Satellite Clock Research Articles

Performance analysis of SBAS ephemeris corrections and integrity algorithms in China region

Satellite Based Augmentation Systems (SBASs) improve the positioning accuracy and integrity by broadcasting to the civil aviation community the corrections and integrity parameters. A snapshot algorithm based on the minimum variance estimation is investigated in this study to calculate the satellite clock and orbit corrections. A chi-square test is performed on the remaining errors in the corrected ephemeris to guarantee the integrity. User Differential Range Error (UDRE) and scaling matrix contained in Message Type 28 are derived using the covariance information based on the assumption that one of the reference stations failed. A software package is developed and applied in the real data collected at 26 stations. International GNSS (Global Navigation Satellite System) Service (IGS) precise clock and orbit products are taken as the references to assess the accuracy of corrections. For both Global Positioning System (GPS) and BeiDou Navigation Satellite System (BDS), the range accuracy of 0.10 m can be achieved with the employment of the derived corrections. No obvious performance difference between GPS and BDS is found. UDREs for all visible satellites are generated with the maximum index of 12 and minimum index of 3. The geometric range differences calculated with IGS precise products and broadcast ephemeris are employed to assess the integrity of UDRE. It is found that the UDRE is able to bound the residuals with 99.9% confidence which meet the requirement of aviation users. With ionospheric delay corrected by Global Ionosphere Map (GIM), the positioning accuracy of 0.98 m with GPS corrections and 0.80 m with multi-constellation augmentation can be achieved which indicates a significant improvement of GPS standalone results.

Assessment of multi-GNSS precise orbit and clock products from different analysis centers based on precise point positioning

Performance of 24h static Precise Point Positioning (PPP) solutions based on multi-GNSS precise satellite orbit and clock products from four analysis centers and seven various constellation combinations was studied to evaluate their quality and characteristics. Data from ten European and four Chinese GNSS stations and 152 days long period from year 2020 were processed. Obtained coordinates were firstly compared with those provided by IGS final weekly combined solution. In Europe, the best agreement with this reference product was reached by solutions including Galileo signals, namely by a combination of GPS+GLONASS+Galileo systems with a mean RMS of 11 mm. This situation was different in China where inclusion of Galileo always led to worse results and the best agreement was achieved by a combination of GPS+GLONASS systems. Although product provided by German Research Center for Geosciences (GFZ) could be selected as the best performing over Europe and product by Center for Orbit Determination in Europe (CODE) over China, differences between individual precise products were mostly at a minimal level. Secondly, coordinates repeatability over the processed period was computed in order to assess the positioning stability. In this regard, the lowest values in both horizontal and vertical direction were reached by GPS+GLONASS solutions. From the perspective of precise products, the repeatability results were dependent on the selected constellation where mainly a specific behavior of product from Wuhan University (WUM) for Galileo system was observed.

Comparisons of CODE and CNES/CLS GPS satellite bias products and applications in Sentinel-3 satellite precise orbit determination

To resolve undifferenced GNSS phase ambiguities, dedicated satellite products are needed, such as satellite orbits, clock offsets and biases. The International GNSS Service CNES/CLS analysis center provides satellite (HMW) Hatch-Melbourne-Wübbena bias and dedicated satellite clock products (including satellite phase bias), while the CODE analysis center provides satellite OSB (observable-specific-bias) and integer clock products. The CNES/CLS GPS satellite HMW bias products are determined by the Hatch-Melbourne-Wübbena (HMW) linear combination and aggregate both code (C1W, C2W) and phase (L1W, L2W) biases. By forming the HMW linear combination of CODE OSB corrections on the same signals, we compare CODE satellite HMW biases to those from CNES/CLS. The fractional part of GPS satellite HMW biases from both analysis centers are very close to each other, with a mean Root-Mean-Square (RMS) of differences of 0.01 wide-lane cycles. A direct comparison of satellite narrow-lane biases is not easily possible since satellite narrow-lane biases are correlated with satellite orbit and clock products, as well as with integer wide-lane ambiguities. Moreover, CNES/CLS provides no satellite narrow-lane biases but incorporates them into satellite clock offsets. Therefore, we compute differences of GPS satellite orbits, clock offsets, integer wide-lane ambiguities and narrow-lane biases (only for CODE products) between CODE and CNES/CLS products. The total difference of these terms for each satellite represents the difference of the narrow-lane bias by subtracting certain integer narrow-lane cycles. We call this total difference “narrow-lane” bias difference. We find that 3% of the narrow-lane biases from these two analysis centers during the experimental time period have differences larger than 0.05 narrow-lane cycles. In fact, this is mainly caused by one Block IIA satellite since satellite clock offsets of the IIA satellite cannot be well determined during eclipsing seasons. To show the application of both types of GPS products, we apply them for Sentinel-3 satellite orbit determination. The wide-lane fixing rates using both products are more than 98%, while the narrow-lane fixing rates are more than 95%. Ambiguity-fixed Sentinel-3 satellite orbits show clear improvement over float solutions. RMS of 6-h orbit overlaps improves by about a factor of two. Also, we observe similar improvements by comparing our Sentinel-3 orbit solutions to the external combined products. Standard deviation value of Satellite Laser Ranging residuals is reduced by more than 10% for Sentinel-3A and more than 15% for Sentinel-3B satellite by fixing ambiguities to integer values.

