3.3 The Extremity of Positioning Error
According to the RTCA DO-253 document standard [8], the integrity risk value of
satellite navigation ground-based augmentation system (GBAS) is 10
−8
–10
−7 . If the
frequency estimation is used to calculate the integrity risk, the required sample number
should be 10
8 at least. Even if the sampling frequency is 1 Hz, the acquisition time will
reach several years. So we can see that the event of positioning error exceeding the
limit is extreme and it is difficult to appear in short-term observation experiments.
Therefore, the integrity evaluation of the system needs to deduce the integrity risk value
by establishing the distribution model of positioning error.
3.4 The Thick Tail of Positioning Error
The integrity risk evaluation of satellite navigation system mainly focuses on the
characteristics of the distribution tail of positioning error as the occurrence of larger
error. Therefore, whether the positioning error has a thick tail is the key to choose the
distribution model. Compared with the normal distribution, if the tail descent rate of a
given distribution is slower than that of the normal distribution, it can be judged that the
distribution is thick-tailed. The hist function of MATLAB software can be used to
make intuitive statistics on the distribution of vertical positioning error in Sect. 3.1 and
the result is shown in Figs. 8 and 9.
Fig. 8. Vertical error distribution of single-point positioning
Analysis and Experimental Research on Data Characteristics …
43
According to the RTCA DO-253 document standard [8], the integrity risk value of
satellite navigation ground-based augmentation system (GBAS) is 10
−8
–10
−7 . If the
frequency estimation is used to calculate the integrity risk, the required sample number
should be 10
8 at least. Even if the sampling frequency is 1 Hz, the acquisition time will
reach several years. So we can see that the event of positioning error exceeding the
limit is extreme and it is difficult to appear in short-term observation experiments.
Therefore, the integrity evaluation of the system needs to deduce the integrity risk value
by establishing the distribution model of positioning error.
3.4 The Thick Tail of Positioning Error
The integrity risk evaluation of satellite navigation system mainly focuses on the
characteristics of the distribution tail of positioning error as the occurrence of larger
error. Therefore, whether the positioning error has a thick tail is the key to choose the
distribution model. Compared with the normal distribution, if the tail descent rate of a
given distribution is slower than that of the normal distribution, it can be judged that the
distribution is thick-tailed. The hist function of MATLAB software can be used to
make intuitive statistics on the distribution of vertical positioning error in Sect. 3.1 and
the result is shown in Figs. 8 and 9.
Fig. 8. Vertical error distribution of single-point positioning
Analysis and Experimental Research on Data Characteristics …
43