Search Results (9)

In global navigation satellite systems (GNSSs)-based positioning, user receiver clock jump is a common phenomenon on the low-cost receiver clocks and can break the continuity of observation time tag, carrier phase and pseudo range. The discontinuity may affect precise point positioning-related parameter estimation, including receiver clock error, position, troposphere and ionosphere parameters. It is important to note that these parameters can be used for timing, positioning, atmospheric inversion and so on. In response to this problem, the receiver clock jumps are divided into two types. The first one can be expressed by the carrier phase and pseudo range having the same scale jump, and the second one is that they are having different scale jumps. For the first type, if a small priori variance of receiver clock error is provided, it can affect the accuracy of ionospheric delay estimation both in static and kinematic mode, while in the latter mode, it also affects position estimation. However, if large process noise is provided, numerical problems may arise since other parameters’ process noises are usually small, it is proposed to use the single point positioning with pseudo ranges to provide a priori value of receiver clock error, and an empiric value is assigned to its prior variance, this handle can avoid the above problems. For the second type, instead of compensating so many raw observations in the traditional methods, it is proposed to compensate the ambiguities at the clock jump epochs only in a new method. The new method corrects the Melbourne–Wubbena (MW) combination firstly in order to avoid the misjudging of cycle slips for current epoch, and the second step is to compensate the corresponding ambiguities, then, after Kalman filtering, the MW and its mean should be corrected back in order to avoid the misjudging of cycle slips at the next epoch. This approach has the advantage of handling the clock jump epoch-wise and can avoid correcting the rest of the observations as the traditional methods used to. With the numerical validation examples both in static and kinematic modes, it shows the new method is simple but efficient for real time precise point positioning (PPP). Full article

The modernization of Global Navigation Satellite System (GNSS) including the transmission of signals on multiple frequencies has greatly promoted the development of the popular PPP (Precise Point Positioning) technique. A key issue of multi-frequency PPP is the handling of the observable-specific signal biases in order to allow for carrier-phase ambiguity resolution (AR). As a result, PPP modeling at a user side in the multi-frequency case varies depending on the definition of the applied phase bias products. In this study, we investigate the positioning performance of GPS L1/L2/L5 and Galileo E1/E5a/E5b/E6 undifferenced ionosphere-float model in the conventional PPP mode and the single-epoch mode using the uncombined code and phase bias products generated at the French CNES (Centre National D’Etudes Spatiales). A series of widelane ambiguities are configured in our multi-frequency PPP functional model instead of forming the classical Melbourne–Wübbena (MW) combination. The best integer equivariant (BIE) estimator is used for the ambiguity resolution in a conventional cascading scheme according to the wavelength of the combined ambiguities for each constellation. Real data collected at IGS stations with a 30-s sampling interval is applied to evaluate the above models. For the conventional kinematic PPP configuration, a significant accuracy improvement of 63% on the east component of the fixed solution is obtained with respect to the ambiguity-float solution. The PPP convergence is accelerated by 17% after the AR. Regarding the single-epoch positioning, an accuracy of 32 and 31 cm for north and east components can be achieved, respectively, (68th percentile) with the instantaneous widelane-ambiguity resolution, which is improved by 13% and 16% compared to multi-frequency code-based or float solution. Full article

