The Control Segment is comprised of a number of ground-based monitoring stations, which continually gather information from the satellites. These data are sent to a Master Control Station in Colorado Springs, CO, which analyzes the constellation and projects the satellite ephemerides and clock behaviour forward for the next few hours. This information is then uploaded into the satellites for retransmission to users.
The User Segment consists of all users who, by receiving signals transmitted from the satellites, are able to determine their position, velocity, and the time on their local clocks.
The GPS is a navigation and timing system that is operated by the United States Department of Defense (DoD), and therefore has a number of aspects to it that are classified. Several organizations monitor GPS signals independently and provide services from which satellite ephemerides and clock behavior can be obtained. Accuracies in the neighborhood of 5-10 cm are not unusual. Carrier phase measurements of the transmitted signals are commonly done to better than a millimeter.
GPS signals are received on earth at two carrier frequencies,
L1 () and L2 (
). The L1 carrier is modulated by two types of pseudorandom noise
codes, one at 1.023 MHz - called the Coarse/Acquisition or
C/A-code - and an encrypted one at 10.23 MHz called the
P-code. P-code receivers have access to both L1 and L2
frequencies and can correct for ionospheric delays, whereas
civilian users only have access to the C/A-code. There are thus
two levels of positioning service available in real time, the
Precise Positioning Service utilizing P-code, and the Standard
Positioning Service using only C/A-code. The DoD has the
capability of dithering the transmitted signal frequencies and
other signal characteristics, so that C/A-code users would be
limited in positioning accuracy to about
meters. This is termed Selective Availability, or SA. SA was
turned off by order of President Clinton in May, 2000.
The technological basis for GPS lies in extremely accurate,
stable atomic clocks. Figure
1
gives a plot of the Allan deviation for a high-performance
Cesium clock, as a function of sample time
. If an ensemble of clocks is initially synchronized, then when
compared to each other after a time
, the Allan deviation provides a measure of the rms fractional
frequency deviation among the clocks due to intrinsic noise
processes in the clocks. Frequency offsets and frequency drifts
are additional systematic effects which must be accounted for
separately. Also on Figure
1
is an Allan deviation plot for a Quartz oscillator such as is
typically found in a GPS receiver. Quartz oscillators usually
have better short-term stability performance characteristics than
Cesium clocks, but after 100 seconds or so, Cesium has far better
performance. In actual clocks there is a wide range of variation
around the nominal values plotted in Figure
1
.
The plot for Cesium, however, characterizes the best orbiting
clocks in the GPS system. What this means is that after
initializing a Cesium clock, and leaving it alone for a day, it
should be correct to within about 5 parts in
, or 4 nanoseconds. Relativistic effects are huge compared to
this.
The purpose of this article is to explain how relativistic effects are accounted for in the GPS. Although clock velocities are small and gravitational fields are weak near the earth, they give rise to significant relativistic effects. These effects include first- and second-order Doppler frequency shifts of clocks due to their relative motion, gravitational frequency shifts, and the Sagnac effect due to earth's rotation. If such effects are not accounted for properly, unacceptably large errors in GPS navigation and time transfer will result. In the GPS one can find many examples of the application of fundamental relativity principles. These are worth careful study. Also, experimental tests of relativity can be performed with GPS, although generally speaking these are not at a level of precision any better than previously existing tests.
The principles of position determination and time transfer in
the GPS can be very simply stated. Let there be four synchronized
atomic clocks that transmit sharply defined pulses from the
positions
at times
, with
j
=1, 2, 3, 4 an index labelling the different transmission events.
Suppose that these four signals are received at position
at one and the same instant
t
. Then, from the principle of the constancy of the speed of
light,
where the defined value of
c
is exactly
. These four equations can be solved for the unknown space-time
coordinates
of the reception event. Hence, the principle of the constancy of
c
finds application as the fundamental concept on which the GPS is
based. Timing errors of one ns will lead to positioning errors of
the order of 30 cm. Also, obviously, it is necessary to
specify carefully the reference frame in which the transmitter
clocks are synchronized, so that Eq. (1
) is valid.
The timing pulses in question can be thought of as places in the transmitted wave trains where there is a particular phase reversal of the circularly polarized electromagnetic signals. At such places the electromagnetic field tensor passes through zero and therefore provides relatively moving observers with sequences of events that they can agree on, at least in principle.
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Relativity in the Global Positioning System
Neil Ashby http://www.livingreviews.org/lrr-2003-1 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |