Satellite Clock Estimation Research Articles

Real-time LEO satellite clock estimation with predicted LEO satellite orbits constrained

Low Earth Orbit (LEO) satellites can augment the traditional GNSS-based positioning, navigation and timing services, which require real-time high-precision LEO satellite clock products. As the complicated systematic effects contained in the LEO satellite clock estimates limit their high-precision mid- to long-term prediction, high-frequency LEO satellite clocks need to be estimated within a Kalman filter, resulting in a short prediction time for real-time applications. Compared to the clock estimation using Batch Least-Squares (BLS) adjustment, filter-based clock estimation experiences a lower precision. Increasing the model strength by introducing external orbital information, thus, de-correlating the orbital and clock parameters, will benefit real-time clock precision. In this contribution, reduced-dynamic LEO satellite orbits are first estimated using BLS adjustment in near real-time and predicted in the short term. The predicted orbits are then constrained during the Kalman-filter-based clock estimation process. The variance–covariance matrix of the introduced orbital errors is tested for different sets of values in the radial, along-track and cross-track directions when constraining orbits of different prediction times. One week of GPS data from the Sentinel-3B satellite in 2018 was used for validation of the proposed method. When weakly constraining high-accuracy predicted orbits within a prediction time of 20 min, i.e., with a standard deviation of the constraint set to 2–3 dm in the radial and cross-track directions, and 4–6 dm in the along-track direction, the estimated clock accuracy can be improved from about 0.27 to 0.23 ns, with a 13.4% improvement. Depending on the prediction period of the introduced orbits, the Signal-In-Space Range Error (SISRE) of the LEO satellite to Earth can also be improved, from about 9.59 cm without constraints, to 7.38–8.07 cm after constraining the predicted orbits, with an improvement of 16–23%. The improvements in the SISRE also indicate a better consistency between the real-time clock and orbital estimates.

Cube: An Open-Source Software for Clock Offset Estimation and Precise Point Positioning with Ambiguity Resolution

Precise point positioning (PPP) is a prevalent, high-precision spatial absolution positioning method, and its performance can be enhanced by ambiguity resolution (AR). To fulfill the growing need for high-precision positioning, we developed an open-source GNSS data processing package based on the decoupled clock model called Cube, which integrates decoupled clock offset estimation and precise point positioning with ambiguity resolution (PPP-AR). Cube is a secondary development based on RTKLIB. Besides the decoupled clock model, Cube can also estimate legacy clocks for the International GNSS Service (IGS), as well as clocks with satellite code bias extraction, and perform PPP-AR using the integer-recovered clock model. In this work, we designed satellite clock estimation and PPP-AR experiments with one week of GPS data to validate Cube’s performance. Results show that the software can produce high-precision satellite clock products and positioning results that are adequate for daily scientific study. With Cube, researchers do not need to rely on public PPP-AR products, and they can estimate decoupled clock products and implement PPP-AR anytime.

Real-time clock estimation using system time offset maintenance aiming at multi-GNSS time interoperability

Time interoperability is one of the important aspects of Global Navigation Satellite System (GNSS) compatibility and interoperability, which will greatly benefit the accuracy and availability of the positioning, navigation and timing (PNT) solution. In this paper, we proposed a real-time satellite clock estimation method using system time offset (STO) maintenance to help users realize GNSS time interoperability. First, receiver inter-system bias (ISB) was investigated and modeled for STO maintenance. Then, we presented clock estimation assessment results, which demonstrate that the new method can make the satellite clock product maintain a stable STO. Finally, precise point positioning (PPP) was used for further validation. The results show that in the condition of a 45° cutoff elevation angle, fixing the ISB can significantly reduce the convergence time, increase the availability by 21.5%, and improve the average positioning accuracy in horizontal and vertical by 37.7% and 44.4%, respectively.

