Determination of GNSS receiver elevation-dependent clock bias accuracy

Abstract

The differentiation of observation equations allows for the elimination of most ofGNSS errors. The receiver clock error (bias) is eliminated by the measurements of two satellites in a single difference observation equation combination. The satellite clock error is eliminated by the observations of two receivers and its magnitude is correlated with geometric error due tothe speed of light. Motivation for this paper was commonly used erroneous statement says that the receiver's clock correction must be known at the same level as satellite’s ones. As previously stated, this is mistakenly treated as a direct derivative of the speed of light, i.e. 1 µs = 300 m, 1 ns = 30 cm etc. This paper presents the method of calculation of receiver clock bias depending on zenith angle. Hypothesis is showed in a theoretical part, where radial velocity of the satellite with relation to the receiver and error in geometric distance generated by receiver with 1 µs clock error were calculated for four different GNSS (GPS, GLONASS, Galileo and Beidou) systems. In a practical part reference station located near equator was selected and together with satellite positions of four GNSS systems, obtained from precise orbit files calculations were made. A result on the base on selected sort of data both theoretical and practical calculations were consistent. Concluding, the receiver is unblinking in relation tothe satellite, thus the receiver clock error is correlated with the satellite zenith angle and must be known within 3–4 orders of magnitude better compared to the satellite one. A novelty and innovation is proved by the fact that these kinds of calculations have never been published before. Both theoretical and practical calculation part proves that receiver clock error at 1 μs level leads to only 1 mm geometrical error and might be eliminated by the usage of precise oscillator providing this level of accuracy.