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Author Topic:   Motion in GPS Position Finding

jimh posted 03-13-2014 06:56 PM ET (US)
It was suggested (by another boater in another discussion) that movement of the antenna of a GPS receiver could affect the performance of the receiver in deducing a position solution. This comment caused me to wonder about the influence of the relative speed between the receiver and the transmitter of the radio signals used to deduce a position in the GPS or any other global navigation satellite system (or GNSS). Perhaps it is useful to remind readers that in a GNSS the signals being used by a receiver come from transmitters that are moving. The signals come from satellites in Earth orbit.
In the specific case of the United States Air Force's Global Positioning System (GPS), the signals come from satellites in low-earth orbit. The Air Force says the satellites are in an orbit with an altitiude of of 20,200-kilometers above the Earth. The Earth has a radius of 6,371-kilometers. This suggests the orbital path is a circle of radius of 26,571-kilometers (the sum of the Earth radius and the satellite altitude).
The circumference of such a circle is 166,950.5-kilometers
The orbital period of a GPS satellite is 12-hours. The speed is thus
= 166,950.5-kilometers/12-hour, or
= 13912.5-kilometers/hour, or
= 3.8645-kilometers/second, or
= 8,644.8-MPH
It seems like any motion of the receiver on a recreational boat would be limited to a speed that is about one one-hundreth (86-MPH) to as little as one one-thousandths (8.6-MPH) of the speed of the transmitter. It does not seem likely that any motion occurring on a recreational boat while underway could have much influence on the accuracy of the position solution obtained with a GNSS signal from a moving satellite.
jimh posted 03-13-2014 07:09 PM ET (US)
In the early stage of testing of what would become the Global Positioning System (GPS), the U.S. Air Force testing the concept of the GPS by using transmitters located on Earth at stationary installations, and a receiver operating in an air plane at altitude and moving at high speed. Having a moving receiver and stationary transmitters is a reversal of the normal GPS application; typically the transmitters are moving and the receiver is stationary (or moving relatively slowly in comparison to the transmitters).
Chuck Tribolet posted 03-13-2014 08:35 PM ET (US)
Except that the motion of the satellite is known and the
motion of the receiver is not.
Chuck
jimh posted 03-14-2014 09:12 AM ET (US)
Chuck--It is the relative speed of motion about which there is confusion. It is not necessary for a GPS receiver to be in a stationary position for it to work. It works as well in motion as it does when stationary. I think this is easily inferred from the consideration that even a stationary GPS receiver is in motion relative to the transmitters sending it signals, and, since the satellites are moving at very high speeds, any motion of the GPS receiver would be only a very small change in the relative motion.
It is also reasonable to consider that any motion of the GPS receiver might actually reduce the relative speed of motion between a particular transmitter and the receiver. The GPS receiver motion could be in the same direction as the satellite, so by moving it would actually be slowing down the relative motion.
jimh posted 03-14-2014 09:14 AM ET (US)
In any radio location system, the location of the transmitters must be known in order to deduce the position of the receiver. That requirement does not change depending on the motion of the receiver.
jimh posted 03-24-2014 10:53 PM ET (US)
I came across a specification in a GPS receiver for dynamic conditions. A modern GPS receiver based on the capable SiRF III chip set specifies the following:
Acceleration limit = less than 4G
Altitude limit = maximum 60,000-feet
Velocity limit - 515-meters/second (1,152-MPH)
Jerk limit = 20-meters/second^3
Cf.: http://www.usglobalsat.com/store/download/62/bu353_ds_ug.pdf
(Note: I corrected an error in their units conversion.)
jimh posted 03-24-2014 11:12 PM ET (US)
Regarding the jerk limit, one study cites the limit for humans as follows:
"The largest jerk an average human can withstand without losing his balance is about 0.60 m/s^3 even if the maximum acceleration is not exceeded."
Cf.: http:/ / search. asee. org/ search/ fetch; jsessionid=1foo7th9uupma?url= file%3A%2F%2Flocalhost%2FE%3A%2Fsearch%2Fconference%2F17%2FAC%25202008Fu ll1330. pdf& index=conference_papers& space=129746797203605791716676178& type=application%2Fpdf& charset=
We see that a typical GPS can continue to function during changes in acceleration that are about 33 times greater than those tolerated by a human.
