The electronic systems in an F1 car are heavily regulated, because teams were using ECU tricks to sneakily add traction control. The teams have no choice but to use the limited number of inputs available, because the ECU is a sealed box.

https://www.wired.com/2013/10/red-bull-f1-traction-control/

My suggestion would be to place the car by distance travelled since last leaving the home straight. Use steering + throttle inputs to determine when you are on the home straight, make a best guess at where the start/finish line is, then guess where you are based on distance travelled since last passing it.

Yeah, are inertial navigation sensors and GPS units disallowed?

It seems like they must be, as that'd be the obvious solution. I wonder what the motivation for that rule is, and how soon it'll change.

Ages ago, they had GPS/INS systems and active suspension that would pick the car's tires up over known bumps in the road. They also had a few spectacular accidents possibly related to misbehaving tech of that sort and it also represented a disproportionate chance to spend money in an arms race, so F1 banned much of that. I don't see them likely going back on it.

What are they using to show the track location graphics? I just assumed they must be using GPS.

Could be equipment that the teams don't have access to the data from.

This was for qualifying though, right? Not a race. So irrelevant

I'm really amazed I had to scroll down this far (past the pedantic supercharger/turbocharger nomenclature arguments) to get to someone making this point.