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Time Precision of Navigation SystemsVydáno dne 20. 03. 2007 (8444 přečtení)This paper will present advantages and potential possibilities of
satellite navigation systems, especially with the emphasis on what makes them so
precise in showing time. Satellite navigation is a type of radio navigation that use radio waves from artificial satellites in order to determine points and moving receivers location, along with their movement parameters, in any place on the Earth. The most popular system of satellite navigation is GPS (Global Positioning System). Principle of operation
Radio waves information about local time is constantly broadcasts by each satellite; time is counted down by four cesiumbeam atomic clocks. To compute the distance from satellite, GPS receiver measure time, which passed between sending and receiving the signal; difference between these two values is multiply by speed of light, which is speed of radio wave propagation. When the distance from first satellite is calculate, it is known, that the GPS receiver’s location is somewhere on sphere’s surface with satellite as a center and radius equal to the distance, Figure 1.a). By knowing distance from second satellite, it is possible to reduce this space to a circle, which is interception point of both spheres, Figure 1.b). Distance from third satellite to receiver makes possible to narrow down search area to two points, where one for being an impossible result can be rejected, Figure 1.c). In theory those data would be sufficient to determine precise distance, but the GPS receiver is equipped with quartz clocks, which are not as accurate as those very expensive atomic clocks on board of satellites with accuracy of 1 nanosecond. That is why the signal from fourth satellite is being use to synchronize quartz clock in receiver with satellite’s atomic clock [2].
GPS radio signals Relativity
where
Using this expression, one obtains a frequency decrease of 8,32 parts in 10^{11} for GPS satellites. General Relativity experiments show that the gravitational potential affects the rate at which clocks run. In order to demonstrate these effects without excessive use of mathematics, scale factor “s” was define, slightly less than one, which is used to multiply or scale the parameter of interest. This scale factor is a direct function of the gravitational potential, and can be computed from it. The lower the gravitational potential the smaller the scale factor becomes. The scale factor is defined as,
where
The clocks run slower (measured time appears dilated) as compared to the rate at which they would run if they were located external to the gravitational field. The comparative clock rate is given in terms of the scale factor, s, defined above as,
where
There is a change in the clock frequency of the GPS satellite clocks at the time of their launch. The change in the gravitational potential at the surface of the earth to the gravitational potential at the satellite orbital height causes an increase in the average rate at which the clock runs of 5,311 parts in 10^{10}. As stated above, the speed of the GPS satellites in orbit causes a clock frequency decrease of 8,32 parts in 10^{11}. These two effects combine to give a net increase in frequency of 4,479 parts in 10^{10}. These two frequencybiasing effects and the additional small mean effects of the earth oblateness, sun and moon are compensated before launch by setting the frequency low by 4,45 parts in 10^{10} [7]. Further, each GPS receiver has built into it a microcomputer that (among other things) performs the necessary relativistic calculation when it is determining the user’s position. Accuracy
where TEC is the total number of electrons, called the Total Electron Content,
along the path from the transmitter to the receiver, c is the velocity of light
in meters per second, and f is the carrier frequency in Hz. TEC common
definition is a number of electrons in a unit crosssection column of 1 m^{2} area
along the path and range from 10^{16} electrons per m^{2} to 10^{19} electrons per m^{2}.
This leads to the delay of 54 ns, for 1,575 GHz C/A carrier frequency for GPS
satellite system and for a TEC of 10^{18} electrons per m^{2}. Obviously, the TEC
parameter is significant for GPS system [8]. Conclusion Acknowledgement References Autor: E. Kozlowska Pracoviště: České vysoké učení technické v Praze, FEL 
Projekty a aktuality
01.03.2012: PROJEKT
Výzkum a vývoj nového komunikačního systému s vícekanálovým přístupem a mezivrstvovou spoluprací pro průmyslové aplikace TA02011015
01.01.2012: PROJEKT Vývoj adaptabilních datových a procesních systémů pro vysokorychlostní, bezpečnou a spolehlivou komunikaci v extrémních podmínkách VG20122014095
09.10.2010: PROJEKT Výzkum a vývoj datového modulu 10 Gbit/s pro optické a mikrovlnné bezdrátové spoje, FRTI2/621
09.01.2010: PROJEKT Sítě s femtobuňkami rozšířené o řízení interference a koordinaci informací pro bezproblémovou konektivitu, FP7ICT20094 248891
09.11.2008: PROJEKT Ochrana člověka a techniky před vysokofrekvenčním zářením, FIIM5/202
20.06.2008: Schválení Radou pro výzkum a vývoj jako recenzovaný časopis
01.04.2007: PROJEKT Pokročilá optimalizace návrhu komunikačních systémů pomocí neuronových sítí, GA102/07/1503
01.07.2006: Doplnění sekce pro registrované 12.04.2005: Zavedeno recenzování článků 30.03.2005: Výzkumný záměr Výzkum perspektivních informačních a komunikačních technologií MSM6840770014
29.11.2004: Přiděleno ISSN 04.11.2004: Spuštění nové podoby Access serveru 18.10.2004: PROJEKT Optimalizace přenosu dat rychlostí 10 Gbit/s, GA102/04/0773
04.09.2004: PROJEKT Specifikace kvalitativních kritérií a optimalizace prostředků pro vysokorychlostní přístupové sítě, NPV 1ET300750402
04.06.2004: PROJEKT Omezující faktory při širokopásmovém přenosu signálu po metalických párech a vzájemná koexistence s dalšími systémy, GA102/03/0434

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