# Full Real-Time Positioning and Attitude System Based on GNSS-RTK Technology
## 2 GNSS-RTK Technology
### GNSS Error Correction  
The position computation method explained above could be enough to obtain an accuracy of centimeters. However, there exist several error sources that degrade the position estimation [12]:  
* Satellites' clocks (\(\pm 2\) m): Satellites' clocks are high-precision atomic clocks, but they have to be periodically readjusted from terrestrial control stations using more precise clocks. At the orbit height of the satellites, an error of 10 nanoseconds causes a positioning error of approximately 3 m.  
Figure 1: Phase difference ambiguity in the carrier signal (single frequency). Figure 2: Phase difference ambiguity in the carrier signal (double frequency). * Orbital errors (\(\pm\)2.5 m): The satellites' orbits are known and periodically retransmitted by other satellites (ephemerides). However, the real orbits are not completely predictable, and their monitoring must be readjusted from terrestrial control stations. * Ionospheric delay (>5 m): The radio signal propagation of the satellites through the ionosphere has important delays due to solar activity, position, time, etc., which are constant within relatively large geographical areas (50 km of radius). * Tropospheric delay (\(\pm\)0.5 m): The radio signal propagation of the satellites through the troposphere has delays with similar causes to those of the ionospheric delays, and they are constant within local geographical areas. * Receiver noise (\(\pm\)0.3 m): Any delay in the signal processing or any error in the oscillator frequency causes position estimation errors. * Multipath propagation (\(\pm\)1 m): When the signal transmitted by a satellite rebounds in an object, the GNSS receiver measures a larger transmission time than the real one [18]. This delay adds an additional position estimation error. There are several methods to reduce the impact of the above sources of errors. Each GNSS receiver model can support some of them; the following are the most usual ones:  
* Advanced multi-frequency and multi-constellation receivers improve the global accuracy and robustness, and are able to reach an accuracy of one meter in ideal conditions. * Satellite-based augmentation systems (SBAS) are geostationary satellites that emit corrections that are valid for specific geographical areas. * The RTK technique described in Section 2.1 provides the best results concerning the global precision. A base, i.e., a receiver whose position is known, may be used to mitigate parts of the errors described above. To know the position of a base with high accuracy, it may be installed over geodesic points of known position, or it can be installed over a point whose position is not initially known, but its average position is computed over a large enough time window. The corrections provided by the base are less effective as the receiver (rover) goes further from the base, since many of these corrections depend on the geographic localization. The accuracy deteriorates at a rate of 2 ppm (parts per million), which corresponds to 2 mm for each kilometer between the base and the rover (baseline). It is important to remark that the absolute position of the rover depends on the absolute position of the base. However, the relative precision of the rover with respect to the base is independent. The installation of a new base requires additional time and equipment, so it is impractical. If infrastructure and Internet connection exist, an alternative solution is to use the GNSS reference station networks. These networks provide corrections by Internet using the NTRIP protocol and allow the rover to move along all the area covered by the networks. In applications where only the relative position between base and rover is important, the absolute position computation of the base may be discarded. In addition, some GNSS receivers can work as a mobile base, which allows the rover to receive corrections from a mobile base with a relative precision of a few centimeters.