Global Navigation Satellite System Clock Research Articles

Reference clock impact on GNSS clock outliers

Abstract With the advent of the Global Navigation Satellite System (GNSS), the need for precise and highly accurate orbit and clock products becomes crucial in processing GNSS data. Clocks in GNSS observations form the basis of positioning. Their high quality and stability enable high accuracy and the reliability of the obtained results. The clock modelling algorithms are continuously improved; thus, the accuracy of the clock products is evolving. At present, 8 Analysis Centers (ACs) contribute to the International GNSS Service final clock products. These products are based on GNSS observations on a network of reference stations, where for a given day one of the reference station clocks is the reference clock. In this paper, the authors determined the impact of the reference clock on the quality of clock product, especially outliers, for the first time. For this purpose, the multi-GNSS final clock products provided by the Center for Orbit Determination in Europe (CODE) for the period 2014–2021 (1773–2190 GPS week, 2921 days) were analysed. Analysis shows that by applying the Median Absolute Deviation (MAD) algorithm for outlier detection, the Passive Hydrogen Maser (PHM) clock installed on board the GALILEO satellites have the lowest level of noise, whereas the Block IIR GPS satellite launched in 1999 appears to have the highest levels of noise. Furthermore, the GNSS station OHIE3, when used as a reference clock, generates an increase in the level of noise, especially noticeable on the G09 and E03 satellites.

Aging of ground Global Navigation Satellite System oscillators

Global Navigation Satellite System (GNSS) are widely used in many areas of human life and activity. The proper functioning of GNSS systems depends on several factors, the most important of which is the correct knowledge of time. The position indirectly is based on the knowledge of the distance, which is determined based on time with the knowledge of the speed of the electromagnetic wave. Thus, proper (accurate) knowledge of time (GNSS clock stability) is a key to precise positioning. In this text, the long-term stability of the GNSS station clocks covering the years 1994-2020 was analysed. For this purpose, the corrections of the clocks at selected permanent stations were used, and their stability was determined for all years separately. Then the change of clock stability over time and the search for correlation were analysed. As the results showed, there are clearly differences between four of the type of oscillators analysed. In case of the comparison on an annual basis, no change over time was found.

Undifferenced Kinematic Precise Orbit Determination of Swarm and GRACE-FO Satellites from GNSS Observations.

Low Earth Orbit (LEO) satellites can be used for remote sensing and gravity field recovery, while precise orbit determination (POD) is vital for LEO satellite applications. However, there are some systematic errors when using the LEO satellite orbits released by different agencies in multi-satellite-based applications, e.g., Swarm and Gravity Recovery and Climate Experiment-Follow-On (GRACE-FO), as different GNSS precise orbit and clock products are used as well as processing strategies and software. In this paper, we performed undifferenced kinematic PODs for Swarm and GRACE-FO satellites simultaneously over a total of 14 days by using consistent International Global Navigation Satellite System (GNSS) Service (IGS) precise orbit and clock products. The processing strategy based on an undifferenced ionosphere-free combination and a least squares method was applied for Swarm and GRACE-FO satellites. Furthermore, the quality control for the kinematic orbits was adopted to mitigate abrupt position offsets. Moreover, the accuracy of the kinematic orbits solution was evaluated by carrier phase residual analysis and Satellite Laser Ranging (SLR) observations, as well as comparison with official orbits. The results show that the kinematic orbits solution is better than 4 cm, according to the SLR validation. With quality control, the accuracy of the kinematic orbit solution is improved by 2.49 % for the Swarm-C satellite and 6.98 % for the GRACE-D satellite when compared with their precise orbits. By analyzing the accuracy of the undifferenced kinematic orbit solution, the reliability of the LEO orbit determination is presented in terms of processing strategies and quality control procedures.

A multi‐frequency method to improve the long‐term estimation of GNSS clock corrections and phase biases

<h3>Abstract</h3> The space segment of the Global Navigation Satellite System (GNSS) is equipped with highly stable atomic clocks. In order to use these clocks as references, their time offsets must be estimated from ground measurements as accurately as possible. This work presents a multi-frequency and multi-constellation method for estimating satellite and receiver clock corrections, starting from unambiguous, uncombined, and undifferenced carrier-phase measurements. A byproduct of the estimation process is phase biases (i.e., the hardware delays of the carrier-phase measurements occurring at receivers and satellites). The stability and predictability of our clock estimates for receivers and satellites (GPS and Galileo) are compared with those obtained by the International GNSS Service (IGS), whereas the phase biases are assessed against two independent determinations involving combinations of carrier-phase measurements. We conclude that the method reduces day boundary discontinuities in the clock corrections, and that the estimated phase biases reproduce variabilities already observed by other authors.

