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.
The alignment of transmitter coils for the three-dimensional electromagnetic articulograph (3D-EMA), an instrument used to measure articulatory movements, was studied. Receiver coils of the 3D-EMA are used as position markers and are placed in alternating magnetic field produced by multiple transmitter coils. The estimation of the state (the position and orientation) of each receiver coil is based on the minimization of the signal error between the measured and predicted receiver signals using a model of the magnetic field. Previous studies report a noticeable increase in the position estimation error irrespective of small signal error at a specific portion of the measurement region. The existence of the non-uniqueness problem in the position estimation is hypothesized to be the cause of this problem. To resolve the problem, we optimized the alignment of the transmitter coils by maximizing the difference between the receiver signals for any pair of states in the measurement region and evaluated the alignment by performing computer simulations and actual measurement. As a result, a measurement accuracy of approximately 0.4 mm was obtained.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.