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GNSS satellites (at least GPS ones) are in Medium Earth Orbit (MEO). LEO satellites can use GNSS for positioning. Is this still possible for satellites in elliptical, such as Molniya, orbits? For geostationary satellites, all GNSS satellites will be in a relatively small solid angle (but still much larger than the earth one), but in principle, it should still be possible to use GNSS. How far up has GNSS-based positioning been used, and how does the precision degrade with distance to Earth, theoretically and in practice?

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The furthest satellite that I have seen use GPS is the AO-40, an amateur built satellite. In fact, they did a research paper on the subject. The paper states that it was able to achieve a navigation solution at 60,000 km, which is about 1/6th of the way to the moon, and well beyond the belt of Geosynchronous satellites. I'm sure there are other satellites which have demonstrated this technology even further, but just to receive the signal beyond the GPS constellation is impressive.

It should be stated that this problem is difficult because the GPS antennas are all focused at the Earth, thus, not much radiation extends beyond the GPS constellation. Still, it can be done, if you do it carefully. Furthermore, there are now special receivers for HEO GPS reception, such as can be found here.

There is at least one mission that continues to try to break the record further away, being NASA's MMS mission. They have gone beyond AO-40's record to hit 70,000 km, since I originally wrote this answer.

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    $\begingroup$ Right, I guess GPS satellite antennas are directional, so you'd need to get the signal from the other side of the Earth? $\endgroup$ – gerrit Jul 21 '13 at 0:32
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    $\begingroup$ @ernestopheles I'd be very interested to see these papers... I've never heard this characterization before. $\endgroup$ – user29 Jul 21 '13 at 14:14
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    $\begingroup$ FYI, the link to the HEO GPS receiver is dead $\endgroup$ – Bohemian Aug 3 '15 at 16:53
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    $\begingroup$ Does that mean there is a sort of orbital GPS "Goldilocks zone"? Too close and you're on the wrong side of near satellites, but eclipsed from the far ones by Earth; too far and there is too little signal available, or perhaps angles get too small to derive an adequate solution? $\endgroup$ – Anthony X Aug 3 '15 at 19:04
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    $\begingroup$ You can update your answer now - the record is now 70,000 km! see space.com/34640-nasa-satellites-gps-world-record.html and sciencedaily.com/releases/2016/11/161104190848.htm $\endgroup$ – uhoh Nov 9 '16 at 13:34

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