When you enter your ITRF2020 cartesian coordinates in EUREF transformation service, you do not have to provide speeds (VX, VY, VZ) as your don’t change coordinates epoch.
Just type SBG1 4141140.548 1388894.707 4632493.710

I made the same transformations with Proj and I get the same results as you at the millimeter level.

Meanwhile he also did 2 calculation using 2 VRS providers
Fömi: 46.87629729 - 18.5408981 159.95
Axiál: 46.87629732 - 18.54089811 159.97
NRCAN + ETRF2000: 46.87629736 18.54089816 161.938

If omnicalculator is good:
Fömi → NRCAN → 9mm
Axiál → NRCAN → 6mm
Fömi → Axiál → 3mm

BUT the height is off by ~2 meters… Which doesn’t matter much for the tractors but if we expect to use this with drones then maybe the height also matters.

Is there anything we could do about the height? does it matter in your opinion?

Thank you for all your help! At least X-Y axis we’re good.

I checked 2 more rinex files + manual calcs (of a different base) → there even the height is spot on. So I’m not sure why we had that 2 meter diff.
XY direction we had 6cm difference compared to VRS so I think this transformation technique should be really accurate.

Now it’s time for me to simplify / automate as much as possible
Ideally end user should just copy-paste the summary from NRCAN and get the ETRF2000 coordinates for the PI.

(Not that the copy-paste approach doesn’t work just I want to reduce the places where they can misplace a number.)

Is anyone aware of a cartesian → WGS84 converter that’s php / API based?
Would love to be able to copy-paste the EUREF conversion to another textbox and then spit out the values for PI.

I used data from the CRO2 centipede station, in France, near Grenoble. I used a first set of data, recorded on the 11/07/2021 and a second set recorded on 01/06/2023 and stored on renag servers.

For each, I made two calculations. The first calculation is done with NRCAN followed by ITRF to ETRF conversion (at recording epoch and without velocity ) with final conversion from XYZ to Latitude/Longitude/Elevation. Please note that NRCAN results are in ITRF2014 for 2021’s data while in ITRF2020 for 2023’s data. The second calculation is done by IGN/RGP service using the network option (not the PPP option). It is directly providing results in ITRF2014 and ETRF2000.

PROJ is a generic coordinate transformation software that transforms geospatial coordinates from one coordinate reference system (CRS) to another. This includes cartographic projections as well as geodetic transformations. https://proj.org/en/9.2/about.html