Performance of Multi-GNSS Real-Time UTC(NTSC) Time and Frequency Transfer Service Using Carrier Phase Observations

The technique of carrier phase (CP), based on the global navigation satellite system (GNSS), has proven to be a highly effective spatial tool in the field of time and frequency transfer with sub-nanosecond accuracy. The rapid development of real-time GNSS satellite orbit and clock determinations has enabled GNSS time and frequency transfer using the CP technique to be performed in real-time mode, without any issues associated with latency. In this contribution, we preliminarily built the prototype system of real-time multi-GNSS time and frequency transfer service in National Time Service Center (NTSC) of the Chinese Academy of Sciences (CAS), which undertakes the task to generate, maintains and transmits the national standard of time and frequency UTC(NTSC). The comprehensive assessment of the availability and quality of the service system were provided. First, we assessed the multi-GNSS state space representation (SSR) correction generated in real-time multi-GNSS prototype system by combining broadcast ephemeris through a comparison with the GeoForschungsZentrum (GFZ) final products. The statistical results showed that the orbit precision in three directions was smaller than 6 cm for global positioning system (GPS) and smaller than approximately 10 cm for BeiDou satellite system (BDS). The root mean square (RMS) values of clock differences for GPS were approximately 2.74 and 6.74 ns for the GEO constellation of BDS, 3.24 ns for IGSO, and 1.39 ns for MEO. The addition, the GLObal NAvigation Satellite System (GLONASS) and Galileo satellite navigation system (Galileo) were 4.34 and 1.32 ns, respectively. In order to assess the performance of real-time multi-GNSS time and frequency transfer in a prototype system, the four real-time time transfer links, which used UTC(NTSC) as the reference, were employed to evaluate the performance by comparing with the solution determined using the GFZ final products. The RMS could reach sub-nanosecond accuracy in the two solutions, either in the SSR or GFZ solution, or in GPS, BDS, GLONASS, and Galileo. The frequency stability within 10,000 s was 3.52 × 10−12 for SSR and 3.47 × 10−12 for GFZ and GPS, 3.63 × 10−12 for SSR and 3.53 × 10−12 for GFZ for BDS, 3.57 × 10−12 for SSR and 3.52 × 10−12 for GFZ for GLONASS, and 3.56 × 10−12 for SSR and 3.48 × 10−12 for GFZ for Galileo.

Accuracy Analysis of GNSS Hourly Ultra-Rapid Orbit and Clock Products from SHAO AC of iGMAS

With the development of the global navigation satellite system(GNSS), the hourly ultra-rapid products of GNSS are attracting more attention due to their low latency and high accuracy. A new strategy and method was applied by the Shanghai Astronomical Observatory (SHAO) Analysis Center (AC) of the international GNSS Monitoring and Assessment Service (iGMAS) for generating 6-hourly and 1-hourly GNSS products, which mainly include the American Global Positioning System (GPS), the Russian Global’naya Navigatsionnaya Sputnikova Sistema (GLONASS), the European Union’s Galileo, and the Chinese BeiDou navigation satellite system (BDS). The 6-hourly and 1-hourly GNSS orbit and clock ultra-rapid products included a 24-h observation session which is determined by 24-h observation data from global tracking stations, and a 24-h prediction session which is predicted from the observation session. The accuracy of the 1-hourly orbit product improved about 1%, 31%, 13%, 11%, 23%, and 9% for the observation session and 18%, 43%, 45%, 34%, 53%, and 15% for the prediction session of GPS, GLONASS, Galileo, BDS Medium Earth Orbit (MEO), Inclined Geosynchronous Orbit (IGSO), and GEO orbit, when compared with reference products with high accuracy from the International GNSS service (IGS).The precision of the 1-hourly clock products can also be seen better than the 6-hourly clock products. The accuracy and precision of the 6-hourly and 1-hourly orbit and clock verify the availability and reliability of the hourly ultra-rapid products, which can be used for real-time or near-real-time applications, and show encouraging prospects.

