From: dank@micrologic.com (Dan Kotlow)
Subject: Re: GPS math
Date: Thu, 18 Jan 2001 06:46:48 GMT
Newsgroups: sci.math
Summary: How does the Global Positioning Satellite system compute locations?

GPS doesn't work the way you assume -- the electronics does not
measure the travel time differences between satellites.  The
earthbound navigation system called LORAN works that way.

Roughly, the satellites issue their signals at known times, and the
receiver notes when they arrive.  The receiver almost never has a
sufficiently accurate clock, however, so its own time is another
unknown to be solved for.  Four satellites (at least) are therefore
needed.

In practice, there are many effects that need to be taken into
account, and there is more information in the signals that can help.
It is a very complicated business.  See the Trimble website for the
basics, or the book by Strang and Borre, "Linear Algebra, Geodesy, and
GPS" for more on the mathematics.

-Dan

On Thu, 18 Jan 2001 04:39:59 GMT, jong7117@my-deja.com wrote:

>For the math to find global position from satellites and other weird
>stuff, visit me at,
>
>http://www.geocities.com/jongiff2000
>
>
>
>Sent via Deja.com
>http://www.deja.com/
==============================================================================

From: jamesrheckman@gateway.netnospam (Jim Heckman)
Subject: Re: GPS math
Date: 18 Jan 2001 10:15:01 GMT
Newsgroups: sci.math

>From: dank@micrologic.com  (Dan Kotlow)
>Date: 1/17/01 10:46 PM Pacific Standard Time
>Message-id: <3a668cbd.3853336986@news.ma.ultranet.com>
>
>GPS doesn't work the way you assume -- the electronics does not
>measure the travel time differences between satellites.

??? I can't figure out what on Earth you mean here. GPS most
certainly does work, at the coarsest level, by measuring travel
time differences between satellites. Maybe you meant that this
is typically done by software, not the "electronics". :-/

>The
>earthbound navigation system called LORAN works that way.
>
>Roughly, the satellites issue their signals at known times, and the
>receiver notes when they arrive.

Correct.

>The receiver almost never has a
>sufficiently accurate clock, however, so its own time is another
>unknown to be solved for.

Correct.

>Four satellites (at least) are therefore needed.

Or some other constraint, such as a known altitude. E.g., by
assuming that one is constantly at sea level -- true for many
applications -- one can get by with just 3 sats.

>In practice, there are many effects that need to be taken into
>account, and there is more information in the signals that can help.
>It is a very complicated business.

All very true.

>See the Trimble website for the
>basics, or the book by Strang and Borre, "Linear Algebra, Geodesy, and
>GPS" for more on the mathematics.

-- 
 
Jim Heckman