On Feb 23, 12:49 pm, koobee.wub...@gmail.com wrote:
> On Feb 20, 4:33 am, "Jon" <jon8...@peoplepc.com> wrote:
>
> > Supposing three satellites transmit signals with time stamps that are picked
> > up by a receiver.  If the clocks on the satellites are closely synchronized,
> > then
>
> > |AD|=|AB|+t_AB
> > |BD|=|BC|+t_BC
> > |CD|=|CA|+t_CA
>
> > Where
> > A,B,C=position vectors of three satellites
> > AB,BC,CA=distances between satellites
> > t_AB,t_BC,t_CA=time differences between signals at D.
> > D=position vector of receiver.
>
> > Once |AD|,|BD|,|CD| are found, the coordinates of D can be derived.
>
> > Is this how it is done?
>
> > summarized at
>
> >http://mypeoplepc.com/members/jon8338/math/id8.html
>
> 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.

Currently, only Block IIR satellites are capable of autonomous
position monitoring and synchronization independent of the ground
control segment. This capability allows Block IIR satellites to
mutually correct their clocks and ephemerides information for a
period of up to several months should the ground segment be
knocked out by, say, nuclear war. For optimum performance under
non-wartime conditions, "ground truth" comparisons are still
performed on a daily basis to correct the satellites for drift.

GPS satellites before the Block IIR series are incapable of such
mutual correction, and require monitoring and daily corrections
by the Ground Segment.

Satellite control requires that the Space Segment and Ground
Segment clocks be synchronized. The only practical way of
synchronizing the world-wide network of ground stations is to
use the network of GPS satellites to disseminate time. The only
way to use the networks of GPS satellites to disseminate time is
if the satellite clocks are adjusted via the GR correction so
that they beat in time with Earth clocks.

Jerry