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.

Galileo precise orbit determination with optical two-way links (OTWL): a continuous wave laser ranging and time transfer concept

In this simulation study we analyze the benefit of ground-space optical two-way links (OTWL) for Galileo precise orbit determination (POD). OTWL is a concept based on continuous wave laser ranging and time transfer with modulated signals from and to ground stations. The measurements are in addition to Global Navigation Satellite System (GNSS) observations. We simulate the measurements with regard to 16 Galileo Sensor Stations. In the simulation study we assume that the whole Galileo satellite constellation is equipped with terminals for OTWL. Using OTWL together with Galileo L-band, in comparison with an orbit solution calculated with L-band-only, demonstrates the advantage of combining two ranging techniques with different influences of systematic errors. The two-way link allows a station and satellite clock synchronization. Furthermore, we compare the ground-space concept with the satellite-to-satellite counterpart known as optical two-way inter-satellite links (OISL). The advantage of OTWL is the connection between the satellite system and the solid Earth as well as the possibility to synchronize the satellite clocks and the ground station clocks. The full network, using all three observation types in combination is simulated as well. The possibility to estimate additional solar radiation pressure (SRP) parameters within these combinations is a clear benefit of these additional links. We paid great attention to simulate systematic effects of all observation techniques as realistically as possible. For L-band these are measurement noise, tropospheric delays, phase center variation of receiver and transmitter antennas, constant and variable biases as well as multipath. For optical links we simulated colored and distance-dependent noise, offsets due to the link repeatability and offsets related to the equipment calibration quality. In addition, we added a troposphere error for the OTWL measurements. We discuss the influence on the formal orbit uncertainties and the effects of the systematic errors. Restrictions due to weather conditions are addressed as well. OTWL is synergetic with the other measurement techniques like OISL and can be used for data transfer and communication, respectively.

Distribution of Reference Stations: Initial Explore on the Optimal Selection Strategy

The Satellite-based augmentation system (SBAS) is intended to provide real-time differential global navigation satellite system corrections with the high accuracy, availability, and integrity required for aviation applications. Since the performance of Satellite clock and ephemeris (SCE) corrections and Ionospheric range delay (IRD) corrections can vary dramatically depending on satellites and Ground reference stations (GRSs) geometry, therefore, we present a GRSs distribution optimized criteria and process to improve SBAS corrections performance. The present step-by-step optimized scheme using the average satellite surveillance dilution of precision and relative centroid metric availability of grid points as fitness values to determine the appropriate GRSs distribution to sufficiently meet the corrections requirements. The results show that the statistical mean RCM availability can reach more than 0.5518 for all IGPs and the coverage depth of GRSs in China and its surrounding areas is more than 25, which fully satisfies the requirement for solving SCE and IRD corrections.

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.

