Multipath error mitigation based on wavelet transform in L1 GPS receivers for kinematic applications

GPS precise point positioning (PPP) approach has been considered for achieving time transfer for a long time. By virtue of GPS/Galileo/BDS FCB products, PPP model has the possibilities for changing phase ambiguities from ‘float’ value to ‘integer’ value. In this study, PPP time/frequency transfer model has been presented and performance of seven links equipped with Hydrogen Masers (H-Masers) and cesium atomic clocks are compared in static and kinematic modes. With partial ambiguity resolution (PAR) enabled, in contrast to GPS, results show that multi-GNSS’s fixing rate is much higher and TTFF(Time To First Fixing) is much shorter. It is verified that the fixing rate and TTFF has nothing to do with the atomic clock type but has strong correlation with the quality of observation. We find that frequency stability of time link is seriously dependent on the type of atomic clock. As far as H-Masers, it has reached the order of 1E-16/1E-15 at the averaging time of 122880 s, respectively. As far as Cesium clock, it has reached the order of 1E-15/1E-14 at the averaging time of 122880 s, respectively. For H-Maser, the long-term frequency stabilities of integer PPP (IPPP) have been improved by roughly 3% at the static mode and 4% at the kinematic mode on average, respectively. For positioning, compared to PPP solutions, the stabilities of the IPPP coordinates are improved after an averaging time of 7680 s in static or kinematic mode.

The Chinese Area Positioning System (CAPS) is a new positioning system developed by the Chinese Academy of Sciences based on the communication satellites in geosynchronous orbit. The CAPS has been regarded as a pilot system to test the new technology for the design, construction and update of the BeiDou Navigation Satellite System (BDS). The system structure of CAPS, including the space, ground control station and user segments, is almost like the traditional Global Navigation Satellite Systems (GNSSs), but with the clock on the ground, the navigation signal in C waveband, and different principles of operation. The major difference is that the CAPS navigation signal is first generated at the ground control station, before being transmitted to the satellite in orbit and finally forwarded by the communication satellite transponder to the user. This design moves the clock from the satellite in orbit to the ground. The clock error can therefore be easily controlled and mitigated to improve the positioning accuracy. This paper will present the performance of CAPS-based relative positioning and velocity estimation as assessed in Beijing, China. The numerical results show that, (1) the accuracies of relative positioning, using only code measurements, are 1.25 and 1.8 m in the horizontal and vertical components, respectively; (2) meanwhile, they are about 2.83 and 3.15 cm in static mode and 6.31 and 10.78 cm in kinematic mode, respectively, when using the carrier-phase measurements with ambiguities fixed; and (3) the accuracy of the velocity estimation is about 0.04 and 0.11 m/s in static and kinematic modes, respectively. These results indicate the potential application of CAPS for high-precision positioning and velocity estimation and the availability of a new navigation mode based on communication satellites.

Performance assessment of real-time multi-GNSS integrated PPP with uncombined and ionospheric-free combined observables

The limit of orbit accuracy associated with processing the ionospheric-free double-differenced (DD) GPS carrier phase observable in pure kinematic mode is investigated. The kinematic orbit determination problem becomes unobservable when the satellite positions at all epochs and all of the DD ambiguities are estimated simultaneously without any constraints. Although searching for some of the DD ambiguities can make the problem observable, this is not practical when the DD ambiguities are not integers. However, if a reasonably accurate a priori satellite orbit solution is available, epoch-by-epoch satellite positions and the DD ambiguities can be estimated by constraining a geometrically strong DD pass. The technique was demonstrated with TOPEX GPS data, which gave a final radial RMS orbit accuracy of 4 cm with respect to a fully dynamic solution.

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.

RTKLIB which is an open source Global Navigation Satellite Systems (GNSS) software has gained rapid acceptance among Surveying professionals thanks to recent developments in UAS (Unmanned Aerial System) technology. RTKLIB enables standard and precise point positioning (PPP) in real-time and post-processing modes to be performed. As such, UAS users utilize this software to analyze GNSS data collected by GNSS systems on UAS. By being versatile and free, RTKLIB is commonly used by many; however, it is not the only freely available GNSS software. There are also freely available online GNSS data processing software running on servers. These online GNSS data processing services provide data processing in static, kinematic and rapid static modes. Because UAS collect data in kinematic mode, in this study, kinematic data processing by aforementioned software (CSRS-PPP, GAPS and APPS) is analyzed. The results coming from these software are compared against the results produced by photogrammetric software (Agisoft Metashape and Pix4Dmapper). The aim of this practical project is to produce generalizable knowledge about the performance of these software. It is found out that RTKLIB and CSRS-PPP achieved cm-level precision. Yet, GAPS and APPS achieved dm-level precision both for horizontal and vertical coordinates. This study demonstrates the precision and accuracy expected from these software if they are used for kinematic GNSS data processing.

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.

Real-time capability , positioning accuracy and convergence time ar e the keys to the performance of Precise Point Positioning (PPP). In recent years, the development of IGS Real-Time Services (RTS) has improved the performance of real-time PPP to a large extent. Meanwhile, the PPP ambiguity resolution technique, which significantly improves the positioning accuracy and convergence time, has become mature gradually. If the advantages of both techniques can be combined to realize real-time PPP with ambiguity resolution, the application of PPP would be greatly expanded. In this paper, a real-time satellite-satellite single-difference fractional cycle bias (FCB) estimation method based on RTS products is proposed. To meet the demand of real-time PPP, narrow-lane FCBs are forecasted by short-term linear extrapolation. Taking accuracy levels and data amount into consideration, the forecasting interval for real-time wide-lane and narrow-lane FCBs are determined. Finally, the performance of real-time PPP with ambiguity resolution using real-time FCBs is evaluated in both static and kinematic modes. The results show that wide-lane FCBs to be forecasted daily and narrow-lane FCBs to be forecasted every 5 min can satisfy the need of real-time PPP with ambiguity resolution. In static mode, the average time to first fix (TTFF) is 15.97 min, and the average precision of the north, east and up components for hourly solution are 1.51, 1.64 and 2.18 cm respectively. As for kinematic mode, an average TTFF of 24.36 min is needed, and the 3D position error in fixed solution is decreased by 42.59% compared with float solution.

