"Wally W." <email@example.com> wrote in message news:firstname.lastname@example.org... > On Sun, 24 Mar 2013 20:02:16 -0000, email@example.com wrote: > >>Sam Wormley <firstname.lastname@example.org> wrote: >>> On 3/24/13 12:04 PM, email@example.com wrote: >>>> Sam Wormley <firstname.lastname@example.org> wrote: >>>>> On 3/23/13 9:15 PM, email@example.com wrote: >>>> >>>>>> For lasers it was 1917 and for GPS it was around 1878. >>>>>> >>>>> >>>>> Thanks be to Albert Einstein. >>>> >>>> For what? >>>> >>>> Nothing Einstein did is necessary to build either. >>>> >>>> Building a laser is pretty trivial once one is aware of the effect and >>>> there are natural lasers. >>>> >>>> Absent Einstein the corrections needed to keep GPS accurate could have >>>> been determined empirically. >>>> >>> >>> Many don't understand the relativistic correction, jimp. There is no >>> shame in that. See: >> >>You are changing the subject, ass hat. > > SOP for warmophobes. > > The news media doesn't notice because their attention span is only 8 > seconds long. > >>The relativistic correction has nothing to do with lasers. >> >>The relativistic correction is nothing more than a set of equations >>that with enough data could be determined empirically. >> >>Does the phrase "curve fitting" mean anything to you ass hat. >> >>Granted such does not give a theoretical explaination of WHY it is so, but >>it does give a working solution to build a system.
It is sad that most people have been brainwashed to believe that General Relativity is a powerful model and was and is essential to the GPS system.
The GPS system engineers designed a ***closed loop system*** that adjusts for all possible effects including the DOPPLER <velocity> EFFECT, and the GALILEO <acceleration> EFFECT.
1. Light travels at a constant speed of 299 792.458 meters per second in the absence of matter, and in media with sparse matter, such as the Earth's atmosphere.
2. Time interval measurements of E-M waves in air, and space, are equivalent to distance measurements.
distance = time interval * C
3. Synchronized clocks can be used to quantize the distance between the points by measuring the time it takes light/radio waves to travel from one point to another.
Clock(A) sends a message that it is time(X). Clock(B) notes that it is time(X) + I1 on its' clock.
The distance between the clocks is I1 * C
In other words, systems of synchronized clocks can quantize the distances between the clocks, by transmitting the time at each clock's location.
Any clock can determine the distances between it and other clocks, by simply determining time(I) for all of the other clocks.
For example, if one measures a time delay of "I1" of a radio wave from New York, they must be somewhere on the surface of a sphere, with a distance radius of I1 * C, centered about New York
If they also measure a time delay of "I2" of a radio wave from San Francisco, they must be somewhere on the surface of a sphere, with a distance radius of I2 * C, centered about San Francisco.
If they measure both, they must be on a circle represented by the intersection of the two spheres.
As can be seen, the measurement of a third point, would be the intersection of the circle with another sphere, and would let tell the observer that they are on one of two points.
A fourth measurement would resolve the situation, and tell them at which of the two points they are located.
4. As the GPS satellites are moving, whereas New York and San Francisco are located at fixed points (With respect to Earth bound observers.), it is necessary that GPS receivers know where the satellites were when they transmitted the time.
This is handled, by having each satellite transmit its' position in space, along with the time data.
Each satellite not only transmits where it is ("ephemeris data"), it transmits its' orbital data ("almanac data"), along with its' time.
The "ephemeris data" serves the same purpose to the GPS receiver, as the Sun does is to a sailor with a sextant.
5. Ground stations continuously monitor the satellites' orbits and transmissions, and when changes exceed certain amounts, signals are sent to the offending satellites, updating their "almanac data", their "ephemeris data", their time settings and drift in their clocks with respect to the master clock on Earth.
In other words, the ground station monitors the data transmitted by the satellites and when necessary sends them signals that tells them, that their clock is x nano-seconds fast, their orbit has changed to such and such (Perhaps because of dust drag, etc.), that their "ephemeris data" should be xxx, etc.
6. As portable GPS receivers do not have extremely stable oscillators, they must derive precision times from the satellites.
