5 ms·

Does the system rely on knowing the position of the satellites to equivalent accuracy? i.e. "millimetres" accuracy for differential GPS. If so, how is this acc

by jbert 12y ago

Does the system rely on knowing the position of the satellites to equivalent accuracy? i.e. "millimetres" accuracy for differential GPS. If so, how is this accuracy achieved? (Obviously the satellites themselves cannot use gps to determine their position...). Measurement from the ground plus manouvering? Are there any events (micro debris strike, solar wind?) which cause drift in our estimate of their position?

Cthulhu_ 12y ago
From what I understand, GPS receivers synchronize their clocks with those of the satellites; triangulation occurs by comparing the timestamps of three or more sattelites. The deviation, times the speed of light or something, gives the receiver a pretty good indication of how far each satellite is. That should be enough to determine a location.
- jbert 12y ago
  > That should be enough to determine a location. Yes, if you know where the satellites are to the same degree of precision. That's what I was wondering about.
- mikeash 12y ago
  That's the basic idea, but note that it takes four satellites, not just three, because you're fixing your position in four dimensions (three space, plus time). If you had an extremely accurate clock locally then you could get away with just three, but without knowing the precise time, you need an extra satellite to fix time as well as space. Basically, GPS doesn't give you distance to the satellites, but the differences in the distances to different satellites. The signal from one satellite gives you nothing much, two satellites fixes your position on a hyperboloid, three satellites fixes your position on a curve, and four fixes you to a point.
TickleSteve 12y ago
The orbits of the satellites are known to a certain accuracy allowing prediction of where the satellite is at any given point. The accuracy of this almanac & ephemeris data is only valid for a short time in the future (hours to days) but is continuously updated from measurements of the satellites actual position. The ephemeris & almanac data is what is transmitted to the GPS receivers on the ground along with the timing information allowing the receiver to calculate their position. An assisted GPS (A-GPS) system can transmit predicted ephemeris for up to a week ahead to a device and store it allowing very quick start ups (Time-To-First-Fix) presuming that the data is preloaded (avoids having to wait for an almanac &ephemeris download which can take up to 13 minutes). In answer to your question, the orbits are affected by everything from the atmospheric weather which causes deflections in the signals to phases of the moon and the shape of the earth that it is passing over causing small deflections in the satellites orbit. Many factors combine to make orbital predictions very difficult, akin to predicting the weather.
- jbert 12y ago
  Thanks for that, this is really interesting. So - there are ground-based observatories continuously determining the absolute position of the satellites? This seems really hard. The satellites are ~20,000Km up. I think that means a 1 millimetre difference would be a 5 x 10^-11 radians difference (theta ~ tan theta), or 0.0001 arc seconds - surely this is beyond any telescope technology? And even if they could resolve at that level, we're trying for an absolute fix, so we're also trying to measure the alignment of a (moving?) telescope with 0.0001 arc second precision (hoping no mice cough nearby?) That can't be right, so what am I missing? Wikipedia says that there are lots (~13?) stations: http://en.wikipedia.org/wiki/Global_Positioning_System#Control_segment http://en.wikipedia.org/wiki/Global_Positioning_System#Contr... Are there potential issues with them being covered by weather etc? [Ah - found the link to 'http://en.wikipedia.org/wiki/Kalman_filter' http://en.wikipedia.org/wiki/Kalman_filter' - this is probably the magic?]
  - TickleSteve 12y ago
    Yeah, its a really hard thing to do... the ground-segment (Monitor stations) isn't my speciality (I worked on an AGPS system using ephemeris predicition for a year or two) but pretty much everything you can think of affects the accuracy, weather (at multiple levels in the atmosphere), landscape, topology, season (planetary motions),etc. The guys who do the ephemeris prediction model at JPL would know more tho. But the take-away message is, yes, its really hard stuff.
  - VLM 12y ago