A computationally efficient prior quality control approach for multi-GNSS real-time satellite clock estimation

A computationally efficient prior quality control approach for multi-GNSS real-time satellite clock estimation

Improved short-term stability for real-time GNSS satellite clock estimation with clock model

Improved short-term stability for real-time GNSS satellite clock estimation with clock model

Relativistic effects of LEO satellite and its impact on clock prediction

Low Earth orbit (LEO) augmentation in the global navigation satellite system has become a focus in the current satellite navigation field. To achieve high precision in positioning, navigation and timing services, relativistic effects should be considered, as they are difficult to distinguish from LEO satellite clock estimates and disturb their predictions. The relativistic effects on LEO satellite clocks are discussed in detail based on both theoretical and empirical results. Two LEO satellite clock prediction strategies are proposed, with and without removing the relativistic effect, using real data from typical LEO satellites: SENTINEL-3B and Gravity Recovery and Climate Experiment Follow-On (GRACE FO-1). For GRACE FO-1 and SENTINEL-3B, the relativistic effects are both on the order of nanoseconds and after removing the relativistic effects, the modified Allan deviations of the clocks are shown to be significantly improved. Based on the prediction strategies proposed, for SENTINEL-3B at around 810 km, with the prediction period increased from 30 to 3600 s, the root mean square error (RMSE) increases from 0.025 ns to about 1.4–1.6 ns. For the lower LEO satellite GRACE FO-1 at around 500 km, the RMSE of the predicted clocks increases more rapidly, i.e. from 0.012 ns at 30 s to about 4.5 ns at 3600 s. Results showed that the LEO satellite relativistic effects developed based on the theory could correct the majority, but not all of the once- and twice-per-revolution terms in the LEO satellite clocks. Although the corrections have exhibited effective improvements in the clock stability, they do not behave better than simply applying the mathematical model to the clock predictions. The latter model, however, does not have physical foundations as the former one.

A Real-Time Linear Prediction Algorithm for Detecting Abnormal BDS-2/BDS-3 Satellite Clock Offsets

Due to space environment interference, imperfect data processing model, and the performance of atomic clocks, real-time satellite clock products often contain outliers or irregular biases. We propose a real-time linear moving short-term prediction algorithm to predict clock offsets and detect abnormalities. The proposed algorithm mainly includes phase/frequency anomaly detection and real-time prediction part. Both the phase and frequency domains are used to detect abnormal clock offsets with previous epochs for building the clock prediction model accurately. The real-time moving prediction module utilizes the high short-term prediction performance to check the clock abnormality. The performance of the algorithm is then evaluated for all satellites with real-time estimated satellite clock offsets. To verify the feasibility and effectiveness of the proposed linear moving model and algorithm, the results of the grey model GM(1,1) and the ARIMA model are also compared. The experimental results indicated that the algorithm can detect clock outliers, frequency modulation, and phase jumps, and the linear model has a better clock performance improvement. After the abnormalities are removed with the proposed algorithm, the average STD accuracy of the real-time clock offsets for all satellites is improved by 15.5%, compared to an improvement of 11.4% by the GM(1,1) model and 11.5% by the ARIMA model. The PPP results demonstrate that the proposed clock prediction algorithm improves the positioning accuracy by 8.1%, 13.3%, and 16.9% in the east, north, and up components, respectively.

Analysis of BDS-3 Real-Time Satellite Clock Offset Estimated in Global and Asia-Pacific and the Corresponding PPP Performances

The quality of satellite clock offset affects the performances of positioning, navigation and timing services, and thus it is essential to the Global Navigation Satellite System (GNSS). This research focuses on the estimation of BeiDou Navigation Satellite System (BDS) real-time precise satellite clock offset by using GNSS stations located in the Global and Asia-Pacific region based on the mixed-difference model. The precision of the estimated BDS clock corrections is then analyzed with the classification of the orbit types, satellite generations, and atomic clock types. The results show that the precision of the BDS clock offset estimated in the Asia-Pacific for Geosynchronous Earth Orbit (GEO), Inclined Geosynchronous Satellite Orbit (IGSO) and Medium Earth Orbit (MEO) satellites are 0.204 ns, 0.077 ns and 0.085 ns, respectively, as compared to those of clock offsets estimated in globally distributed stations. The average precision of the BDS-3 satellites clock offset estimated in global region is 0.074 ns, which is much better than the 0.130 ns of BDS-2. Furthermore, analyzing the characteristics of the corresponding atomic clocks can explain the performance of the estimated satellite clock offset, and the stability and accuracy of various parameters of the Passive Hydrogen Maser (PHM) atomic clocks are better than those of Rubidium (Rb) atomic clocks. In the positioning domain, the real-time clocks estimated in the global/Asia-Pacific have been applied to BDS kinematic Precise Point Positioning (PPP) in different regions. The Root Mean Square (RMS) of positioning results in global real-time kinematic PPP is within 4 cm in the horizontal direction and about 6 cm in the vertical direction. Hence, the BDS real-time clock offset can supply the centimeter-level positioning demand around the world.

