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Date: Tue, 24 Feb 2009 05:16:45 +0100
From: "\\frac{1}{R}\\sqrt{\\frac{L}{C}}" <bla@bla.org>
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Subject: Re: GPS question
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koobee.wublee@gmail.com wrote:
> On Feb 23, 11:09 am, PD <TheDraperFam...@gmail.com> wrote:
>> On Feb 23, 12:49 pm, koobee.wub...@gmail.com wrote:
> 
>>> You need four satellites where each satellite should know its time and
>>> position.  Time can just be a counter with all the satellites
>>> synchronized to within a count of each other.  Each satellite then
>>> just broadcast its time and position information as almanac signal to
>>> whoever wants to receive it.
>>> Since the distance is traveled by light with a known speed, you can
>>> then easily form a set of four equations with four unknowns.  The four
>>> unknowns are your time (relative to the counter in each satellite) and
>>> position.
>>> **  c^2 (t1 – t)^2 = (x1 – x)^2 + (y1 – y)^2 + (z1 – z)^2
>>> **  c^2 (t2 – t)^2 = (x2 – x)^2 + (y2 – y)^2 + (z2 – z)^2
>>> **  c^2 (t3 – t)^2 = (x3 – x)^2 + (y3 – y)^2 + (z3 – z)^2
>>> **  c^2 (t4 – t)^2 = (x4 – x)^2 + (y4 – y)^2 + (z4 – z)^2
>>> Where
>>> **  (t1, x1, y1, z1) = Time and position of satellite 1
>>> **  (t2, x2, y2, z2) = Time and position of satellite 2
>>> **  (t3, x3, y3, z3) = Time and position of satellite 3
>>> **  (t4, x4, y4, z4) = Time and position of satellite 4
>>> **  (t, x, y, z) = Time and position of the receiver
>>> Notice that relativistic effect is never needed.
>> Except that t1, t2, t3, and t4 are Earth-referenced times, not the
>> native time of the clocks on the satellites, which are t1', t2', t3',
>> t4'. To get from t1', t2', t3', t4' to t1, t2, t3, t4, the satellites
>> have programmed in a correction that comes from understanding
>> relativistic effects.
> 
> There are two ways to synchronize t1, t2, t3, and t4.  Ground-
> satellite synchronization introduces much more errors than satellite-
> satellite synchronization.  The latter does not have the ionosphere
> and other atmospheric anomalies to consider.  That latter also does
> not have high speed to worry about since all satellites are either at
> rest or moving very slowly relative to each other.
> 
> For precision GPS design, one must use the satellite-satellite
> synchronization.  In doing so, there is no relativistic correction
> needed in the design.  <shrug>
> 
> 

You don't need satellite to satellite synchronization in GPS, although
the newer satellites have this capability (block III i think they are
called, these guys could operate independently for a while)

Since the 70's any single GPS satellite in orbit is tracked with a few
stations on ground forming a ground segment.

In this way you get the orbit of the satellite, a master oscillator at
just one tracking station is good enough to synchronize all satellite
clocks to the same time system.

Q

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