Abstract
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.
Highlights
Global Navigation Satellite System (GNSS) relative positioning has been widely applied in many fields, such as structural health monitoring [1], crustal motion monitoring [2], mine deformation monitoring [3], and attitude determination [4]
In order to verify the consistency between orbital period and multipath periods of Global Position System (GPS) satellites and the feasibility of the regularization method, we calculated the residuals and extracted the multipath model with respect to each satellite, and evaluated the baseline results
To ensure that the base station is not affected by multipath effects and the rover station has a significant multipath effect, we turned off the anti-multipath function of the rover station, while switching on the function of the base station
Summary
GNSS relative positioning has been widely applied in many fields, such as structural health monitoring [1], crustal motion monitoring [2], mine deformation monitoring [3], and attitude determination [4]. Multipath errors and some other random noises are still remained. This can be clearly seen in the carrier phase measurement residual series, as shown in the following figures. Systematic patterns can be seen even by the naked eye, which violates the assumption of purely random noises. These systematic patterns are deemed the effect of multipath errors. The magnitude of multipath error can be as high as a quarter of the signal wavelength [5,6,7]. The effects of multipath errors cannot be ignored in the above-mentioned high precision applications. Work should be conducted to model and mitigate the influences of the multipath errors
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