## 2 Satellite Systems and Errors in Position Determination
### Errors in Position Determination  
Satellite systems should be treated as advanced technologies. The problem is that the individual components of the system are separated from each other by thousands of kilometers. This complicates the reach of adequate accuracy in position determination. The satellite signal has to travel a very long distance, during which it encounters interference related to Earth's atmosphere, as well as problems caused by, for example, urban agglomeration (large buildings can block the simplest path to the receiver). All in all, there are many factors affecting the accuracy of satellite systems. In this paper, the greatest attention was paid to errors arising from weather conditions (especially solar flares) and related to the Earth's atmosphere. Satellite navigation systems in various applications require high positioning accuracy. Then, appropriate methods should be used to eliminate errors in determining the position, which can reach even several dozen meters. However, first, it is necessary to know what error types are the most common. These are [54]:  
* Ephemeris errors--satellite position errors, basically, the difference between their real and identified positions; they are caused by the Earth's gravitational field, atmospheric drag, the gravitational effects of the Sun, Moon, and other celestial bodies, solar radiation, crustal tides, oceanic tides, electromagnetic forces, and relativistic effects; the error caused by the ephemeris can be about 2 m, but can be reduced;
* Inaccuracy of the time standard--position determination is mainly related to the measurement of the time, in which the signal reaches the receiver from the satellite; since the speed of wave propagation in vacuum is 300,000 km/s, it is important to know the propagation time of the signal, because a small deviation of the time can cause errors of several meters;
* Signal multipath--multipath errors are related to secondary wave inference; the phenomenon occurs when the satellite signal does not reach the receiver directly, but through various paths due to reflections from all kinds of objects standing in the way of the signal; in particular, the phenomenon of multipathing can be seen in large cities, where big buildings are present in high numbers, and when the satellites are low on the horizon;
* Variation of the antenna phase center--this error appears when the physical center is not compatible with the phase center of the receiver's antenna; the phase center is constantly changing; due to the constant change in the height and azimuth of the satellites, the angle of signal transmission also changes; deviations caused by this phenomenon are generally small and the newer the antenna, the smaller the deviation, up to several millimeters;
* Receiver's noise--noise is nothing different then a voltage peak of random frequency and amplitude, generated on current-carrying elements; the satellite receiver itself is a source of unwanted noise; noise affects accuracy and cannot be eliminated;
* Geometric errors of the satellite alignment--this type of error is affected by the satellites' position versus the receiver; the error is described by dilution of precision (DOP)--a parameter characterizing the influence of satellite constellation geometry on positioning; if any of the coefficients are equal to zero, it means that the measurement is impossible due to interference, weak signal from the satellites, or too few visible satellites;
* Errors in the design of the satellite system--satellites' location has a significant impact on their visibility to the receiver; four visible satellites are indispensable for positioning, however, this is the minimum vital number and may cause positioning errors;
* Errors related to the Earth's atmosphere (which are discussed hereinafter). An atmosphere is a gaseous shell that surrounds a celestial body, with enough mass to hold a layer of gases as a result of gravity.