Efficient, High-Fidelity Modeling and Simulation of Global Navigation Satellite System Constellations

This paper presents a method for modeling and simulation of Global Navigation Satellite System (GNSS) constellations by the use of Chebyshev polynomials fit to publicly available precision data. The Global Positioning System (GPS) is used to demonstrate the method, but the method applies to all GNSS with precise ephemeris data including Galileo and GLONASS. The method facilitates highly accurate satellite orbit and clock modeling, including relativistic effects, with mean fit differences of the order in position, in velocity, and microseconds in clock offset. The method also improves simulation run time by using a fast technique for evaluating the Chebyshev polynomials. Runtime comparisons demonstrate the polynomial method reduces runtime by up to 72% of more traditional methods. The speed of the method makes it well suited for practical, accurate Monte Carlo simulation techniques. The method can be used in simulations for the verification and validation of GNSS receivers embedded in autonomous aerospace navigation systems, for uncertainty analysis, and for other purposes. Details for validating the precision data are given. Pseudocode algorithms are provided for fitting and evaluating Chebyshev polynomials. Also provided are high-level concepts of one approach for integrating the method into larger, multisystem aerospace simulations, including the effects of signal propagation delay and Earth blockage.

LEO satellite clock analysis and prediction for positioning applications

ABSTRACT The positioning service aided by low Earth orbit (LEO) mega-constellations has become a hot topic in recent years. To achieve precise positioning, accuracy of the LEO clocks is important for single-receiver users. To bridge the gap between the applicable time of the clock products and the time of positioning, the precise LEO clocks need to be predicted over a certain period depending on the sampling interval of the clock products. This study discusses the prediction errors for periods from 10 s to 1 h for two typical LEO clock types, i.e. the ultra-stable oscillator (USO) and the oven-controlled crystal oscillator (OCXO). The prediction is based on GNSS-determined precise clock estimates, where the clock stability is related to the GNSS estimation errors, the behaviors of the oscillators themselves, the systematic effects related to the environment and the relativistic effects, and the stability of the time reference. Based on real data analysis, LEO clocks of the two different types are simulated under different conditions, and a prediction model considering the systematic effects is proposed. Compared to a simple polynomial fitting model usually applied, the proposed model can significantly reduce the prediction errors, i.e. by about 40%-70% in simulations and about 5%-30% for real data containing different miss-modeled effects. For both clock types, short-term prediction of 1 min would result in a root mean square error (RMSE) of a few centimeters when using a very stable time reference. The RMSE amounts to about 0.1 m, when a typical real-time time reference of the national center for space studies (CNES) real-time clocks was used. For long-term prediction of 1 h, the RMSE could range from below 1 m to a few meters for the USOs, depending on the complexity of the miss-modeled effects. For OCXOs, the 1 h prediction could lead to larger errors with an RMSE of about 10 m.

Ultra-Low-Cost Tightly Coupled Triple-Constellation GNSS PPP/MEMS-Based INS Integration for Land Vehicular Applications

The rapid rise of ultra-low-cost dual-frequency GNSS chipsets and micro-electronic-mechanical-system (MEMS) inertial sensors makes it possible to develop low-cost navigation systems, which meet the requirements for many applications, including self-driving cars. This study proposes the use of a dual-frequency u-blox F9P GNSS receiver with xsens MTi670 industrial-grade MEMS IMU to develop an ultra-low-cost tightly coupled (TC) triple-constellation GNSS PPP/INS integrated system for precise land vehicular applications. The performance of the proposed system is assessed through comparison with three different TC GNSS PPP/INS integrated systems. The first system uses the Trimble R9s geodetic-grade receiver with the tactical-grade Stim300 IMU, the second system uses the u-blox F9P receiver with the Stim300 IMU, while the third system uses the Trimble R9s receiver with the xsens MTi670 IMU. An improved robust adaptive Kalman filter is adopted and used in this study due to its ability to reduce the effect of measurement outliers and dynamic model errors on the obtained positioning and attitude accuracy. Real-time precise ephemeris and clock products from the Centre National d’Etudes Spatials (CNES) are used to mitigate the effects of orbital and satellite clock errors. Three land vehicular field trials were carried out to assess the performance of the proposed system under both open-sky and challenging environments. It is shown that the tracking capability of the GNSS receiver is the dominant factor that limits the positioning accuracy, while the IMU grade represents the dominant factor for the attitude accuracy. The proposed TC triple-constellation GNSS PPP/INS integrated system achieves sub-meter-level positioning accuracy in both of the north and up directions, while it achieves meter-level positioning accuracy in the east direction. Sub-meter-level positioning accuracy is achieved when the Stim300 IMU is used with the u-blox F9P GNSS receiver. In contrast, decimeter-level positioning accuracy is consistently achieved through TC GNSS PPP/INS integration when a geodetic-grade GNSS receiver is used, regardless of whether a tactical- or an industrial-grade IMU is used. The root mean square (RMS) errors of the proposed system’s attitude are about 0.878°, 0.804°, and 2.905° for the pitch, roll, and azimuth angles, respectively. The RMS errors of the attitude are significantly improved to reach about 0.034°, 0.038°, and 0.280° for the pitch, roll, and azimuth angles, respectively, when a tactical-grade IMU is used, regardless of whether a geodetic- or low-cost GNSS receiver is used.

