Optimal Hatch Filter with an Adaptive Smoothing Window Width

Abstract

The Hatch filter is a code-smoothing technique using integrated carrier phase observations. It is an easy technique that non-experts can use to reduce receiver noise on the pseudorange. This paper suggests a new algorithm for the optimal Hatch filter whose smoothing window width varies adaptively depending on the regional, diurnal and seasonal ionospheric variation and satellite elevation angle. We consider both quiet and storm conditions of the ionosphere. Using the well-known quiet ionospheric model, a conservative boundary value for ionospheric storm and the receiver noise statistics function of the satellite elevation angle, this algorithm can mathematically solve the optimal averaging constant for each satellite in every epoch. From a 24 hr data process result and real-time experiment, we found that the position accuracy of the optimal Hatch filter is better and more robust than that of the traditional Hatch filter. The optimal Hatch filter algorithm and its results are expected to provide a new solution for a single-frequency DGPS receiver and a thorough understanding of the relationship between the position error and the averaging constant. Furthermore, a DGPS user who applies this algorithm to a low-cost single-frequency receiver can obtain a more accurate and robust position result than via the classical Hatch filter.