Measurement system of jaw movements by using BP neural networks method and a nonlinear least-squares method

The jaw movements can be measured by estimating the position and orientation of two small permanent magnets attached on the upper and lower jaws. It is a difficult problem to estimate the positions and orientations of the magnets from magnetic field because it is a typical inverse problem. The back propagation neural networks (BPNN) are applicable to solve this problem in short processing time. But its precision is not enough to apply to practical measurement. In the other hand, precise estimation is possible by using the nonlinear least-square (NLS) method. However, it takes long processing time for iterative calculation, and the solutions may be trapped in the local minima. In this paper, we propose a precise and fast measurement system which makes use of the estimation algorithm combining BPNN with NLS method. In this method, the BPNN performs an approximate estimation of magnet parameters in short processing time, and its result is used as the initial value of iterative calculation of NLS method. The cost function is solved by Gauss-Newton iteration algorithm. Precision, processing time and noise immunity were examined by computer simulations. These results shows the proposed system has satisfactory ability to be applied to practical measurement.