The effect of navigation frequency on smoothed pseudorange variance in SBAS

In Satellite Based Augmentation Systems (SBAS), reference stations are equipped with dual-frequency receivers to obtain pseudorange and carrier phase measurements, since carrier phase measurement is less affected by multipath and noise than pseudorange, it could be used to smooth the pseudorange, and simultaneously ionospheric delay estimation could be got. The Hatch filter is an averaging filter that can smooth pseudorange measurements with carrier phase. The ionosphere is the largest remaining error source affecting GPS. It also has some of the largest predictable spatial and temporal variations. As such the ionosphere becomes the determining factor in system performance for SBAS. Thus in this paper, pseudorange are smoothed by continuous carrier phase measurements, non-divergence Hatch filter is adopted to compensate for the ionospheric variation. Then the ionospheric delay correction can be got with smoothed measurements. As an important element of integrity in SBAS, the ionospheric measurement variance will be calculated and verified in this paper. In the simulation, the ionospheric delay measurements are generated through Klobuchar model, which is added by two items of high-frequency variety, the observation noise is of Gaussian distribution with zero mean value. The simulation result suggests that the variance of smoothed pseudorange gradually decreases with the smoothing time, and tends to be a stable value, which fits the theoretical analysis well. Furthermore, regardless of the ionospheric effect, the variance equals to the carrier phase measurement variance; however, due to the ionospheric delay, the variance is somewhat enlarged and has relevance to the frequency of navigation signal.