Single-frequency Divergence-free Hatch Filter for the Low-cost Single-Frequency GNSS Receiver

Abstract

The Hatch filter is a code-smoothing technique that uses the variation of the carrier phase. It can effectively reduce the noise of a pseudorange with a very simple filter construction, but it occasionally causes an ionosphere-induced error for low-lying satellites. To find out the optimal smoothing constant for the conventional Hatch filter, various algorithms have been recently suggested. It is difficult to estimate the ionospheric-error by SF (Single-Frequency) measurement for a single epoch, thus recently proposed methods focus on bounding the divergence due to the ionospheric error, rather than on reducing it. To minimize the effect of the ionosphere-induced error, we propose an SF divergence-free Hatch filter that can compensate for the divergence due to ionospheric variation by the grid ionospheric vertical error (GIVE) from the SBAS message type (MT) 26, which can be easily obtained from typical low-cost single-frequency GNSS receivers. Even though we assume that the SBAS has modelled current ionospheric delay sufficiently, it is necessary to consider the residual error due to the coarse resolution of the ionospheric vertical delay, 0.125 m. Considering the quantization error, we derived the error equation of the SF divergence-free Hatch filter, and found out the optimal smoothing width as a function of pseudorange CNMP (Code Noise and Multi-Path) and Obliquity factor. To verify the suggested SF divergence-free Hatch filter algorithm and to evaluate its performance, we applied MSAS correction to the U-blox M8, which is located in Sejong Unversity, Seoul, S. Korea. 3hr position-domain analysis shows that the optimal SF divergence-free Hatch filter with a smoothing constant of 500 can reduce the RMS error of the conventional Hatch filter with a constant of 300 by 4 cm. 95% percentile error also decreased from 1.28m to 1.19m by enlarging the averaging constant from 300 to 500 for the SF divergence-free Hatch filter. Considering that SF receivers dominate the GNSS market and that most of these receivers include the SBAS function, the filter suggested in this paper is very practical to improve the performance of most receivers while maintaining the recursive and simple form of the conventional Hatch filter. It is also of great value in that it can make the DGPS performance of the low-cost SF receivers comparable to that of DF receivers.