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The Hatch filter is a code-smoothing technique using integrated carrier phase observations. It is an averaging filter that can smooth pseudorange measurements with continuous carrier phase. It is well known that if the smoothing window is an averaging constant, the filter diverges because of opposite signs of the ionospheric error in the code pseudorange and carrier phase. To solve the problem, this paper suggests a new algorithm for the optimal Hatch filter whose smoothing window width varies adaptively depending on the ionospheric delay variation and the satellite elevation. We use the ionosphere mesh model of the SBAS to calculate the ionosphere delay variation. Based a single day’s GPS data, the position accuracy of the pseudorange using optimal Hatch filter outperforms both the pseudorange calculation using classical Hatch filter and the pseudorange calculation without smoothing. Keywords-Global Navigation Satellite System (GNSS), Hatch filter, SBAS, Carrier Phase, Ionospheric delay , Pseudorange smoothing

Optimal Hatch Filter with an Adaptive Smoothing Time Based on SBAS