Inter-system Bias Research Articles

Determining inter-system bias of GNSS signals with narrowly spaced frequencies for GNSS positioning

Relative positioning using multi-GNSS (global navigation satellite systems) can improve accuracy, reliability, and availability compared to the use of a single constellation system. Intra-system double-difference (DD) ambiguities (ISDDAs) refer to the DD ambiguities between satellites of a single constellation system and can be fixed to an integer to derive the precise fixed solution. Inter-system ambiguities, which denote the DD ambiguities between different constellation systems, can also be fixed to integers on overlapping frequencies, once the inter-system bias (ISB) is removed. Compared with fixing ISDDAs, fixing both integer intra- and inter-system DD ambiguities (IIDDAs) means an increase of positioning precision through an integration of multiple GNSS constellations. Previously, researchers have studied IIDDA fixing with systems of the same frequencies, but not with systems of different frequencies. Integer IIDDAs can be determined from single-difference (SD) ambiguities, even if the frequencies of multi-GNSS signals used in the positioning are different. In this study, we investigated IIDDA fixing for multi-GNSS signals of narrowly spaced frequencies. First, the inter-system DD models of multi-GNSS signals of different frequencies are introduced, and the strategy for compensating for ISB is presented. The ISB is decomposed into three parts: 1) a float approximate ISB number that can be considered equal to the ISB of code pseudorange observations and thus can be estimated through single point positioning (SPP); 2) a number that is a multiple of the GNSS signal wavelength; and 3) a fractional ISB part, with a magnitude smaller than a single wavelength. Then, the relationship between intra- and inter-system DD ambiguity RATIO values and ISB was investigated by integrating GPS L1 and GLONASS L1 signals. In our numerical analyses with short baselines, the ISB parameter and IIDDA were successfully fixed, even if the number of observed satellites in each system was small.

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.

Mixed GPS–BeiDou RTK with inter-systems bias estimation aided by CSAC

It is now common to use multiple GNSS constellations (multi-GNSS) for precise positioning. When GPS and BeiDou satellites are used in real-time kinematic GNSS (RTK-GNSS), the normal approach is to construct separate sets of double differences for each satellite constellation. Since QZSS is designed to be the same as GPS in terms of frequency and timing, a QZSS satellite can be used as another GPS satellite for positioning. The normal approach ("normal RTK") requires one primary satellite for each constellation and thus removes one usable satellite. We developed a mixed GPS + BeiDou model by differencing BeiDou carrier phase and pseudorange observations from those of the primary GPS satellites. This approach introduces inter-system (GPS-to-BeiDou) biases, which must be estimated and removed. In addition, the difference between GPS and BeiDou signal frequencies means that receiver clock error has to be estimated precisely in this approach, and a chip-scale atomic clock (CSAC) was utilized to aid this estimation. The proposed mixed GPS + BeiDou RTK method was evaluated using static data and kinematic data. Kinematic data were collected in both normal and dense urban areas in Tokyo using a small car. The kinematic tests were conducted using an external CSAC as an input to the receiver, which allowed precise estimation of receiver clock error while in motion. The resulting fix rate of mixed GPS + BeiDou RTK-GNSS was approximately 10% better than normal RTK-GNSS.

An Enhanced Multi-GNSS Navigation Algorithm by Utilising a Priori Inter-System Biases

The integration of multi-constellation Global Navigation Satellite System (GNSS) measurements can effectively improve the accuracy and reliability of navigation and positioning solutions, while the Inter-System Bias (ISB) is a key issue for compatibility. The ISB is traditionally estimated as an unknown parameter along with three-dimensional position coordinates and a receiver clock offset with respect to Global Positioning System (GPS) time. ISB estimation of this sort will sacrifice a satellite observation for each integrated GNSS system. These sacrificed observations could be vital in situations of limited satellite visibility. In this study, an enhanced multi-GNSS navigation algorithm is developed to avoid sacrificing observations under poor visibility conditions. The main idea of this algorithm is to employ a moving average filter to smooth the ISBs estimated at previous epochs. The filtered value is utilised as a priori information at the current epoch. Experimental tests were conducted to evaluate the enhanced algorithm under open and blocked sky conditions. The results show that the enhanced algorithm effectively improves the accuracy and availability of navigation solutions under the blocked sky condition, with performance being comparable to traditional ISB estimation algorithms in open sky conditions. The improvement rates of the three-dimensional position accuracy and availability reach up to 63% and 21% in the blocked sky environment. Even in the case of only four different GNSS satellites, a position solution can still be obtained using the enhanced algorithm.