Analysis of Galileo five-frequency precise satellite clock estimation models and its effect on multi-frequency PPP

The Global Navigation Satellite System (GNSS) multi-frequency observations are widely used in positioning applications, while precise orbit determination and precise clock estimation (PCE) techniques typically employ dual-frequency undifferenced (UD) ionospheric-free (IF) observations from global networks. To fully utilize the multi-frequency GNSS observations for generating satellite products at the server-end, we develop some new five-frequency PCE models based on Galileo data, which are five-frequency uncombined FFUC model, FFIF0 model combining the E1/E5a, E1/E5b, E1/E5 and E1/E6 IF observables, FFIF1 model combining E1/E5a and E1/E5a/E5b/E5/E6 IF observables, respectively. The traditional dual-frequency UD IF and triple-frequency PCE models are also introduced for comparison. The new multi-frequency PCE models can not only make full use of the modern GNSS multi-frequency observations, but also obtain satellite clock offsets and inter-frequency clock bias (IFCB) at the same time, which can better support multi-frequency precise point positioning (PPP) applications. The multi-frequency models can improve the stability of GNSS satellite clock estimation, the precision of satellite clock offsets can be improved by 8–12% for triple-frequency models, and 19–27% for five-frequency PCE models compared with the traditional dual-frequency IF model. The PPP positioning accuracy using only multi-frequency satellite clock offsets can be improved by 7–18% for dual-frequency PPP, 8–15% for triple-frequency PPP, 4–16% for five-frequency PPP. The positioning accuracy can be further improved by 11–28% for triple-frequency PPP and 7–20% for five-frequency PPP. Therefore, the new multi-frequency PCE models are demonstrated to support PPP applications with better performance.

Improving undifferenced precise satellite clock estimation with BDS-3 quad-frequency B1I/B3I/B1C/B2a observations for precise point positioning

Improving undifferenced precise satellite clock estimation with BDS-3 quad-frequency B1I/B3I/B1C/B2a observations for precise point positioning

A Kalman filter-based online fractional cycle bias determination method for real-time ambiguity-fixing GPS satellite clock estimation

Integer ambiguity resolution (IAR) is one of the most powerful methods to improve the precision and the convergence of estimating real-time satellite clocks, which is an indispensable prerequisite to support the real-time precise point position (PPP) service. In this study, a Kalman filter-based online fractional cycle bias (FCB) determination method is proposed to facilitate the real-time IAR for satellite clock estimation. A real-time recursive algorithm for smoothing the average float wide-lane (WL) ambiguity is developed to mitigate the impact of pseudorange noise. Quality control procedures are established throughout the entire FCB filter process to remove low-quality observations and mitigate the impact of incorrect integer ambiguities. This method is designed as an embedded module in the clock estimation procedure to fix both integer WL and narrow-lane (NL) ambiguities in an epoch-by-epoch way for recovering the integer property of the undifferenced ionosphere-free (IF) ambiguities in real-time. The performance of the FCB filter and the ambiguity-fixing clock estimation is validated with a GPS network from the international GNSS service (IGS). Experiments show that the WL and NL FCB estimation accuracy reaches 0.004 cycles and 0.080 cycles for GPS satellites. The WL and NL residuals fit the normal distribution well after several minutes and 1.5 h, respectively, making the ambiguity-fixing clocks converge rapidly in about two hours. The online FCB filter method improves real-time ambiguity-fixing clock estimation accuracy significantly. Compared to the ambiguity-float solution, the STD of the ambiguity-fixing real-time satellite clocks is averagely improved by 31.0 % to 0.040 ns with the ultra-rapid orbits. The ambiguity-fixing satellite clocks can be applied in the real-time kinematic PPP ambiguity resolution, and the positioning accuracy is improved by 24.1 % to 51.7 % compared to that of using the ambiguity-float clock products.

