Optimal Divergence-Free Hatch Filter for GNSS Single-Frequency Measurement

The Hatch filter is a code-smoothing technique that uses the variation of the carrier phase. It can effectively reduce the noise of a pseudo-range with a very simple filter construction, but it occasionally causes an ionosphere-induced error for low-lying satellites. Herein, we propose an optimal single-frequency (SF) divergence-free Hatch filter that uses a satellite-based augmentation system (SBAS) message to reduce the ionospheric divergence and applies the optimal smoothing constant for its smoothing window width. According to the data-processing results, the overall performance of the proposed filter is comparable to that of the dual frequency (DF) divergence-free Hatch filter. Moreover, it can reduce the horizontal error of 57 cm to 37 cm and improve the vertical accuracy of the conventional Hatch filter by 25%. Considering that SF receivers dominate the global navigation satellite system (GNSS) market and that most of these receivers include the SBAS function, the filter suggested in this paper is of great value in that it can make the differential GPS (DGPS) performance of the low-cost SF receivers comparable to that of DF receivers.