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.

Ionospheric and receiver DCB-constrained multi-GNSS single-frequency PPP integrated with MEMS inertial measurements

Single-frequency precise point positioning (SF-PPP) is a potential precise positioning technique due to the advantages of the high accuracy in positioning after convergence and the low cost in operation. However, there are still challenges limiting its applications at present, such as the long convergence time, the low reliability, and the poor satellite availability and continuity in kinematic applications. In recent years, the achievements in the dual-frequency PPP have confirmed that its performance can be significantly enhanced by employing the slant ionospheric delay and receiver differential code bias (DCB) constraint model, and the multi-constellation Global Navigation Satellite Systems (GNSS) data. Accordingly, we introduce the slant ionospheric delay and receiver DCB constraint model, and the multi-GNSS data in SF-PPP modular together. In order to further overcome the drawbacks of SF-PPP in terms of reliability, continuity, and accuracy in the signal easily blocking environments, the inertial measurements are also adopted in this paper. Finally, we form a new approach to tightly integrate the multi-GNSS single-frequency observations and inertial measurements together to ameliorate the performance of the ionospheric delay and receiver DCB-constrained SF-PPP. In such model, the inter-system bias between each two GNSS systems, the inter-frequency bias between each two GLONASS frequencies, the hardware errors of the inertial sensors, the slant ionospheric delays of each user-satellite pair, and the receiver DCB are estimated together with other parameters in a unique Kalman filter. To demonstrate its performance, the multi-GNSS and low-cost inertial data from a land-borne experiment are analyzed. The results indicate that visible positioning improvements in terms of accuracy, continuity, and reliability can be achieved in both open-sky and complex conditions while using the proposed model in this study compared to the conventional GPS SF-PPP.

BDS–GPS inter-system bias of code observation and its preliminary analysis

Navigation applications will benefit significantly from the improved reliability, availability, and accuracy offered by combining BeiDou Navigation Satellite System (BDS) and Global Positioning System (GPS). In the BDS/GPS navigation data fusion model, the effect of inter-system bias (ISB) must be considered. We present a detailed analysis of the pseudorange measurements for BDS and GPS and demonstrate the existence of code ISB in BDS/GPS measurements. The ISB mainly consists of the time system offset, the coordinate system difference, and the inter-system hardware delay bias. A method based on statistical hypothesis testing is proposed to assess the stability and difference of the BDS–GPS ISB. Real data from 18 stations equipped with six types of receivers are used to compute the ISB. The results illustrate that (a) receiver-dependent ISBs are evident and comparatively consistent, with the maximum ISB observed in our experiments being −1516 ns, (b) these receiver-dependent ISBs exhibit great stability in terms of their standard deviation and intra-day variation, and (c) the estimated ISBs for each BDS satellite type with respect to GPS are consistent.

Comparative analysis of multi-constellation GNSS single-frequency precise point positioning