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.

Assessing IGS GPS/Galileo/BDS-2/BDS-3 phase bias products with PRIDE PPP-AR

Ambiguity Resolution in Precise Point Positioning (PPP-AR) is important to achieving high-precision positioning in wide areas. The International GNSS (Global Navigation Satellite System) Service (IGS) and some other academic organizations have begun to provide phase bias products to enable PPP-AR, such as the integer-clock like products by Centre National d’Etudes Spatials (CNES), Wuhan University (WUM) and the Center for Orbit Determination in Europe (CODE), as well as the Uncalibrated Phase Delay (UPD) products by School of Geodesy and Geomatics (SGG). To evaluate these disparate products, we carry out Global Positioning System (GPS)/Galileo Navigation Satellite System (Galileo) and BeiDou Navigation Satellite System (BDS-only) PPP-AR using 30 days of data in 2019. In general, over 70% and 80% of GPS and Galileo ambiguity residuals after wide-lane phase bias corrections fall in ± 0.1 cycles, in contrast to less than 50% for BeiDou Navigation Satellite (Regional) System (BDS-2); moreover, around 90% of GPS/Galileo narrow-lane ambiguity residuals are within ± 0.1 cycles, while the percentage drops to about 55% in the case of BDS products. GPS/Galileo daily PPP-AR can usually achieve a positioning precision of 2, 2 and 6 mm for the east, north and up components, respectively, for all phase bias products except those based on German Research Centre for Geosciences (GBM) rapid satellite orbits and clocks. Due to the insufficient number of BDS satellites during 2019, the BDS phase bias products perform worse than the GPS/Galileo products in terms of ambiguity fixing rates and daily positioning precisions. BDS-2 daily positions can only reach a precision of about 10 mm in the horizontal and 20 mm in the vertical components, which can be slightly improved after PPP-AR. However, for the year of 2020, BDS-2/BDS-3 (BDS-3 Navigation Satellite System) PPP-AR achieves about 50% better precisions for all three coordinate components.

Initial Assessment of BDS PPP-B2b Service: Precision of Orbit and Clock Corrections, and PPP Performance

On 31 July 2020, the Beidou global navigation satellite system (BDS-3) was officially announced as being commissioned. In addition to offering global positioning, navigation, and timing (PNT) services, BDS-3 also provides precise point positioning (PPP) augmentation services. The satellite orbit correction, clock correction and code bias correction of BDS-3 and other global navigation satellite systems (GNSS) are broadcast by the BDS-3 geostationary earth orbit (GEO) satellites through the PPP-B2b signal. The PPP-B2b service is available for users in China and the surrounding area. In this study, an initial assessment of the PPP-B2b service is presented, with collected 3-day PPP-B2b messages. Based on broadcast ephemeris and PPP-B2b messages, the precise satellite orbits and clock offsets can be recovered. This precision is evaluated with the precise ephemeris from the GeoForschungsZentrum Potsdam (GFZ) analysis center as references. The results indicate that the accuracy of BDS-3 satellite orbits in the direction of radial, along-track, and cross-track is 0.138, 0.131, and 0.145 m, respectively, and for GPS a corresponding accuracy of 0.104, 0.160, and 0.134 m, respectively, could be obtained. The precision of clock offsets can reach a level of several centimeters for both GPS and BDS-3. Both the performance of static PPP and kinematic PPP are evaluated using the observations from four international GNSS monitoring assessment service (iGMAS) stations. Regarding static PPP, the average convergence time is 17.7 min to achieve a horizontal positioning accuracy of better than 0.3 m, and a vertical positioning accuracy of better than 0.6 m. The average positioning accuracy in the direction of east, north, and up-directions are 2.4, 1.6, and 2.3 cm. As to kinematic PPP, the average RMS values of positioning errors in the direction of east, north, and up are 8.1 cm, 3.6 cm, and 8.0 cm after full convergence.