Removing day-boundary discontinuities on GNSS clock estimates: methodology and results

Global navigation satellite system (GNSS) satellites are equipped with very stable atomic clocks that can be used for assessing the models and strategies involved in the estimation processes, where the clock estimates should present high stability. For instance, GNSS products (including satellite and receiver clocks) are computed on daily basis, i.e., with the data of each day being processed independently from other days. This choice produces the well-known day-boundary discontinuities (DBDs) on clock estimates that stem from the estimation process, rather than to the nature of the atomic clock itself. The aim of the present contribution is to propose a strategy to estimate the satellite and receiver clock offsets that is capable to reduce the DBDs observed in the products of different analysis centers (ACs) within the International GNSS Service (IGS), ultimately improving the accuracy of clock estimates. Our approach relies on the use of unambiguous, undifferenced and uncombined carrier phase measurements collected by a network of permanent receivers on ground. The strategy considers the carrier phase hardware delays and assumes their possible variations along time. Our daily data processing aims to maintaining the natural continuity over days of the carrier phase measurements after integer ambiguity resolution (IAR), even if IAR is performed on daily batches. We compare our clock estimations with those computed by different IGS ACs, evaluating the linear behavior of the satellite atomic clocks on the day change. The results show the removal of DBD on clock estimates computed with the continuous and unambiguous carrier phase measurements. This DBD improvement may benefit the statistical characterization of long-term phenomena correlated with the on-board clocks.

High-Rate Monitoring of Satellite Clocks Using Two Methods of Averaging Time

Knowledge of the global navigation satellite system (GNSS) satellite clock error is crucial in real-time precise point positioning (PPP), seismology, and many other high-rate GNSS applications. In this work, the authors show the characterisation of the atomic GNSS clock’s stability and its dependency on the adopted orbit type using Allan deviation with two methods of averaging time. Four International GNSS Service (IGS) orbit types were used: broadcast, ultra-rapid, rapid and final orbit. The calculations were made using high-rate 1 Hz observations from the IGS stations equipped with external clocks (oscillators). The most stable receiver oscillator was chosen as a reference clock. The results show the advantage of the newest GPS satellite block with respect to the other satellites. Significant differences in the results based on the orbit type used have not been recorded. Many averaging time methods used in Allan deviation (ADEV) show the clock’s fluctuations, usually smoothed in 2n s averaging times.

Assessment of Multiple GNSS Real-Time SSR Products from Different Analysis Centers

The real-time State Space Representation (SSR) product of the GNSS (Global Navigation Satellite System) orbit and clock is one of the most essential corrections for real-time precise point positioning (PPP). In this work, the performance of current SSR products from eight analysis centers were assessed by comparing it with the final product and the accuracy of real-time PPP. Numerical results showed that (1) the accuracies of the GPS SSR product were better than 8 cm for the satellite orbit and 0.3 ns for the satellite clock; (2) the accuracies of the GLONASS (GLObalnaya NAvigatsionnaya Sputnikovaya Sistema) SSR product were better than 10 cm for orbit RMS (Root Mean Square) and 0.6 ns for clock STD (Standard Deviation); and (3) the accuracies of the BDS (BeiDou Navigation Satellite System) and Galileo SSR products from CLK93 were about 14.54 and 4.42 cm for the orbit RMS and 0.32 and 0.18 ns for the clock STD, respectively. The simulated kinematic PPP results obtained using the SSR products from CLK93 and CLK51 performed better than those using other SSR products; and the accuracy of PPP based on all products was better than 6 and 10 cm in the horizontal and vertical directions, respectively. The real-time kinematic PPP experiment carried out in Beijing, Tianjin, and Shijiazhuang, China indicated that the SSR product CLK93 from Centre National d’Etudes Spatiales (CNES) had a better performance than CAS01. Moreover, the PPP with GPS + BDS dual systems had a higher accuracy than those with only a GPS single system.

