Topic: Lightning location computation based on Blitzortung received signal TOGAs

[CF20852]

I was reorganizing some files a few weekends ago and found some old program listings for LORAN-C and Transit satellite navigation programs I wrote back in the late 70's and early 80's.  I decided to see if I could write a version of the algorithm for finding the location of a lightning stroke given an initial guesstimate of the stroke location and time-of-group-arrival (TOGA) measurements from several (up to 15) receivers.  I decided to put it in the form of a macro-enabled Excel 2010 workbook, with the algorithm implemented as Visual Basic for Applications (VBA) macros.  I posted a writeup and the spreadsheet at https://github.com/CF20852/Lightning-Location-Algorithm .  It's not what I'd call production-ready code by any stretch of the imagination, but it works as a pedagogical aid.  Note that it works a little differently than the Blitzortung documentation says the algorithm the Blitzortung servers use.  The Blitzortung documentation says that their system is based on the computation of hyperbolic curves, in other words, based on the differences in times of arrival of the lightning signal at several stations.  I decided to base my version on times of group arrival per se, rather than differences in times of group arrival, which means my algorithm also solves for the time the stroke occurred in addition to its latitude and longitude.  Strokes and folks, as they say... (sorry).

My thanks to Bob, Station 1189, Clifton, for helpful comments about the organization of the writeup.

Chip, Station 1093, North Bethesda

[Cutty Sark Sailor]

Another algorithm you might have overlooked would be the TOGA, and the zero crossings of the sferics pulse trains.  I'm not sure how many iterations Egon et.al. process to compare expected vs actual timing, and it's not fully implemented, since, especially in some areas, there is a lack of overall signal quality. I suspect it will be fully implemented with the next generation systems. RED should be able to be processed that way... one issue is high gains and too many skywaves from distant sferics for most stations to record with accuracy.  Answer? Back off gain, dense number of stations operating with much less 'distant' reception.  In other words, as a network, rather than a single station.
Zero Crossings illustrated here...: Note it's looking at pre-discharge, and post discharge signals.

[CF20852]

Thanks, Mike,

I have read the paper by Dowden, Brundell, and Rodger (http://wwlln.net/publications/dowden.toga.article.pdf) describing the time-of-group-arrival (TOGA)  algorithm a couple of times.  The TOGA algorithm is used to determine the precise time of arrival of the lightning waveform at the receiver.  The algorithm I describe could be used in the next step of locating the lightning strike, which is computing its position based on the information generated by running the TOGA algorithm on the stroke signals received by several non-co-located receivers.

Incidently, in Section 1.2 of their paper, Dowden et al describe the algorithm they use to locate the lightning stroke once the TOGA algorithm has done its thing as the "downhill simplex method," and mention that the algorithm typically requires about 100 iterations.  The least-squares algorithm I describe typically achieves a solution in five or six iterations, even if the initial guesstimate of stroke location is hundreds of miles off.

Chip

[CF20852]

After I posted this yesterday (January 2, 2015), it occurred to me that some folks might wonder about the advantages/disadvantages of the range-range least-squares algorithm versus the hyperbolic least-squares algorithm.  So I took a few hours today to add the hyperbolic algorithm code to the Excel 2010 VBA macro code, and restructured the spreadsheet accordingly.  I also updated the readme file with a brief discussion of the advantages/disadvantages of the hyperbolic algorithm.  See https://github.com/CF20852/Lightning-Location-Algorithm for details.

Chip

[CF20852]

One additional thought, stimulated by Mike's post above:

If you could determine the quality of the output of the TOGA measurement for each lightning receiver, you might be able to use a technique called "weighted least squares" to improve the final stroke location estimate.  There's an article on Wikipedia about least squares that includes a section on weighted least squares; you can find it at http://en.wikipedia.org/wiki/Least_squares#Weighted_least_squares .  A fairly obvious factor that might make one want to weight a particular station's measurements lower, at least on one channel, is the presence of strong interference at that station.  That's pretty easy to detect in the spectra of the received signals.  (Sorry, you guys near Fort Collins, Cutler, Jim Creek, etc.) 

I stopped working in the navigation field in the early 1980's, and it would take me some time to get up to speed on weighted least squares.  Moreover, I want to spend my remaining use-or-lose leave time on another hobby project.  I have an idea of how I'd modify my Excel VBA code to test the implementation of weighted least squares suggested above that I'd be willing to share, though.

A final note:  I haven't had any discussions with Egon, Richo, or Tobi about any of this, so I have no idea of what algorithms they're using (other than TOGA).   I don't have a lot more time to spend on this.  I just wanted to refresh my memory on the least-squares technique, see if I could modify it for a system like the Blitzortung system, and get it to the point where I could share it with my fellow hobbyists.

Chip

[davidgamble]

Great stuff Chip.
I see that LORAN is making a come back in the UK. If the GPS satellites are knocked out by a "Carrington Event" (Solar mass ejection) then the plan is to use LORAN as a backup. Good luck! If we get another Carrington Event then my guess is that everything will get cooked.