I wonder if this can be used for navigation? At the very least, for sanity checking GPS data.

20th-century navigation used to operate like that, except using artificial radio sources—fixed beacons. I guess you could answer a lot of technical questions by looking at OMEGA, which, similar to lightning-generated RF, used the VLF range (3–30 kHz), and had global range bouncing off the ionosphere,

https://en.wikipedia.org/wiki/Hyperbolic_navigation ("Hyperbolic navigation")

https://en.wikipedia.org/wiki/Omega_(navigation_system) ("Omega (navigation system)")

> "OMEGA was the first global-range radio navigation system, operated by the United States in cooperation with six partner nations. It was a hyperbolic navigation system, enabling ships and aircraft to determine their position by receiving very low frequency (VLF) radio signals in the range 10 to 14 kHz, transmitted by a global network of eight fixed terrestrial radio beacons, using a navigation receiver unit. It became operational around 1971 and was shut down in 1997 in favour of the Global Positioning System."