We develop new single-frequency PPP models, which combine the observations of the current GNSS constellations, including GPS, GLONASS, Galileo and BeiDou. Four single-frequency GNSS PPP models are developed, namely, the undifferenced single-frequency GNSS PPP model, the undifferenced ionosphere-free (IF) code and phase model known as quasi-phase model, the between-satellite-single-difference model (BSSD) and the between-satellite-single-difference ionosphere-free (BSSDIF) model. The IGS final precise products are used to account for the orbital and clock errors. For both undifferenced and BSSD models, the IGS final global ionospheric maps (GIM) model is used to correct the ionospheric delay. The GNSS inter-system biases are treated as additional unknowns in the estimation process for the undifferenced models, while a loosely coupled technique is used for the BSSD models. Various GNSS combinations are considered in the assessment for each PPP model, including GPS/GLONASS, GPS/Galileo, GPS/BeiDou and quad-constellation GNSS observations. It is shown that the multi-GNSS observations enhance the PPP solution accuracy in comparison with the GPS-only solution. Furthermore, the use of IF-PPP technique enhances the positioning accuracy by 25, 20, 24, 20 and 19% compared with the GIM-based PPP model for the GPS-only, GPS/GLONASS, GPS/Galileo, GPS/BeiDou and quad-GNSS combinations, respectively, for 1 h of GNSS data processing. In addition, an average of 15% positioning accuracy improvement can be obtained when the BSSD techniques are used compared with the undifferenced techniques. However, for 6 h of processing, comparable positioning accuracy can be obtained from all four single-frequency models.

Research Article. Improved Dual Frequency PPP Model Using GPS and BeiDou Observations

Abstract This paper introduces a new dual-frequency precise point positioning (PPP) model, which combines GPS and BeiDou observations. Combining GPS and BeiDou observations in a PPP model offers more visible satellites to the user, which is expected to enhance the satellite geometry and the overall PPP solution in comparison with GPSonly PPP solution. However, combining different GNSS constellations introduces additional biases, which require rigorous modelling, including GNSS time offset and hardware delays. In this research, ionosphere-free linear combination PPP model is developed. The additional biases, which result from combining the GPS and BeiDou observables, are lumped into a new unknown parameter identified as the inter-system bias. Natural Resources Canada’s GPSPace PPP software is modified to enable a combined GPS/BeiDou PPP solution and to handle the newly introduced biases. A total of four data sets at four IGS stations are processed to verify the developed PPP model. Precise satellite orbit and clock products from the IGS-MGEX network are used to correct both of the GPS and BeiDou measurements. It is shown that a sub-decimeter positioning accuracy level and 25% reduction in the solution convergence time can be achieved with combining GPS and Bei-Dou observables in a PPP model, in comparison with the GPS-only PPP solution.

Accounting for Inter-System Bias in DGNSS Positioning with GPS/GLONASS/BDS/Galileo

Code Differential Global Positioning System (DGPS) is widely used in satellite navigation and positioning because of its simple algorithm and preferable precision. Multi-Global Navigation Satellite System (GNSS) is expected to enhance the accuracy, reliability and availability of Differential GNSS (DGNSS) positioning. Traditional DGNSS models should set separate clock parameters due to the clock differences between the different systems. Awareness of the Inter-System Bias (ISB) could help to maximise the redundancy of the positioning model, thus improving the performance of multi-GNSS positioning. This paper aims to examine the inter-system bias of GPS/GLONASS/BeiDou (BDS)/Galileo and their benefits in DGNSS positioning. Results show that Differential ISB (DISB) characteristics vary with different receiver types and systems. The size of DISB could reach metre-level and the precision of estimated DISBs can reach approximately several centimetres within tens of epochs. Therefore, a new real-time DGNSS model that accounts for ISB is proposed. After differential ISBs are initialised, positioning with four satellites from arbitrarily the same or different systems can be realised. Moreover, compared with the traditional DGNSS model, the precision of the positioning results with the new model are obviously improved, especially in harsh environments.

Particle filter-based estimation of inter-system phase bias for real-time integer ambiguity resolution

