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Suppose I have a GPS unit attached to an antenna through a 50 meter coax cable.

How would the location as calculated by the GPS unit be affected by the cable length? As a bonus question, how would the time accuracy of the GPS be affected by the cable?

David Gardner
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    I'm doubtful there'd be much signal left at the end of 50m of coax at 1.5GHz, unless it's really good coax. – gbarry Jul 01 '15 at 06:55
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    @gbarry: It depends on the antenna, most datacenter grade gps disciplined oscillators have antennas that mix down the signal so you can run up to 300m of cable. – PlasmaHH Jul 01 '15 at 08:35
  • We use 100 m cable with active amplifiers for GPS – User323693 Jul 01 '15 at 08:49

4 Answers4

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The exact position is the phase center of the antenna independent of the length of the cable and location of the chip.

The time delay has to be calibrated by measuring the delay of the cable for the band. (L1 band). Many GPS receivers provide option to key in the delay parameter.

Nicolas Raoul
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User323693
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    Cable delay could be calibrated, calculated or ignored depending on timing requirements. I'd say most commodity receivers jitter enough not to go beyond a simple cable delay calculation. – Eugene Ryabtsev Jul 01 '15 at 08:52
  • @Eugene Yeah. That is subjective. – User323693 Jul 01 '15 at 08:55
  • No one stated this was a commodity receiver. This could be a static installation which would be for a differential reference station of a time-source. That would usual mean a high quality receiver is in use and the delays for the cable would be noticeable in the calculations. Additional delays could suggest you are ~cable length lower. GPS is a generic term could mean NAVSTAR, GLONASS or Galileo systems (usually NAVSTAR in the engish speaking world). GLONASS uses different frequencies so phase repose of cable should have significant effects too. – TafT Jul 01 '15 at 09:25
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    @TafT GPS is GPS from US. (https://en.wikipedia.org/wiki/Global_Positioning_System) GNSS refers to all in general. – User323693 Jul 01 '15 at 09:33
  • @Umar as hard as the industry tries for that to be the case I am not sure most end users realise the distinction. That did not matter in the past but as GLONASS receivers are now present in many mobile phones (& presumably other consumer grade products) it could be significant. – TafT Jul 01 '15 at 10:05
  • Please could @David-Gardner confirm he was thinking specifically of the US GNSS system which uses the NAVSTAR constellation or if he meant any system that a GPS Receiver (which is really as GNSS receiver) might use? – TafT Jul 01 '15 at 10:05
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Cable delay adds an equal offset to the pseudoranges for all satellites. Since GPS uses the difference in the pseudoranges to each satellite to calculate the position, positioning isn't affected by cable delay.

The position calculated will be at the antenna, not at the receiver, which you can see by realizing that moving the antenna has a different effect on the pseudoranges to different satellites due to geometry, but moving the receiver has no effect at all (the cable length stays the same and so does the cable delay).

The time calculated by the GPS receiver will have an error equal to the cable delay, which is the length of the cable divided by the propagation velocity of the cable. The RG174 commonly used on "puck" antennas has a velocity of 0.66 c, which is about 5 nanoseconds per meter.

hobbs
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    I liked your answer but it seems to contradict @umar - any thoughts? – Andy aka Jul 01 '15 at 07:38
  • @Andyaka: where does it contradict? It seems both say its at the antenna and there is a time delay due to cable length. – PlasmaHH Jul 01 '15 at 08:39
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    The position is that of the antenna. The time is that of the signal arriving at the antenna plus a delay down the cable. – pjc50 Jul 01 '15 at 08:47
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    @PlasmaHH if the position is determined by the ratio of two (or more?) signals at the antenna then why should taking into consideration the cable's time delay matter. That's the contradiction as it appears to me. – Andy aka Jul 01 '15 at 09:39
  • @Andyaka: "positioning isn't affected by cable delay." is what this answer says. Or maybe I am not seeing what you do and you can quote two contradicting sentences? – PlasmaHH Jul 01 '15 at 09:49
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    @Andy GPS receiver gives both position and very accurate time. Time information gets affected by cable delay, but not the position. Hope i have understood your point. – User323693 Jul 01 '15 at 10:40
  • @umar - that makes complete sense. – Andy aka Jul 01 '15 at 10:40
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    Point worth noting about "GPS time": _Since GPS time does not adjust for leap seconds, it is ahead of UTC(USNO) by the integer number of leap seconds that have occurred since January 6, 1980 plus or minus a small number of nanoseconds. However, the time offset from UTC is contained in the GPS broadcast message and is usually applied automatically by GPS receivers._ Source: http://www.nist.gov/pml/div688/utcnist.cfm – Floris Jul 01 '15 at 20:49
  • @Floris The time correction happened this week. :) – User323693 Jul 02 '15 at 02:02
  • @Umar - actually, the "correction" that happened was the addition of another leap second, making the difference with GPS time even worse. But I just checked - even my cheap GPS knows what the right time is... despite the increasing difference. – Floris Jul 02 '15 at 02:56
  • @FLoris The correction has nothing to do with the accuracy of time and position. Every GPS knows whats the difference and correct them in the firmware automatically. – User323693 Jul 02 '15 at 03:13
  • @Umar my point was that "GPS time" is different than UTC time although an internal correction is made. So while a GPS can accurately report UTC it does so by not reporting GPS time. Oh never mind. – Floris Jul 02 '15 at 03:55
  • @Andyaka In the second sentence: "GPS uses the *difference* in the pseudoranges [emphasis original]". This statement is incorrect. GPS uses time of arrival (ToA), not time difference of arrival (TDoA). – Nick Alexeev Jul 02 '15 at 21:07
  • @NickAlexeev if you added a constant to the time transmitted by every SV, no receiver would report a different position, only a different time. Receivers don't generally have an external time reference outside of GPS. That's a degree of freedom, and it means that whatever you want to call things, it's only the differences that matter in an ordinary positioning application. – hobbs Jul 02 '15 at 21:23
  • @NickAlexeev (that said, a GPS receiver attached to an accurate atomic clock could eliminate one degree of freedom and get a 3SV 3D fix, in theory at least) – hobbs Jul 02 '15 at 21:25
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As already mentioned, the position is determined by differences in signals received by the antenna. So the cable and chip will be irrelevant for that.

However, when it comes to timing things get tricky.

As mentioned, you can calculate how long it takes for your signal to travel through the cable and correct for that, but when I did an experience a few years ago, we actually found the variability in timing to be in the order of microseconds.

So you can correct a few nanoseconds for your theoretical cable delay, but in practice the uncertainty in timing may be much larger.

dennis
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    The uncertainty is mostly determined by whatever you use to calculate the time. The time information in the analog signal is clearly a lot more accurate than microseconds or the whole location thing would never work. Your receiver and whatever you use to check the times (actual computer running a non-real-time OS like Windows or Linux, maybe?) however may very well introduce uncertainties in that range. If that is what you use, correcting nanoseconds might really be in vain. If your timestamp consumer is something faster (FPGA, analog) it might not be. – DeVadder Jul 02 '15 at 13:50
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Although I agree that the phase center of the antenna is the calculated position. the real/actual GPS position is affected by the cable length.
A person holding the GPS can move anywhere within a radius of 50m from the center of the antenna and the GPS will not register any difference. Therefore the cable length does affect the accuracy of the GPS position, but because the cable length only causes a signal delay (about 300 ns), it does not affect the signal accuracy!

Guill
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