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In ambiguity resolution, the Hatch–Melbourne–Wübbena code and carrier phase combination is usually used to fix the wide-lane (WL) ambiguity, and thus, the quality of the code observations directly affects the fixing success rate, especially when there are some kind of serious bias errors. Unfortunately, we found that the P1 code multipath (MP) errors of the Haiyang-2B calculated using the MP combination formula rapidly increases from sub-meter to several meters at elevation less than 40°. These rapid variations lead to biases in the fixed WL ambiguities. In this article, we create a static correction map on a grid with 5° x 5° resolution. Using this correction map, we reduced the root mean square of the P1 code bias errors from 1.04 to 0.47 m, which corresponds to an improvement of 54.8%. By comparing the different precise orbit determination solutions, we found that the ambiguity resolution significantly reduced the satellite laser ranging (SLR) residuals from 1.63 to 1.31 cm with an average improvement of 19.6%. However, because of the code errors, the ambiguity fixing rate of the P1 ambiguity-fixed solutions was much lower than that of the C1 solutions. By modeling this static correction, the impact of these errors was effectively reduced. The ambiguity fixing rate for the P1 solutions was improved by 15.6% and a 1–3 mm reduction in the SLR residuals was small but noticeable.

The proper handling of code biases is essential for realizing precise ionospheric modeling, positioning and timing. It is common to treat code biases in a differential mode as a differential code bias (DCB). With the modernization of GPS and GLONASS and the implementation of Galileo and BDS, the traditional DCB calibrations are complex and not easily extendable to different frequencies and modulations. An alternative treatment of code biases is to use observable-specific signal biases (OSBs). In this contribution, all possible OSBs are estimated for the latest GNSS and analyzed from the perspectives of precision, consistency and stability. The precisions of the GPS and Galileo OSBs are significantly better than those of the GLONASS and BDS OSBs. Considering the inter-frequency bias (IFB) of GLONASS and the inter-system bias (ISB) of BDS can improve the precisions of their OSB estimates. OSB comparisons among different agencies reveal that GPS and Galileo show good agreement at the level of 0.2–0.3 ns, while the differences of the GLONASS and BDS OSBs reach 0.5–1.0 ns. In addition, agreement of 0.4–0.5 ns is demonstrated for IGSO and MEO OSBs, while the consistency of GEO OSBs is worse by a factor of 2–3. The stability of the OSB estimates is at the level of 0.03–0.09 ns for GPS, 0.10–0.25 ns for Galileo, 0.14–0.48 ns for GLONASS, and 0.16–0.44 ns for BDS. In general, the BDS-3 OSB estimates show better stability than the BDS-2 OSBs. Moreover, the code biases at the same or at a close central frequency show similar performance. This is particularly obvious for Galileo and BDS, which adopt the dual-frequency constant envelope multiplexing (DCEM) technique. For instance, the code bias estimates of C5Q, C5X, C7Q, and C8Q are close to each other for individual Galileo satellites, and the BDS code biases of C5P, C7Z, and C8X are comparable to each other. [ABSTRACT FROM AUTHOR]

Global navigation satellite systems and positioning, navigation, and timing services, such as the newly developed BeiDou satellite system (BDS), require high-accuracy satellite observations. Satellite-induced code bias is present in BDS-2 satellite observations while it is negligibly present in BDS-3 satellite observations. The traditional method of mitigating BDS code bias involves two steps, first addressing multipath delay and then code bias, and does not obtain optimal results. A one-step strategy is therefore proposed to model and eliminate code bias and multipath delay considering BDS-2 and BDS-3 integrated processing. A combined least-square and autoregressive strategy is selected to estimate the model coefficients of code bias and construct the multipath delay with one solution. Moreover, inter-satellite correlations of BDS-2 and BDS-3 are extracted to improve the weight matrix in the estimation of model coefficients. To verify the proposed strategy, experiments are designed for eight schemes to analyze the coefficients and residuals of modelling code bias. Experimental results indicate that a more stable and accurate code bias model is acquired by introducing inter-satellite correlation; with the one-step strategy, the model residuals are reduced and a more optimal code bias model is output. Meanwhile, the single-frequency precise point positioning (PPP) and real-time PPP of BDS-2 and BDS-3 combined estimations are tested for different stations, frequencies, and code bias models. The results of final positions reveal that accuracy in the Up (U) direction is improved compared with that in the East (E) and North (N) directions; improvements are greater for B1I than for B3I. In general, the one-step strategy enhances the precision of single-frequency (B1I/B3I) PPP, especially in the U direction. However, the effects on BDS ultra-rapid orbit determination are negligible. Equally, the double-frequency real-time PPP solution is improved, compared with adopting the traditional method, by 10.6–64.9%, 0.0–59.1%, and 12.6–67.2% for E, N, and U directions, respectively, through BDS-2/BDS-3 integrated processing. The proposed one-step strategy therefore outperforms the two-step strategy in terms of rapidly processing high-precision BDS observations. [ABSTRACT FROM AUTHOR]

