Differential Inter-system Biases Research Articles

A new inter-system double-difference RTK model applicable to both overlapping and non-overlapping signal frequencies

Aiming at the problem that the traditional inter-system double-difference model is not suitable for non-overlapping signal frequencies, we propose a new inter-system double-difference model with single difference ambiguity estimation, which can be applied for both overlapping and non-overlapping signal frequencies. The single difference ambiguities of all satellites and Differential Inter-System Biases (DISB) are first estimated, and the intra-system double difference ambiguities, which have integer characteristics, are then fixed. After the ambiguities are successfully fixed, high-precision coordinates and DISB can be obtained with a constructed transformation matrix. The model effectively avoids the DISB parameter filtering discontinuity caused by the reference satellite transformation and the low precision of the reference satellite single difference ambiguity calculated with the code. A zero-baseline using multiple types of receivers is selected to verify the stability of the estimated DISB. Three baselines with different lengths are selected to assess the positioning performance of the model. The ionospheric-fixed and ionospheric-float models are used for short and medium-long baselines, respectively. The results show that the Differential Inter-System Code Biases (DISCB) and Differential Inter-System Phase Biases (DISPB) have good stability regardless of the receivers type and the signal frequency used and can be calibrated to enhance the strength of the positioning model. The positioning results with three baselines of different lengths show that the proposed inter-system double-difference model can improve the positioning accuracy by 6–22% compared with the intra-system double-difference model which selects the reference satellite independently for each system. The Time to First Fix (TTFF) of the two medium-long baselines is reduced by 30% and 29%, respectively.

Tight Integration Kinematic PPP-AR Using GPS/Galileo/QZSS Overlapping Frequency Signals and Its Performance in High-Shade Environments

Several global navigation satellite systems (GNSS) broadcast overlapping frequencies to enhance interoperability, allowing tight integration with only one reference satellite for every system with the same frequency. The key to realizing tight integration is estimating and utilizing differential intersystem biases, which allows the integer characteristic of the differenced ambiguity of two satellites from different systems to be retrieved. In this study, a detailed algorithm flow of a tight integration kinematic uncalibrated phase delay (UPD)-based PPP ambiguity resolution (PPP-AR) method, which includes multiple parts, is introduced. Subsequently, PPP-AR numerical experiments were conducted in a high-shade observation environment to determine the performance. In comparison with traditional methods, our results indicate that the average success fix rate improves from 83% to 100% after using the tight integration method in an environment where only three satellites are observed for each system. Moreover, for fewer than nine satellites, the tight integration method can still consistently maintain a fixed state. However, for comparison, the traditional loose integration method could no longer be implemented.

Accounting for BDS-2/BDS-3 inter-system biases in PPP and RTK models

Inter-system Biases (ISBs) between BDS-2 and BDS-3 is of great importance for BDS-2/BDS-3 joint processing, which is meaningful to make full use of BDS observations and improves PNT (positioning, navigation, timing) performance. In this contribution, we derive ISBs models with undifferenced ionospheric-free (IF) combination and double-differenced model, corresponding to the IF-PPP and RTK technologies respectively. To analyze code ISB in PPP, we processed data from 55 multi-GNSS experimental (MGEX) stations including 7 receiver types and conduct a detailed analysis on the effect of frequency, receiver types and precise products from 4 IGS Analysis Centers (ACs). It is concluded that both the overlapping frequency and the non-overlapping frequency of BDS-2/BDS-3 exist code ISB. The code ISB of overlapping frequency is within 10 ns, and that of the non-overlapping frequency can reach 100 ns. Moreover, code ISB is influenced by receiver types as well as satellite geometry. The average ISB of stations with the same manufactures tend to be the same while that of stations from different manufactures are different. Affected by the satellite geometry, the ISB characteristics exhibit periodicity and correlation with the location of stations. By comparing ISB calculated by different precise clock products from the GeoForschungsZentrum (GFZ), European Space Agency (ESA), Center for Orbit Determination in Europe (CODE) and Wuhan University (WHU), the results show that the daily STD of ISBCOD, ISBWHU,ISBESA and ISBGFZ is about 0.2 ns, which means that ISB can be calibrated by constant estimation when these products are used. As for Differential Inter-system Biases (DISBs) in RTK, it is discovered that the BDS-2/BDS-3 joint differenced system has a Differential Inter-system Code Bias (DISCB) that exceeds 3.4 ns when the rover and base receivers are made by different manufactures and the hardware delay characteristics for BDS-2 and BDS-3 are different. However, the Differential Inter-system Phase Bias (DISPB) doesn’t exist and can be neglected in RTK.

