Multipath Mitigation Method in GPS/BDS Deformation Monitoring Based on Observation Domain

The multipath effect is a crucial error source caused by the environment around the station and cannot be eliminated or mitigated by differential algorithms. Theoretically, the maximum value for the carrier phase is a quarter the wavelength, i.e., about 4.8 cm for the GPS L1 signal. Considering the increasing demands of high-precision applications, the multipath error has become a major factor affecting the accuracy and reliability of GPS millimeter-level data processing. This paper proposes a multi-point hemispherical grid model (MHGM) to mitigate the multipath effect. In this method, the hemisphere centered on each station is divided into a grid, and the multipath error at the station is estimated based on the parameterization of the grid points. The double-differenced (DD) observed-minus-calculated (OMC) values on some previous days are treated as the observation values to model the present multipath error. Contrary to the present methods which rely much on the platform of data collection and processing, MHGM can be potentially applied to GPS data processing with the existing hardware and software. Experiments in high-multipath and low-multipath environments are designed by mounting a baffle or not. The experimental results show that MHGM is effective in mitigating the multipath effect. When using data from the previous day, an average improvement of about 63.3% in the RMS of DD OMC can be made compared with that without correction, and this is basically consistent with the sidereal filtering (SF) method which is 63.0%. Furthermore, the effectiveness of the above two methods is better than that of the empirical site model (ESM). The kinematic positioning results are also basically consistent with the statistical results of the RMS values of DD OMC. Historical data from more than one day can more explicitly and effectively model the MHGM. Furthermore, compared with the SF method, the MHGM can be used not only to mitigate the multipath error, but also to orientate the sources of the multipath error around the station, and give guidance in the physical elimination of these sources.

In view of the problem of the long-term variation of code multipath error (called code multipath bias) in the IGSO and MEO satellite observable, code multipath bias of BDS is analyzed using iGMAS data of multiple earth stations. In addition, the GPS and BDS multipath error variation is analyzed comparatively. The results show that the variation of BDS multipath error is related to the elevation angle, satellite orbit type and carrier frequency, but independent with the location of the receivers. And for the carrier frequency B1, B2, and B3, the code multipath bias for MEO satellite is 1.66, 1.05 and 0.53 m, respectively. For IGSO satellite the code multipath bias is 0.65, 0.44, and 0.31 m accordingly, which are smaller than that reported by earlier papers. Especially, for IGSO at frequency B2 and B3, the code multipath bias is smaller than half of that reported earlier. At the same time, in order to reduce the multipath bias, a two-order polynomial fitting algorithm is proposed in this paper. The results show that: compared with the results of piecewise linear model with 10 correction parameters, the two-order polynomial correction algorithm with three correction parameters can correct the multipath error and reduce the RMS of the multipath error more effectively. The two-order polynomial model in this paper is more convenient considering broadcasting the correction information to the users.

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.

Multipath, where GPS signals arrive by more than one path and thereby create a range error, has remained the long-lasting major error source in GPS solutions although having been a target of the GPS research community since the day the system started operating. Seeking to understand the GPS multipath errors, this report aims to ef?ciently mitigate multipath effects at observable levels to improve the accuracy and precision of GPS solutions.Based on an analysis of the geometry of a multipath signal's reflections, and the principle of GPS receiver's tracking loop, geometrical models of multipath errors are developed at observable levels (both code and carrier-phase multipath). More specifically, multipath errors corresponding to a satellite are mathematically proven to be functions of the satellite's geometry with respect to a receiver which is parameterized by azimuth and elevation angles. Hence, the problem of multipath error estimation amounts to a regression problem where the multipath functions are approximated using training data. Whereas the theory behind regression problem is robust, the regression problem solution would be feasible as long as a priori data (e.g. training data) is available. As code multipath errors can be easily isolated using a combination of GPS measurements and satellites' geometrical information can be computed using orbital information broadcast from the satellites, training data for the problem code multipath error estimation can be extracted. An experiment was conducted to demonstrate the performance of the proposed method. A real data set was recorded at 0.1 Hz during 5 days to use for the experiment. After training the multipath estimators with data from 31 visible satellites over four days using the epsilon-SVR algorithm, multipath estimation and correction have been performed on the data from the successive day. Results show approximately 80% reduction in term of code multipath error standard deviation, the proposed method shows great promise for understanding and removing multipath errors. Advantageously, while being scalable with data rate, the proposed method is shown to be not harmful to other signals (simulation). An analogous experiment was also conducted to address carrier-phase multipath error. Unfortunately, for a standalone receiver, carrier-phase multipath error cannot be isolated by a combination of measurements as has been done with code multipath error, a carrier-phase double difference between two short-basedlined receivers needs to be made. It results in combinatorial carrier-phase multipath error of 4 satellite-receiver pairs involved in double-difference. Mitigation of this error is beneficial for relative positioning applications. With the same rationale, the multipath error is modeled as a function of the geometries of 4 satellite-receiver pairs. Training the multipath estimation using 1-Hz data from two short-baselined stations of IGS network, preliminary experimental result showed 57% reduction in multipath error for a pair of satellites. My next target is to unify an evaluation framework for multipath mitigation problems with well-defined tests, and evaluation criteria, as this is missing in the literature. Whereas further experiments on carrier-phase multipath mitigation as well as on data recorded from the field need to be done, there is also still room for improvement in multipath estimation algorithms with the focus on computational complexity reduction and incremental learning ability. Integration of the new signals in GPS modernization plans is also worth exploring.

