TY - JOUR
T1 - Three-dimensional electromagnetic articulography
T2 - A measurement principle
AU - Kaburagi, Tokihiko
AU - Wakamiya, Kohei
AU - Honda, Masaaki
N1 - Funding Information:
The authors wish to thank Mr. A. Zierdt and Dr. P. Hoole for their valuable discussions. We also thank Mr. T. Mochida for his support given to record the magnetic data at NTT Communication Science Laboratories. This research was partly supported by the Grant-in-Aid for Scientific Research from the JSPS (Grant No. 14101001). 1
PY - 2005/7
Y1 - 2005/7
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.
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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 -