Although double-differenced (DD) observations between satellites from different systems can be used in multi-GNSS relative positioning, the inter-system DD ambiguities cannot be fixed to integer because of the existence of the inter-system bias (ISB). Obviously, they can also be fixed as integer along with intra-system DD ambiguities if the associated ISBs are well known. It is critical to fix such inter-system DD ambiguities especially when only a few satellites of each system are observed. In most of the existing approaches, the ISB is derived from the fractional part of the inter-system ambiguities after the intra-system DD ambiguities are successfully fixed. In this case, it usually needs observations over long times depending on the number of observed satellites from each system. We present a new method by means of particle filter to estimate ISBs in real time without any a priori information based on the fact that the accuracy of a given ISB value can be qualified by the related fixing RATIO. In this particle filter-based method, the ISB parameter is represented by a set of samples, i.e., particles, and the weight of each sample is determined by the designed likelihood function related to the corresponding RATIO, so that the true bias value can be estimated successfully. Experimental validations with the IGS multi-GNSS experiment data show that this method can be carried out epoch by epoch to provide precise ISB in real time. Although there are only one, two, or at most three Galileo satellites observed, the successfully fixing rate increases from 75.5% for GPS only to 81.2%. In the experiment with five GPS satellites and one Galileo satellites, the first successfully fixing time is reduced to half of that without fixing the inter-system DD ambiguities.

Multi-GNSS precise point positioning (MGPPP) using raw observations

A joint-processing model for multi-GNSS (GPS, GLONASS, BDS and GALILEO) precise point positioning (PPP) is proposed, in which raw code and phase observations are used. In the proposed model, inter-system biases (ISBs) and GLONASS code inter-frequency biases (IFBs) are carefully considered, among which GLONASS code IFBs are modeled as a linear function of frequency numbers. To get the full rank function model, the unknowns are re-parameterized and the estimable slant ionospheric delays and ISBs/IFBs are derived and estimated simultaneously. One month of data in April, 2015 from 32 stations of the International GNSS Service (IGS) Multi-GNSS Experiment (MGEX) tracking network have been used to validate the proposed model. Preliminary results show that RMS values of the positioning errors (with respect to external double-difference solutions) for static/kinematic solutions (four systems) are 6.2 mm/2.1 cm (north), 6.0 mm/2.2 cm (east) and 9.3 mm/4.9 cm (up). One-day stabilities of the estimated ISBs described by STD values are 0.36 and 0.38 ns, for GLONASS and BDS, respectively. Significant ISB jumps are identified between adjacent days for all stations, which are caused by the different satellite clock datums in different days and for different systems. Unlike ISBs, the estimated GLONASS code IFBs are quite stable for all stations, with an average STD of 0.04 ns over a month. Single-difference experiment of short baseline shows that PPP ionospheric delays are more precise than traditional leveling ionospheric delays.

Un-differenced precise point positioning model using triple GNSS constellations

AbstractThis paper introduces a dual-frequency precise point positioning (PPP) model, which combines the observations of three different global navigation satellite system (GNSS) constellations, namely GPS, Galileo, and BeiDou. A drawback of a single GNSS system such as GPS, however, is the availability of sufficient number of visible satellites in urban areas. Combining GNSS observations offers more visible satellites to users, which in turn is expected to enhance the satellite geometry and the overall positioning solution. However, combining several GNSS observables introduces additional biases, which require rigorous modeling, including the GNSS time offsets and hardware delays. In this paper, un-differenced ionosphere-free linear combination PPP model is developed. The additional biases of the GPS, Galileo, and BeiDou combination are accounted for through the introduction of a new unknown parameter, which is identified as the inter-system bias, in the PPP mathematical model. Natural Resources Canada’s...

Modeling and Assessment of GPS/BDS Combined Precise Point Positioning.

Precise Point Positioning (PPP) technique enables stand-alone receivers to obtain cm-level positioning accuracy. Observations from multi-GNSS systems can augment users with improved positioning accuracy, reliability and availability. In this paper, we present and evaluate the GPS/BDS combined PPP models, including the traditional model and a simplified model, where the inter-system bias (ISB) is treated in different way. To evaluate the performance of combined GPS/BDS PPP, kinematic and static PPP positions are compared to the IGS daily estimates, where 1 month GPS/BDS data of 11 IGS Multi-GNSS Experiment (MGEX) stations are used. The results indicate apparent improvement of GPS/BDS combined PPP solutions in both static and kinematic cases, where much smaller standard deviations are presented in the magnitude distribution of coordinates RMS statistics. Comparisons between the traditional and simplified combined PPP models show no difference in coordinate estimations, and the inter system biases between the GPS/BDS system are assimilated into receiver clock, ambiguities and pseudo-range residuals accordingly.