Abstract There are code biases on the pseudo-range observations of the Beidou Navigation Satellite System (BDS) that range in size from several decimeters to larger than one meter. These biases can be divided into two categories, which are the code biases in the pseudo-range observations of Inclined Geo-Synchronous Orbit (IGSO) satellites and Medium Earth Orbit (MEO) satellites and the code biases in the pseudo-range observations of Geosynchronous Earth Orbit (GEO) satellites. In view of the code bias of the IGSO/MEO satellites, the code bias correction model is established using the weighted least square curve fitting method. After the correction, the code biases of the IGSO and MEO satellites are clearly mitigated. A methodology of correcting GEO code bias is proposed based on the empirical mode decomposition (EMD)-wavelet transform (WT) coupled model. The accuracies of the GEO multipath combination of the B1, B2 and B3 frequencies are improved by 39.9%, 17.9%, and 29.4%, respectively. Based on the corrections above, the ten days observations of three Multi-GNSS Experiment (MGEX) stations are processed. The results indicate that the convergence time of the precise point positioning (PPP) can be improved remarkably by applying a code bias. The mean convergence time can be improved by 14.67% after the IGSO/MEO code bias correction. By applying the GEO code bias, the mean convergence time can be further improved by 17.42%. [ABSTRACT FROM AUTHOR]

Satellite chip shape distortions lead to signal tracking errors in pseudorange measurements, which are related to the receiver manufacturers, called receiver-related pseudorange biases. Such biases will lead to adverse effects for differential code bias (DCB) and satellite clock estimation, single point positioning (SPP) and precise point positioning (PPP) applications with pseudoranges. In order to assess the characteristics of receiver-related pseudorange biases for global positioning system (GPS), Galileo navigation satellite system (Galileo) and BeiDou navigation satellite system (BDS), seven short baselines from the Multi-GNSS experiment (MGEX) network are tested. The results demonstrate that there are significant inconsistences of pseudorange biases according to satellites, frequencies, receiver and antenna types. For the baselines using the same receivers of TRIMBLE, pseudorange biases are within ±0.2 ns with the same antennas, while they increase to ±0.6 ns with the different antennas. As for baselines with mixed receiver types, pseudorange biases can reach up to 2.5 ns. Among GPS/Galileo/BDS, Galileo shows the smallest pseudorange biases, and the obvious inconsistences of pseudorange biases are observed between BDS-2 and BDS-3, and Galileo in-orbit validation (IOV) satellites and full operational configuration (FOC) satellites. In order to validate receiver-related pseudorange biases, we carry out relative positioning experiments using short baselines. The results show that the RMS values of position errors are reduced 12.6% and 11.4% in horizontal and vertical components with biases correction. The impacts of receiver-related pseudorange biases on wide-lane (WL) ambiguity are also discussed. The results indicate that the percentage of the fractional parts within ±0.1 cycles have an obvious increase with the pseudorange biases correction, and RMS values of the fractional parts are reduced 28.9% and 67.6% for GPS and BDS, respectively.

An empirical mode decomposition (EMD) model for BeiDou Navigation Satellite System (BDS) code bias has been established upon the observation model of multiple global navigation satellite systems (multi-GNSS). To validate the correctness and effectiveness of the model, seven days from day of year (DOY) 213-219, 2015 from eight Multi-GNSS Experiment (MGEX) stations were processed. Results show that after code bias correction, the standard deviation of the multipath combination (MP) series on B1 and B2 frequencies decreased by 38.63 % and 17.4 %, respectively. The timespan needed for convergence in BDS precise point positioning (PPP) was improved by 7.9 % after inclined geosynchronous orbit (IGSO) and medium earth orbit (MEO) code bias correction, and another improvement of 11.4 % was generated by applying geostationary orbit (GEO) code bias correction. Despite the improvement of convergence time, the accuracy of the single-day solution barely increased for PPP in multi-GNSS as compared to the single GNSS. A continuous decrease in percentage along with prolonged timespan for PPP convergence was observed with increasing cut-off elevation angle. However, the performance of multi-GNSS PPP, which was superior to that of the single GNSS, shows that it is extremely valuable for practical applications in mountainous or sheltered areas. [ABSTRACT FROM AUTHOR]