    Two ways to do it 1) You have a defined position of your antenna... make the ephemeris "work" such that your antenna gets the right signal from the satellite. In a philosophical sense, where is the satellite? Well... does it really matter? This ephemeris says your antenna is in the right place, so... I'm not implying this is how it work or its a good idea, but it certainly is a good unit test if your "real" method when run thru a test bench implies you're on the moon instead of at the (note singular) base station... 2) Those numbers are no big deal with doppler / frequency ranging. If you transmit at 1500 MHz its a little higher as it approaches and lower as it leaves. Ask a ham radio operator to demonstrate with their 144/440-ish MHz satellites, the doppler in low earth orbit is maybe 15 KHz or so. Anyway sub-Hz accuracy measurement (no big deal) of a 1.5e9 Hz signal for a couple seconds gives you the -11th class of accuracy you're looking for. The absolute freq would be nice to know, but you can figure out the instant the satellite passed zenith (or any other elevation relative to your position) as long as the freq is "short term more or less constant". Of course giant and heavy earth bound clocks can give you that precise freq you're looking for, which is also cool. The doppler of a satellite pass is pleasingly non-linear and they're high up enough so make for long passes and proper data analysis means you can downsample maybe 10000 samples to find the theoretical best RMS zenith instant for all 10000 samples, so oversampling and averaging gives you another couple orders of magnitude. Maybe another way to say it, is if you have basically perfect accuracy clocks, and you sample and literally count every incoming cycle of a 1.5e9 RF signal for only 100 seconds even if you ignore phase data (why would you? But for the sake of the argument...) then thats 1.5e11 cycles in a given time, a bit of division and you have a freq accurate to one cycle or part in 10 to the 11th. Its more complicated in reality because the GPS signal is not a simple RF carrier but is a spread spectrum signal so you need a reasonably low noise and stable PLL to lock onto the SS signal and then you actually measure the SS signal.
michaelt 12y ago
Does the system rely on knowing the position of the satellites to equivalent accuracy? Base stations calculate the satellites' orbital parameters, and estimates of errors due to satellite clock error, and the ionosphere and troposphere, and transmit them to the satellites; the satellites send them on to receivers. The orbital parameters don't perfectly describe everything about the orbits, so they're updated every 30 minutes or so. Back in 2000, the RMS error was about 5m [1], with inaccuracies distributed in such a way that the user equivalent range error was around 2m. It may have improved since then. i.e. "millimetres" accuracy for differential GPS. The orbital parameters transmitted by the satellites are not millimetre-position - but for differential GPS, the same differential approach that can cancel out errors due to the ionosphere and troposphere can also cancel out errors due to inaccuracy in satellite position reports. From the user's perspective, an error due to inaccurate ephemerides looks a lot like an error due to an inaccurate satellite clock or a signal delayed by the atmosphere. If so, how is this accuracy achieved? (Obviously the satellites themselves cannot use gps to determine their position...). Satellites are tracked by a network of base stations at known locations, called the 'control segment' of the GPS system (the other parts being the 'space segment' (satellites) and the 'user segment' (receivers)). Satellite position is tracked by working backwards from the received GPS signal, and the satellites can also be tracked optically (the satellites carry retroreflectors [2] so they can be tracked with special laser range finders). The most recent satellite position measurements are extrapolated forward to work out near future positions, which are then transmitted to the satellites. Are there any events (micro debris strike, solar wind?) which cause drift in our estimate of their position? Loads of things have to be taken into account [3]. From the gravity of jupiter to the fact there are reflected photons on one side of the earth but not the other (the latter is admittedly only 30cm per day). For more information, the satellite orbits are called 'ephemerides' or 'ephemeris' and you'll find lots of info on Google now you know the right keyword to look for! [1] http://gauss.gge.unb.ca/papers.pdf/COSPAR2000.pdf http://gauss.gge.unb.ca/papers.pdf/COSPAR2000.pdf [2] http://gpsworld.com/expert-advice-laser-reflectors-to-ride-on-board-gps-iii/ http://gpsworld.com/expert-advice-laser-reflectors-to-ride-o... [3] http://www.colorado.edu/ASEN/asen6090/broadcast_vs_precise.pdf http://www.colorado.edu/ASEN/asen6090/broadcast_vs_precise.p... http://igscb.jpl.nasa.gov/igscb/center/analysis/noaa.acn http://igscb.jpl.nasa.gov/igscb/center/analysis/noaa.acn

by jbert 12y ago

Cthulhu_ 12y ago

From what I understand, GPS receivers synchronize their clocks with those of the satellites; triangulation occurs by comparing the timestamps of three or more sattelites. The deviation, times the speed of light or something, gives the receiver a pretty good indication of how far each satellite is. That should be enough to determine a location.

