Overview of Global Positioning Systems (GPSs)

The recent Navstar Global Positioning System (GPS) developed as a Joint Services Program by the Department of Defense uses a constellation of 24 satellites (including three spares) orbiting the earth every 12 hours at a height of about 10,900 nautical miles. Four satellites are located in each of six planes inclined 55 degrees with respect to the plane of the earth’s equator [Getting, 1993]. The absolute three-dimensional location of any GPS receiver is determined through simple trilateration techniques based on time of flight for uniquely coded spread-spectrum radio signals transmitted by the satellites. Precisely measured signal propagation times are converted to pseudoranges representing the line-of-sight distances between the receiver and a number of reference satellites in known orbital positions. The measured distances have to be adjusted for receiver clock offset, as will be discussed later, hence the term pseudoranges. Knowing the exact distance from the ground receiver to three satellites theoretically allows for calculation of receiver latitude, longitude, and altitude. Although conceptually very simple (see [Hurn, 1993]), this design philosophy introduces at least four obvious technical challenges:

& Time synchronization between individual satellites and GPS receivers.
& Precise real-time location of satellite position.
The recent Navstar Global Positioning System (GPS) developed as a Joint Services Program by theDepartment of Defense uses a constellation of 24 satellites (including three spares) orbiting the earthevery 12 hours at a height of about 10,900 nautical miles. Four satellites are located in each of sixplanes inclined 55 degrees with respect to the plane of the earth’s equator [Getting, 1993]. Theabsolute three-dimensional location of any GPS receiver is determined through simple trilaterationtechniques based on time of flight for uniquely coded spread-spectrum radio signals transmitted bythe satellites. Precisely measured signal propagation times are converted to pseudorangesrepresenting the line-of-sight distances between the receiver and a number of reference satellites inknown orbital positions. The measured distances have to be adjusted for receiver clock offset, as willbe discussed later, hence the term pseudoranges. Knowing the exact distance from the groundreceiver to three satellites theoretically allows for calculation of receiver latitude, longitude, andaltitude.Although conceptually very simple (see [Hurn, 1993]), this design philosophy introduces at leastfour obvious technical challenges:

& Time synchronization between individual satellites and GPS receivers.

& Precise real-time location of satellite position.

& Accurate measurement of signal propagation time.

& Sufficient signal-to-noise ratio for reliable operation in the presence of interference and possible jamming.

The first of these problems is addressed through the use of atomic clocks (relying on the vibration period of the cesium atom as a time reference) on each of the satellites to generate time ticks at a frequency of 10.23 MHz. Each satellite transmits a periodic pseudo-random code on two different frequencies (designated L1 and L2) in the internationally assigned navigational frequency band. The L1 and L2 frequencies of 1575.42 and 1227.6 MHz are generated by multiplying the cesium-clock time ticks by 154 and 128, respectively. The individual satellite clocks are monitored by dedicated ground tracking stations operated by the Air Force, and continuously advised of their measured offsets from the ground master station clock. High precision in this regard is critical since electromagnetic radiation propagates at the speed of light, roughly 0.3 meters (1 ft) per nanosecond. To establish the exact time required for signal propagation, an identical pseudocode sequence is generated in the GPS receiver on the ground and compared to the received code from the satellite.

The locally generated code is shifted in time during this comparison process until maximum correlation is observed, at which point the induced delay represents the time of arrival as measured by the receiver’s clock. The problem then becomes establishing the relationship between the atomic clock on the satellite and the inexpensive quartz-crystal clock employed in the GPS receiver. This T is found by measuring the range to a fourth satellite, resulting in four independent trilateration equations with four unknowns. Details of the mathematics involved are presented by Langley [1991].

The precise real-time location of satellite position is determined by a number of widely distributed tracking and telemetry stations at surveyed locations around the world. Referring to Figure 3.4, all measured and received data are forwarded to a master station for analysis and referenced to universal standard time. Change orders and signal-coding corrections are generated by the master station and then sent to the satellite control facilities for uploading [Getting, 1993]. In this fashion the satellites are continuously advised of their current position as perceived by the earth-based tracking stations, and encode this ephemeris information into their L1 and L2 transmissions to the GPS receivers. (Ephemeris is the space vehicle orbit characteristics, a set of numbers that precisely describe the vehicle’s orbit when entered into a specific group of equations.)

