Path: csiph.com!weretis.net!feeder6.news.weretis.net!panix!.POSTED.panix2.panix.com!not-for-mail From: Hul Tytus Newsgroups: comp.arch.embedded Subject: Re: navigation math Date: Sat, 20 Nov 2021 20:55:49 -0000 (UTC) Organization: PANIX Public Access Internet and UNIX, NYC Message-ID: References: Injection-Date: Sat, 20 Nov 2021 20:55:49 -0000 (UTC) Injection-Info: reader1.panix.com; posting-host="panix2.panix.com:166.84.1.2"; logging-data="4175"; mail-complaints-to="abuse@panix.com" Xref: csiph.com comp.arch.embedded:30917 Don - At this point just the basics are of need, but the various subleties are worth looking at. Thanks. Hul Don Y wrote: > On 11/19/2021 1:28 PM, Hul Tytus wrote: > > Anyone know the method for calculating a reciever's position from the time > > difference between three rf pulse transmiters of known positions? This has > > apparantly been in use since the second world war but a description of the > > mathematics involved is hiding. Maybe a text on navagation methods? > You will be dealing with families of "concentric" hyperbolae > (as the equation for a hyperbola involves maintaining a constant > difference between lengths of vectors to foci). > LORAN was renowned for using this -- on a global scale. It has > since been decommissioned in the wild but there's an abundance > of information regarding its use and deployment. > Note, however, that there are many subtleties buried in the > LORAN implementation that make it differ from a theoretical > approach. E.g., there are intentional delays introduced > to make the numbers cleaner. > If you are truly looking to navigate on a *large* scale > (hundreds of miles), then you will have to consider things > like changes in propagation delays over different types > of terrain and the "shape" of that terrain (e.g., the Earth > is an oblate sphere). Again, LORAN has these covered but > you'll have to dig for details. > Similar problems exist "in the small" for position > resolution within a structure! (I use similar technology > to determine where, in an "arena" -- home or office, in > my case -- the user is sited) > [If you look at a preprinted maritime map augmented with > LORAN "lines of constant time difference", you'd see > that they differ from what you would otherwise expect > from a more naive mathematical/geometric treatment]