Single-epoch RTK performance assessment of tightly combined BDS-2 and newly complete BDS-3

The BeiDou global navigation satellite system (BDS-3) constellation deployment has been completed on June 23, 2020, with a full constellation comprising 30 satellites. In this study, we present the performance assessment of single-epoch Real-Time Kinematic (RTK) positioning with tightly combined BeiDou regional navigation satellite system (BDS-2) and BDS-3. We first investigate whether code and phase Differential Inter-System Biases (DISBs) exist between the legacy B1I/B3I signals of BDS-3/BDS-2. It is discovered that the DISBs are in fact about zero for the baselines with the same or different receiver types at their endpoints. These results imply that BDS-3 and BDS-2 are fully interoperable and can be regarded as one constellation without additional DISBs when the legacy B1I/B3I signals are used for precise relative positioning. Then we preliminarily evaluate the single-epoch short baseline RTK performance of tightly combined BDS-2 and the newly completed BDS-3. The performance is evaluated through ambiguity resolution success rate, ambiguity dilution of precision, as well as positioning accuracy in kinematic and static modes using the datasets collected in Wuhan. Experimental results demonstrate that the current BDS-3 only solutions can deliver comparable ambiguity resolution performance and much better positioning accuracy with respect to BDS-2 only solutions. Moreover, the RTK performance is much improved with tightly combined BDS-3/BDS-2, particularly in challenging or harsh conditions. The single-frequency single-epoch tightly combined BDS-3/BDS-2 solution could deliver an ambiguity resolution success rate of 96.9% even with an elevation cut-off angle of 40°, indicating that the tightly combined BDS-3/BDS-2 could achieve superior RTK positioning performance in the Asia–Pacific region. Meanwhile, the three-dimensional (East/North/Up) positioning accuracy of BDS-3 only solution (0.52 cm/0.39 cm/2.14 cm) in the kinematic test is significantly better than that of the BDS-2 only solution (0.85 cm/1.02 cm/3.01 cm) due to the better geometry of the current BDS-3 constellation. The tightly combined BDS-3/BDS-2 solution can provide the positioning accuracy of 0.52 cm, 0.22 cm, and 1.80 cm, respectively.

Particle Filter-Based Inter-System Positioning Model for Non-Overlapping Frequency Code Division Multiple Access Systems

In the process of composing a double-differenced positioning model, it is difficult to separate different frequency signals between code division multiple access (CDMA) systems, the single-difference ambiguity of the pivot satellite and phase differential inter-system biases (PDISBs). Hence it is difficult to calibrate in advance the bias between systems in order to build an inter-system model which only needs one pivot satellite. Based on analysis of the stability of PDISB parameters for non-overlapping frequency CDMA systems, this study adopts a particle filter to estimate the fractional part of the PDISBs (F-PDISBs) between the systems and proposes a particle filter-based inter-system positioning model. Results show that the F-PDISBs and code DISBs for the baselines with the same receiver types and some with different receiver types are rather stable over time and for these baselines it is feasible to use a particle filter to estimate the F-PDISB parameters in the initial stage. Having attained the F-PDISBs, the inter-system model can be constructed to improve positioning accuracy in complex operational environments.

