Multipath extraction and mitigation for static relative positioning based on adaptive layer wavelet packets, bootstrapped searches and CNR constraints

Abstract

Multipath is one of the major error sources in high-precision GNSS positioning since it cannot be mitigated by double differences or corrected by empirical models. Considering that the multipath error is related to the carrier-to-noise ratio (CNR) of the signal strength, an enhanced multipath extraction and mitigation method based on an adaptive layer wavelet packets, bootstrapped searches strategy and CNR constraints is proposed. The key concept of the proposed method is to use the adaptive layer-selecting wavelet packets transform to improve the precision of the multipath correction model, which is extracted from the reference day. In addition, to improve the accuracy and effectiveness of multipath mitigation on the subsequent observation day, a bootstrap search strategy based on CNR constraints is adopted. Real data sets are collected to assess the performance of the denoising and the static relative positioning of the proposed method; experimental results show that: (1) the multipath residuals of the carrier phase maintain a strong relationship with the CNR. Thus, the proposed method based on CNR constraints is feasible. Moreover, based on analysis of the distribution of multipath residuals, it can be found that constant layer wavelet packets transform denoising can not only lead to inefficiency for most epochs with low residuals but can also reduce the effectiveness of denoising for epochs with large residuals. (2) The average improvement rate of the root mean square (RMS) of the single-difference residuals after adopting the proposed method can reach approximately 25.33% compared with the original residuals and approximately 10.37% compared with the constant layering method, which indicates that the proposed method can improve the accuracy of the multipath correction model effectively; (3) For the positioning results, after applying the proposed method, the RMS of bias can improve 30.77, 31.25 and 38.20% in the east, north and up components compared with the original result. Even compared with the constant layering multipath mitigation method, the improvement rate can also reach approximately 29.79% for 3D positioning. It is worth noting that this proposed method is also suitable for other GNSS static relative positioning applications such as BDS and Galileo.