Enabling ambiguity resolution in CSRS‐PPP

<h3>Abstract</h3> Precise point positioning (PPP) uses precise satellite orbits, clock corrections and biases derived from a global network of reference stations to enable accurate positioning worldwide. Natural Resources Canada’s Canadian Spatial Reference System (CSRS) PPP is a free Web service offering automated PPP processing. A critical factor limiting the adoption of PPP in many applications is the convergence time needed to reach centimeter-level accuracies. To address this issue, CSRS-PPP now implements PPP with ambiguity resolution (PPP-AR). This feature required the development of new algorithms, such as sequential normal stacking for least-squares filtering/smoothing, and the weighted integer decision concept for ambiguity validation. New satellite product lines (ultra-rapid, rapid, final) also have been deployed to enable PPP-AR processing with various latencies. This analysis demonstrates that sub-centimeter horizontal accuracies can be obtained in less than one hour for both static and kinematic modes. Using product lines with longer latencies is beneficial, although improvements are typically within the reported uncertainties.

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.

Estimation of fractional cycle bias for GPS/BDS-2/Galileo based on international GNSS monitoring and assessment system observations using the uncombined PPP model

The Fractional Cycle Bias (FCB) product is crucial for the Ambiguity Resolution (AR) in Precise Point Positioning (PPP). Different from the traditional method using the ionospheric-free ambiguity which is formed by the Wide Lane (WL) and Narrow Lane (NL) combinations, the uncombined PPP model is flexible and effective to generate the FCB products. This study presents the FCB estimation method based on the multi-Global Navigation Satellite System (GNSS) precise satellite orbit and clock corrections from the international GNSS Monitoring and Assessment System (iGMAS) observations using the uncombined PPP model. The dual-frequency raw ambiguities are combined by the integer coefficients (4,− 3) and (1,− 1) to directly estimate the FCBs. The details of FCB estimation are described with the Global Positioning System (GPS), BeiDou-2 Navigation Satellite System (BDS-2) and Galileo Navigation Satellite System (Galileo). For the estimated FCBs, the Root Mean Squares (RMSs) of the posterior residuals are smaller than 0.1 cycles, which indicates a high consistency for the float ambiguities. The stability of the WL FCBs series is better than 0.02 cycles for the three GNSS systems, while the STandard Deviation (STD) of the NL FCBs for BDS-2 is larger than 0.139 cycles. The combined FCBs have better stability than the raw series. With the multi-GNSS FCB products, the PPP AR for GPS/BDS-2/Galileo is demonstrated using the raw observations. For hourly static positioning results, the performance of the PPP AR with the three-system observations is improved by 42.6%, but only 13.1% for kinematic positioning results. The results indicate that precise and reliable positioning can be achieved with the PPP AR of GPS/BDS-2/Galileo, supported by multi-GNSS satellite orbit, clock, and FCB products based on iGMAS.

Global Navigational Satellite System Seismic Monitoring

ABSTRACTWe have developed a global earthquake deformation monitoring system based on subsecond-latency measurements from ∼2000 existing Global Navigational Satellite System (GNSS) receivers to rapidly characterize large earthquakes and tsunami. The first of its kind, this system complements traditional seismic monitoring by enabling earthquake moment release and, where station density permits, fault-slip distribution, including tsunamigenic slow slip, to be quantified as rupture evolves. Precise point position time series from globally distributed GNSS stations are continuously estimated within an Earth center of mass-fixed reference frame and streamed as local north, east, and vertical coordinates with 1 s updates and global subsecond receiver-to-positions latency. Continuous waveforms are made available via messaging exchanges to third-party users (U.S. Geological Survey, National Oceanic and Atmospheric Administration, network operators, etc.) and internally filtered to trigger coseismic offset estimation that drive downstream point-source and finite-fault magnitude and slip characterization algorithms. We have implemented a corresponding analytics system to capture ∼100 million positions generated per day per thousand global stations positioned. Assessed over one typical week using 1270 globally distributed stations, the latency of position generation at a central analysis center from time of data acquisition in the field averages 0.52 s and is largely independent of station distance. Position variances from nominal in north, east, and vertical average 8, 9, and 12 cm, respectively, predominantly caused by random-walk noise peaking in a ∼4–5min spectral band introduced by global satellite clock corrections. Solutions completeness over the week within 0.5, 1, and 2 s latency is 55%, 90%, and 99%, respectively. This GNSS analysis platform is readily scalable, allowing the accelerating proliferation of low-cost phase-tracking GNSS receivers, including those increasingly embedded in consumer devices such as smartphones, to offer a new means of characterizing large earthquakes and tsunami far more quickly than existing systems allow.

