[time-nuts] Re: Timestamping counter techniques : phase computation question

[Magnus Danielson]

Erik,

On 2022-01-31 20:32, Erik Kaashoek wrote:
> Thanks all for the good input.
>
> @Magnus, I need some time to understand the math as it has been over 30
> years since when I used to do this kind of math.
> There is no intention to store the collected captures, only to present a
> measurement at the measurement interval, so currently I'm calculating
> the 5 running sums from the captures and at the end of the interval I do
> the regression calculation using these running sums like described in
> the Wikipedia article on linear regression.
> This is what I am storing now (Sum means running sum from start of
> measurement interval till capture number n):  Sum(X), Sum(Y), Sum(X*X),
> Sum (Y*Y) and Sum (X*Y) and n.

You end up not needing to use the linear algebra part, as it is removed 
and reduced.

You form two sums, then process them through one of the two rules 
depending on phase or frequency estimated and you are done.

This performs an very cheap least square estimation. The decimation 
rules allow hierarchial decimation, so you end up in Fast Least Square 
space just as you do with Fast Fourier Transform.

Cheers,
Magnus