It’s an interesting approach using the envelope of the tilted vertical lobe. I haven’t made any calculation of the possible accuracy but I think it has been used so it probably works, but I’ve failed to find any source. Probably described by P J D Gething in his book “Radio Direction-finding and the Resolution of Multicomponent Wave-fields” but I hesitate to buy it due to the high cost and that it is very theoretical.
Obviously there are three ways to go: https://books.google.se/books?id=qdWUKSj5PCcC&pg=PA93&lpg=PA93&dq=vertical+angle+measuring+radio+lobe&source=bl&ots=4v2fCxDwr9&sig=HMKM1J_7iAsmDmNn-f_OQ5rUzx4&hl=en&sa=X&ved=0ahUKEwjpg42354PSAhWEFZoKHbYVA1oQ6AEIIDAB#v=onepage&q=vertical%20angle%20measuring%20radio%20lobe&f=false
Another practical solution was used by Dr Harry Whale in New Zealand (and probably others) in the fifties and sixties. There were two short dipoles at the tip of a rotating bar and the system was an Interferometer. Described here http://www.qsl.net/zl1bpu/IONO/iono101.htm
. I’ve failed to find any description of the system. Of course one thinks of the possible use of an electronically rotating antenna like in Doppler RDF systems.
A third system is using three Orthogonal loops described here http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.486.1746&rep=rep1&type=pdf
. No description of the “inner workings” found.
And of course the Rohde & Schwarz way:https://cdn.rohde-schwarz.com/pws/dl_downloads/dl_common_library/dl_news_from_rs/155/n155_ddf01x.pdf
73, Roland SM0BRF