Precise Clock Research Articles

Assessment of Real-Time GPS/BDS-2/BDS-3 Single-Frequency PPP and INS Tight Integration Using Different RTS Products

Due to the virtues of low-cost and high positioning accuracy, Single-Frequency Precise Point Positioning (SF-PPP) is becoming a prospective technique. However, SF-PPP is not as widely used as dual-frequency and triple-frequency PPP at present, owing to the effect of ionospheric delay residuals after model rectification. In recent years, with the evolution of multi-constellation Global Navigation Satellite Systems (multi-GNSS, i.e., GPS, BDS-2, and BDS-3), it has become possible to obtain credible and continuous positioning results using SF-PPP. However, such performance would be significantly degraded in challenging environments (i.e., boulevards, tunnels, and tall buildings). Under these circumstances, GNSS signals are obstructed, and it is difficult to provide sufficient observations for SF-PPP. Therefore, the Inertial Navigation System (INS) is employed to promote the positioning performance of SF-PPP. The PPP/INS integration is regarded as one of the most efficient approaches in GNSS-denied environments. To satisfy the request of supplying real-time positioning information, the Real-Time Services (RTS) of the International GNSS Service (IGS) provide real-time precise orbit and clock products for globally distributed users through the internet. In this paper, a real-time GPS/BDS-2/BDS-3 SF-PPP and INS tight integration model is proposed, and it is assessed using the data gathered by vehicle and real-time products afforded by CAS (Chinese Academy of Sciences), GFZ (Deutsche GeoForschungsZentrum), and WHU (Wuhan University). The outcomes illustrate the following: (1) GPS + BDS SF-PPP/INS can provide more accurate and continuous positioning solutions compared with those of GPS + BDS SF-PPP, with improvements of 52.8%, 31.1%, and 42.8% in the north, east, and vertical components, respectively. (2) In general, the orbit and clock products’ accuracies in terms of GPS afforded by the three analysis centers are consistent with each other. For BDS, the orbit product from WHU is more accurate compared to those of CAS and GFZ. However, the accuracy of the clock product afforded by WHU is lower compared with those provided by the other two centers, especially for BDS-2 satellites. (3) The positioning accuracy in terms of Root Mean Square (RMS) values based on GFZ products are much higher than the results based on CAS and WHU products in the three directions.

A Short-Term Forecasting Method of Inter-Frequency Clock Bias for GPS Block IIF Satellites

The time-varying biases within carrier phase observations are integrated into satellite clock offset parameters for precise clock estimation. Consequently, when the precise satellite clock bias is applied to the third frequency observation for precise point positioning (PPP), a new type of inter-frequency clock bias (IFCB) with satellite dependence should be noticed. If the IFCB is estimated together with the receiver coordinates, tropospheric wet delay, ambiguity and other parameters, it will increase the computational burden and lead to more time consumption. In order to solve this problem, the IFCB of GPS Block IIF satellites were estimated using 162 global uniformly distributed Multi-GNSS Experiment (MGEX) stations. By analyzing the time-varying characteristic of each satellite IFCB and combining the lag characteristics of the final ephemeris products, a modeling method of short-term IFCB prediction based on the epoch-by-epoch sliding Pearson autocorrelation function is proposed. The feasibility of this method was verified through the Student’s t-distribution, comparison with the measured IFCB, the posteriori residual of the third frequency carrier phase and the kinematic/static PPP solutions. The results showed that since the IFCB period was not a complete 24 h, the difference in the IFCBs time series on different days was increasingly significant with the passage of lag time, and the correlation constantly decreased. The peak-to-peak amplitudes of the IFCB difference reached 1.13, 3.44, 6.86 and 11.25 cm when the lag time was 1, 9, 19 and 29 days, respectively. In addition, based on the lag characteristic of final precise ephemerides released by the International GNSS Service (IGS) analysis centers, the prediction accuracy of the IFCB was evaluated with a time lag of 7 days. The root mean square of the posteriori residuals at the third-frequency observation decreased by approximately 51.3% compared to that without considering for IFCB correction. The triple-frequency uncombined PPP in the horizontal and vertical directions improved by approximately 33.2% and 17.2% for the static PPP solutions and 50.2% and 39.7% for the kinematic PPP solutions, respectively. In general, the accuracy and convergence time of the triple-frequency uncombined PPP were equivalently improved when the predicted IFCB and the measured IFCB were used.