Chronothyroidology: Chronobiological Aspects in Thyroid Function and Diseases.

Chronobiology is the scientific discipline which considers biological phenomena in relation to time, which assumes itself biological identity. Many physiological processes are cyclically regulated by intrinsic clocks and many pathological events show a circadian time-related occurrence. Even the pituitary–thyroid axis is under the control of a central clock, and the hormones of the pituitary–thyroid axis exhibit circadian, ultradian and circannual rhythmicity. This review, after describing briefly the essential principles of chronobiology, will be focused on the results of personal experiences and of other studies on this issue, paying particular attention to those regarding the thyroid implications, appearing in the literature as reviews, metanalyses, original and observational studies until 28 February 2021 and acquired from two databases (Scopus and PubMed). The first input to biological rhythms is given by a central clock located in the suprachiasmatic nucleus (SCN), which dictates the timing from its hypothalamic site to satellite clocks that contribute in a hierarchical way to regulate the physiological rhythmicity. Disruption of the rhythmic organization can favor the onset of important disorders, including thyroid diseases. Several studies on the interrelationship between thyroid function and circadian rhythmicity demonstrated that thyroid dysfunctions may affect negatively circadian organization, disrupting TSH rhythm. Conversely, alterations of clock machinery may cause important perturbations at the cellular level, which may favor thyroid dysfunctions and also cancer.

Punctuality Algorithm Based on BP Neural Network PID Control

In the modern information society, high-precision clocks are particularly important in the fields of electric power, communications, aviation, and finance, and have very strict objective requirements in terms of frequency accuracy. Currently, the technology of using GPS satellite clock sources to synchronize local clocks has become one of the mainstream methods for generating high-precision clocks at home and abroad. The core idea of this technology is to use the satellite clock to tame the local clock. Due to the development and application of 5G, the accuracy of the system's punctuality have higher requirements, Through analysis, it is found that the combination of BP neural network and PID control can be used to optimize the control of the constant temperature crystal oscillator and improve the precision of punctuality. Finally, the simulation results show that the method has a significant effect in improving the accuracy of punctuality.

An efficient clock offset datum switching compensation method for BDS real-time satellite clock offset estimation

The quality of real-time satellite clock offsets products is one of the key elements for real-time satellite clock performance monitoring and real-time precise point positioning (PPP). However, impacted by the station location, environment, communication equipment, receiver performance, network delay, temporary modem failure or other reasons, the observation data of clock offset datum receiver occasionally outage, resulting in all satellite clocks offset cannot be estimated. In this contribution, an efficient clock offset datum switching compensation method for BDS real-time satellite clock offset estimation is proposed. One hundred stations distributed around the world, from day of year (DOY) 074 to 075 in 2019 are used to estimate BDS real-time satellite clock offset. Four schemes: clock offset datum switching without compensation (S1), clock offset datum switching with satellite clock offset jump compensation (S2), clock offset datum switching with satellite clock offset jump and receiver clock drift compensation (S3, the proposed method), clock offset datum without switching (S4), are used to validate the proposed method. By using the proposed method, the satellite clock offset jump can be eliminated and the satellite clock offset consistency can be maintained. The satellite clock offsets STD for S1, S2, S3 and S4 are 0.184, 0.183, 0.183 and 0.150 ns, respectively. The fitting precision of S1, S2, S3 and S4 are 70907.344, 0.731, 0.502 and 0.543 ns, respectively. The frequency stability of S3 shows the best performance among S2, S3 and S4 when the averaging interval time is 10,000 and 20,000 s, which can be attributed to the effectiveness of proposed method and frequency stability difference of clock offset datum receiver. The fitting precision and frequency stability cannot be reflected correctly by clock offset due to the satellite clock offset jump in S1. For precise point positioning (PPP), the coordinates jump and re-convergence can be eliminated by using the proposed method. Thus, this method can provide a reference for obtaining real-time, continuous and reliable BDS satellite clock offset products.