[time-nuts] Two questions about counters

[Erik Kaashoek]

Pardon me for asking two highly specialized questions.

In his may 2012 presentation  (see 
http://athome.kaashoek.com/time-nuts/Counter%20Principles.pdf ) Rubiola 
describes on slide 40 the enhanced resolution counter and compares it to 
a Linear-regression counter on slide 45. Unfortunately my match 
capabilities have disappeared in the 40 years since I left university 
and I'm not able to understand the statement he makes ("The linear 
regression estimator is asymptotically equivalent to the enhanced 
resolution count") and the math is too complex for me to understand if 
the enhanced resolution counter has any advantages over the linear 
regression counter.
I think I understand that the enhanced resolution counter has a well 
defined decimation approach allowing a step wise decimation.
The enhanced resolution counter however seems to require a lot more 
memory related to the amount of decimation where a  linear regression 
only needs a small set of running sums
Is there someone in this community that can  explain the (dis)advantages 
of these counter approaches in a simple way?

In their 2016 paper "On temporal correlations in high-resolution 
frequency counting" ( 
http://athome.kaashoek.com/time-nuts/Measuring%20Counter%20Noise.pdf ) 
the authors describe how using the undocumented RCON mode instead of the 
CONT mode when using a Keysight 53230A can have certain advantages, one 
seems to be the phase stability realized when using the RCON mode
The CONT mode is described as continuous resolution enhanced gap free 
measurements and, although it is not formally known, the method used 
could be a linear regression or enhanced resolution approach given the 
slope of the ADEV when measuring the noise floor of the counter in that 
mode.
The RCON method without using internal averaging seems to have the 
advantage for phase measurement that there is no cumulative error, 
although the frequency resolution may be lower and it may be purely 
based on the interpolated timestamps thus avoiding a cumulative phase error.
It is however possible to use the linear regression method to calculate 
a phase relative to the counter reference so the output of the counter 
(phase instead of frequency) is resolution enhanced but the phase output 
does not have an accumulative error as would occur when using the 
frequency output after resolution enhancement as it is always referred 
to the counter reference.
For a counter that should be usable for ADEV and/or phase measurements, 
would having a phase output mode without cumulative error, either using 
a method similar to RCON or a linear regression approach with phase hard 
linked to the reference, be an advantage?
Erik.