Continuous quantum clock with high precision and long recurrence time

Continuous clocks, i.e., clocks that measure time in a continuous manner, are regarded as an essential component of sensing technology. Precision and recurrence time are two basic features of continuous clocks. In this paper, in the framework of quantum estimation theory various models for continuous quantum clocks are proposed, and all tools of quantum estimation theory are employed to seek the characteristics of clocks with high precision and long recurrence time. Then, in a resource-based approach, the performances of the proposed models are compared. It is shown that quantum clocks based on an $n$ two-qubit system not only can have better precision than quantum clocks based on a $2n$ one-qubit system but also support long recurrence time. Finally, it is shown that while employing $n$ entangled qubits improves the precision of clocks by a factor of $1/\sqrt{n}$, it inevitably worsens the recurrence time of the clock.

Sea ice out of time: Reckoning with environmental change

In September 2007, Arctic sea ice plummeted to a shocking record minimum at the time. The amount of ice lost that summer was equal to that lost over the previous 25 years. As Arctic sea ice escapes scientists’ predictions, scholars in the social sciences and humanities have critically interrogated “nature”/“culture” divides that treat the time of nature as unchanging and distinct from human beings. This essay examines what concept of time emerges through Arctic sea ice as an analytic lens. By this, I mean scientific knowledge of sea ice and the conceptual possibilities for thinking ice temporalities and environmental time-reckoning that it opens up. Attending to these possibilities suggests different kinds of “clocks” to help reckon the time of environmental changes in the form of (1) climate anomalies (e.g., deviations in ice thickness), which offer a different way of telling environmental time that attends to the physical specificity of substances; and (2) the Arctic Oscillation, a semi-periodic world weather pattern that emerges from the thick of relationships among ice, atmosphere, ocean, and now humans, generating a collective planetary time. Finally, I argue that the relational human–nonhuman production of planetary time shifts the focus in social studies of time from collective time-reckoning, which assumes entities have a socioculturally determined concept of time, toward temporal coordination as a less anthropocentric mode of ordering shared realities. Coordination decenters “the Human” as an epistemic ordering principle and enlarges ordering to include a diversity of nonhuman ways of being. Through temporal coordination, environmental prediction would be the ordering of a collective reality that a multiplicity of human and nonhuman ways of being make together rather than the search for a more precise clock, or development of better technoscientific means to capture nonhuman temporalities external to human beings.

Evaluation and comparison of the performance of BDS-3 space-borne atomic clocks

At present, most of the space-borne atomic clocks used by the major global navigation satellite systems include rubidium atomic clocks, passive hydrogen master (PHM) clocks and cesium atomic clocks. The new independently developed space-borne rubidium atomic clocks and PHM clocks on BeiDou Global Navigation Satellite System (BDS-3) are important hardware improvements. In this paper, performances of new Beidou domestic atomic clocks are evaluated using precise clock offset data from September 2019 to September 2021 and compared with the mainstream space-borne atomic clocks of other satellite navigation systems. The results show that the BDS-3 space-borne PHM clocks have low drift rate and high stability at 86400s interval, which respectively reaches 8.26 × 10−16 and 5.13 × 10−15. These performances are only slightly lower than Galileo PHM clocks. The frequency stability at 86400s interval of BDS-3 rubidium clock is up to 9.03 × 10−15, which is 27.76% higher than GPS rubidium clocks.

Combining VGOS, legacy S/X and GNSS for the determination of UT1

We perform a combination on the observation level (COL) between VLBI and co-located GNSS in the context of VLBI intensive sessions. Our approach revolves around an estimation procedure which uses 3 h of GNSS data that uniformly encapsulate the 1-h VLBI data, in order to provide consistent troposphere information. We test this approach on both VGOS and Legacy S/X using the VGOS-B and concurrently observed INT1 sessions. The COL strategy is found to increase the precision by 15 % over both session types and leads to an increase of 65 % in the agreement between the sessions when estimating tropospheric gradients every 3 h. A more frequent estimation of the gradients every 1 h, which can be rigorously pursued with the utilization of multi-GNSS, results in a further convergence of the two session types by 30 %. The COL-aided length-of-day (LOD) products also show a 55 % better agreement to external GNSS-derived LOD. In the light of the increasing precision of broadcast GNSS orbits and clocks, this COL strategy can be used to derive rapid UT1-UTC products.

