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(17.2)
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where c is the speed of light. Substituting this in Eq. (17.1) gives: O (xn x0 )2 (yn y0)2 (zn z0)2 c2(tdn t)2 (17.3)
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The unknowns here are the location (x0, y0, z0) and the timing difference t. For satellite n the position (xn, yn, zn) is known and delay time tdn is measured by the receiver. Since there are four unknowns, the receiver must be capable of measuring tdn for four satellites simultaneously (n 1, 2, 3, 4) to yield four simultaneous equations of the form (17.3). These can be solved to find the unknowns t and (x0, y0, z0). The latter, of course, are the required position coordinates for the receiver, and these would be converted into local coordinates (latitude, longitude, and altitude). All this requires quite sophisticated microprocessing in the receiver. Also, the composition of the GPS signal is much more complex than indicated here, utilizing spread-spectrum techniques. The free-space value for c is used where high precision is not required. However, the free-space value cannot be used for radio waves traveling through the ionosphere and the troposphere. Although the change in propagation velocity is small in absolute terms, it can introduce significant timing errors in certain applications. Also, the satellites clocks, although highly accurate will have their own timing errors. The dilution of position errors, described previously, combined with these timing errors set a limit on the accuracy of location determination. Where very high accuracy is required differential GPS (DGPS) can be used. Two receivers are used, one of which is placed at an accurately known location. Thus, the reference receiver makes a measurement in the usual way, but since the coordinates for the location are known, the only unknown in Eq. (17.1) is the range On, which can now be calculated. Comparing the reference value with the value obtained from the receiver correlator enables the errors to be determined. The reference receiver is linked by radio to the receiver at the unknown location, which can now correct for the errors. The two receivers may be up to a few hundred kilometers apart but this is insignificant in comparison with the distances to the satellites, and it may be assumed also that the signal paths through the ionosphere and troposphere are the same. Further details of the GPS system will be found in: Langley (1990a, 1991b, 1991c), Kleusberg and Langley (1990), and Mattos (1992, 1993a, 1993b, 1993c, 1993d, 1993e) and at http://www.trimble.com/gps/why.html
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17.6 Orbcomm The Orbital Communications Corporation (Orbcomm) system is a LEO satellite system, which provides two-way message and data communications services and position determination. The satellite constellations are shown in Table 17.3
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TABLE 17.3
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Orbital Parameters for ORBCOMM A 12/23/97 8 7.178 800 45 101 B 8/2/98 8 7.178 800 45 101 C 9/23/98 6 7.178 800 45 101 D 12/4/99 6 7.178 800 45 101 E 4/3/95 1 7.078 710 70 99 F 2/10/98 1 7.178 820 108 101
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Orbital plane Launch date No. of Satellites Semimajor axis, km Altitude, km Inclination, deg Period, min
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SOURCE:
http://www.orbcomm.com/wwwroot/
A number of gateway control centers (GCC) in various countries provide the switching necessary to link subscribers with terrestrial networks. The GCCs also provide a performance and status monitoring service for the system. The network control center (NCC) located in Dulles, VA serves as the U.S. GCC and also manages the satellite constellation. Gateway earth stations (GES) throughout the world link the ground segment with the satellites. Users have a subscriber communicator for fixed and mobile messaging. Figure 17.4 illustrates the system and Table 17.4 shows some of the parameters used in link-budget calculations. The satellites are small compared with the geostationary satellites in use, as shown in Fig. 17.5. The VHF/UHF antennas are seen to extend in a lengthwise manner, with the solar panels opening like lids top and bottom. Before launch, the satellites are in the shape of a disk, and the launch vehicle, a Pegasus XL space booster [developed by Orbital Sciences Corporation (OSC), the parent company of Orbcomm] can deploy eight satellites at a time into the same orbital plane. For launch, the satellites are stacked like a roll of coins, in what the company refers to as an eight-pack. Attitude control is required to keep the antennas pointing downward and at the same time to keep the solar panels in sunlight (battery backup is provided for eclipse periods). A three-axis magnetic control system, which makes use of the earth s magnetic field, and gravity gradient stabilization are employed. A small weight is added at the end of the antenna extension to assist in the gravity stabilization. Thus, the satellite antennas hang down as depicted in Fig. 17.4. At launch, the initial separation velocity is provided by springs used to separate the satellites, and a braking maneuver is used when the satellites reach their specified 45 in-plane separation. Intraplane spacing is maintained by a proprietary station-keeping technique which, it is claimed, has no cost in terms of fuel usage (Orbcomm, 1993). Because no onboard fuel is required to maintain the intraplane spacing between satellites, the satellites have a design lifetime of 4 years, which is based on the projected degradation of the power subsystem (solar panels and batteries).
574 The Orbcomm system. (Courtesy of Orbital Communications Corporation.)
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