I believe it's now usually a combination of multiple sources (e.g. ground-based navaids like VORs and DMEs, GNSSs/GPS, and INS to reject most spoofed signals or in case everything else fails).
But, as it always was, it is regularly corrected with GNSS or navaid corrections. As far as I know most airliners still don't automatically enter corrections for INS and require manual input (basically retyping of GNSS data from a screen into a keypad) to put human into the loop which can verify if GNSS is being spoofed. The pilots can alternatively do the correction using VOR/DME navaids or even their eyes if they feel like it.
As far as I know, it's becoming much more common to have INS with ability to automatically correct drift from GNSS in smaller planes (and I'm sure that will make it to airliners sooner than later).
However the autopilots inner loop and Flight Direction Indicator (artificial horizon) are going to be driven almost entirely by INS. This is because GPS positions can't update fast enough, are noisy, and don't provide velocity, acceleration, or orientation (outside of even slower position integration). Also those systems are not particularly involved in where the aircraft is, rather they care about where it is going.
I haven't looked into what the requirements of ADSB position information is, I don't suspect that they mandate GNSS but they may mandate a degree of accuracy. From an ATC perspective within crowded airspaces ADSB would be augmented by primary surveillance radar to prevent mishaps, spoofing, and errors.
For what it's worth my day job is aircraft avionics, navigation equipment is pretty much daily for me.
Ps. Hi HN, Reddit refugee and my first post here.
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I suspect much or all of the data boradcast is GPS derived. Would be nice to have some hard data there.
For almost all general aviation aircraft in the USA the data source for ADS-B Out is GPS. All the GA STCs I've seen are GPS only position sources. Many modern GA aircraft will have AHRS but not a full INS, and so INS is not an option for them. Even on larger business jets that may have INS with GPS integration I am not clear any actually use it to drive ADS-B Out, the few installations I've looked at were all GPS.
Boeing was an early advocate for GNSS alone driving ADS-B Out. I think their argument was simplicity, everybody has the same data, and not dependent on erroneous INS or INS settings. I'm not sure what they ended up doing with all their actual installations. If the intent is to send more exotic data such as roll-angle they'll need some INS or at least AHRS integration, but there is no requirement to broadcast that data. The few early third party STCs I saw for ADS-B Out installations in Boeing aircraft only used GPS data sources.
