dtuuri, in an early post pointed out that a completely new ADF concept that was microprocessor based, did all the thinking inside, had a data base of all the USA broadcast stations, and a fixed but directional antenna, could solve the problem.
Operationally, when you turned on the radio power, and the display came up, input the airport you are on, and it has a fix for a stating point. As you fly, the fix should remain very good. With a database of airports, it would also be capable oe 'direct to' guidance to any airport, or search and display 'Nearest airport'. My old database RNAV LORAN, had this capability, but it is now in the College Park Aviation Museum,
This could pass the resolved position to whatever nav display you have in the same format as GPS, or to a dedicated display for continuous normal navigation.
This might not be limited to either AM, or FM, as identifying with audio would not be required, and the basic frequency would be the only signal needed to pinpoint the direction. Errors of as much as 10 degrees in areas with many stations would be smoothed out by normal surveying algorithms, to provide a position with a precision of a fraction of a mile, and high degree of certainty.
In areas with fewer transmitters, the motion of your aircraft would move the direction of the signal, and processing would gradually pin down an accurate position, and that accuracy would generally continue as long as the unit continued calculating.
Strikefinder technology achieves directional information with fixed antenna, so that technology is readably available. Standard AM has longer range, useful in less populated areas, but there are a lot more FM stations, and at our altitudes, they can be received well outside their normal service circle.
I have lived in the ADF world of home brew approaches, and have flown them in VFR conditions, to make sure that I was aware of the limitations and risks they had. Anybody here heard of he WTOP, or KXEO approaches? Both were popular, in widely different parts of the USA. WTOP morphed into a GPS approach.
Edited to add, the location of the transmit towers is already in a Federal database, Lat/Long/height MSL and AGL. Frequencies are there too.