Combined BDS-2/BDS-3 real-time satellite clock estimation with the overlapping B1I/B3I signals

With the deployment of the global BeiDou navigation satellite system (BDS-3) constellation completed, the positioning service performance is significantly improved relative to the regional system (BDS-2). As one of the key prerequisite products for precise point positioning (PPP), the combined BDS-2/BDS-3 real-time satellite clock estimation method is investigated in this study. Since the code hardware delays of BDS-2/BDS-3 satellites might be inconsistent for some receiver types, the inter-system bias (ISB) is considered in the combination although the overlapping B1I/B3I signal is employed. The combination processing is comprehensively evaluated in terms of satellite tracking coverage, clock precision, and convergence time. The experiment results indicate that the standard deviation (STD) precision of the estimated clocks for BDS-2 medium Earth orbit (MEO) satellites is improved by 52.0% from 0.150 ns to 0.072 ns due to the improvement of satellite tracking coverage. Introducing the ISB parameter as piece-wise constants improves the STD of all clocks from 0.076 ns to 0.067 ns and BDS-3 clocks achieve a significant improvement from 0.065 ns to 0.053 ns. The real-time clock estimation is demonstrated to be robust for the clock datum transformation, and it converges after one hour to a stable precision but needs a long time to achieve the best performance. The BDS real-time clocks are estimated with the proposed strategy to support real-time PPP based on the predicted satellite orbits. Results show that the clock STD is about 0.1 ns for most BDS satellites and the positioning accuracy of about 10 cm is achieved after the convergence time of about half an hour. The clock precision for BDS-2 geostationary Earth orbit (GEO) satellites is degraded to 0.303 ns due to the impact of poor orbit prediction errors. The exclusion of GEO satellites improves the positioning accuracy by about 15% and reduces the convergence time by 22–34%.

A Method to Accelerate the Convergence of Satellite Clock Offset Estimation Considering the Time-Varying Code Biases

Continuous and stable precision satellite clock offsets are an important guarantee for real-time precise point positioning (PPP). However, in real-time PPP, the estimation of a satellite clock is often interrupted for various reasons such as network fluctuations, which leads to a long time for clocks to converge again. Typically, code biases are assumed to stay constant over time in clock estimation according to the current literature. In this contribution, it is shown that this assumption reduces the convergence speed of estimation, and the satellite clocks are still unstable for several hours after convergence. For this reason, we study the influence of different code bias extraction schemes, that is, taking code biases as constants, extracting satellite code biases (SCBs), extracting receiver code biases (RCBs) and simultaneously extracting SCBs and RCBs, on satellite clock estimation. Results show that, the time-varying SCBs are the main factors leading to the instability of satellite clocks, and considering SCBs in the estimation can significantly accelerate the filter convergence and improve the stability of clocks. Then, the products generated by introducing SCBs in the clock estimation based on undifferenced observations are applied to PPP experiments. Compared with the original undifferenced model, clocks estimated using the new method can significantly accelerate the convergence speed of PPP and improve the positioning accuracy, which illustrates that our estimated clocks are effective and superior.

The CODE ambiguity-fixed clock and phase bias analysis products: generation, properties, and performance

The generation and use of GNSS analysis products that allow—particularly for the needs of single-receiver applications—precise point positioning with ambiguity resolution (PPP-AR) are becoming more and more popular. A general uncertainty concerns the question on how the necessary phase bias information should be provided to the PPP-AR user. Until now, each AR-enabling clock/bias representation method had its own practice to provide the necessary bias information. We have generalized the observable-specific signal bias (OSB) representation, as introduced in Villiger (J Geod 93:1487–1500, 2019) originally exclusively for pseudorange measurements, to carrier phase measurements. The existing common clock (CC) approach has been extended in a way that OSBs allowing for flexible signal and frequency handling between multiple GNSS become possible. Advantages of the proposed OSB-based PPP-AR approach are: GNSS biases can be provided in a consistent way for phase and code measurements and it is capable of multi-GNSS and suitable for standardization. This new, extended PPP-AR approach has been implemented by the Center for Orbit Determination in Europe (CODE). CODE clock products that adhere to the integer-cycle property have been submitted to the International GNSS Service (IGS) since mid of 2018 for three analysis lines: Rapid, Final, and MGEX (Multi-GNSS Extension). Ambiguity fixing is performed not only for GPS but also for Galileo. The integer-cycle property of between-satellite clock differences is of fundamental importance when comparing satellite clock estimates among various analysis lines, or at day boundaries. Both kinds of comparisons could be exploited at a very high level of consistency. Any retrieved comparison essentially indicated a standard deviation for between-satellite clocks from CODE of the order of 5 ps (1.5 mm in range). Finally, the integer-cycle property that may be recovered between the CODE Final clock and the accompanying bias product of consecutive daily sessions (using clock estimates additionally provided for the second midnight epoch) allows us to deduce GPS satellite clock and phase bias information that is consistent and continuous with respect to carrier phase observation data over two, three, or, in principle, yet more days. Phase-based clock densification from initially estimated integer-cycle-conform clock corrections at intervals of 300 s to 30 s (5 s in case of our Final clock product) is a matter of particular interest. Based on direct product comparisons and GRACE K-band ranging (KBR) data analysis, the quality of accordingly densified clock corrections could be confirmed to be on a level similar to that of “anchor” (300 s) clock corrections.