A statistical characterization of the Galileo-to-GPS inter-system bias

Global navigation satellite system operates using independent time scales and thus inter-system time offsets have to be determined to enable multi-constellation navigation solutions. GPS/Galileo inter-system bias and drift are evaluated here using different types of receivers: two mass market and two professional receivers. Moreover, three different approaches are considered for the inter-system bias determination: in the first one, the broadcast Galileo to GPS time offset is used to align GPS and Galileo time scales. In the second, the inter-system bias is included in the multi-constellation navigation solution and is estimated using the measurements available. Finally, an enhanced algorithm using constraints on the inter-system bias time evolution is proposed. The inter-system bias estimates obtained with the different approaches are analysed and their stability is experimentally evaluated using the Allan deviation. The impact of the inter-system bias on the position velocity time solution is also considered and the performance of the approaches analysed is evaluated in terms of standard deviation and mean errors for both horizontal and vertical components. From the experiments, it emerges that the inter-system bias is very stable and that the use of constraints, modelling the GPS/Galileo inter-system bias behaviour, significantly improves the performance of multi-constellation navigation.

Single-Frequency Precise Point Positioning Using Multi-Constellation GNSS: GPS, GLONASS, Galileo and BeiDou

Single-frequency precise point positioning (PPP) presents a cost-effective positioning technique for a large number of users. However, it possesses low positioning accuracy and convergence time compared with the dual-frequency PPP. Single-frequency PPP commonly employs GPS satellite systems that suffer from poor satellite geometry, especially in dense urban areas. We develop a new single-frequency PPP model that combines the observations of current GNSS constellations, including GPS, GLONASS, Galileo and Beidou. The MGEX IGS final precise products are utilized to account for the orbital and clock errors, while the IGS final global ionospheric maps (GIM) model is used to correct for the ionospheric delay. The GNSS inter-system biases are treated as additional unknowns in the estimation process. The con tri bution of the additional GNSS observations to single-frequency PPP is assessed through solution comparison with its traditional GPS-only counterpart. Various GNSS combinations are considered in the assessment, including GPS/GLONASS, GPS/Galileo, GPS/BeiDou and all-constellation GNSS. It is shown that the additional GNSS observations enhance the PPP solution accuracy and convergence time in comparison with the tra di tional GPS-only solution. Except for stations with a sufficient number of tracked BeiDou satellites, both Galileo and BeiDou have marginal effects on the positioning accuracy due to their limited number of satel lites. However, for stations with a sufficient number of visible BeiDou satellites, an average of 40% PPP accuracy improvement is obtained. The major contribution to the PPP accuracy enhancement is obtained from GLONASS satellite observations.

Precise Point Positioning Using Triple GNSS Constellations in Various Modes.

This paper introduces a new dual-frequency precise point positioning (PPP) model, which combines the observations from three different global navigation satellite system (GNSS) constellations, namely GPS, Galileo, and BeiDou. Combining measurements from different GNSS systems introduces additional biases, including inter-system bias and hardware delays, which require rigorous modelling. Our model is based on the un-differenced and between-satellite single-difference (BSSD) linear combinations. BSSD linear combination cancels out some receiver-related biases, including receiver clock error and non-zero initial phase bias of the receiver oscillator. Forming the BSSD linear combination requires a reference satellite, which can be selected from any of the GPS, Galileo, and BeiDou systems. In this paper three BSSD scenarios are tested; each considers a reference satellite from a different GNSS constellation. Natural Resources Canada’s GPSPace PPP software is modified to enable a combined GPS, Galileo, and BeiDou PPP solution and to handle the newly introduced biases. A total of four data sets collected at four different IGS stations are processed to verify the developed PPP model. Precise satellite orbit and clock products from the International GNSS Service Multi-GNSS Experiment (IGS-MGEX) network are used to correct the GPS, Galileo, and BeiDou measurements in the post-processing PPP mode. A real-time PPP solution is also obtained, which is referred to as RT-PPP in the sequel, through the use of the IGS real-time service (RTS) for satellite orbit and clock corrections. However, only GPS and Galileo observations are used for the RT-PPP solution, as the RTS-IGS satellite products are not presently available for BeiDou system. All post-processed and real-time PPP solutions are compared with the traditional un-differenced GPS-only counterparts. It is shown that combining the GPS, Galileo, and BeiDou observations in the post-processing mode improves the PPP convergence time by 25% compared with the GPS-only counterpart, regardless of the linear combination used. The use of BSSD linear combination improves the precision of the estimated positioning parameters by about 25% in comparison with the GPS-only PPP solution. Additionally, the solution convergence time is reduced to 10 minutes for the BSSD model, which represents about 50% reduction, in comparison with the GPS-only PPP solution. The GNSS RT-PPP solution, on the other hand, shows a similar convergence time and precision to the GPS-only counterpart.