CSAC Characterization and Its Impact on GNSS Clock Augmentation Performance

Chip Scale Atomic Clocks (CSAC) are recently-developed electronic instruments that, when used together with a Global Navigation Satellite Systems (GNSS) receiver, help improve the performance of GNSS navigation solutions in certain conditions (i.e., low satellite visibility). Current GNSS receivers include a Temperature Compensated Cristal Oscillator (TCXO) clock characterized by a short-term stability (τ = 1 s) of 10−9 s that leads to an error of 0.3 m in pseudorange measurements. The CSAC can achieve a short-term stability of 2.5 × 10−12 s, which implies a range error of 0.075 m, making for an 87.5% improvement over TCXO. Replacing the internal TCXO clock of GNSS receivers with a higher frequency stability clock such as a CSAC oscillator improves the navigation solution in terms of low satellite visibility positioning accuracy, solution availability, signal recovery (holdover), multipath and jamming mitigation and spoofing attack detection. However, CSAC suffers from internal systematic instabilities and errors that should be minimized if optimal performance is desired. Hence, for operating CSAC at its best, the deterministic errors from the CSAC need to be properly modelled. Currently, this modelling is done by determining and predicting the clock frequency stability (i.e., clock bias and bias rate) within the positioning estimation process. The research presented in this paper aims to go a step further, analysing the correlation between temperature and clock stability noise and the impact of its proper modelling in the holdover recovery time and in the positioning performance. Moreover, it shows the potential of fine clock coasting modelling. With the proposed model, an improvement in vertical positioning precision of around 50% with only three satellites can be achieved. Moreover, an increase in the navigation solution availability is also observed, a reduction of holdover recovery time from dozens of seconds to only a few can be achieved.

Distribution and mitigation of higher‐order ionospheric effects on precise GNSS processing

Higher‐order ionospheric effects (I2+) are one of the main limiting factors in very precise Global Navigation Satellite Systems (GNSS) processing, for applications where millimeter accuracy is demanded. This paper summarizes a comprehensive study of the I2+ effects in range and in GNSS precise products such as receiver position and clock, tropospheric delay, geocenter offset, and GNSS satellite position and clock. All the relevant higher‐order contributions are considered: second and third orders, geometric bending, and slant total electron content (dSTEC) bending (i.e., the difference between the STEC for straight and bent paths). Using a realistic simulation with representative solar maximum conditions on GPS signals, both the effects and mitigation errors are analyzed. The usage of the combination of multifrequency L band observations has to be rejected due to its increased noise level. The results of the study show that the main two effects in range are the second‐order ionospheric and dSTEC terms, with peak values up to 2 cm. Their combined impacts on the precise GNSS satellite products affects the satellite Z coordinates (up to +1 cm) and satellite clocks (more than ±20 ps). Other precise products are affected at the millimeter level. After correction the impact on all the precise GNSS products is reduced below 5 mm. We finally show that the I2+ impact on a Precise Point Positioning (PPP) user is lower than the current uncertainties of the PPP solutions, after applying consistently the precise products (satellite orbits and clocks) obtained under I2+ correction.

Ground-based GNSS ZTD/IWV estimation system for numerical weather prediction in challenging weather conditions

The Global Navigation Satellite Systems (GNSS) are one of the very few tools that can provide continuous, unbiased, precise and robust atmosphere condition information. The extensive research of GNSS space-based segment (e.g. available precise, real-time satellite orbits and clocks), unlimited access to the ground-based Continuously Operating Reference Stations (CORS) GNSS networks along with the well established data processing methods provides an unprecedented opportunity to study the environmental impacts on the GNSS signal propagation. GNSS measurements have been successfully used in precise positioning, tectonic plate monitoring, ionosphere studies and troposphere monitoring. However all GNSS signals recorded on the ground by CORS are subject to ionosphere delay, troposphere delay, multipath and signal strength loss. Nowadays, the GNSS signal delays are gradually incorporated into the numerical weather prediction (NWP) models. Usually the Zenith Total Delay (ZTD) or Integrated Water Vapour (IWV) have been considered as an important source of water vapour contents and assimilated into the NWP models. However, successful assimilation of these products requires strict accuracy assessment, especially in the challenging severe weather conditions.In this study a number of GNSS signal processing strategies have been verified to obtain the best possible estimates of troposphere delays using a selection of International GNSS Service (IGS) orbit and clock products. Three different severe weather events (severe storm, flash flooding, flooding) have been investigated in this paper. The strategies considered are; 1) Double Differenced (DD) network solution with shortest baselines, 2) DD network solution with longest baselines, 3) DD baseline-by-baseline solution (tested but not considered), 4) Zero Differenced (ZD) Precise Point Positioning (PPP) based on ambiguity float solutions, all with precise orbits and clocks, and real time clocks and predicted orbits. The quality of the estimates obtained has been evaluated against radiosonde measurements, Automatic Weather Station (AWS) observations, NWP (assimilation step without ground-based GNSS data) and ZTD estimates from the well established IGS processing centre, the Center of Orbit Determination in Europe (CODE). It shows that the ZTD and IWV estimates from the DD short baseline solution are robust with usually a very small bias (−2.7 to −0.8mm) and errors of less than 10mm (7.6–8.5) (ZTD) or 3mm (2.6–2.7) (IWV). The DD short baseline network solution was found to be the most reliable method in the considered case studies, regardless of the type of orbits and clocks applied.

