[time-nuts] Can the ADEV of a GPSDO output ever be lower than the minimum of the ADEV of the internal oscilator and the ADEV of the GPS PPS?

[Erik Kaashoek]

I'm doing some simulations to understand the impact of a filter between the
TIC measurement and the PI controller steering the Vtune of the OCXO.
With a well tuned PI controller without filter the best ADEV I can get is
just above the minimum ADEV of an actual measured  OCXO and an actual
measured GPS PPS.
When I add an alpha-beta filter, similar to a first order Kalman filter
with a manually tuned Kalman gain, and using similar Kp, Ki, the overall
performance does not change (much)
However with the filter its is possible to increase the Kp, Ki with a
factor 10 and when I use in the simulation instead of a measured PPS an
artificial PPS created from noise with the same ADEV as the GPS PP but with
a very constant phase (different from the varying phase of a GPS PPS)  the
ADEV of the GPSDO output in my simulation seems to drops below the ADEV of
the PPS. Am I correct to assume this is a hint there is still something
wrong in the simulation or was my initial assumption about the possible
range of the GPSDO ADEV wrong?
Erik.