustics 2012},
  year = {2012},
  address = {Nantes, France},
  month = apr,
  abstract = {This article addresses the problem of 2D localization of acoustics
	source in a plate. This localization is based on Time Difference
	of Arrival (TDOA) measurements thanks to an array of three sensors
	arbitrary distributed on the 2D plane. Some previous works proposed
	approximated solutions or maximum likelihood methods. In order to
	obtain a fast, but robust and accuracy, algorithm, allowing an online
	estimation of the location of hits or Acoustic Emission (AE) events
	in a composite plate for example, the authors propose an exact solution
	of the TDOA problem by solving a nonlinear system of coupled equations.
	The exact analytical Cramer-Rao Bounds (CRBs) on the variance of
	the estimations is then presented. Moreover, the statistical performances
	of the method are illustrated by means of Monte-Carlo simulations
	and are compared to the CRBs. These last expressions can be very
	useful in order to justify the accuracy of TDOA measurements and
	for guiding the choice of the sensors position.},
  owner = {gplantier},
  timestamp = {2012.11.11}
}