INRIM Tool for Satellite Clock Characterization: Frequency Drift Estimation and Removal

In Global Navigation Satellite Systems (GNSS), atomic clocks are fundamental for their excellent stability. Being the distance measured from the time, any error on the measure of time leads to an error in the positioning: accurate and stable atomic clocks need to be employed on board satellites. Hence, the on board clock behaviour has to be continuously monitored and any malfunctioning has to be immediately detected. In this work, we illustrate a software tool developed at the National Institute of Metrological Research (INRIM) for GNSS clock characterization and monitoring. In particular we focus on the functionality of frequency drift estimation and removal, including the uncertainty evaluation. Actually, the frequency drift evaluation and the monitoring of its evolution over time is extremely important in GNSS applications to ensure the adequacy of the timing system to the integrity requirements of the positioning service. The software has been optimized for space clock data, which are different from the ones from timing laboratories, since often present missing data and outliers. The tool allows to easily handle satellite clock data, and get a quick estimate and graphic representation of clock key parameters, such as the clock frequency drift.

Acousto-optic devices using lead molybdate and related compounds: Bell Telephone Labs Inc US patent 3617931 (1971) filed 5 May 1969

The Global Navigation Satellite Systems (GNSS) are one of the very few tools that can provide continuous, unbiased, precise and robust atmosphere condition information. The extensive research of GNSS space-based segment (e.g. available precise, real-time satellite orbits and clocks), unlimited access to the ground-based Continuously Operating Reference Stations (CORS) GNSS networks along with the well established data processing methods provides an unprecedented opportunity to study the environmental impacts on the GNSS signal propagation. GNSS measurements have been successfully used in precise positioning, tectonic plate monitoring, ionosphere studies and troposphere monitoring. However all GNSS signals recorded on the ground by CORS are subject to ionosphere delay, troposphere delay, multipath and signal strength loss. Nowadays, the GNSS signal delays are gradually incorporated into the numerical weather prediction (NWP) models. Usually the Zenith Total Delay (ZTD) or Integrated Water Vapour (IWV) have been considered as an important source of water vapour contents and assimilated into the NWP models. However, successful assimilation of these products requires strict accuracy assessment, especially in the challenging severe weather conditions.In this study a number of GNSS signal processing strategies have been verified to obtain the best possible estimates of troposphere delays using a selection of International GNSS Service (IGS) orbit and clock products. Three different severe weather events (severe storm, flash flooding, flooding) have been investigated in this paper. The strategies considered are; 1) Double Differenced (DD) network solution with shortest baselines, 2) DD network solution with longest baselines, 3) DD baseline-by-baseline solution (tested but not considered), 4) Zero Differenced (ZD) Precise Point Positioning (PPP) based on ambiguity float solutions, all with precise orbits and clocks, and real time clocks and predicted orbits. The quality of the estimates obtained has been evaluated against radiosonde measurements, Automatic Weather Station (AWS) observations, NWP (assimilation step without ground-based GNSS data) and ZTD estimates from the well established IGS processing centre, the Center of Orbit Determination in Europe (CODE). It shows that the ZTD and IWV estimates from the DD short baseline solution are robust with usually a very small bias (− 2.7 to − 0.8 mm) and errors of less than 10 mm (7.6–8.5) (ZTD) or 3 mm (2.6–2.7) (IWV). The DD short baseline network solution was found to be the most reliable method in the considered case studies, regardless of the type of orbits and clocks applied.