In 2015, the plan for global coverage by the Chinese BeiDou Navigation Satellite System was launched. Five global BeiDou experimental satellites (BeiDou-3e) are in orbit for testing. To analyze the performances of precise orbit determination (POD) and precise point positioning (PPP) of onboard BeiDou satellites, about two months of data from 24 tracking stations were used. According to quality analysis of BeiDou-2/BeiDou-3e data, there is no satellite-induced code bias in BeiDou-3e satellites, which has been found in BeiDou-2 satellites. This phenomenon indicates that the quality issues of pseudorange data in BeiDou satellites have been solved well. POD results indicate that the BeiDou-3e orbit precision is comparable to that of BeiDou-2 satellites. The ambiguity fixed solution improved the orbit consistency of inclined geosynchronous orbit satellites in along-track and cross-track directions, but had little effect in the radial direction. Satellite laser ranging of BeiDou-3e medium Earth orbit satellites (MEOs) achieved a standard deviation of about 4 cm. Differences in clock offset series after the removal of reference clock in overlapping arcs were used to assess clock quality, and standard deviation of clock offset could reach 0.18 ns on average, which was in agreement with the orbit precision. For static PPP, when BeiDou-3e satellites were included, the positioning performance for horizontal components was improved slightly. For kinematic PPP, when global positioning satellites (GPS) were combined with BeiDou-2 and BeiDou-3e satellites, the convergence time was 13.5 min with a precision of 2-3 cm for horizontal components, and 3-4 cm for the vertical component. [ABSTRACT FROM AUTHOR]

The successful launch of five new-generation experimental satellites of the China's BeiDou Navigation Satellite System, namely BeiDou I1-S, I2-S, M1-S, M2-S, and M3-S, marks a significant step in expanding BeiDou into a navigation system with global coverage. In addition to B1I (1561.098 MHz) and B3I (1269.520 MHz) signals, the new-generation BeiDou-3 experimental satellites are also capable of transmitting several new navigation signals in space, namely B1C at 1575.42 MHz, B2a at 1176.45 MHz, and B2b at 1207.14 MHz. For the first time, we present an initial characterization and performance assessment for these new-generation BeiDou-3 satellites and their signals. The L1/L2/L5 signals from GPS Block IIF satellites, E1/E5a/E5b signals from Galileo satellites, and B1I/B2I/B3I signals from BeiDou-2 satellites are also evaluated for comparison. The characteristics of the B1C, B1I, B2a, B2b, and B3I signals are evaluated in terms of observed carrier-to-noise density ratio, pseudorange multipath and noise, triple-frequency carrier-phase ionosphere-free and geometry-free combination, and double-differenced carrier-phase and code residuals. The results demonstrate that the observational quality of the new-generation BeiDou-3 signals is comparable to that of GPS L1/L2/L5 and Galileo E1/E5a/E5b signals. However, the analysis of code multipath shows that the elevation-dependent code biases, which have been previously identified to exist in the code observations of the BeiDou-2 satellites, seem to be not obvious for all the available signals of the new-generation BeiDou-3 satellites. This will significantly benefit precise applications that resolve wide-lane ambiguity based on Hatch-Melbourne-Wübbena linear combinations and other applications such as single-frequency precise point positioning (PPP) based on the ionosphere-free code-carrier combinations. Furthermore, with regard to the triple-frequency carrier-phase ionosphere-free and geometry-free combination, it is found that different from the BeiDou-2 and GPS Block IIF satellites, no apparent bias variations could be observed in all the new-generation BeiDou-3 experimental satellites, which shows a good consistency of the new-generation BeiDou-3 signals. The absence of such triple-frequency biases simplifies the potential processing of multi-frequency PPP using observations from the new-generation BeiDou-3 satellites. Finally, the precise relative positioning results indicate that the additional observations from the new-generation BeiDou-3 satellites can improve ambiguity resolution performance with respect to BeiDou-2 only positioning, which indicates that observations from the new-generation BeiDou-3 satellites can contribute to precise relative positioning. [ABSTRACT FROM AUTHOR]