The release of the world’s first dual-frequency GPS/Galileo smartphone, Xiaomi mi 8, in 2018 provides an opportunity for high-precision positioning using ultra low-cost sensors. In this research, the GNSS precise point positioning (PPP) accuracy of the Xiaomi mi 8 smartphone is tested in post-processing and real-time modes. Raw dual-frequency observations are collected over two different time windows from both of the Xiaomi mi 8 smartphone and a Trimble R9 geodetic-quality GNSS receiver using a short baseline, due to the lack of a nearby reference station to the observation site. The data sets are first processed in differential modes using Trimble business center (TBC) software in order to provide the reference positioning solution for both of the geodetic receiver and the smartphone. An in-house PPP software is then used to process the collected data in both of post-processing and real-time modes. Precise ephemeris obtained from the multi-GNSS experiment (MGEX) is used for post-processing PPP, while the new NAVCAST real-time GNSS service, Germany, is used for real-time PPP. Additionally, the real-time PPP solution is assessed in both of static and kinematic modes. It is shown that the dual-frequency GNSS smartphone is capable of achieving decimeter-level positioning accuracy, in both of post-processing and real-time PPP modes, respectively. Meter-level positioning accuracy is achieved in the kinematic mode.

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.

Image denoising always is one of important research topics in the image processing field. In this paper, fast discrete curvelet transform (FDCT) and undecimated wavelet transform (UDWT) are proposed for image denoising. A noisy image is first denoised by FDCT and UDWT separately. The whole image space is then divided into edge region and non-edge regions. After that, wavelet transform is performed on the images denoised by FDCT and UDWT respectively. Finally, the resultant image is fused through using both of edge region wavelet cofficients of the image denoised by FDCT and non-edge region wavelet cofficients of the image denoised by UDWT. The proposed method is validated through numerical experiments conducted on standard test images. The experimental results show that the proposed algorithm outperforms wavelet-based and curvelet-based image denoising methods and preserve linear features well.

Objectives:  To develop an image enhancement technique that includes both resolution and contrast enhancement. Resolution is the ability of an image to show its details.  In this method, Stationary Wavelet Transform (SWT) is used in combination with Lifting Wavelet Transform (LWT) for resolution enhancement and SWT with the combination of Contrast limited adaptive Histogram Equalization (CLAHE) for contrast enhancement. SWT is used in combination with LWT improves the resolution and also minimizes the execution time drastically. SWT is combined with CLAHE to enhance the Contrast and mitigate the noise effects than existing methods. The proposed method gives superior results, and it is proved with Peak Signal to Noise Ratio (PSNR), Noise Estimation and Root Mean Square Error (RMSE), and pictorial results.

In GNSS real-time high-precision monitoring, the multipath spatial correlation is weak, it is difficult to eliminate the multipath error by double difference, and the traditional method based on the sidereal filtering in the coordinate domain to mitigate multipath error of MEO satellite will no longer be applicable. Aiming at the above problem, this paper storage single difference observation residuals after ambiguity resolved in real-time baseline resolution, where storage residual information for 1d in GPS, BDS GEO, IGSO, and BDS MEO satellite for 7d. When the residual information database initialization is complete, each satellite multipath error sequence model will be established from the residual database by using the low-pass filter method, then mitigating multipath error of the corresponding satellite carrier phase observations in real time. The measured data show that, based on the mitigating multipath of observation domain, the real-time monitoring accuracy of the 3D position can be improved by about 50% after mitigating multipath error in real-time.

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.

Global navigation satellite system (GNSS) has been widely used in many deformation monitoring fields in recent years and can achieve centimeter-level or even sub-centimeter-level real-time monitoring accuracy through the carrier phase double-differenced technique. However, this technique cannot eliminate or weaken multipath errors, which become the main error source for GNSS deformation monitoring. Therefore, extracting deformation information from coordinate series mixed with multipath errors has become a key issue for further improving the accuracy of GNSS deformation monitoring. In this paper, we propose an approach to overcome this issue called empirical wavelet transform-independent component analysis with reference (EWT-ICA-R). The specific process is as follows. First, EWT is employed to model the multipath errors from a priori GNSS coordinate series, and the model is input to ICA-R as a reference signal. Then, the GNSS deformation monitoring series mixed with multipath errors and deformation information is decomposed into sub-series of different scales using EWT, and these sub-series are input to ICA-R as multi-channel signals. Finally, ICA-R is used to calculate the input signals together to obtain the multipath errors in the GNSS deformation monitoring series and then subtract the multipath errors from the GNSS deformation monitoring series to obtain accurate deformation information. Experiments show the following: (1) For the vibration deformation experiments, the correlation coefficients between the deformation information extracted by the proposed method and the real values reached 0.981, 0.981, and 0.885 in the E, N, and U directions, respectively, and the corresponding root mean square errors decrease to 0.694 mm, 0.694 mm, 1.852 mm, respectively. (2) For the slow-deformation experiment, the correlation coefficients in the three directions were all higher than 0.98, and the corresponding root mean square errors decrease to 1.345 mm, 1.546 mm, and 3.866 mm, respectively. The experiments verified the feasibility of the proposed method to accurately extract deformation information, which makes it possible to obtain sub-millimeter GNSS deformation information and provide effective technical support for deformation monitoring in related fields.