The multipath error is the primary pseudorange measuring error factor in Compass system, in dual-frequency positioning mode, it is difficult to be eliminated by modeling methods, and on the contrary, it is always amplified because of the combination of measuring error. As a result, certain kind of user terminal has lower vertical positioning precision under dual-frequency mode than under single-frequency mode. This paper makes simulation of the impact of multipath error on pseudorange UERE under single-band mode and dual-band mode, obtains the interrelation of ionosphere modeling error, multipath error and the vertical positioning precision of single-band and dual-band respectively. This paper extracts multipath error in pseudorange of GEO and IGSO satellite by pseudorange carrier phase combination method, and uses the ionosphere delay calculated by dual-band carrier phase measurements as a benchmark, makes assessment of the ionosphere delay calculated by dual-band pseudorange combination method and ionospheric delay model correction method, analyses the amount of error correction brought into the Compass system by pseudorange of distinct orbit satellite. Data processing results show that, under current multipath mitigation measures, the pseudorange multipath error will cause that the error of GEO satellite ionosphere delay correction measured by dual-band is larger than by single-band, make a reasonable interpretation of the phenomena that dual-band vertical positioning accuracy is lower than single-band vertical positioning accuracy, and the ionospheric delay correction errors brought by pseudorange multipath error of GEO satellites are greater than the IGSO satellites, verify the phenomenon of “standing multipath error” brought by GEO satellite orbital characteristics.

Regarding the problem of systematic multipath bias on BeiDou navigation system code observations, ten days BeiDou triple-frequency observations of multi-stations were collected, the relationships between the characteristic of multipath bias and the type of the satellite, the signal frequency and the satellite elevation angle were analyse d. In order to solve this problem, a modified sidereal filtering based on zero-phase filter was proposed to mitigate the multipath bias on GEO and IGSO satellites code observations, and elevation-angle correction method was introduced to decrease the multipath bias of IGSO and MEO satellite code observations. The experimental results show that the modified sidereal filtering can decrease the multipath bias of B1, B2 and B3 frequencies code observations for GEO and IGSO satellites over 17.0, 18.6 and 10.5%, respectively, and the elevation-angle correction method can reduce the multipath bias of IGSO and MEO satellite B1, B2 and B3 frequencies code measurements by 5.0, 6.8, and 4.1%, respectively. After mitigating the multipath bias of BeiDou code observations, the precision of single point position for east, north and up directions can be improved about 34, 45 and 51%, respectively.

A GPS multipath mitigation method in coordinate-domain considering the effects of gross errors and missing data

With the first phase of COMPASS/BeiDou-2 (BDS) completed, the assessment of positioning performance and the characterization of its system are analyzed and presented. Pseudo-range and carrier phase measurements modulated on B1 and B2 have been collected in Shanghai, from 00:00 to 24:00 on 28 December, 2012. Compared with GPS, visibility and measurement quality of BDS's GEO, IGSO and MEO satellites are analyzed. DOP during the whole orbital period is also analyzed the results demonstrate that BDS's HDOP is better than GPS's one, but VDOP opposite. Furthermore, the result of positioning is also presented and analyzed. Short baselines are estimated by standalone BDS and GPS's carrier phase measurement, respectively, using 48 segmentations of observations during a whole day (24 hours, each segmentation, is about 30 minutes observation). The analysis of static relative positioning demonstrates that BDS could achieve to millimeter level, corresponding to GPS. Kinematic result is produced by double differenced carrier phase observations with the ambiguities fixed under the constraint of precise short baseline.The result shows that the centimeter accuracy could be achieved. When comparing the results of kinematic baseline solutions, performance of BDS is worse than GPS on North and Up components, but oppositely on the component of East in the kinematic baseline processing.

