Characteristics of BeiDou Navigation Satellite System Multipath and Its Mitigation Method Based on Kalman Filter and Rauch-Tung-Striebel Smoother

BDS Dual-Frequency Carrier Phase Multipath Hemispherical Map Model and Its Application in Real-Time Deformation Monitoring

The BDS multipath delay error is highly related to the surrounding monitoring environment, which cannot be eliminated or mitigated by applying the double difference observation model. In the actual monitoring environment, due to the complexity of the BDS constellation, it is difficult for existing algorithms to consider GEO, IGSO, MEO and other different orbital types of satellites for real-time and efficient multipath error reduction. Therefore, we propose a novel BDS dual-frequency multipath error reduction method for real deformation monitoring for BDS considering various satellite orbit types. This method extracts the single error residual of each satellite based on the assumption of "zero mean" and divides the appropriate grid density of GEO and IGSO/MEO, respectively, to construct a dual-frequency multipath hemispherical map model suitable for BDS satellites with different orbital types. This method can realize the multipath error elimination of the observed values of different orbits and different frequencies. The results of simulation experiments and real deformation monitoring data demonstrate that this method can effectively eliminate low-frequency multipath delay errors in the observation domain and coordinate domain. After multipath correction, the precision of the horizontal coordinates and height coordinates are 1.7 mm and 4.6 mm. The precision of the horizontal coordinate and height coordinate is increased by 50% and 60%, respectively. The fixed rate of ambiguity increased by 5-7%.

A Single-Difference Multipath Hemispherical Map for Multipath Mitigation in BDS-2/BDS-3 Short Baseline Positioning

The BeiDou Navigation Satellite System (BDS) features a heterogeneous constellation so that it is difficult to mitigate the multipath in the coordinate-domain. Therefore, mitigating the multipath in the observation-domain becomes more important. Sidereal filtering is commonly used for multipath mitigation, which needs to calculate the orbit repeat time of each satellite. However, that poses a computational challenge and damages the integrity at the end of the multipath model. Therefore, this paper proposes a single-difference model based on the multipath hemispherical map (SD-MHM) to mitigate the BDS-2/BDS-3 multipath in a short baseline. The proposed method is converted from double-difference residuals to single-difference residuals, which is not restricted by the pivot satellite transformation. Moreover, it takes the elevation and the azimuth angles of the satellite as the independent variables of the multipath model. The SD-MHM overcomes the unequal observation time of some satellites and does not require specific hardware. The experimental results show that the SD-MHM reduces the root mean square of the positioning errors by 56.4%, 63.9%, and 67.4% in the east, north, and vertical directions; moreover, it contributes to an increase in the baseline accuracy from 1.97 to 0.84 mm. The proposed SD-MHM has significant advantages in multipath mitigation compared with the advanced sidereal filtering method. Besides, the SD-MHM also features an excellent multipath correction capability for observation data with a period of more than seven days. Therefore, the SD-MHM provides a universal strategy for BDS multipath mitigation.

Detection and Monitoring of Tunneling-Induced Riverbed Deformation Using GPS and BeiDou: A Case Study

Shield tunneling under rivers often requires monitoring riverbed deformations in near real-time. However, it is challenging to measure riverbed deformation with conventional survey techniques. This study introduces a comprehensive method that uses the Global Positioning System (GPS) of the USA and the BeiDou navigation satellite system (BeiDou) of China to monitor riverbed deformation during the construction of twin tunnels beneath the Hutuo River in Shijiazhuang, China. A semi-permanent GPS network with one base station outside the river and six rover stations within the river was established for conducting near real-time and long-term monitoring. The distances between the base and the rover antennas are within two kilometers. The network was continuously operating for eight months from April to December 2018. The method is comprised of three components: (1) Monitoring the stability of the base station using precise point positioning (PPP) method, a stable regional reference frame, and a seasonal ground deformation model; (2) monitoring the relative positions of rover stations using the carrier-phase double-difference (DD) positioning method in near real-time; and (3) detecting abrupt and gradual displacements at both base and rover stations using an automated change point detection algorithm. The method is able to detect abrupt positional-changes as minor as five millimeters in near real-time and gradual positional-changes at a couple of millimeters per day within a week. The method has the flexibility of concurrent processing different GPS and BeiDou data sessions (e.g., every 15 minutes, 30 minutes, one hour, one day) for diffident monitoring purposes. This study indicates that BeiDou observations can also achieve few-millimeter-accuracy for measuring displacements. Parallel processing GPS and BeiDou observations can improve the reliability of near real-time structural deformation monitoring and minimize false alerts. The method introduced in this article can be applied to other urban areas for near real-time and long-term structural health monitoring.

Tikhonov Regularization Based Modeling and Sidereal Filtering Mitigation of GNSS Multipath Errors

In Global Navigation Satellite System (GNSS) relative positioning applications, multipath errors are non-negligible. Mitigation of the multipath error is an important task for precise positioning and it is possible due to the repeatability, even without any rigorous mathematical model. Empirical modeling is required for this mitigation. In this work, the multipath error modeling using carrier phase measurement residuals is realized by solving a regularization problem. Two Tikhonov regularization schemes, namely with the first and the second order differences, are considered. For each scheme, efficient numerical algorithms are developed to find the solutions, namely the Thomas algorithm and Cholesky rank-one update algorithm for the first and the second differences, respectively. Regularization parameters or Lagrange multipliers are optimized using the bootstrap method. In experiment, data on the first day are processed to construct a multipath model for each satellite (except the reference one), and then the model is used to correct the measurement on the second day, namely following the sidereal filtering approach. The smoothness of the coordinates calculated using the corrected measurements is improved significantly compared to those using the raw measurement. The efficacy of the proposed method is illustrated by the actual calculation.