Estimability analysis of differential inter-system biases and differential inter-frequency biases for dual-frequency GPS and BDS combined RTK

Inter-system biases (ISBs) and inter-frequency biases (IFBs) are critical for the data processing of multi-frequency and multi-constellation global navigation satellite systems (GNSS). Calibration of the ISB and IFB makes it possible to enhance the accuracy, integrity, and availability of multi-GNSS positioning, navigation, and timing. In this study, we investigate the magnitude and stability of the code and carrier phase differential inter-system biases (DISBs) between the GPS/BeiDou navigation satellite system (BDS) L1–B1/L2–B2 and differential inter-frequency biases (DIFBs) between L1–L2/B1–B2 using zero and short baseline data collected using both identical and different receiver types in real-time kinematic (RTK) positioning. We verify that the code and carrier phase DISBs of GPS/BDS L1–B1/L2–B2 and DIFBs of L1–L2/B1–B2 are both approximately constant on the timescale of a consecutive five-day observation period from a statistical perspective, and can thus be corrected by a priori DISB and DIFB, respectively. Moreover, the performance of the a priori model correction and real-time estimation strategies for the DISB and DIFB are compared. Both can precisely correct the DISB and DIFB and achieve significantly improved performance for multi-GNSS inter-system and inter-frequency combined RTK positioning compared to the classical intra-system and intra-frequency combined RTK approach. The DISB and DIFB using the a priori model correction and real-time estimation effectively improve the positioning model strength, thereby enabling superior performance for multi-GNSS positioning.

Differential Inter-System Biases Estimation and Initial Assessment of Instantaneous Tightly Combined RTK with BDS-3, GPS, and Galileo

In this contribution, we assess, for the first time, the tightly combined real-time kinematic (RTK) with GPS, Galileo, and BDS-3 operational satellites using observations from their overlapping L1-E1-B1C/L5-E5a-B2a frequencies. First, the characteristics of B1C/B2a signals from BDS-3 operational satellites is evaluated compared to GPS/Galileo L1-E1/L5-E5a signals in terms of observed carrier-to-noise density ratio, pseudorange multipath and noise, as well as double-differenced carrier phase and code residuals using data collected with scientific geodetic iGMAS and commercial M300Pro receivers. It’s demonstrated that the observational quality of B1C/B2a signals from BDS-3 operational satellites is comparable to that of GPS/Galileo L1-E1/L5-E5a signals. Then, we investigate the size and stability of phase and code differential inter-system bias (ISB) between BDS-3/GPS/Galileo B1C-L1-E1/B2a-L5-E5a signals using short baseline data collected with both identical and different receiver types. It is verified that the BDS-3/GPS/Galileo ISBs are indeed close to zero when identical type of receivers are used at both ends of a baseline. Moreover, they are generally present and stable in the time domain for baselines with different receiver types, which can be easily calibrated and corrected in advance. Finally, we present initial assessment of single-epoch tightly combined BDS-3/GPS/Galileo RTK with single-frequency and dual-frequency observations using a formal and empirical analysis, consisting of ambiguity dilution of precision (ADOP), ratio values, the empirical ambiguity resolution success rate, and the positioning accuracy. Experimental results demonstrate that the tightly combined model can deliver much lower ADOP and higher ratio values with respect to the classical loosely combined model whether for GPS/BDS-3 or GPS/Galileo/BDS-3 solutions. The positioning accuracy and the empirical ambiguity resolution success rate are remarkably improved as well, which could reach up to approximately 10%∼60% under poor observational conditions.

Tightly combined GPS and GLONASS for RTK positioning with consideration of differential inter-system phase bias