Though widely used to generate the global navigation satellite system (GNSS) ultra-rapid orbit products for real-time applications, the batch least-squares (LSQ) adjustment and precise orbit determination (POD) prediction is limited for satellites undergoing maneuvers. To generate the truly real-time orbit products, we introduce the square root information filter (SRIF) real-time POD strategy, in which a real-time satellite maneuver handling algorithm that adapts the stochastic model for irregular satellite behaviors is implemented. The performance of the SRIF POD strategy is first evaluated with 1-month of data from multi-GNSS experiment (MGEX) network and BDS experimental tracking stations (BETS). Compared with the MGEX final products provided by GFZ (GBM), the SRIF solutions show higher precision than the ultra-rapid solutions. The averaged 3D RMS of the orbit differences between the SRIF solutions and the GBM final product is about 29.1 cm and 22.5 cm for the BDS IGSO and MEO satellites. The BDS orbits generated by SRIF are continuous over all the time, while the ultra-rapid orbits exhibit obvious jumps and discontinuity at the orbit update time. Validation by satellite laser ranging (SLR) shows that for GEO satellites, the SRIF solutions have better stability and continuity, whereas the GBM final products exhibit obvious accuracy degradation around the day boundary. To evaluate the performance of maneuver handling, the proposed method is further tested on 10 maneuver cases of BDS GEO and IGSO satellites. The start and end time of all maneuver events in different cases are precisely detected, which are consistent with the officially announced ones. Using the proposed strategy, the filter avoids divergence and outputs continuous orbit solutions during the maneuver periods and restores the normal POD within about 7.5 h after the maneuver is finished.

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.

In the Global Navigation Satellite System (GNSS), the multipath error affected by many aspects is the main error source that affects satellite navigation, and it is difficult to establish a much more accurate model to analyze it. Based on the ground multipath reflection model, it firstly deeply studies the influence of GNSS satellite orbit parameters on multipath fading frequency and establishes a multipath signal model related to satellite orbit parameters. Secondly, the influence of carrier phase cycle slip, receiver clock adjustment, and GNSS satellite orbit on multiparameter- (MP-) combined observations is analyzed in detail based on the measured data. Finally, aiming at the common phenomenon of code-carrier divergence in the Beidou system, the elevation-based pseudorange correction model and a sidereal filtering are built to correct the MP errors; experiments with measured data show that there is a fluctuation range reduction of 35.7% after sidereal filtering when the receiver reaches a steady state.

Triple-frequency observations will introduce an inter-frequency clock bias (IFCB) between the new frequency and the original dual-frequency observations. It has been verified that satellite IFCB can reach dozens of centimeters and several centimeters for GPS Block IIF satellite and BDS satellite, respectively. The existence of satellite IFCB will significantly affect undifferenced triple-frequency data processing. Based on 4-year data collected from 80 globally distributed stations, the long-term characteristics of IFCB coefficients obtained by using harmonic analysis have been studied. The results demonstrate that the coefficients of IFCB periodic model cannot be well fitted only by using sun elevation angle. Also, coefficients have obvious periodic characteristics and their periods differ among different satellites. Thus, a new linear-plus-periodic model is proposed to fit the long-term coefficients. Then, IFCB empirical correction models for 12 GPS Block IIF satellites and BDS GEO and IGSO satellites are built. In order to validate the correction model, IFCB standard deviation (STD), triple-frequency precise point positioning (PPP) and undifferenced extra-wide-lane (EWL) ambiguity resolution are employed. The results based on more than 4-year observations show that, with correction model applied, the average IFCB STD decreases by about 65.5% and 45.5% for GPS and BDS satellites, respectively. Compared to triple-frequency PPP without IFCB correction, triple-frequency PPP results with IFCB correction show that Up, North and East components accuracy are improved by 12.3%, 16.0% and 13.2%, respectively. Besides, IFCB correction will greatly improve the consistence of EWL fractional cycle bias among different stations and improve the success rate of EWL ambiguity resolution.