Due to different designs of receiver correlators and front ends, receiver-related pseudorange biases, called signal distortion biases (SDBs), exist. Ignoring SDBs that can reach up to 0.66 cycles and 10 ns in Melbourne-Wübbena (MW) and ionosphere-free (IF) combinations can negatively affect phase bias estimation. In this contribution, we investigate the SDBs and evaluate the impacts on wide-lane (WL) and narrow-lane (NL) phase bias estimations, and further propose an approach to eliminating these SDBs to improve phase bias estimation. Based on a large data set of 302 multi-global navigation satellite system (GNSS) experiment (MGEX) stations, including 5 receiver brands, we analyze the characteristics of these SDBs The SDB characteristics of different receiver types for different GNSS systems differ from each other. Compared to the global positioning system (GPS) and BeiDou navigation satellite system (BDS), SDBs of Galileo are not significant; those of BDS-3 are significantly superior to BDS-2; Septentrio (SEPT) receivers show the most excellent consistency among all receiver types. Then, we apply the corresponding corrections to phase bias estimation for GPS, Galileo and BDS. The experimental results reveal that the calibration can greatly improve the performance of phase bias estimation. For WL phase biases estimation, the consistencies of WL phase biases among different networks for GPS, Galileo, BDS-2 and BDS-3 improve by 89%, 77%, 76% and 78%, respectively. There are scarcely any improvements of the fixing rates for Galileo due to its significantly small SDBs, while for GPS, BDS-2 and BDS-3, the WL ambiguity fixing rates can improve greatly by 13%, 27% and 14% after SDB calibrations with improvements of WL ambiguity fixing rates, the corresponding NL ambiguity fixing rates can further increase greatly, which can reach approximately 16%, 27% and 22%, respectively. Additionally, after the calibration, both WL and NL phase bias series become more stable. The standard deviations (STDs) of WL phase bias series for GPS and BDS can improve by more than 46%, while those of NL phase bias series can yield improvements of more than 13%. Ultimately, the calibration can make more WL and NL ambiguity residuals concentrated in ranges within ±0.02 cycles. All these results demonstrate that SDBs for phase bias estimation cannot be ignored and must be considered when inhomogeneous receivers are used. Full article

Many Beidou navigation satellite system (BDS) receivers or boards provide dual-frequency measurements to conduct precise positioning and navigation for low-power consumption. Cycle-slip processing is a primary work to guarantee consistent, precise positioning with the phase data. However, the cycle-slip processing of BDS dual-frequency phases still follows with those of existing GPS methods. For single-satellite data, cycle-slip detection (CSD) with the geometry-free phase (GF) is disturbed by severe ionospheric delay variations, while CSD or cycle-slip repair (CSR) with the Melbourne–Wubbena combination (MW) must face the risk of the tremendous disturbance from large pseudorange errors. To overcome the above limitations, a new cycle-slip repair method for BDS dual-frequency phases (BDCSR) is proposed: (1) An optimal model to minimize the variance of the cycle-slip calculation was established to the dual-frequency BDS, after correcting the ionospheric variation with a reasonable and feasible way. (2) Under the BDS dual-frequency condition, a discrimination function was built to exclude the adverse disturbance from the pseudorange errors on the CSR, according to the rankings of the absolute epoch-difference GFs calculated by the searched cycle-slip candidates after correcting the ionospheric variation. Subsequently, many compared CSR tests were implemented in conditions of low and medium elevations during strong geomagnetic storms. Comparisons from the results of different methods show that: (1) The variations of ionospheric delays are intolerable in the cycle-slip calculation during the geomagnetic storm, and the tremendous influence from the ionospheric variation should be corrected before calculating the cycle-slip combination with the BDS dual-frequency data. (2) Under the condition of real dual-frequency BDS data during the geomagnetic storm, the actual success rate of the conventional dual-frequency CSR (CDCSR) by employing the optimized combinations, but absenting from the discrimination function, is lower than that of BDCSR by about 2%; The actual success rate of the CSD with MW (MWCSD), is lower than that of BDCSR by about 2%. (3) After adding gross errors of 0.7 m to all real epoch-difference pseudoranges epoch-by-epoch, results of CDCSR and MWCSD showed many errors. However, BDCSR achieved a higher actual success rate than those of CDCSR and MWCSD, about 43% and 16%, respectively, and better performance of refraining the disturbance of large pseudorange error on the cycle-slip determination was achieved in the BDCSR methodology. Full article

