3 point navigation

   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?

Hul

On Fri, 19 Nov 2021 20:32:34 -0000 (UTC), Hul Tytus <ht@panix.com>
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?

Hyperbolic navigation.  

.<https://en.wikipedia.org/wiki/Hyperbolic_navigation>

Joe Gwinn

On Fri, 19 Nov 2021 20:32:34 -0000 (UTC), Hul Tytus <ht@panix.com>
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?
>
>Hul

The old terms and tech (i.e. LORAN) have changed since WWII.
Hyperbolic navigation is still with us, but with the advent of
cellular and ADS-B, it's now called MLAT (multilateration), TOA, TDOA
(time difference of arrival), or a multitude of other term.  Note that
the GPS system uses the flight time between the GPS receiver and the
known positions of at least 3 GPS satellites.

These should supply a list of buzzwords to research:
<https://en.wikipedia.org/wiki/Multilateration>
<https://en.wikipedia.org/wiki/True-range_multilateration>
<https://www.sciencedirect.com/topics/engineering/multilateration>

-- 
Jeff Liebermann                 jeffl@cruzio.com
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Skype: JeffLiebermann      AE6KS    831-336-2558

On Friday, November 19, 2021 at 4:32:40 PM UTC-4, 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? 

The only parameter you can determine without a highly directional antenna is the difference in arrival time which places the transmitter on a hyperbola with two receiving antennas at the foci.  Add a third antenna and you get intersecting hyperbolæ which will resolve the transmitter's location to a point.  

But you are asking to locate a receiver from the time difference of arrival of known transmitters.  Same problem with the transmitters at the foci.  I believe this is the basis of locating a commercial aircraft based on the TACAN signal.  

The math is just algebra and trig, solving simultaneous hyperbolic equations.  I think two baselines give you only two points as solutions and the remaining baseline resolves between those two. 

-- 

Rick C.

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