### Abstract

A measurement principle of the three-dimensional electromagnetic articulographic device is presented. The state of the miniature receiver coil is described by five variables representing the position in the three-dimensional coordinate system and the rotation angles relative to it. When the receiver coil is placed in the magnetic field produced from the distributed transmitter coils, its state can be optimally estimated by minimizing the difference between the measured strength of the received signal and the predicted one using the known spatial pattern of the magnetic field. Therefore, the design and calibration of the field function inherently determine the accuracy in estimating the state of the receiver coil. The field function in our method is expressed in the form of a multivariate B spline as a function of position in the three-dimensional space. Because of the piecewise property of the basis function and the freedom in the selection of the rank and the number of basis functions, the spline field function has a superior ability to flexibly and accurately represent the actual magnetic field. Given a set of calibration data, the spline function is designed to form a smooth curved surface interpolating all of these data samples. Then, an iterative procedure is employed to solve the nonlinear estimation problem of the receiver state variables. Because the spline basis function is a polynomial, it is also shown that the calculation of the Jacobian or Hessian required to obtain updated quantities for the state variables can be efficiently performed. Finally, experimental results reveal that the measurement accuracy is about 0.2 mm for a preliminary condition, indicating that the method can achieve the degree of precision required for observing articulatory movements in a three-dimensional space. It is also experimentally shown that the Marquardt method is a better nonlinear programming technique than the Gauss-Newton or Newton-Raphson method for solving the receiver state problem.

Original language | English |
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Pages (from-to) | 428-443 |

Number of pages | 16 |

Journal | Journal of the Acoustical Society of America |

Volume | 118 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jul 1 2005 |

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### All Science Journal Classification (ASJC) codes

- Arts and Humanities (miscellaneous)
- Acoustics and Ultrasonics

### Cite this

**Three-dimensional electromagnetic articulography : A measurement principle.** / Kaburagi, Tokihiko; Wakamiya, Kohei; Honda, Masaaki.

Research output: Contribution to journal › Article

*Journal of the Acoustical Society of America*, vol. 118, no. 1, pp. 428-443. https://doi.org/10.1121/1.1928707

}

TY - JOUR

T1 - Three-dimensional electromagnetic articulography

T2 - A measurement principle

AU - Kaburagi, Tokihiko

AU - Wakamiya, Kohei

AU - Honda, Masaaki

PY - 2005/7/1

Y1 - 2005/7/1

N2 - A measurement principle of the three-dimensional electromagnetic articulographic device is presented. The state of the miniature receiver coil is described by five variables representing the position in the three-dimensional coordinate system and the rotation angles relative to it. When the receiver coil is placed in the magnetic field produced from the distributed transmitter coils, its state can be optimally estimated by minimizing the difference between the measured strength of the received signal and the predicted one using the known spatial pattern of the magnetic field. Therefore, the design and calibration of the field function inherently determine the accuracy in estimating the state of the receiver coil. The field function in our method is expressed in the form of a multivariate B spline as a function of position in the three-dimensional space. Because of the piecewise property of the basis function and the freedom in the selection of the rank and the number of basis functions, the spline field function has a superior ability to flexibly and accurately represent the actual magnetic field. Given a set of calibration data, the spline function is designed to form a smooth curved surface interpolating all of these data samples. Then, an iterative procedure is employed to solve the nonlinear estimation problem of the receiver state variables. Because the spline basis function is a polynomial, it is also shown that the calculation of the Jacobian or Hessian required to obtain updated quantities for the state variables can be efficiently performed. Finally, experimental results reveal that the measurement accuracy is about 0.2 mm for a preliminary condition, indicating that the method can achieve the degree of precision required for observing articulatory movements in a three-dimensional space. It is also experimentally shown that the Marquardt method is a better nonlinear programming technique than the Gauss-Newton or Newton-Raphson method for solving the receiver state problem.

AB - A measurement principle of the three-dimensional electromagnetic articulographic device is presented. The state of the miniature receiver coil is described by five variables representing the position in the three-dimensional coordinate system and the rotation angles relative to it. When the receiver coil is placed in the magnetic field produced from the distributed transmitter coils, its state can be optimally estimated by minimizing the difference between the measured strength of the received signal and the predicted one using the known spatial pattern of the magnetic field. Therefore, the design and calibration of the field function inherently determine the accuracy in estimating the state of the receiver coil. The field function in our method is expressed in the form of a multivariate B spline as a function of position in the three-dimensional space. Because of the piecewise property of the basis function and the freedom in the selection of the rank and the number of basis functions, the spline field function has a superior ability to flexibly and accurately represent the actual magnetic field. Given a set of calibration data, the spline function is designed to form a smooth curved surface interpolating all of these data samples. Then, an iterative procedure is employed to solve the nonlinear estimation problem of the receiver state variables. Because the spline basis function is a polynomial, it is also shown that the calculation of the Jacobian or Hessian required to obtain updated quantities for the state variables can be efficiently performed. Finally, experimental results reveal that the measurement accuracy is about 0.2 mm for a preliminary condition, indicating that the method can achieve the degree of precision required for observing articulatory movements in a three-dimensional space. It is also experimentally shown that the Marquardt method is a better nonlinear programming technique than the Gauss-Newton or Newton-Raphson method for solving the receiver state problem.

UR - http://www.scopus.com/inward/record.url?scp=22144448561&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=22144448561&partnerID=8YFLogxK

U2 - 10.1121/1.1928707

DO - 10.1121/1.1928707

M3 - Article

C2 - 16119363

AN - SCOPUS:22144448561

VL - 118

SP - 428

EP - 443

JO - Journal of the Acoustical Society of America

JF - Journal of the Acoustical Society of America

SN - 0001-4966

IS - 1

ER -