Recently, some smartphone manufacturers have subsequently released dual-frequency GNSS smartphones. With dual-frequency observations, the positioning performance is expected to be significantly improved. Cycle-slip detection and correction play an important role in high-precision GNSS positioning, such as precise point positioning (PPP) and real-time kinematic (RTK) positioning. The TurboEdit method utilizes Melbourne–Wübbena (MW) and phase ionospheric residual (PIR) combinations to detect cycle-slips, and it is widely used in the data processing applications for geodetic GNSS receivers. The smartphone pseudorange observations are proved to be much noisier than those collected with geodetic GNSS receivers. Due to the poor pseudorange observation, the MW combination would be difficult to detect small cycle-slips. In addition, some specific cycle-slip combinations, where the ratio of cycle-slip values at different carrier frequencies is close to the frequency ratio, are also difficult to be detected by PIR combination. As a consequence, the traditional TurboEdit method may fail to detect specific small cycle-slip combinations. In this contribution, we develop a modified TurboEdit cycle-slip detection and correction method for dual-frequency smartphone GNSS observations. At first, MW and PIR combinations are adopted to detect cycle-slips by comparing these two combinations with moving-window average values. Then, the epoch-differenced wide-lane combinations are used to estimate the changes of smartphone position and clock bias, and the cycle-slip is identified by checking the largest normalized residual whether it exceeds a predefined threshold value. The process of estimation and cycle-slip identification is implemented in an iterative way until there is no over-limit residual or there is no redundant measurement. At last, the cycle-slip values at each frequency are estimated with the epoch-differenced wide-lane and ionosphere-free combinations, and the least-square ambiguity decorrelation adjustment (LAMBDA) method is adopted to further obtain an integer solution. The proposed method has been verified with 1 Hz dual-frequency smartphone GNSS data. The results show that the modified TurboEdit method can effectively detect and correct even for specific small cycle-slip combinations, e.g., (4, 3), which is difficult to be detected with the traditional TurboEdit method. Full article

Ambiguity resolution (AR) is critical for achieving a fast, high-precision solution in precise point positioning (PPP). In the standard uncombined PPP (S-UPPP) method, ionosphere-free code biases are superimposed by ambiguity and receiver clock offsets to be estimated. However, besides the time-constant part of the receiver code bias, the complex and time-varying term in receivers destroy the stability of ambiguities and degrade the performance of the UPPP AR. The variation of receiver code bias can be confirmed by the analysis in terms of ionospheric observables, code multipath (MP) of the Melbourne–Wübbena (MW) combination and the ionosphere-free combination. Therefore, the effect of receiver code biases should be rigorously mitigated. We introduce a modified UPPP (M-UPPP) method to reduce the effects of receiver code biases in ambiguities and to decouple the correlation between receiver clock parameters, code biases, and ambiguities parameters. An extra receiver code bias is set to isolate the code biases from ambiguities. The more stable ambiguities without code biases are expected to achieve a higher success rate of ambiguity resolution and a shortened convergence time. The variations of the receiver code biases, which are the unmodeled errors in measurement residuals of the S-UPPP method, can be estimated in the M-UPPP method. The maximum variation of the code biases is up to 16 ns within two-hour data. In the M-UPPP method, the averaged epoch residuals for code and phase measurements recover their zero-mean features. For the ambiguity-fixed solutions in the M-UPPP method, the convergence times are 14 and 43 min with 17.7% and 69.2% improvements compared to that in the S-UPPP method which are 17 and 90 min under the 68% and 95% confidence levels. Full article

Many strategies for treating dual-frequency cycle slip, which can seriously affect the performance of a carrier-phase-based positioning system, have been studied over the years. However, the legacy method using the Melbourne-Wübbena (MW) combination and ionosphere combination is vulnerable to pseudorange multipath effects and high ionospheric storms. In this paper, we propose a robust algorithm to detect and repair dual-frequency cycle slip for the network-based real-time kinematic (RTK) system which generates high-precision corrections for users. Two independent and complementary carrier-phase combinations, called the ionospheric negative and positive combinations in this paper, are employed for avoiding insensitive pairs. In addition, they are treated as second-order time differences to reduce the impact of ionospheric delay even under severe ionospheric storm. We verified that the actual error distributions of these monitoring values can be sufficiently bounded by the normal Gaussian distribution. Consequently, we demonstrated that the proposed method ensures high-integrity performance with a maximum probability of missed detection of 7.5 × 10⁻⁹ under a desired false-alarm probability of 10⁻⁵. Furthermore, we introduce a LAMBDA-based cycle slip compensation method, which has a failure rate of 1.4 × 10⁻⁸. Through an algorithm verification test using data collected under a severe ionospheric storm, we confirmed that artificially inserted cycle slips are successfully detected and compensated for. Thus, the proposed method is confirmed to be effective for handling dual-frequency cycle slips of the network RTK system. Full article

