I'm working on a Kalman filter for estimating the position of a point in 3D space. I know that I can measure its 3D position directly with a variance of about 2 mm (in other words: the variance of the norm of the measured x, y, z vector is about 2 mm).
I'd like to fill my measurement noise covariance matrix based on this, so my question is:
How does this relate to the variance of the individual x, y, z measurements? I'm looking for three equal variances, assuming independency.