A tightly combined inter-system model between two global navigation satellite systems can improve the performance of real-time kinematic (RTK) positioning, if the associated differential inter-system biases (DISBs) are processed well, especially for the severely obstructed environment. In recent years, tightly combined models among code division multiple access (CDMA) systems (e.g. Global Positioning System (GPS), BeiDou Navigation Satellite System (BDS), Quasi-Zenith Satellite System (QZSS)) have been extensively studied. However, when there is tightly combined use of CDMA systems and Global Navigation Satellite System (GLONASS), which adopts frequency-division multiple access (FDMA), we need to process not only the DISBs between systems, but the problem caused by the different wavelengths of the GLONASS satellites. In this paper, we propose a new model for the tight combination of GPS and GLONASS. First, we adopt the model with two reference satellites to maintain the integer ambiguity resolution of GLONASS. Then, an inter-system model between GPS and GLONASS is proposed with a total of three ‘reference satellites’ involved. Using several zero and ultra-short baselines, the stability of GPS and GLONASS differential inter-system phase biases (DISPBs) will be evaluated. The results indicated that the DISPBs between GPS and GLONASS are generally stable, although low-frequency variations may appear in the baselines with different receiver types. Using the stability of DISPBs, the combined GPS and GLONASS single-frequency RTK positioning performance is evaluated with simulated obstructed environments with no more than four GPS and four GLONASS satellites visible. It will be shown that compared with the intra-system model, the proposed inter-system model can improve the positioning accuracies by 13.5%, 15.0% and 46.2%, respectively, in three directions.

Accounting for the differential inter-system bias (DISB) of code observation in GPS+BDS positioning

Abstract If the associated differential inter-system biases (DISBs) are priori known, only one common reference satellite is sufficient, which is called the inter-system model. The inter-system model can help to maximize the redundancy of the positioning model, and thus can improve the positioning performance, especially in harsh environment. However, in practice use not all receivers can be calibrated with DISBs in advance. In this paper, taking combined GPS and BDS pseudorange positioning as the example, we compare three positioning models and their positioning performance. One is traditional intra-system model, and the other two belongs to the inter-system models, i. e. the model with calibration of DISB and the model with real-time estimation of DISB parameter. Positioning performance using the three models is evaluated with simulated obstructed environments. It will be shown that besides the model with calibration of DISB, the model with real-time estimation of DISB parameter can also effectively improve positioning accuracy and reliability compared with the traditional intra-system model, especially for the severely obstructed environment with only a few satellites observed. When no more than 7 satellites visible, the positioning accuracies in each directions can be improved by no less than 15 %. The proposed model can be used alternatively when no priori DISB calibration is available.

Combined GPS and BDS for single-frequency continuous RTK positioning through real-time estimation of differential inter-system biases

Double-differenced (DD) ambiguities between overlapping frequencies from different GNSS constellations can be fixed to integers if the associated differential inter-system biases (DISBs) are well known. In this case, only one common pivot satellite is sufficient for inter-system ambiguity resolution. This will be beneficial to ambiguity resolution (AR) and real-time kinematic (RTK) positioning especially when only a few satellites are observed. However, for GPS and current operational BDS-2, there are no overlapping frequencies. Due to the influence of different frequencies, the inter-system DD ambiguities still cannot be fixed to integers even if the DISBs are precisely known. In this contribution, we present an inter-system differencing model for combined GPS and BDS single-frequency RTK positioning through real-time estimation of DISBs. The stability of GPS L1 and BDS B1 DISBs is analyzed with different receiver types. Along with parameterization and using the short-term stability of DISBs, the DD ambiguities between GPS and BDS pivot satellites and the between-receiver single-difference ambiguity of the GPS pivot satellite can be estimable jointly with the differential phase DISB term from epoch to epoch. Then the inter-system differencing model can benefit from the near time-constant DISB parameters and thus has better multi-epoch positioning performance than the classical intra-system differencing model. The combined GPS and BDS single-frequency RTK positioning performance is evaluated with various simulated satellite visibilities. It will be shown that compared with the classical intra-system differencing model, the proposed model can effectively improve the positioning accuracy and reliability, especially for severely obstructed situations with only a few satellites observed.

Inter-System Differencing between GPS and BDS for Medium-Baseline RTK Positioning

