No. In the current SI, Planck's constant and the speed of light are defined, fixed constants, not subject to measurement. You use those definitions to reduce measurements to a comparison of time to that kept by a cesium clock.

@JohnDoty that is indeed the point. You do experiments, like the photoelectric effect, black body spectra, or a Kibble balance, that previously measured Planck's constant, and now they measure the mass in kilograms instead

What you're saying is quite misleading. The SI, for historical continuity, chose definitions compatible with previous measurements, but there was no physical or mathematical requirement to do so. At the present time, it is literally meaningless to measure the speed of light or Planck's constant within the SI context. So your statement that reproducing the meter and kilogram "requires a measurement of Planck’s constant [and] the speed of light" is false and profoundly misleading.

@JohnDoty said "At the present time, it is literally meaningless to measure the speed of light or Planck's constant within the SI context" That is a good point. I have revised the statement to be more clear about my intention.

What historical measurement of the speed of light corresponds to using GPS to measure distance?

Any one-way measurement of the speed of light using synchronized clocks

Not a common sort of method for measuring the speed of light. But if you ignore all physical reality in the experimental protocol, you can find an experiment vaguely analogous in the abstract mathematics (which one?). The problem is, physics isn't abstract, it's physical. In an experiment, the machinery and the protocol matter.

I am not sure what you are complaining about. You made the correct point earlier that it is meaningless to talk about measuring c or h in the current SI. I agree with that point and edited my answer accordingly. However, it is an historical fact that previous experiments did measure c and h (using previous versions of the SI). Those same experiments now are still experiments. They now measure distance or time or mass rather than c or h. That is experimental fact, not abstract math

They are not the same experiments. Nothing like GPS was ever used to measure c. Nobody uses Fizeau's toothed wheel to measure distance. In some cases, the experiments used similar machinery, but the experimental designs, protocols, error analysis, etc. were different. That is experimental fact.

I still don't know what you are complaining about. You are the one who brought up GPS. So don't complain to me that you brought in a weird example. That the protocols and analysis is different is trivially obvious since you are getting a different number in the end. So I don't get your objection.

There is nothing weird about GPS: it's an extremely commonplace example of using a clock-based method to measure space. Protocols and analyses aren't trivia: they are crucial parts of experiments, the foundations of physics.

It is a weird example in the context of historical measurements of c since it was not historically used for that purpose. I am not going to read a whole book to try to understand your complaint.

You make my point. You said "To reproduce the meter ... from the definitions requires performing experiments that historically would be considered as measurements of ... the speed of light". But GPS reproduces the meter from the definition, principally using the "master" cesium clock at USNO, and, as you say, nothing like it was ever used to measure c.

Ah, I see your point. But I am ok with my wording. Although the GPS was never historically used to measure c, if you used the historical SI it could indeed be used for that purpose. The same as any other one-way measurement of c using synchronized clocks. At least now I finally understand your objection, but I just don’t agree that it is a problem

"The same as any other one-way measurement of c using synchronized clocks." What historical experiment is anything like GPS?