GPS: what does a satellite send out?
Hello,
A GPS satellite sends out ephemeris and almanac data, on that subjects all sources I've read agree. But it's about the health data, the ionospheric delays, and the offset of satellite clock from GMT that a lot of books disagree. I asume health data is being transmitted by the satellite. The ionospheric delay can only be corrected by differential GPS or by comparing the L1 and L2 signal. So it isn't send out by the satellite. How would a satellite even know what that delay is? And the receiver receives the satellite's clock, and corrects its own internal clock to match that satellite's clock. Otherwise the correction to the receiver's internal clock would become bigger and bigger over time. Am I right about those items? 
I can't give you chapter and verse, but I do know that the GPS constellation is monitored by a 'mission control'. I used to know where this was but can't remember now.
So each satellite is regularly checked for errors, health, clock accuracy, orbital accuracy, etc. and corrections are sent to each satellite via a data link if required. I don't know about the ionospheric delay, but you've said yourself that it can be corrected for by comparing the L1 and L2 signals, so presumably the satellite doesn't need to 'get involved'? 
It's not my area of boffinry, but in 2 minutes on Google I found a load of textbooks on the subject, some readable online.

Regarding if the satellite knows the ionospheric delay:
To some extent it does. How? We on ground are making predictions of how the ionosphere will affect the signal on a particular day. This data is sent up along with the corrections to the satellite. 
Do some reading on WAAS (And EGNOS for Europe).

My impression was ionospheric delay was entirely a DGPS correction. A ground station knows what its position is supposed to be and if the calculation yields another we know the propagation velocity error.

As has been noted, the GPS Signal includes satellite health information.
It is not true that Ionospheric correction is solely the domain of dual frequency or DGPS positioning. The ionospheric delays can be estimated by ionosphere modelling. This ionosphere information is included in the Navigation message and allows an independent (nonDGPS) single frequency receiver to apply ionosphere delay corrections to the received signals. There actually are 2 time corrections encoded in the GPS signal. The clocks in the GPS satellites are very accurate, but not perfect. (cesium and rubidium atomic clocks, IIRC) The errors are small but significant for precise applications. When your measuring stick is traveling at the speed of light, a very small timing error translates to a fairly large distance error. So the GPS signal includes clock correction data for each satellite. And because the GPS system operates in its own time system, which is independent of UTC, the signal includes an offset for GPS time to UTC time. This offset is not constant, as GPS time is a stable atomic based time system, and UTC, while also an atomic time system, is adjusted periodically with leap seconds to keep it close to astronomic time based on the earth's rotation. 
Originally Posted by Ross_M
My impression was ionospheric delay was entirely a DGPS correction. A ground station knows what its position is supposed to be and if the calculation yields another we know the propagation velocity error.

The data that is send down from the satellites is described in the GPS interface specification document: GPS interface specification
You'll find the message specification in appendix II (page 65 and beyond). Parameters of an ionosperic model are transmitted as well, even a single frequency receiver can take it into account. The ionospheric parameters are generated by the control segments and are uploaded to the satellites from the ground stations. The transmitted time and related synchronization is perhaps the most difficult part to understand. GPS is based on the accurate measurement of time. The distance between the satellite and the receiver is determined by looking at the time difference between transmission and reception which after multiplying by the speed of light gives the range. In order for this method to work, the receiver clock has to be precisely synchronised to the satellite's clock. The problem is that, in order to do that, one has to know the distance to at least one satellite in order to take account for the effect of the distance traveled by the signal. It is running in circles. Therefore a slightly different approach is taken. To solve the problem, the mathematical relation between receiver position (lat, lon, h), time offset and the timestamps in the received signals is established. That requires amongst other the almanac and ephimeris data, since these allow the receiver to calculate the positions of the satellites as a function of time. In order to solve a mathematical problem with four uknowns (lat,lon,h,time), at least 4 independent equations are needed. That is the reason that GPS requires at least 4 satellites to work properly (you can do with 3 if you assume you are at the earth's surface). When the problem is solved, you get lat,lon,h and time all at once. Note that aviation GPS receivers require at least 5 satellites. The extra satellite is needed for the RAIM function to work; it basically determines whether the extra measurement is in agreements with the rest. If one of the 5 measurements is wrong, there will be no agreement and the receiver will flag a fault. 
The calculation is also compounded by the fact that the time reference of the satellite is different from the time reference of the GPS receiver.
Not only is the "starting point" of time measurement different but also is the rate at which the time flows. That's relativity. Special relativity states that the satellite clock (tsv in the document) beats slowlier than the GPS receiver clock when evaluated in the GPS receiver reference frame (when evaluated in the satellite reference, it is the opposite ; the GPS receiver clock beats slowlier). (drifting rate ~= 7000 ns per day) On top of that, general relativity states that clocks at the satellite altitude beat quicker than clocks at the level of the ground. (drifting rate ~= +45000 ns per day) In total, the satellite clock is quicker. The exact correction depends on the relative speed of the satellite and GPS receiver, thus on the position of the GPS receiver relative to the satellite trajectory. This is what is computed in equation (2) of page 102. Coefficients af0, af1 and af2 express the dependency to the satellite trajectory and, thus, the 3 first items contain the special relativity correction. The fourth item Δtr contain the general relativity correction. 
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