Function filter and tolerance for the forecast uncertainty threshold

Hi, I would like to better understand how does filter function regularises the forecast uncertainty matrix to avoid singularity? (https://nl.mathworks.com/help/econ/dssm.filter.html?searchHighlight=singular%20kalman%20&s_tid=srchtitle_singular%20kalman%20_6#buzf397-3)

The function allows to specify the tolerance for the procedure, which if activated, applies the correction. I was wondering does it use cholesky inversion for the correction or what? I tried to look into the function but it says that is in-built and does not show the code.

I appreciate your help.