Performance Evaluation of Different GNSS Positioning Modes

This paper gives a comparison of different GPS positioning modes using RTKLIB which is free and open-source software. The modes tested in this work are Single point positioning ( SPP), precise point positioning (PPP), Satellite-based augmentation system ( SBAS), Differential GPS (DGPS), and Real-Time Kinematic (RTK). The data for tests were obtained from NetR9 receivers, these types of receivers are multi-frequencies and multi-constellation receivers that provide carrier and phase measurements. The SPP mode is the very simplest mode, it can be used for applications where accuracy is not less than 5m, and it can be improved to achieve 1m by using SBAS corrections but only in the coverage area of the system. The DGPS can also provide 1m accuracy using a second receiver as a base station which can increase the cost of the operation. For applications that need very high accuracy, RTK and PPP can be used to reach centimeter-level accuracy. RTK needs a base station in addition to the rover receiver used for the positioning; PPP uses precise orbital and clock solutions which are not available in real time for all users.

Continuous-Variable Quantum Key Distribution Without Synchronized Clocks

It is well known that accurate clock synchronization is the backbone of quantum information processing tasks. Continuous-variable quantum key distribution (CV QKD), when proposed, benefited from its natural synchronization signals, i.e., local oscillator (LO), which provides a precise and automatic clock synchronization without a special clock board. The application of LO, however, incurs security loopholes, exposing the system to the risk of being attacked. We resolve this unsafe synchronization by proposing a virtual clock synchronization method for the CV QKD protocol without sending a real LO. The proposed method, which is based on the interpolation algorithm, extracts the clock information from the measured quadrature of the quantum signal rather than the classical LO. By formulating the measured quadrature as the synchronization signal, Bob recovers the clock information without both security loopholes and a specific clock board. Numerical results test the robustness of our method and show its potential in a real CV QKD implementation.

Results of the Deep Space Atomic Clock Deep Space Navigation Analog Experiment

The timing and frequency stability provided by the Deep Space Atomic Clock (DSAC) is nearly commensurate to the Deep Space Network’s ground clocks and enables one-way radiometric measurements with accuracy equivalent to current two-way tracking data. A demonstration unit of the clock was launched into low Earth orbit on June 25, 2019, for the purpose of validating DSAC’s performance in the space environment. Global Positioning System (GPS) data collected throughout the two-year mission was utilized not only for precise clock estimation but also as a proxy for deep space tracking data to conduct the Deep Space Navigation Analog Experiment. Through careful selection and processing of GPS Doppler data and limited modeling fidelity representative of deep space navigation capabilities, the analog orbit solutions are compared to higher-fidelity solutions, demonstrating DSAC’s viability as a navigation instrument in conditions typical for a low-altitude Mars orbiter. Onboard telemetry quantifying the ultrastable oscillator (USO) frequency correction is processed to demonstrate the orbit determination performance degradation when utilizing USO-based one-way radiometric tracking data.

Gene copy number and negative feedback differentially regulate transcriptional variability of segmentation clock genes

SummaryTimely progression of a genetic program is critical for embryonic development. However, gene expression involves inevitable fluctuations in biochemical reactions leading to substantial cell-to-cell variability (gene expression noise). One of the important questions in developmental biology is how pattern formation is reproducibly executed despite these unavoidable fluctuations in gene expression. Here, we studied the transcriptional variability of two paired zebrafish segmentation clock genes (her1 and her7) in multiple genetic backgrounds. Segmentation clock genes establish an oscillating self-regulatory system, presenting a challenging yet beautiful system in studying control of transcription variability. In this study, we found that a negative feedback loop established by the Her1 and Her7 proteins minimizes uncorrelated variability whereas gene copy number affects variability of both RNAs in a similar manner (correlated variability). We anticipate that these findings will help analyze the precision of other natural clocks and inspire the ideas for engineering precise synthetic clocks in tissue engineering.

