A multipath error is one of the main sources of GNSS positioning errors. It cannot be eliminated by forming double-difference and other methods, and it has become an issue in GNSS positioning error processing, because it is mainly related to the surrounding environment of the station. To address multipath errors, three main mitigation strategies are employed: site selection, hardware enhancements, and data processing. Among these, data processing methods have been a focal point of research due to their cost-effectiveness, impressive performance, and widespread applicability. This paper focuses on the review of data processing mitigation methods for GNSS carrier-phase multipath errors. The paper begins by elucidating the origins and mitigation strategies of multipath errors. Subsequently, it reviews the current research status pertaining to data processing methods using stochastic and functional models to counter multipath errors. The paper also provides an overview of filtering techniques for extracting multipath error models from coordinate sequences or observations. Additionally, it introduces the evolution and algorithmic workflow of sidereal filtering (SF) and multipath hemispherical mapping (MHM), from both coordinate and observation domain perspectives. Furthermore, the paper emphasizes the practical significance and research relevance of multipath error processing. It concludes by delineating future research directions in the realm of multipath error mitigation.

The Kalman filter is an optimal estimator with numerous applications in technology, especially in systems with Gaussian distributed noise. Moreover, the adaptive Kalman filtering algorithms, based on the Kalman filter, can control the influence of dynamic model errors. In contrast to the adaptive Kalman filtering algorithms, the H-infinity filter is able to address the interference of the stochastic model by minimization of the worst-case estimation error. In this paper, a novel adaptive H-infinity filtering algorithm, which integrates the adaptive Kalman filter and the H-infinity filter in order to perform a comprehensive filtering algorithm, is presented. In the proposed algorithm, a robust estimation method is employed to control the influence of outliers. In order to verify the proposed algorithm, experiments with real data of the Global Positioning System (GPS) and Inertial Navigation System (INS) integrated navigation, were conducted. The experimental results have shown that the proposed algorithm has multiple advantages compared to the other filtering algorithms.

The Kalman filter has been widely applied in the field of dynamic navigation and positioning. However, its performance will be degraded in the presence of significant model errors and uncertain interferences. In the literature, the fading filter was proposed to control the influences of the model errors, and the H-infinity filter can be adopted to address the uncertainties by minimizing the estimation error in the worst case. In this paper, a new multiple fading factor, suitable for the Global Positioning System (GPS) and the Inertial Navigation System (INS) integrated navigation system, is proposed based on the optimization of the filter, and a comprehensive filtering algorithm is constructed by integrating the advantages of the H-infinity filter and the proposed multiple fading filter. Measurement data of the GPS/INS integrated navigation system are collected under actual conditions. Stability and robustness of the proposed filtering algorithm are tested with various experiments and contrastive analysis are performed with the measurement data. Results demonstrate that both the filter divergence and the influences of outliers are restrained effectively with the proposed filtering algorithm, and precision of the filtering results are improved simultaneously.

Single receiver positioning has been widely used as a standard and standalone positioning technique for about 25 years. To detect the slowly growing faults caused by satellite and receiver clocks in single receiver positioning, the Autonomous Integrity Monitoring with an Extrapolation method (AIME) was proposed based on the Kalman filter measurement domain. However, AIME was designed with the assumption of there is the same number of visible satellites at each epoch, which limits its application. To address this issue, this paper proposes a state-domain Robust Autonomous Integrity Monitoring with the Extrapolation Method (SRAIME). The slowly growing fault detection statistics is established based on the difference between the estimates of the state propagator and the posterior state estimation in Kalman filtering. Meanwhile, singular value decomposition is adopted to factor the covariance matrix of the difference to increase computational robustness. Besides, the relevant formulas of the proposed method are theoretically derived, and it is proven that the proposed method is suitable for any positioning model based on the Kalman filter. Additionally, the results of two experiments indicate that SRAIME can detect slowly growing faults in single receiver positioning earlier than AIME.

Global Navigation Satellite System (GNSS) carrier phase measurement for short baseline meets the requirements of deformation monitoring of large structures. However, the carrier phase multipath effect is the main error source with double difference (DD) processing. There are lots of methods to deal with the multipath errors of Global Position System (GPS) carrier phase data. The BeiDou navigation satellite System (BDS) multipath mitigation is still a research hotspot because the unique constellation design of BDS makes it different to mitigate multipath effects compared to GPS. Multipath error periodically repeats for its strong correlation to geometry of satellites, reflective surface and antenna which is also repetitive. We analyzed the characteristics of orbital periods of BDS satellites which are consistent with multipath repeat periods of corresponding satellites. The results show that the orbital periods and multipath periods for BDS geostationary earth orbit (GEO) and inclined geosynchronous orbit (IGSO) satellites are about one day but the periods of MEO satellites are about seven days. The Kalman filter (KF) and Rauch-Tung-Striebel Smoother (RTSS) was introduced to extract the multipath models from single difference (SD) residuals with traditional sidereal filter (SF). Wavelet filter and Empirical mode decomposition (EMD) were also used to mitigate multipath effects. The experimental results show that the three filters methods all have obvious effect on improvement of baseline accuracy and the performance of KT-RTSS method is slightly better than that of wavelet filter and EMD filter. The baseline vector accuracy on east, north and up (E, N, U) components with KF-RTSS method were improved by 62.8%, 63.6%, 62.5% on day of year 280 and 57.3%, 53.4%, 55.9% on day of year 281, respectively.