PPP-RTK and inter-system biases: the ISB look-up table as a means to support multi-system PPP-RTK

PPP-RTK has the potential of benefiting enormously from the integration of multiple GNSS/RNSS systems. However, since unaccounted inter-system biases (ISBs) have a direct impact on the integer ambiguity resolution performance, the PPP-RTK network and user models need to be flexible enough to accommodate the occurrence of system-specific receiver biases. In this contribution we present such undifferenced, multi-system PPP-RTK full-rank models for both network and users. By an application of $$\mathcal {S}$$ -system theory, the multi-system estimable parameters are presented, thereby identifying how each of the three PPP-RTK components are affected by the presence of the system-specific biases. As a result different scenarios are described of how these biases can be taken into account. To have users benefit the most, we propose the construction of an ISB look-up table. It allows users to search the table for a network receiver of their own type and select the corresponding ISBs, thus effectively realizing their own ISB-corrected user model. By applying such corrections, the user model is strengthened and the number of integer-estimable user ambiguities is maximized.

A new method to improve the performance of multi-GNSS pseudorange positioning in signal-degraded environment

There are two existing multi-GNSS positioning methods, (1) separate receiver clock parameter is set for each constellation, (2) estimating intersystem biases (ISBs) in advance to obtain position solutions with only four unknowns. The former is the regular method and its unknowns include three receiver-coordinate parameters and several receiver clock parameters (depend on the number of participant constellations), so that it may disable when few satellites belonging to different GNSS are in view. The latter is one workable way to obtain position solution with only four visible satellites. In addition to the disabled regular method, the positioning results by the ISB-corrected method are often unsatisfactory for navigation users in signal-degraded environment. Both the deviation of ISB-solutions and the remaining measurement errors of the need corrected observations are factors to degrade location precision. Apart from these, fewer visible satellites usually cause a low robustness of the positioning model, which cause the negative influence of various errors is amplified. Based on the variation of various measurement errors, we propose a new ISSB-corrected method with observations corrected by corresponding satellite-dependent parameters. The new parameter contains the difference of time scales, hardware delays and uncorrected measurement errors between the corresponding satellite and reference, in other words, it can synthetically consider measurement errors and the ISB. By the ISSB-corrected method, we not only achieve positioning solutions with four satellites, but also significantly reduce the accuracy loss. Many experiments are conducted to present the superiority of the ISSB-corrected method. In open-area, the accuracies of regular and ISB-corrected methods are nearly equal. Apart from a similar accuracy in horizontal, the accuracy is improved by approximate 10% in up direction with respect to the two existing methods. Given the high redundancy of model in open-area, the new method may not improve the accuracy remarkably. However, it can make great contributions in signal-degraded environments. In order to compare the performance of ISB- and ISSB-corrected methods in environment with limited visible satellites, we simulate several scenarios (different satellites participant or various receivers) with only four participant satellites in the positioning solution. By the ISSB-corrected method, the 3D RMS of positioning results with four satellites is about 15m, while it is usually worse than 25m for the ISB-corrected method. In an urban vehicular test, the horizontal positioning error of the ISSB-corrected method is less than 20m; and the ISB-corrected method may reach up to 70m.