As the satellites are at an altitude of about 11,000 miles, (From the center of the Earth.) and radio waves travel 186,000 miles in one second, it takes about .006 seconds for the time, ephemeris, and almanac data to reach a sea level receiver.
This means that in a typical transmission, the GPS receiver must subtract about .006 seconds from its' clock, in order to set its' clock. GPS receivers receive and average the times from several satellites, and recursively home in on the master time, and make an adjustment for recursively computed position of the satellite.
In other words, at the reception of the first data, the GPS receiver knows the master time to about .006 seconds higher than the first time it receives, and as it picks up signals from other satellites, and recursively computes the distances to the satellites, and averages out multi-path signal variations, its' own clock homes in on the master clock time.
As the satellites take about 12 hours (43200 seconds) to orbit the Earth, and the ephemeris data takes about .006 seconds to reach the receiver, this means that the GPS receiver knows where the satellite is to an accuracy of about one part in 43000 / .006 = 71600000 parts, even without clock and ephemeris corrections.
Considering that the Earth is about 24,000 miles or 126,000,000 feet in circumference, this amounts to a sphere of uncertainty of about 1.76 feet at sea level.
7. The clocks used in the GPS system are extremely stable. They have a long term and short term stability of about 1 part in 10^14 over one day and even months.
As there are about 3 x 10^13 MICROseconds in a year, this means that the GPS clocks can maintain microsecond agreement for over a year, even if no corrections are made.
But of course, adjustments are made to the clocks on a regular basis by a ground clock, to which all of the GPS clocks are referenced to.
( The adjustments are not actually made to the clocks and the oscillators that drive the clocks but data is sent to each satellite that it in turn transmits to GPS receivers informing them what offsets must be applied to correct that satellite's data to the master ground data.)
8. As the satellites have a life expectancy of about 10 years, their orbits are very stable. In other words, when ground stations get a fix on a satellite's orbit, we know pretty much where the satellite will be for a long time, and GPS receivers on the ground have an extremely dependable target to reference.
9. There is some variation in the time it takes the signal to reach the receiver due to multi paths taken by the radio wave to the GPS receiver, so GPS receivers are programmed to compute out the multi-path variations, and to compute the time, using the most reliable data it gets from several satellites.
10. The GPS satellites broadcast on two carrier frequencies: L1 at 1575.42 MHz and L2 at 1227.6 MHz. They transmit a "coarse acquisition code" at 1.0 bits per nanosecond and a "precision code" at a bit rate of 10.230 bits per nanosecond.
Frankly the usefullness of the "precision code" is vastly overrated as modern GPS receivers have the capacity to phase lock with the carrier frequency.
As light travels at about 300,000,000 meters per second, or 300 meters in one micro-second, a one nano second error would result in an error sphere of about .3 meters ( One foot), and a 10 nanosecond error would result in an error of about 3 meters or ten feet.
By averaging data from multiple satellites, a receiver can reduce the timing uncertainty due to multipaths, and can reduce the error sphere by only averaging where the error spheres of several satellites overlap.
In order to identify each satellite, and to measure the time interval most accurately, a "quasi-random code" is used.
Part of the code includes a "Gold Code" with good correlation properties. and part of the code includes the satellite ID and the data.
To eliminate the jitter in the leading edge of the transmitted signal, caused by transmitter noise, receiver noise, environmental noise, multipath signal combining, jamming, etc.,
and to delineated the signal, GPS receivers perform an auto-correlation on the signal.
A segment of the quasi-random signal is incrementally delayed, and multiplied by the signal stream.
If two strings of random numbers are multiplied, a maximum occurs when and if the strings match, otherwise the product tends toward zero.
After the signal is delineated using "auto-correlation",
it is further delineated by "cross-correlating" the delineated blocks with the quasi-random codes used to identify the satellites,
and the data associated with each satellite. can thus be identified and decoded.
In summary, the largest contributor to time transfer uncertainty is caused by variations in path delay, due to signals reflected off mountains, buildings, etc., and as noted, much of the path delay errors can be averaged out, because the satellites are moving, and signals are received from several satellites.
The accuracy of the GPS system is limited mainly by the random, non-homogenity of the air.
The best GPS receivers can, by using the methods described above, reduce the uncertainty in time to about one nanosecond, which amounts to a sphere of uncertainty of about one foot.