Error in source localization simulation using dipole fitting and LCMV

Hello,

I used a single dipole source to simulate the raw data obtained from the OPM magnetometer planar array measurement (which did not add noise). The first issue is that when using the current dipole fitting as the source localization method, I found that the dipole fitting result is only correct when the sensor sensitive axis direction is orthogonal to the dipole direction. I didn’t understand why.

In addition, when I use the LCMV method for source localization, stc.data is a complex matrix, and each row has the same result, with only positive and negative differences (theoretically fitting data for different source space coordinates). This means that each dipole in the predefined source space is the theoretically optimal source, which is clearly incorrect. Then I found that the rank of the activity covariance matrix is only 1. Is the reason for the error that the rank of the covariance matrix is too small? What should I do?
image

In the case shown in the figure, red represents the source dipole and blue represents the sensor array. When the dipole direction is along the z or y direction, the source estimation result is incorrect. The source estimation result is only correct when the dipole direction is along the x direction.

Looking forward to your reply!

After adding noise to the simulated measurement signal, the rank of the signal covariance matrix is consistent with the number of sensor channels. When the input dipole source direction is orthogonal to the measurement direction, the dipole fitting is correct, and the LCMV traceability result is also correct. However, this issue still exists, which is why the direction of the dipole source and the sensitive direction of the sensor need to meet a certain relationship in order for the traceability result to be correct.