A Height Constrained Adaptive Kalman Filtering Based on Climbing Motion Model for GNSS Positioning

In the past decades, short multipath effect is one of the most important error sources in global navigation satellite systems (GNSS) navigation, and seriously affects the positioning precision. Therefore, some algorithms based on traditional Kalman filtering (KF) have been proposed to overcome the short multipath effect, for example extended KF (EKF), adaptive KF (AKF) and constrained KF (CKF). However, height positioning accuracy of EKF and AKF is lower than that of horizontal. On the other hand, CKF requires additional height information from a barometer or location service system. To overcome the limitations of current algorithms, this paper first proposes an empirical multipath residual model after GNSS baseband processing, which shows that pseudo range error exhibits “rectangular” distribution or “shock” distribution. This paper also demonstrates that GNSS positioning error has the same distribution as the pseudo range error, and the height positioning error is higher than the horizontal positioning error in influence of short multipath effect. To improve the height positioning accuracy and suppress the short multipath effect, we propose a practical climbing motion model to constrain the height estimation in the AKF, which can effectively suppress short multipath effect and achieve an improved positioning result. Field tests illustrate that the proposed height constrained AKF (HCAKF) improves the height positioning accuracy by 85.1% over traditional EKF, 85.4% over AKF, and improves the total positioning accuracy by 56.9% over traditional EKF, 37.8% over AKF. Furthermore, the height estimate from HCAKF is smoother than those from traditional EKF and AKF.