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Re: navigation math

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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]

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navigation math Hul Tytus <ht@panix.com> - 2021-11-19 20:28 +0000
  Re: navigation math Dennis <dennis@none.none> - 2021-11-19 16:12 -0600
    Re: navigation math Hul Tytus <ht@panix.com> - 2021-11-20 20:45 +0000
  Re: navigation math Grant Edwards <invalid@invalid.invalid> - 2021-11-19 22:54 +0000
    Re: navigation math Grant Edwards <invalid@invalid.invalid> - 2021-11-19 23:03 +0000
    Re: navigation math Don Y <blockedofcourse@foo.invalid> - 2021-11-19 16:28 -0700
    Re: navigation math Hul Tytus <ht@panix.com> - 2021-11-20 20:50 +0000
  Re: navigation math Don Y <blockedofcourse@foo.invalid> - 2021-11-19 16:19 -0700
    Re: navigation math Hul Tytus <ht@panix.com> - 2021-11-20 20:55 +0000
      Re: navigation math Don Y <blockedofcourse@foo.invalid> - 2021-11-20 15:38 -0700
  Re: navigation math Paul Rubin <no.email@nospam.invalid> - 2021-11-19 18:17 -0800
    Re: navigation math Hul Tytus <ht@panix.com> - 2021-11-20 20:59 +0000
  Re: navigation math Robert Roland <fake@ddress.no> - 2021-11-20 14:27 +0100

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