MEVSİMSEL DEĞİŞİMLERİN HASSAS NOKTA KONUMLAMAYA ETKİSİ

Hassas Nokta Konumlama (Precise Point Positioning-PPP), tek bir GNSS alıcısıyla hassas uydu yörünge ve saat bilgilerini kullanarak santimetre doğruluğunda konum bilgisi sağlayan bir yöntemdir. Son zamanlarda bu yöntem pek çok bilimsel çalışmaya konu olmaktadır. Bu çalışmada, mevsimlerin PPP konum belirleme doğruluğu üzerindeki etkisini araştırmak amacıyla kuzey yarım kürede yer alan yüksek enlem (KIR8 (İsveç), NYA2 (Norveç)), orta enlem (ANKR(Türkiye), DLF1(Hollanda)) ve ekvatoral bölgede (NKLG(Gabon), SIN1(Singapur)) bulunan Uluslararası GNSS Servisi (International GNSS Service: IGS) istasyonları seçilmiştir. Seçilen istasyonlara ait 365 gün 24 saat 30 saniyelik RINEX verileri çözümlerde kullanılmak üzere elde edilmiştir. 01.12.2019-30.11.2020 tarihleri arasında elde edilen veriler çözümlerin yapılabildiği web tabanlı PPP servislerinden CSRS-PPP, MagicGNSS ve APPS ile değerlendirilmiştir. Web tabanlı servislerden elde edilen koordinatların hassasiyetlerini araştırmak amacıyla her ay için ortalama koordinat değerleri kullanılarak karesel ortalama hatalar (KOH) hesaplanmış, daha sonra mevsimlere bağlı doğrulukları ortaya koymak için istasyonların IGS’den temin edilen bilinen koordinatları kullanılarak konum ortalama hataları hesaplanmıştır. Aynı istasyonlar ve servisler için farklı mevsimlerde elde edilen konum ortalama hataları Bartlett testi ile karşılaştırılmıştır. Karşılaştırma sonunda ANKR istasyonu hariç diğer istasyonlarda konum ortalama hatalarının uyuşum içinde olduğu, konum doğruluklarının mevsimlerden ziyade kullanılan servislere bağlı olduğu ve en iyi sonuçların MagicGNSS ile elde edildiği görülmüştür.

Relational evolution with oscillating clocks

A fundamental description of time can be consistent not only with the usual monotonic behavior but also with an oscillating physical clock variable, coupled to the degrees of freedom of a system evolving in time. Generically, one would in fact expect some kind of oscillating motion of a system that is dynamical and interacts with its surroundings, as required for a fundamental clock that can be noticed by any other system. Unitary evolution does not require a monotonic clock variable and can be achieved more generally by formally unwinding the oscillating clock movement, keeping track not only of the value of the clock variable but also of the number of cycles it has gone through at any moment. The specific treatment used here employs concatenations of evolution operators, alternating between forward and backward evolution of the oscillating clock. Because the clock and an evolving system have a common conserved energy, the clock is in different cycles for different energy eigenstates of the system state. As a result, the clock is generically in a quantum state with a superposition of different clock cycles, a key feature that distinguishes oscillating clocks from monotonic time. In addition, coherence could be lost faster than observed, for instance if a system that would be harmonic in isolation is made anharmonic by interactions with a fundamental clock, implying observational bounds on fundamental clocks. Numerical computations show that coherence is maintained over long timescales provided the clock period is much smaller than the system period. A small loss of coherence nevertheless remains and, measured in terms of the relative standard deviation of the system period, is proportional to the ratio of the system period and the clock period. Since the precision of atomic clocks could not be achieved if atomic frequencies would be subject to additional variations from coupling to a fundamental clock, an upper bound on the clock period can be obtained that turns out to be much smaller than currently available direct or indirect measurements of time.