With the rapid development of the Beidou satellite navigation system (BDS), assessment of its signal quality and navigation performance becomes more and more important. The pseudo-range multipath, carrier-phase signal-to-noise ratio (SNR) and accuracy of standard point positioning are usually taken as the indicators for assessment. In this research, we compared the signal quality and navigation performance of BDS with other three Global Navigation Satellite System (GPS, GLONASS, Galileo). The results of the Asia-Pacific region show that the pseudo-range multipath error for BDS is similar with GPS whereas the GLONASS code measurements exhibit a higher level. The level of carrier-phase signal-to-noise ratio for Galileo is largest, but similar for BDS, GPS and GLONASS. The standard point navigation and positioning performance of BDS is slightly lower than GPS, but it is better than GLONASS, and the accuracy of BDS, GPS and GLONASS standard point positioning is about 10 m. The pseudo-range multipath error of BDS increases as the satellites elevation decreases, but the carrier-phase signal-to-noise ratio is opposite. The variation of pseudo-range multipath error of BDS GEO satellites is small except for low satellites elevation, but the variation of signal-to-noise ratio of GEO satellites is relatively stable. The variation of multipath and signal-to-noise ratio of BDS IGSO and MEO satellites is relatively stable when the satellites elevation is larger than a certain value.

The satellite receiver chain is analysed to perform an assessment of the Delay-Locked Loop (DLL) error in a multipath environment. For this purpose, a test bench is created and two multipath models are used. The first one is the fixed-offset model. It is a straight-forward implementation which allows to study the behaviour of the receiver regarding a constant error case. The second model is deterministic-stochastic and it is based on an existing one which is further developed. A deterministic model is appropriate when the system is well-known, whereas a stochastic one describes the uncertainties. Thus, for a multipath environment the mixture of these two leads to a result which is closer to reality. Within this paper, the deterministic part allows the environment modeling and the statistical one models the random scattering. The multipath channel impact on the signal is described on the three observables: signal strength, carrier shift and code phase shift. These quantitative changes which result from the multipath channel modeling are implemented to real hardware signals using the signal generator Spirent GSS7000. This signal generator allows the user to model the channel using input batch files describing signal attenuation as well as code and carrier shifts. The output signal is digitized by the 50 MHz RF front-end of a software receiver, IFEN SX3. Given its modular construction, the tracking engine of the receiver is further parametrized in order to evaluate the multipath error. With a code and carrier accuracy up to 20 cm, respectively one mm, the assessment results can be validated. Signal simulations with and without the implemented multipath models at different receiver velocities are performed. The multipath error is detected and quantified by means of multiple correlators. The behaviour of the Delay-Lock Loop in presence and absence of multipath is analysed.

Multipath effects are the most challenging error sources for the Global Navigation Satellite System receiver, affecting observation quality and positioning accuracy. Due to the non-linear and time-varying nature, multipath error is difficult to process. Previous studies used a homogeneous indicator to characterize multipath effects and only revealed the temporal or spatial correlations of the multipath, resulting in limited correction performance. In this study, we consider the code multipath to be influenced not only by the elevation and azimuth angle of certain stations to satellites but also to be related to satellite characteristics such as nadir angle. Hence, azimuth angle, elevation angle, nadir angle and carrier-to-noise power density ratio are taken as multiple indicators to characterize the multipath significantly. Then, we propose an Attention-based Convolutional Long Short-Term Memory (AT-Conv-LSTM) that fully exploits the spatiotemporal correlations of multipath derived from multiple indicators. The main processing procedures using AT-Conv-LSTM are given. Finally, the AT-Conv-LSTM is applied to a station for 16 consecutive days to verify the multipath mitigation effectiveness. Compared with sidereal filtering, multipath hemispherical map (MHM) and trend-surface analysis-based MHM, the experimental results show that using AT-Conv-LSTM can decrease the root mean square error and mean absolute error values of the multipath error more than 60% and 13%, respectively. The proposed method can correct the code multipath to centimeter level, which is one order of magnitude lower than the uncorrected code multipath. Therefore, the proposed AT-Conv-LSTM network could be used as a powerful alternative tool to realize multipath reduction and will be of wide practical value in the fields of standard and high-precision positioning services.