jbert 12y ago
> That should be enough to determine a location. Yes, if you know where the satellites are to the same degree of precision. That's what I was wondering about.
mikeash 12y ago
That's the basic idea, but note that it takes four satellites, not just three, because you're fixing your position in four dimensions (three space, plus time). If you had an extremely accurate clock locally then you could get away with just three, but without knowing the precise time, you need an extra satellite to fix time as well as space. Basically, GPS doesn't give you distance to the satellites, but the differences in the distances to different satellites. The signal from one satellite gives you nothing much, two satellites fixes your position on a hyperboloid, three satellites fixes your position on a curve, and four fixes you to a point.

TickleSteve 12y ago

The orbits of the satellites are known to a certain accuracy allowing prediction of where the satellite is at any given point. The accuracy of this almanac & ephemeris data is only valid for a short time in the future (hours to days) but is continuously updated from measurements of the satellites actual position. The ephemeris & almanac data is what is transmitted to the GPS receivers on the ground along with the timing information allowing the receiver to calculate their position. An assisted GPS (A-GPS) system can transmit predicted ephemeris for up to a week ahead to a device and store it allowing very quick start ups (Time-To-First-Fix) presuming that the data is preloaded (avoids having to wait for an almanac &ephemeris download which can take up to 13 minutes). In answer to your question, the orbits are affected by everything from the atmospheric weather which causes deflections in the signals to phases of the moon and the shape of the earth that it is passing over causing small deflections in the satellites orbit. Many factors combine to make orbital predictions very difficult, akin to predicting the weather.

jbert 12y ago
Thanks for that, this is really interesting. So - there are ground-based observatories continuously determining the absolute position of the satellites? This seems really hard. The satellites are ~20,000Km up. I think that means a 1 millimetre difference would be a 5 x 10^-11 radians difference (theta ~ tan theta), or 0.0001 arc seconds - surely this is beyond any telescope technology? And even if they could resolve at that level, we're trying for an absolute fix, so we're also trying to measure the alignment of a (moving?) telescope with 0.0001 arc second precision (hoping no mice cough nearby?) That can't be right, so what am I missing? Wikipedia says that there are lots (~13?) stations: http://en.wikipedia.org/wiki/Global_Positioning_System#Control_segment http://en.wikipedia.org/wiki/Global_Positioning_System#Contr... Are there potential issues with them being covered by weather etc? [Ah - found the link to 'http://en.wikipedia.org/wiki/Kalman_filter' http://en.wikipedia.org/wiki/Kalman_filter' - this is probably the magic?]
- TickleSteve 12y ago
  Yeah, its a really hard thing to do... the ground-segment (Monitor stations) isn't my speciality (I worked on an AGPS system using ephemeris predicition for a year or two) but pretty much everything you can think of affects the accuracy, weather (at multiple levels in the atmosphere), landscape, topology, season (planetary motions),etc. The guys who do the ephemeris prediction model at JPL would know more tho. But the take-away message is, yes, its really hard stuff.
- VLM 12y ago
  Two ways to do it 1) You have a defined position of your antenna... make the ephemeris "work" such that your antenna gets the right signal from the satellite. In a philosophical sense, where is the satellite? Well... does it really matter? This ephemeris says your antenna is in the right place, so... I'm not implying this is how it work or its a good idea, but it certainly is a good unit test if your "real" method when run thru a test bench implies you're on the moon instead of at the (note singular) base station... 2) Those numbers are no big deal with doppler / frequency ranging. If you transmit at 1500 MHz its a little higher as it approaches and lower as it leaves. Ask a ham radio operator to demonstrate with their 144/440-ish MHz satellites, the doppler in low earth orbit is maybe 15 KHz or so. Anyway sub-Hz accuracy measurement (no big deal) of a 1.5e9 Hz signal for a couple seconds gives you the -11th class of accuracy you're looking for. The absolute freq would be nice to know, but you can figure out the instant the satellite passed zenith (or any other elevation relative to your position) as long as the freq is "short term more or less constant". Of course giant and heavy earth bound clocks can give you that precise freq you're looking for, which is also cool. The doppler of a satellite pass is pleasingly non-linear and they're high up enough so make for long passes and proper data analysis means you can downsample maybe 10000 samples to find the theoretical best RMS zenith instant for all 10000 samples, so oversampling and averaging gives you another couple orders of magnitude. Maybe another way to say it, is if you have basically perfect accuracy clocks, and you sample and literally count every incoming cycle of a 1.5e9 RF signal for only 100 seconds even if you ignore phase data (why would you? But for the sake of the argument...) then thats 1.5e11 cycles in a given time, a bit of division and you have a freq accurate to one cycle or part in 10 to the 11th. Its more complicated in reality because the GPS signal is not a simple RF carrier but is a spread spectrum signal so you need a reasonably low noise and stable PLL to lock onto the SS signal and then you actually measure the SS signal.

