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[aprssig] How gps works

Stephen H. Smith wa8lmf2 at aol.com
Sun May 6 04:28:34 UTC 2012

On 5/5/2012 11:21 PM, Andrew Rich wrote:
> Hello
> I am learning how gps works
> I understand that gps satellites contain accurate clocks
> How does the receiver know the distance to the bird ?

Basically, the very simplified concept:

1) All the super-accurate atomic clocks in all the satellites "tick" in 
unison.    These "ticks" are "broadcast on spread-spectrum signals at 1575 MHz 
(for the civilian GPS service).  The signals for all satellites are "stacked" 
on top of each other on the same center frequency.  Each satellite uses a 
different spreading code, which allows it's signal to be separated from others 
by the receiver on the ground.

2) The "ticks" for all the satellites travel outward at the speed of light 
(300,000,000 meters/sec --or-- about 300 meters/uSecond --or-- about 0.3 
meters/nanosecond.   I.e. about 1 foot / nanosecond.

3) Each satellite is also constantly broadcasting it it's OWN location.   (The 
US Air Force measures the precise location of each satellite several times a 
day with ground-based radar, and uploads updated orbital data into each 
satellite several times a day, which the satellites broadcast continuously 
until the next update.)

4) The receiver compares the DIFFERENCE in time-of-arrival of "ticks" from 
several satellites.   The receiver, based on knowing where each satellite was 
at the time of the tick, computes the one location in 3D space where this 
particular combination of delays, due to   differing-distances-traveled,    
must be.     Differences of 5 or 10 nano seconds in time of arrival  
(corresponding to delta distance of  1.5-3 meters) are quite easily measured 
with basic logic circuits.

5)  Comparing the DIFFERENCE is easy; having a reference clock in a cheap 
device, not endowed with a rubidium time standard, that can provide the 
ABSOLUTE time to compare to, is not.   Instead GPS receivers "cheat" by using 
the ticks from one satellite as the triggering absolute time reference, and 
then compare three or more others against the first one.

Compared to a reference time, the delay for a SINGLE satellite says you must be 
somewhere on the surface of a sphere of approx 10,000 miles radius from that 
satellite.    (GPS satellites orbit about 10,000 miles above the earth's surface.)

Measuring the delay for TWO satellites will define two intersecting spheres. 
You must now be somewhere on the circle where the two spheres intersect.

Measuring the delay for THREE satellites will define three intersecting spheres 
where only two unique points will match the time delays observed for all three. 
   One of these will be an obviously impossible solution because it is located 
deep inside the earth, which leaves a single point that is your location.

> Does it look at the pattern coming from the gps sat ?
> Can it work out when comparing the code from others sats to know the difference in time between the different birds, much like trying to line up a set of rulers ?
> What does sending empheris data do to help ? Does that help the receiver picture the constellation ?

More or less.  This is how the receiver "knows" where each satellite is at a 
given instant.

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