This seems to suggest that any loss of function in a GPS receiver due to change in acceleration would occur long after the human occupant of a boat had fallen down, however, the study also showed that riding in certain subway cars in American cities produced jerk values of about 12 m/sec^3.
AZdave posted 03-31-2014 06:29 PM ET (US)
My first thought was that for signals traveling at the speed of light, satellite motion would not be a big factor. I then started finding references to data streams that took 30 sec to transmit. At Jimh's calculated orbital speed of 3.9 km/sec, there is a large displacement of the satellite. I finally ran down this page http://www.navsync.com/notes2.html which seems to give a good explanation of the position and velocity data which the satellite transmits for itself.
jimh posted 04-01-2014 01:53 PM ET (US)
Dave--I read the material at the link you gave. It did not shed any light on the notion of how a GPS receiver might be moving relative to the satellite.
In order to find your position by reception of a signal from a remote transmitting source, the position of the remote transmitter must be known. Since the transmitters in the global positioning system are satellites in motion, the satellite orbits must be known. I do not believe the satellites themselves are self-aware of their orbit or position, but rather that the controlling system, the United States Air Force, measures the orbits and positions of the satellites very precisely, and then uploads that information to the satellites. The satellites then send the most recent data about their orbits and position in the ephemeris information that is included in their signals.
As far as I know, an individual satellite does not deduce its instantaneous position and send that position as data in real time.
jimh posted 04-01-2014 01:58 PM ET (US)
For more on how a GPS receiver calculates its position, see
http://en.wikipedia.org/wiki/Pseudorange
The precise position of an individual satellite is deduced by the GPS receiver by knowing the orbital parameters of the satellite and the precise time. See
http://en.wikipedia.org/wiki/Orbital_parameters
The precise time is not actually known by the GPS receiver with sufficient precision to be useful at all in solving the range solution problem, but by using crafty mathematics, the necessity to know the time can be avoided by using four psuedo-ranges and solving for the time as part of the solution of the four equations.

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Author	Topic: Motion in GPS Position Finding
jimh	posted 03-13-2014 06:56 PM ET (US) It was suggested (by another boater in another discussion) that movement of the antenna of a GPS receiver could affect the performance of the receiver in deducing a position solution. This comment caused me to wonder about the influence of the relative speed between the receiver and the transmitter of the radio signals used to deduce a position in the GPS or any other global navigation satellite system (or GNSS). Perhaps it is useful to remind readers that in a GNSS the signals being used by a receiver come from transmitters that are moving. The signals come from satellites in Earth orbit. In the specific case of the United States Air Force's Global Positioning System (GPS), the signals come from satellites in low-earth orbit. The Air Force says the satellites are in an orbit with an altitiude of of 20,200-kilometers above the Earth. The Earth has a radius of 6,371-kilometers. This suggests the orbital path is a circle of radius of 26,571-kilometers (the sum of the Earth radius and the satellite altitude). The circumference of such a circle is 166,950.5-kilometers The orbital period of a GPS satellite is 12-hours. The speed is thus = 166,950.5-kilometers/12-hour, or = 13912.5-kilometers/hour, or = 3.8645-kilometers/second, or = 8,644.8-MPH It seems like any motion of the receiver on a recreational boat would be limited to a speed that is about one one-hundreth (86-MPH) to as little as one one-thousandths (8.6-MPH) of the speed of the transmitter. It does not seem likely that any motion occurring on a recreational boat while underway could have much influence on the accuracy of the position solution obtained with a GNSS signal from a moving satellite.
jimh	posted 03-13-2014 07:09 PM ET (US) In the early stage of testing of what would become the Global Positioning System (GPS), the U.S. Air Force testing the concept of the GPS by using transmitters located on Earth at stationary installations, and a receiver operating in an air plane at altitude and moving at high speed. Having a moving receiver and stationary transmitters is a reversal of the normal GPS application; typically the transmitters are moving and the receiver is stationary (or moving relatively slowly in comparison to the transmitters).