Inter-satellite link augmented BeiDou-3 orbit determination for precise point positioning

Precise Point Positioning (PPP) requires precise products, including high-accuracy satellite orbit and clock parameters. It is impossible to obtain an orbit solution that is sufficiently accurate for PPP services with a regional tracking network; therefore, satellite orbits are usually estimated by a global tracking network with a large number of ground stations. However, it is expensive to build globally distributed stations. Fortunately, BeiDou-3 satellites carry an Inter-Satellite Link (ISL) payload, which can track the whole arc of the BeiDou-3 satellites and enhance the orbit determination accuracy with regional ground stations. In this contribution, a novel orbit determination strategy for BeiDou-3 PPP is proposed, in which the BeiDou-3 satellite orbits are enhanced by the ISL. First, the generation of precise satellite products is demonstrated in detail. In addition, the products are assessed by Satellite Laser Ranging (SLR) residuals and overlap comparisons. Moreover, the products are used for receivers in mainland China to carry out the static and kinematic modes to research the PPP performance of BeiDou-3′s 3IGSO/24MEO constellation. The SLR validations of the satellite orbits demonstrate an accuracy better than 0.1 m in the radial component, and the orbit overlap comparisons show accuracies of 0.016 m in the radial component, 0.088 m in the along-track component and 0.087 m in the cross-track component. The Standard Deviation (STD) in the differences in overlapping arcs for the estimated satellite clocks is approximately 0.10 ns. The static PPP results demonstrate that the error in both the horizontal and vertical components is smaller than 10 cm after 30 minutes of convergence. After 24 hours of convergence, the errors are 0.70 cm, 0.63 cm and 1.99 cm for the north, east and up components, respectively. The kinematic PPP experiment illustrates that the Root Mean Square (RMS) position errors in the north, east and up components are approximately 3.23 cm, 5.27 cm and 8.64 cm, respectively, after convergence. The obtainable positioning and convergence performances are comparable to those using products generated by global tracking networks.

Simulation of Inter-Satellite Link schemes for use in precise orbit determination and clock estimation

Inter-Satellite Links (ISL) are considered a key technology which might improve the accuracy of the Global Navigation Satellite System (GNSS) and navigation satellites orbit determination. This research aims at evaluation of advantages of the ISLs with special consideration of the Galileo, as a contribution to precise orbit determination and satellite clock estimation. The performed analysis will also pave the way to more advanced processing including more sophisticated modifications of the current orbit determination approach and development of the algorithms for the ISL system.

GNSS Receiver-Related Pseudorange Biases: Characteristics and Effects on Wide-Lane Ambiguity Resolution

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.

