When they say "may vary", they mean by a fraction of a degree! Astronomers care a lot about precisely accounting for atmospheric refraction because if you want to look at a specific star or whatever, it kind of matters that you point your telescope in exactly the right direction. But for just pointing a solar panel roughly towards the sun, the simplified model from that site should be more than sufficient.
Only if the additional cost and complexity of such a setup is worth said cost. It can also be used to move the panels into approximately the correct location then allow the other techniques to fine tune it. If the more complex systems have a fault it may be possible to fall back to the more simple method which, while probably not as good, would be more efficient then just a static panel.
You're forgetting about orientation (and altitude)? The observed position also varies a bit with air pressure and temperature, but iirc that's less than a few degrees.
Anyway, you grab yourself a nice ephemeris library like skyfield, do a little bit of your_location.at(now).observe(sun).apparent().altaz('standard'), and there's your angles.
The trickiest part might be getting an accurate time on whatever cheap controller your using.
Radio time signal stations broadcast time and I would hope it would be cheap enough as we have radio controlled clocks, that do not cost a fortune. Otherwise a small battery and a RTC would be enough and probably a better solution.
A GPS receiver can be had for like $15 these days. That will give you time and position, and require less maintenance than an RTC.
Of course, a $15 receiver might not have the best sensitivity, so reception might actually be a practical concern. On the other hand, you only need 4 satellites for a coarse fix, and you could seemingly tolerate a many minute cold fix time.
Comments are speaking to it like it wasn't even addressed. Do you need data to understand that moving a cell out of a shadow would increase its capacity?
If that's the core proposition, yes, I want data on it. If that data is obvious and boring, then so is the proposition.
Besides, the panel can't move, only rotate and tilt. Have you actually read the article?
(With rotate and tilt only, pointing directly at the sun should maximize the power output from a single panel even with shade from other objects. You can get a very small amount of movement from the fact that the point of rotation is outside of the plane of the panel. But that's not mentioned at all, is it?)
In any case, if you solve a problem with machine learning that already has a non-machine learning solution, you will get this kind of comment. If on top of that you don't compare the existing solution and yours and show that yours significantly improves performance, it just looks like doing ML for the kicks.
Here is how they do it. https://gml.noaa.gov/grad/solcalc/calcdetails.html