An inter-system differencing model between two Global Navigation Satellite Systems (GNSS) enables only one reference satellite for all observations. If the associated differential inter-system biases (DISBs) are priori known, double-differenced (DD) ambiguities between overlapping frequencies from different GNSS constellations can also be fixed to integers. This can provide more redundancies for the observation model, and thus will be beneficial to ambiguity resolution (AR) and real-time kinematic (RTK) positioning. However, for Global Positioning System (GPS) and the regional BeiDou Navigation Satellite System (BDS-2), there are no overlapping frequencies. Tight combination of GPS and BDS needs to process not only the DISBs but also the single-difference ambiguity of the reference satellite, which is caused by the influence of different frequencies. In this paper, we propose a tightly combined dual-frequency GPS and BDS RTK positioning model for medium baselines with real-time estimation of DISBs. The stability of the pseudorange and phase DISBs is analyzed firstly using several baselines with the same or different receiver types. The dual-frequency ionosphere-free model with parameterization of GPS-BDS DISBs is proposed, where the single-difference ambiguity is estimated jointly with the phase DISB parameter from epoch to epoch. The performance of combined GPS and BDS RTK positioning for medium baselines is evaluated with simulated obstructed environments. Experimental results show that with the inter-system differencing model, the accuracy and reliability of RTK positioning can be effectively improved, especially for the obstructed environments with a small number of satellites available.

Tightly Combined BeiDou B2 and Galileo E5b Signals for Precise Relative Positioning

In precise relative positioning applications, an effective approach to improve the interoperability of GNSS systems is the tightly combining or inter-system double-differencing of observations from the common frequencies that are shared by different constellations. As the BeiDou satellites are currently transmitting a B2 signal at 1207.14 MHz that is identical to the Galileo E5b signal, the inter-system double-differenced observations can also be created between observations from both systems at that particular frequency. In this paper, we will focus on the instantaneous ambiguity resolution performance analysis of tightly combining BeiDou B2 and Galileo E5b observations. The size and stability of phase and code Differential Inter-System Biases (DISBs) between BeiDou B2 and Galileo E5b signals are first investigated, in which the new BeiDou and Galileo satellites launched recently will also be included. Then, first results of the Tightly Combined Model (TCM) with a priori corrected DISBs (TCM_C) are evaluated in comparison to the Loosely Combined Model (LCM) and tightly combined model with unknown DISBs (TCM_F) in an instantaneous approach. It is demonstrated that the instantaneous integer ambiguity resolution performance can be improved using the TCM_C with respect to LCM and TCM_F.

GPS, Galileo, QZSS and IRNSS differential ISBs: estimation and application

Knowledge of inter-system biases (ISBs) is essential to combine observations of multiple global and regional navigation satellite systems (GNSS/RNSS) in an optimal way. Earlier studies based on GPS, Galileo, BDS and QZSS have demonstrated that the performance of multi-GNSS real-time kinematic positioning is improved when the differential ISBs (DISBs) corresponding to signals of different constellations but transmitted at identical frequencies can be calibrated, such that only one common pivot satellite is sufficient for inter-system ambiguity resolution at that particular frequency. Recently, many new GNSS satellites have been launched. At the beginning of 2016, there were 12 Galileo IOV/FOC satellites and 12 GPS Block IIF satellites in orbit, while the Indian Regional Navigation Satellite System (IRNSS) had five satellites launched of which four are operational. More launches are scheduled for the coming years. As a continuation of the earlier studies, we analyze the magnitude and stability of the DISBs corresponding to these new satellites. For IRNSS this article presents for the first time DISBs with respect to the L5/E5a signals of GPS, Galileo and QZSS for a mixed-receiver baseline. It is furthermore demonstrated that single-frequency (L5/E5a) ambiguity resolution is tremendously improved when the multi-GNSS observations are all differenced with respect to a common pivot satellite, compared to classical differencing for which a pivot satellite is selected for each constellation.

First results of mixed GPS+GIOVE single-frequency RTK in Australia

First results are presented for precise (mm/cm-level) short-baseline RTK positioning based on single-frequency GPS data combined with data of GIOVE-A/B, the two experimental Galileo satellites, collected in Australia. The paper first focuses on the model of GPS+Galileo observation equations and addresses the issues that arise when combining data of both systems, in particular the inter-system biases (ISBs). Our results indicate that the differential ISBs are quite stable in time, potentially enabling calibration and a priori correction of the Galileo phase and code observations. Based on ISB-corrected data, the reliability of single-frequency GPS+GIOVE ambiguity resolution is significantly improved, when compared to GPS only.