Improving GPS and Galileo precise data processing based on calibration of signal distortion biases

The quality of pseudorange observations plays an important role in Global Navigation Satellite System (GNSS) data processing, especially for satellite clock estimation, differential code bias (DCB) estimation and wide-lane ambiguity resolution. It is validated that receivers with different correlator spaces and front-end designs will bring signal distortion bias (SDB) in pseudorange observations, which will affect GNSS data processing based on inhomogenous receivers, such as receivers from Multi-GNSS EXperiment (MGEX) network. We firstly evaluate the consistency of GPS and Galileo satellite clock and DCB products among different International GNSS Service (IGS) Analysis Centers (ACs). The results show that inconsistency exists in both satellite clocks and DCB products among different ACs. For example, the difference of GPS satellite DCB (C1C-C1W) between two ACs, which is free of ionospheric delay, can reach up to 0.31 ns. To improve GPS and Galileo precise data processing based on inhomogenous receivers, pseudorange biases caused by receiver signal distortion are analyzed and calibrated for 5 receiver brands and 19 receiver models. The maximum pseudorange biases of ionospheric-free combination caused by receiver SDBs can reach up to ±3 ns and ±1 ns for GPS and Galileo, respectively. Then, bias corrections of GPS and Galileo raw pseudorange observations are divided into 11 groups and estimated by each receiver group. Finally, several experiments are carried out for the validation of GPS and Galileo SDB correction models. For example, the GPS and Galileo satellite clock offset differences estimated by different receiver brands are decreased by 86.59% and 50.0% for specific receiver type, respectively. The improvement ratio of satellite DCB accuracy is related to satellite systems and signal types, and the maximum improvement can reach up to 95%. Moreover, the maximum improvement of GPS undifferenced wide-lane ambiguity resolution success rate can reach up to 22% for specific receiver types. All these results prove that the bias corrections proposed could greatly eliminate the effect of receiver SDBs on GPS and Galileo precise data processing. Hence, we suggest the corrections of SDBs should be taken into consideration for IGS data reprocessing.

BDS Real-time Satellite Clock Offsets Estimation with Three Different Datum Constraints

A clock offset datum should be selected to separate the satellite and receiver clock offset when estimating the Global Navigation Satellite System (GNSS) satellite clock offset. However, the applicable conditions and performance of the estimated satellite clock offset vary for different clock offset datums. In this paper, the BeiDou Navigation Satellite System (BDS) real-time satellite clock offset is estimated by using the undifferenced (UD) model with three datum constraints: receiver clock datum, satellite clock datum, and zero-mean condition (ZMC) datum. The constraint conditions of three clock offset datums are discussed, the transformation relationship among the three datums constraints is derived, and the characteristics of three clock offset datums are analyzed. One hundred stations were used to perform the experiments, and the results show mean standard deviation (STD) values of ±0.118, ±0.124, and ±0.101 ns for the receiver clock, satellite clock, and ZMC datum, respectively. The mean clock offset model precisions with the three datum are ±0.497, ±0.646, and ±0.442 ns, respectively. The frequency stability with ZMC datum results showed the best performance when the integration time is less than 10,000 s. For precise point positioning (PPP), the ZMC datum results show better performance among the three datum constraints. This study can provide a reference for clock offset datum selection for GNSS satellite clock offset estimation.

The application of inter-satellite links connectivity schemes in various satellite navigation systems for orbit and clock corrections determination: simulation study

Inter-Satellite Links (ISLs) are intended to improve precision of orbit determination and satellite clock estimation. The ISLs provide a precise pseudorange measurements between satellites in a specific constellation. The study is a preparatory assessment of exploitation of seven connectivity schemes in the terms of the precise orbit determination for three types of constellations—Galileo-like with 24 satellites on three orbital planes, GPS-like with 24 satellites on six orbital planes, and GPS with real positions. The first part of the study focused on detailed analysis of the various ISL connectivity schemes, considering the geometry of ISL observations. The selected results of ranging were examined in the context of the precise orbit determination based on weighted least squares adjustment. The second part of the analysis was based on simulated measurements with two approaches. First approach focuses on geometrical dependencies and the second is performed with ISL measurement biases estimation. It was found that the use of the ISL technique with GNSS measurements in orbit determination improves the results by reducing the RMS error in the along-track and cross-track components. Choice of connectivity schemes does not have a significant impact on the total results of orbit determination, but give different contribution to particular components. Introducing constant bias in ISL measurements occurs in slightly worse estimation results. However, the relations between connectivity schemes is very similar to approach without simulation of ISL bias, the differences are at the level of 10%. Satellite and station clock estimation errors are almost equal for all used connectivity schemes. Results of clocks are also not influenced by ISL bias. This study showed that the ISL technique is a highly promising addition for future generations of satellite navigation systems and that sequential and ring connectivity schemes can be recommended for use in future navigation constellations.