Dale, you do have an 'inquiring' mind... just go read stuff... a lot of the info comes from the reference I mentioned at the top of the PDF.... that article is cited in the Blitzortung Project manual, so it's not an obscure publication.... there are other things out there... just search for them. Now, I don't know exactly how many of the principles the developers are actually using, or planning to use, and I strongly suspect there are some innovative new approaches being applied, or about to be used, that are not presently in literature. I do know a few things that have been mentioned specifically that I noted, and some is 'suspicion'.
Don, I don't understand the 'regression' to zero slope... I've not studied that, and am not a mathematician... for now, I'm thinking that it's where the different frequencies' phases are 'added' together until they flatten out to either 'zero' or a perfect square wave, with no slope... and that would give a pretty exact time difference from the original first trigger time, which can then be compared to arrive at a much more precise time of actual stroke.... I'm not sure it works with the 'peak' of any single frequency, but the 'group' of frequencies. If you look at the e field signals, you can see points where the three frequency band signals attempt to get rising or falling edges 'in sync' instead of the initial phase shifts between them at first reception. I think that might be a hint at what the math is doing, much faster... computing a point where they all level out together. I need to think back into my old ECM days, but I think some sophisticated tracking radars do something similar...
I don't have access to the Book written by Watt, and could not find a fast reference when I was writing those thoughts. I believe the discussion there refers to 'group velocity' and centers around 'skywaves' rather than ground waves. I think it's referring more to the Ionosphere layers' different thicknesses and altitude day vs. night, and the effect that has on certain frequencies...and which Ionospheric region reflects them. I can see an easy 10 mile+ timing error occurring as the Ionosphere changes in altitude and strength, if we're just triggering on the first pulse's arrival. Station A gets a ground wave pulse, and station be gets a reflection... over simplified a bit, say the pulse has reflected and travelled an extra 10 miles to get to B.... and arrives considerably later than would be expected if a straight line.