Thecode-phase divergences, which are absent for GPS, GLONASS, and Galileo,are com- monlyfound in BDS geostationary (GEO), Inclined GeoSynchronous Orbit (IGSO) and Medium Earth Orbit (MEO) satellites. Several precise applications that use code observations are severely affected by these code biases; therefore, it is necessary to correct biases in BDS code observations. Since the BeiDou satellite-induced code bias is confirmed to he orbit type-, frequency-, and elevation-dependent, an improved code bias correction model for IGSO and MEO satellites based on a large amount of the data was developed. To obtain the best filling results, we analyzed the effect of the number and distri­bution of stations and observation time on model estimation, and also considered the different influ­ence of multipath at different elevations. A robust estimation method controlled the observation quali­ty. A dataset from 18 stations during one year period in 2015 was employed to estimate the correction model for MEO satellites and four stations for IGSO satellite. To validate the improved correction model, the effect of the code bias on precise point positioning (PPP) l>efore and after correction is ana­lyzed and compared. Results show that systematic variations were eliminated more clearly after apply­ing the improved correction model as compared to the traditional model. After correction, the positio­ning accuracy of PPP solution was improved and the convergence time decreasedshowing a better per­formance than results using thetraditional model as proposed by Wanninger and Beer. [ABSTRACT FROM AUTHOR]

The Beidou navigation satellite system is a very important sensor for positioning in the Asia-Pacific region. The Beidou inclined geosynchronous orbit (IGSO) and medium Earth orbit (MEO) satellites have been analysed in some studies previously conducted by other researchers; this paper seeks to gain more insight regarding the geostationary earth orbit (GEO) satellites. Employing correlation analysis, Fourier transformation and wavelet decomposition, we validate whether there is a systematic bias in their multipath combinations. These biases can be observed clearly in satellites C01, C02 and C04 and have a great correlation with time series instead of elevation, being significantly different from those of the Beidou IGSO and MEO satellites. We propose a correction model to mitigate this bias based on its daily periodicity characteristic. After the model has been applied, the performance of the positioning estimations of the eight stations distributed in the Asia-Pacific region is evaluated and compared. The results show that residuals of multipath series behaves random noise; for the single point positioning (SPP) and precise point positioning (PPP) approaches, the positioning accuracy in the upward direction can be improved by 8 cm and 6 mm, respectively, and by 2 cm and 4 mm, respectively, for the horizontal component. [ABSTRACT FROM AUTHOR]

Satellite chip shape distortions lead to signal tracking errors in pseudorange measurements, which are related to the receiver manufacturers, called receiver-related pseudorange biases. Such biases will lead to adverse effects for differential code bias (DCB) and satellite clock estimation, single point positioning (SPP) and precise point positioning (PPP) applications with pseudoranges. In order to assess the characteristics of receiver-related pseudorange biases for global positioning system (GPS), Galileo navigation satellite system (Galileo) and BeiDou navigation satellite system (BDS), seven short baselines from the Multi-GNSS experiment (MGEX) network are tested. The results demonstrate that there are significant inconsistences of pseudorange biases according to satellites, frequencies, receiver and antenna types. For the baselines using the same receivers of TRIMBLE, pseudorange biases are within ±0.2 ns with the same antennas, while they increase to ±0.6 ns with the different antennas. As for baselines with mixed receiver types, pseudorange biases can reach up to 2.5 ns. Among GPS/Galileo/BDS, Galileo shows the smallest pseudorange biases, and the obvious inconsistences of pseudorange biases are observed between BDS-2 and BDS-3, and Galileo in-orbit validation (IOV) satellites and full operational configuration (FOC) satellites. In order to validate receiver-related pseudorange biases, we carry out relative positioning experiments using short baselines. The results show that the RMS values of position errors are reduced 12.6% and 11.4% in horizontal and vertical components with biases correction. The impacts of receiver-related pseudorange biases on wide-lane (WL) ambiguity are also discussed. The results indicate that the percentage of the fractional parts within ±0.1 cycles have an obvious increase with the pseudorange biases correction, and RMS values of the fractional parts are reduced 28.9% and 67.6% for GPS and BDS, respectively. [ABSTRACT FROM AUTHOR]