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

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

GNSS real-time precise point positioning with BDS-3 global short message communication devices

Global short-message communication (GSMC) service is a new function of BeiDou-3 global navigation satellite system (BDS-3). Broadcasting precise orbit and clock corrections via GSMC provides an opportunity for real-time precise point positioning (PPP), especially in the areas where internet-based communication is not available, such as deserts and oceans. This research achieves a real-time multi-GNSS PPP based on the precise orbit and clock corrections broadcast via BDS-3 GSMC. To reduce the data size, the precise corrections of only visible GNSS satellites are broadcast, and three messages are used to broadcast the corrections of GPS, Galileo and BDS satellites. The encoding strategy of corrections is designed and a procedure for real-time PPP with BDS-3 GSMC is described. To evaluate the positioning performance of the proposed real-time PPP scheme, the simulated kinematic real-time PPP experiments with BDS-3 GSMC corrections and Centre National d’Etudes Spatiales (CNES) real-time precise orbit and clock products are carried out by using observations of 7 days from 12 globally distributed IGS stations. The positioning accuracy in E, N and U components reach up to 3.3, 3.8 and 5.9 cm with GSMC corrections, which is comparable to that with CNES real-time products. Furthermore, a vehicle real-time PPP experiment is conducted using the devices with the function of BDS-3 GSMC and the positioning accuracy reach up to 4.1, 2.2 and 7.1 cm in E, N and U components after convergence.

Entropy of timekeeping in a mechanical clock.

The dynamics of a unique type of clock mechanism known as grasshopper escapement is investigated with the aim of evaluating its accuracy in a noisy environment. It is demonstrated that the clock's precision scales linearly with the rate of its entropy production, consistently with recently reported results regarding nanoscale and quantum clocks. Moreover, it is shown that the inevitable force variations present in the mechanism can be modeled with a Maxwell-Boltzmann statistic. Finally, the function of clock error is compared with Brownian motion and its fractal-like properties are discussed. The numerical results are confirmed with experimental data.

A Novel Clock Parameterization and Its Implications for Precise Point Positioning and Ionosphere Estimation.

By convention, IGS precise clock products are computed using the ionosphere-free linear combination. Due to the broad use of IGS products, this convention is exploited in PPP-RTK models not using such a linear combination. So, in different carrier phase combinations, the code hardware biases are contained in different combinations, thus making the problem of separating biases from integer ambiguities more complicated. In this paper, we proposed a novel clock parameterization which allows facilitating this problem. Based on the proposed parameterization, we derived a dual-frequency PPP-RTK model for the undifferenced measurements and assessed this model for the static positioning case in terms of positioning accuracy, convergence, and ambiguity resolution performance. The results showed that a cm-level accuracy level is achievable with the derived models with nearly instant convergence and almost 100% successfully resolved ambiguities. We demonstrated the use of this parameterization for slant ionosphere estimation. We derived the analog of the equation linking the wide-lane, geometry-free, and ionosphere-free biases from the Fast-PPP system and used it to retrieve slant ionosphere information. Our TEC estimates showed some evidence of capability to reach an agreement of 1–2 TECU and the standard deviation of 3–4 TECU with GIM TEC values.

A Test Platform for UWB-Based Localization of Dynamic Multi-Agent Systems

Despite recent developments in Ultra-wideband (UWB)-based algorithms, notably in relative localization, existing multi-UWB platforms can only test these algorithms on small or static networks. This work proposes a multi-UWB platform using a novel protocol that improves upon prior works and accommodates large mobile networks by enabling: rapid local network reconfiguration, increased ranging rate among multiple UWB nodes, and bi-directional communication links, which removes precise clock synchronization requirements between UWBs. The proposed UWB platform performance is evaluated using Decawave EVB1000 boards for node addition and removal, and meeting of three networks. These experiments demonstrate increased local reconfiguration rate over prior work and maximization of ranging rate between node pairs. In addition, the supporting firmware and Robot Operating System (ROS) packages for the platform are made publicly available.

