An improved Hatch filter and its application in kinematic positioning with single-frequency GPS

Abstract

The Hatch filter has been widely used in GNSS kinematic positioning and navigation. However, the classic carrier smoothing of code pseudorange observations often results in filter divergence and accuracy degradation in the positioning solution due to the influence of ionospheric delay. One solution is to reduce the impact of ionospheric delay by using the Klobuchar model, which has low correction accuracy. Another solution is to use differential ionospheric delay correction data provided by third parties, which have a high correction accuracy. However, this solution requires the support of obtaining precise ionospheric data through a customized data network. In this study, the authors model the ionospheric delay from the observations themselves and build a mathematical model of the ionospheric delay and its variations. A new and improved Hatch filtering algorithm is proposed. The carrier smoothing of code pseudorange observations in this algorithm has high accuracy and stability because it eliminates the influence of ionospheric delay and variation simultaneously. A sliding average window with an overlap segment is designed for this algorithm, which eliminates the discontinuity in the smoothed data. The analyses in this paper have been performed by means of a set of experimental tests using Trimble, some NETR9 receivers, and a GNSS data processing platform called GNSSer. The executed field tests cover two low kinematic experiments: a ship experiment and a trolley experiment. The results show that the improved Hatch filtering algorithm eliminates most of the influence of the ionosphere and obtains carrier-smoothing pseudorange observations with smoothness and high accuracy. In the kinematic experiment of the ship position, single-frequency pseudorange observations are used to establish an observation equation. The horizontal accuracy of the ship position is approximately 50 cm, and the vertical accuracy is less than 1 m, which is an order of magnitude higher than the accuracy of the classic Hatch filter. However, the kinematic positioning of the trolley is better, the accuracy is within 10 cm in the horizontal and 10–15 cm in the vertical. Both tests show consistent results that the improved Hatch filter has excellent single-frequency, single-epoch positioning performance under low kinematic conditions.