michaelt 12y ago

Does the system rely on knowing the position of the satellites to equivalent accuracy? Base stations calculate the satellites' orbital parameters, and estimates of errors due to satellite clock error, and the ionosphere and troposphere, and transmit them to the satellites; the satellites send them on to receivers. The orbital parameters don't perfectly describe everything about the orbits, so they're updated every 30 minutes or so. Back in 2000, the RMS error was about 5m [1], with inaccuracies distributed in such a way that the user equivalent range error was around 2m. It may have improved since then. i.e. "millimetres" accuracy for differential GPS. The orbital parameters transmitted by the satellites are not millimetre-position - but for differential GPS, the same differential approach that can cancel out errors due to the ionosphere and troposphere can also cancel out errors due to inaccuracy in satellite position reports. From the user's perspective, an error due to inaccurate ephemerides looks a lot like an error due to an inaccurate satellite clock or a signal delayed by the atmosphere. If so, how is this accuracy achieved? (Obviously the satellites themselves cannot use gps to determine their position...). Satellites are tracked by a network of base stations at known locations, called the 'control segment' of the GPS system (the other parts being the 'space segment' (satellites) and the 'user segment' (receivers)). Satellite position is tracked by working backwards from the received GPS signal, and the satellites can also be tracked optically (the satellites carry retroreflectors [2] so they can be tracked with special laser range finders). The most recent satellite position measurements are extrapolated forward to work out near future positions, which are then transmitted to the satellites. Are there any events (micro debris strike, solar wind?) which cause drift in our estimate of their position? Loads of things have to be taken into account [3]. From the gravity of jupiter to the fact there are reflected photons on one side of the earth but not the other (the latter is admittedly only 30cm per day). For more information, the satellite orbits are called 'ephemerides' or 'ephemeris' and you'll find lots of info on Google now you know the right keyword to look for! [1] http://gauss.gge.unb.ca/papers.pdf/COSPAR2000.pdf http://gauss.gge.unb.ca/papers.pdf/COSPAR2000.pdf [2] http://gpsworld.com/expert-advice-laser-reflectors-to-ride-on-board-gps-iii/ http://gpsworld.com/expert-advice-laser-reflectors-to-ride-o... [3] http://www.colorado.edu/ASEN/asen6090/broadcast_vs_precise.pdf http://www.colorado.edu/ASEN/asen6090/broadcast_vs_precise.p... http://igscb.jpl.nasa.gov/igscb/center/analysis/noaa.acn http://igscb.jpl.nasa.gov/igscb/center/analysis/noaa.acn