Analysis of BDS-3 Onboard Clocks Based on GFZ Precise Clock Products

The characteristics and performance of satellite clocks are important to the positioning, navigation, and timing (PNT) services of Global Navigation Satellite System (GNSS) users. Although China’s BeiDou-3 Navigation Satellite System (BDS-3) has been fully operational for more than one year, there is still a lack of comprehensive research on the onboard clocks of the entire BDS-3 constellation. In this study, the precise clock products of GeoForschungsZentrum (GFZ) from day-of-year (DOY) 1, 2021 to DOY 300, 2021 were used to analyze the characteristics and performance of BDS-3 onboard clocks from the following aspects: clock bias, frequency, drift rate, fitting residuals, periodicity, and frequency stability. Compared with BDS-2, the clock quality of BDS-3 satellites has been greatly improved, but there are still jumps in the clock offsets and frequency series of BDS-3 clocks. The drift rate of BDS-3 clocks varies within the range between −2×10−18 and 2×10−18 s/s2. The daily model fitting residuals of passive hydrogen masers (PHM) on BDS-3 medium Earth orbit (MEO), inclined geosynchronous orbit (IGSO), and geostationary (GEO) satellites are 0.15, 0.28, and 0.46 ns, respectively. The overlapping Allan deviation (OADEV) of BDS-3 MEO clocks is 4.0 × 10−14 s/s at a time interval of 1000 s. The PHMs on BDS-3 MEO satellites exhibit fewer periodic signals than those of Rb clocks. In addition, the precise clock offsets of the BDS-3 PHMs carried on the MEO, IGSO, and GEO satellites show different periodicities, which are similar to those of the corresponding types of BDS-2 satellites.

Improved Timing for better performance of distributed data acquisition systems - a further refinement

Continuing the works debuted in the previous work “Improved Timing for better performance of distributed data acquisition systems” the present paper refines and revisits the concept of a local oscillator with GPS corrections as a source of long-term stable reference clock signals with direct application in distributed data acquisition systems. The system as described herein can generate precise and repeatable clock source signals for trigger and sync of various data acquisition equipment when used in mixed and distributed architectures. These timing signals are a vital part of data acquisition as oftentimes raw data is processed as time series and correlations are made based on timestamps. This paper details improvements in implementation of a cost-effective high precision time base (reference clock) using a GPS receiver as a primary time source and a local high precision real time clock as a secondary oscillator. The improvements to the previous version come both from hardware refinements and from updated software with reduced latencies and reconfigured structure that allows for compensation of internal delays and internal process offsets.

High-Rate One-Hourly Updated Ultra-Rapid Multi-GNSS Satellite Clock Offsets Estimation and Its Application in Real-Time Precise Point Positioning

The requirement of timeliness is increasing while obtaining precise tempo-spatial information with the development of global navigation satellite systems (GNSSs). Due to the poor network environment and communication conditions in some regions or application scenarios, it is difficult for users to receive real-time (RT) precise products. The hourly updated ultra-rapid products with low latency and high accuracy are of great interest in GNSS real-time and near-real-time fields. However, it is difficult to achieve the high-rate one-hourly updated precise clock estimation (PCE); since many ambiguity parameters need to be estimated, the computation is time-consuming. At present, the highest time resolution of ultra-rapid clock offsets is 15 min. The low samplings affect the prediction accuracy of clock offsets and the precise point positioning (PPP) performances. To meet these requirements, we proposed an efficient method and design a new framework for high-rate one-hourly updated ultra-rapid PCE. We modified the epoch-difference (ED) PCE model in the parameter estimation. According to the characteristics of the modified ED PCE model, the Open Multi-Processing (OpenMP) and Intel Math Kernel Library (MKL) technologies are used to construct a parallel system to realize the parallelism among satellites, epochs, and stations. The comprehensive assessment in the precision of clock offsets and PPP performances is conducted. The result demonstrates that the one-hourly updated multi-GNSS clock offsets with 30 s sampling can be obtained within 20 min. The estimated clock offsets accuracy increases with the improvement of the time resolution. The STD and RMS are improved by (0.97 to 9.09% and 0.12 to 5.56%) in the observation session, (2.82 to 23.08% and 0.95 to 9.09%) in the first hour of the prediction session, and (0.11 to 3.85% and 0.12 to 4.19%) in the second hour of the prediction session compared with low-rate products, respectively. The high-rate one-hourly updated ultra-rapid clock offsets significantly improves the RT-PPP performances. The positioning accuracy can be improved by 1.52~25.74%, and the convergence time can be improved by 21.96~65.75%. The RT-PPP performances are basically the same as GeoForschungsZentrum Potsdam (GFZ) rapid products and slightly better than the Center National d’Etudes Spatiales (CNES) RT products (CLK93). The one-hourly updated ultra-rapid products with low latency, high accuracy, and not limited by network conditions can be well applied to real-time or near real-time applications and research.