These last few days I worked on the software prototype. I did many calculations and spent a lot of time using Octave. It paid out and now the software prototype on Octave to get the location and the rotation of the receiver is done. It works without using a converging method, which is good because it is fast.
It works this way:
- The 9 (3 emitters vand 3 receivers) voltages are put in a matrix
- Using this matrix, the normalized-field matrix is computed. It is the matrix with the values we get when we get rid of the emmiter and receiver gains and the physic constants. This matrix depends only on the position and orientation of the receiver, not on the emitter nor the receiver characteristics.
- Then this matrix is symetrized because theoritically it is symetric.
- With the symetric matrix we compute the position of the receiver.
- To get the orientation we compare the symetric matrix we measured, which in the base of the receiver, with the theoritical field matrix,which is in the base of the emmiter at the position we just computed, which is in the base of the emmiter. We get the rotation matrix of the receiver.
With this method, I think we get as much precision as we can.
Now, I am working on the calibration. The values obtained from it will be used to get the normalized-field matrix with the voltages. We could compute the calibration values using the characteristics of the coils but we are almost sure it won’t work as expected.