Chuck Tribolet	posted 03-13-2014 08:35 PM ET (US) Except that the motion of the satellite is known and the motion of the receiver is not. Chuck
jimh	posted 03-14-2014 09:12 AM ET (US) Chuck--It is the relative speed of motion about which there is confusion. It is not necessary for a GPS receiver to be in a stationary position for it to work. It works as well in motion as it does when stationary. I think this is easily inferred from the consideration that even a stationary GPS receiver is in motion relative to the transmitters sending it signals, and, since the satellites are moving at very high speeds, any motion of the GPS receiver would be only a very small change in the relative motion. It is also reasonable to consider that any motion of the GPS receiver might actually reduce the relative speed of motion between a particular transmitter and the receiver. The GPS receiver motion could be in the same direction as the satellite, so by moving it would actually be slowing down the relative motion.
jimh	posted 03-14-2014 09:14 AM ET (US) In any radio location system, the location of the transmitters must be known in order to deduce the position of the receiver. That requirement does not change depending on the motion of the receiver.
jimh	posted 03-24-2014 10:53 PM ET (US) I came across a specification in a GPS receiver for dynamic conditions. A modern GPS receiver based on the capable SiRF III chip set specifies the following: Acceleration limit = less than 4G Altitude limit = maximum 60,000-feet Velocity limit - 515-meters/second (1,152-MPH) Jerk limit = 20-meters/second^3 Cf.: http://www.usglobalsat.com/store/download/62/bu353_ds_ug.pdf (Note: I corrected an error in their units conversion.)
jimh	posted 03-24-2014 11:12 PM ET (US) Regarding the jerk limit, one study cites the limit for humans as follows: "The largest jerk an average human can withstand without losing his balance is about 0.60 m/s^3 even if the maximum acceleration is not exceeded." Cf.: http:/ / search. asee. org/ search/ fetch; jsessionid=1foo7th9uupma?url= file%3A%2F%2Flocalhost%2FE%3A%2Fsearch%2Fconference%2F17%2FAC%25202008Fu ll1330. pdf& index=conference_papers& space=129746797203605791716676178& type=application%2Fpdf& charset= We see that a typical GPS can continue to function during changes in acceleration that are about 33 times greater than those tolerated by a human. This seems to suggest that any loss of function in a GPS receiver due to change in acceleration would occur long after the human occupant of a boat had fallen down, however, the study also showed that riding in certain subway cars in American cities produced jerk values of about 12 m/sec^3.
AZdave	posted 03-31-2014 06:29 PM ET (US) My first thought was that for signals traveling at the speed of light, satellite motion would not be a big factor. I then started finding references to data streams that took 30 sec to transmit. At Jimh's calculated orbital speed of 3.9 km/sec, there is a large displacement of the satellite. I finally ran down this page http://www.navsync.com/notes2.html which seems to give a good explanation of the position and velocity data which the satellite transmits for itself.
jimh	posted 04-01-2014 01:53 PM ET (US) Dave--I read the material at the link you gave. It did not shed any light on the notion of how a GPS receiver might be moving relative to the satellite. In order to find your position by reception of a signal from a remote transmitting source, the position of the remote transmitter must be known. Since the transmitters in the global positioning system are satellites in motion, the satellite orbits must be known. I do not believe the satellites themselves are self-aware of their orbit or position, but rather that the controlling system, the United States Air Force, measures the orbits and positions of the satellites very precisely, and then uploads that information to the satellites. The satellites then send the most recent data about their orbits and position in the ephemeris information that is included in their signals. As far as I know, an individual satellite does not deduce its instantaneous position and send that position as data in real time.
jimh	posted 04-01-2014 01:58 PM ET (US) For more on how a GPS receiver calculates its position, see http://en.wikipedia.org/wiki/Pseudorange The precise position of an individual satellite is deduced by the GPS receiver by knowing the orbital parameters of the satellite and the precise time. See http://en.wikipedia.org/wiki/Orbital_parameters The precise time is not actually known by the GPS receiver with sufficient precision to be useful at all in solving the range solution problem, but by using crafty mathematics, the necessity to know the time can be avoided by using four psuedo-ranges and solving for the time as part of the solution of the four equations.