Correction Model of BDS-3 Satellite Pseudorange Multipath Delays and Its Impact on Single-Frequency Precise Point Positioning

Precise point positioning (PPP) is used in many fields. However, pseudorange multipath delay is an important error that restricts its accuracy. Pseudorange multipath delay can be considered as the combination of effective information and observation noise; it can be modeled after removing the observation noise. In this work, elastic nets (EN) regularization denoising method is proposed and compared with L2-norm regularization denoising method. Then, quadratic polynomial (QP) model plus autoregressive (AR) model (QP + AR) are used to model the denoised pseudorange multipath delays. Finally, the modeling results are corrected to the observations to verify the improvement of BDS-3 single-frequency PPP accuracy. Three single-frequency PPP schemes are designed to verify the effectiveness of denoising method and QP + AR model. The experimental results show that the accuracy improvement of B3I and B2a is more obvious than that of B1I and B1C when the modeling values are corrected to the pseudorange observations. The improvement of B3I and B2a in the east (E) and up (U) directions can reach 10.6%∼34.4% and 5.9%∼65.7%, and the improvement of the north (N) direction is mostly less than 10.0%. The accuracy of B1I and B1C in E and U directions can be improved by 0%∼30.7% and 0.4%∼28.6%, respectively, while the accuracy of N direction can be improved slightly or even decreased. Using EN regularization denoising and QP + AR model correction, single-frequency PPP performs better at B3I and B2a, while L2-norm regularization denoising and QP + AR model correction perform better at B1I and B1C. The accuracy improvement of B2a and B3I is more obvious than that of B1I and B1C. The convergence time after MP correction of each frequency is slightly shorter. Overall, the proposed pseudorange multipath delays processing strategy is beneficial in improving the single-frequency PPP of BDS-3 satellite.

Improved Mitigation Method for the Multipath Delays of BDS-3 Code Observations with the Aid of a Sparse Modeling Algorithm

Global navigation satellite systems are essential for positioning, navigation, and timing services. The quality and reliability of satellite observations determine the system performance, especially in the case of the newly launched global BDS-3 service. However, analyses of multipath delays in BDS-3 satellite observations suggest that there are appreciable errors at different frequencies. Improvement of the accuracy and precision of positioning, navigation, and timing services provided by BDS-3 requires the mitigation of multipath delays of the satellite observations. This paper models the multipath delays of BDS-3 observations using a least-squares combined autoregressive method. Furthermore, a sparse modeling algorithm is proposed to obtain a multipath delay series using total variation and elastic net terms for denoising and eliminating the effect of limited original observations. The estimated coefficients of multipath delays are then set as prior information to correct the next-arc code observations, where the square-root information filter is used in the coefficient estimation. Moreover, four groups of experiments are conducted to analyze the results of modeling the BDS-3 multipath delay using the proposed methods, with single-frequency precise point positioning (PPP) and real-time PPP solutions being selected to test the correction of multipath delays in BDS-3 code observations. The residuals of iGMAS and MGEX station coordinates indicate improvements in eastward, northward, and upward directions of at least 4.1%, 9.6%, and 1.2%, respectively, for the frequency B1I; 6.6%, 5.3%, and 0.2%, respectively, for B3I, 12.5%, 14.3%, and 3.8%, respectively, for B1C; and 5.9%, 7.4%, and 18.1%, respectively, for B2a relative to the use of the traditional method in BDS-3 single-frequency PPP. Furthermore, the real-time double-frequency PPP is optimized by at least 10% for B 1 I + B 3 I and B 1 C + B 2 a . An improved result was obtained with the proposed strategy in a standard point positioning experiment. The proposed multipath delay mitigation method is therefore effective in improving BDS-3 satellite code observations.