Numerical stability and accuracy of PLL blocks


does anyone know if any stability and accuracy evaluation of the digital
PLL as implemented in GNU Radio exist?

I’m trying to measure the frequency of a very low phase-noise signal and
I see strange artifacts for certain combinations of detuning (residual
frequency difference between the signal and the N210 center frequency)
and PLL bandwidth.

I already have re-implemented the PLL blocks to measure phase using a
more accurate arctan2() function than the one provided by Volk (which
uses a linear approximation for small angles) but I still see strange
things that I believe are due to the control loop going nuts due to
numerical problems.

If some work has already been done in this regard I could probably save
some time.

Thanks. Cheers,