In a timestamping counter I'm trying to calculate phase and frequency
using statistical techniques.
The counter has two counters, one for the input events and one for an
internal clock.
The capturing of these counters happens synchronized with an event.
The counter takes the timestamps at more or less regular, but not
identical, intervals
An example of 20 captures is:
Events Clock
280707207 1693452332
280708207 1693473665
280709207 1693494999
280710207 1693516332
280711207 1693537665
280712207 1693558999
280713207 1693580332
280714206 1693601644
280715207 1693622999
280716206 1693644310
280717206 1693665644
280718206 1693686977
280719206 1693708311
280720206 1693729644
280721206 1693750977
280722206 1693772311
280723206 1693793644
280724206 1693814977
280725206 1693836310
280726206 1693857644
By subtracting the counts at the first capture one gets:
Events Clock
0 0
1000 21333
2000 42667
3000 64000
4000 85333
5000 106667
6000 128000
6999 149312
8000 170667
8999 191978
9999 213312
10999 234645
11999 255979
12999 277312
13999 298645
14999 319979
15999 341312
16999 362645
17999 383978
18999 405312
It is visible the clock count interval is not completely constant and
the mathematical method used should be able to deal with these interval
variations.
To calculate the ratio between the frequency of the events and the
frequency of the clock a linear regression is calculated where the event
capture is the X and the clock capture is the Y.
The slope of the linear regression is the ratio between the frequency of
the events and the frequency of the clock.
To calculate the phase between the clock and the events it is assumed
that the regression also provides the Y intersect for X is zero as the
fractional correction of the clock count at event count zero as the
capture happened synchronized with the event (and NOT with the clock)
This leads me to my questions:
1: Is using linear regression as described above a good method to
calculate the phase relation between events and clock? If not, what
method to use?
2: For highest accuracy of the calculation output, is it best the
captures are at (almost) regular intervals (as above) or is some form of
dithering of the interval better? And what form of dithering is best?
3: Assuming it is possible to have a large amount (1e+5) of captures per
measurement interval, are there other or additional methods to further
improve the accuracy?
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