In addition to its own timing offset and orbital information, each satellite transmits data on all other satellites in the constellation to enable any ground receiver to build up an almanac after a “cold start.” Diagnostic information with respect to the status of certain onboard systems and expected range-measurement accuracy is also included. This collective “housekeeping” message is superimposed on the pseudo-random code modulation at a very low (50 bits/s) data rate, and requires 12.5 minutes for complete downloading [Ellowitz, 1992]. Timing offset and ephemeris information is repeated at 30 second intervals during this procedure to facilitate initial pseudorange measurements.

To further complicate matters, the sheer length of the unique pseudocode segment assigned to each individual Navstar Satellite (i.e., around 6.2 trillion bits) for repetitive transmission can potentially cause initial synchronization by the ground receiver to take considerable time. For this and other reasons, each satellite broadcasts two different non-interfering pseudocodes. The first of these is called the coarse acquisition, or C/A code, and is transmitted on the L1 frequency to assist in acquisition. There are 1023 different C/A codes, each having 1023 chips (code bits) repeated 1000 times a second [Getting, 1993] for an effective chip rate of 1.023 MHz (i.e., one-tenth the cesium clock rate). While the C/A code alone can be employed by civilian users to obtain a fix, the resultant

gps nastar global positioning system

positional accuracy is understandably somewhat degraded. The Y code (formerly the precision or P code prior to encryption on January 1st, 1994) is transmitted on both the L1 and L2 frequencies and scrambled for reception by authorized military users only with appropriate cryptographic keys and equipment. This encryption also ensures bona fide recipients cannot be “spoofed” (i.e., will not inadvertently track false GPS-like signals transmitted by unfriendly forces).

Another major difference between the Y and C/A code is the length of the code segment. While the C/A code is 1023 bits long and repeats every millisecond, the Y code is 2.35×1014 bits long and requires 266 days to complete [Ellowitz, 1992]. Each satellite uses a one-week segment of this total code sequence; there are thus 37 unique Y codes (for up to 37 satellites) each consisting of 6.18×1012 code bits set to repeat at midnight on Saturday of each week. The higher chip rate of 10.23 MHz (equal to the cesium clock rate) in the precision Y code results in a chip wavelength of 30 meters for the Y code as compared to 300 meters for the C/A code [Ellowitz, 1992], and thus facilitates more precise time-of-arrival measurement for military purposes.

Brown and Hwang [1992] discuss a number of potential pseudorange error sources as summarized below in Table 3.3. Positional uncertainties related to the reference satellites are clearly a factor, introducing as much as 3 meters (9.8 ft) standard deviation in pseudo-range measurement accuracy. As the radiated signal propagates downward toward the earth, atmospheric refraction and multi-path reflections (i.e., from clouds, land masses, water surfaces) can increase the perceived time of flight beyond that associated with the optimal straight-line path (Figure 3.5).

Additional errors can be attributed to group delay uncertainties introduced by the processing and passage of the signal through the satellite electronics. Receiver noise and resolution must also be  taken into account. Motazed [1993] reports fairly significant differences of 0.02 to 0.07 arc minutes in calculated latitudes and longitudes for two identical C/A-code receivers placed side by side. And finally, the particular dynamics of the mobile vehicle that hosts the GPS receiver plays a noteworthy role, in that best-case conditions are associated with a static platform, and any substantial velocity and acceleration will adversely affect the solution.

For commercial applications using the C/A code, small errors in timing and satellite position have been deliberately introduced by the master station to prevent a hostile nation from using GPS in support of precision weapons delivery. This intentional degradation in positional accuracy to around 100 meters (328 ft) best case and 200 meters (656 ft) typical spherical error probable (SEP) is termed selective availability [Gothard, 1993]. Selective availability has been on continuously (with a few exceptions) since the end of Operation Desert Storm. It was turned off during the war from August 1990 until July 1991 to improve the accuracy of commercial hand-held GPS receivers used by coalition ground forces.

There are two aspects of selective availability: epsilon and dither. Epsilon is intentional error in the navigation message regarding the location (ephemeris) of the satellite. Dither is error in the timing source (carrier frequency) that creates uncertainty in velocity measurements (Doppler). Some GPS receivers (for example, the Trimble ENSIGN) employ running-average filtering to statistically reduce the epsilon error over time to a reported value of 15 meters SEP [Wormley, 1994]. At another occasion (October 1992) SA was also turned off for a brief period while the Air Force was conducting tests. Byrne [1993] conducted tests at that time to compare the accuracy of GPS with SA turned on and off. The static measurements of the GPS error as a function of time shown in Figure 3.6 were taken before the October 1992 test, i.e., with SA “on” (note the slowly varying error in Figure 3.6, which is caused by SA). By contrast, Figure 3.7 shows measurements from the October 1992 period when SA was briefly “off.”

gps measuring error

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