The Chinese BeiDou Navigation Satellite System (BDS) has been an important constitute of the Global Navigation Satellite System (GNSS), and the combination of GPS and BDS shows significant improvements when compared with single GPS system for real-time kinematic (RTK) positioning, and improves on availability and fixing rates, especially in the East Asian area. While network RTK might have different types of receivers, both for global and regional networks, different types of receiver may adopt different internal multipath mitigation methods and other techniques that result in different pseudorange characteristics, especially for a multipath. Then, the performance of wide-lane ambiguity resolution (WL AR) is affected. In this study, we first analyze and compare the characteristics of BDS dual-frequency observations for different types of receivers, including Trimble, Leica, Javad, and Septentrio, based on multipath (MP) observables, and then we assess their influence on double-differenced (DD) WL AR. The numerical results show that an obvious low-frequency component exists in MP observables of BDS geostationary earth-orbit satellites (GEOs) for Leica receivers, while its high-frequency measurement noise is very small. For geosynchronous orbit satellites (IGSOs) and medium earth-orbit satellites (MEOs), a slight fluctuation can also be observed that is similar to that of GPS satellites, except for the satellite-included code bias. In Trimble, Javad, and Septentrio receivers, the MP series are dominated by high-frequency measurement noise, both for GEOs and non-GEOs, except for satellite-included code bias. Furthermore, the characteristic of Leica receivers for BDS GEOs seriously affects WL AR and, even for a short baseline, it takes a long time for WL ambiguities to converge, or not converge for many GEO-related DD WL ambiguities, while Trimble, Javad, and Septentrio receivers perform well for short and medium baselines. Then, a time-difference method is proposed to mitigate the multipath of BDS GEOs for a Leica receiver. After applying the proposed method, WL ambiguity fixing rates of GEO-related satellite pairs are improved significantly and the convergence time is shortened from several hours to ten minutes. Full article

The BeiDou satellite-induced code biases have been confirmed to be orbit type-, frequency-, and elevation-dependent. Such code-phase divergences (code bias variations) severely affect absolute precise applications which use code measurements. To reduce their adverse effects, an improved correction model is proposed in this paper. Different from the model proposed by Wanninger and Beer (2015), more datasets (a time span of almost two years) were used to produce the correction values. More importantly, the stochastic information, i.e., the precision indexes, were given together with correction values in the improved model. However, only correction values were given while the precision indexes were completely missing in the traditional model. With the improved correction model, users may have a better understanding of their corrections, especially the uncertainty of corrections. Thus, it is helpful for refining the stochastic model of code observations. Validation tests in precise point positioning (PPP) reveal that a proper stochastic model is critical. The actual precision of the corrected code observations can be reflected in a more objective manner if the stochastic model of the corrections is taken into account. As a consequence, PPP solutions with the improved model outperforms the traditional one in terms of positioning accuracy, as well as convergence speed. In addition, the Melbourne-Wübbena (MW) combination which serves for ambiguity fixing were verified as well. The uncorrected MW values show strong systematic variations with an amplitude of half a wide-lane cycle, which prevents precise ambiguity determination and successful ambiguity resolution. After application of the code bias correction models, the systematic variations can be greatly removed, and the resulting wide lane ambiguities are more likely to be fixed. Moreover, the code residuals show more reasonable distributions after code bias corrections with either the traditional or the improved model. Full article