Clock Parameters Research Articles

LEO satellite clock modeling and its benefits for real-time LEO PPP timing

In the kinematic Precise Orbit Determination (POD) process for low earth orbit (LEO) satellites, a significant correlation exists between the orbital and clock parameters. Here, a LEO satellite clock model is proposed to enhance the Precise Point positioning (PPP) timing and time synchronization during the LEO orbit/clock determination. The GRACE-FO satellite was utilized to achieve PPP timing and time transfer for LEO satellites with the real-time (RT) products provided by three analysis centers, namely Centre National d’Etudes Spatiales (CNES), GMV Aerospace and Defense (GMV), and Wuhan Technical University (WHU). For the frequency stability of the PPP timing for LEO satellites, the short-term stability (1280 s) is about 10−13 level, and the long-term stability (10,240 s) is about 10−14 level. Compared with the traditional PPP method (Scheme1), the LEO satellite clock model (Scheme2) is capable of significantly reducing the noise, regardless of whether it is PPP timing or PPP time synchronization. The frequency stability of Scheme 1 shows an improvement in short-term stability (1280 s) by about 8 %-72 % and the max improvement of the long-term stability (10240 s) by approximately 39 %, the result also shows a better improvement in LEO time synchronization.

A cooperative timestamp-free clock synchronization scheme based on fast unscented Kalman filtering for time-sensitive networking

Clock synchronization, built on the classical two-way message exchange scheme, is the key prerequisite for the normal operation of time-sensitive networking (TSN). In practical TSN, the imperfect oscillator caused by environmental changes leads to clock parameters drift. Moreover, synchronization errors accumulate in multi-hop networks, making it difficult for nodes at the edge of the network to achieve precise synchronization performance. Additionally, in some industrial and vehicular scenarios, the energy consumption and complexity of clock synchronization are important factors that need to be considered. To address these problems, this paper proposes a cooperative synchronization clock offset and clock skew joint tracking algorithm based on fast Unscented Kalman filter (FUKF). To further reduce the computation and energy consumption caused by clock synchronization, we introduce randomized singular value decomposition and timestamp-free exchange. The former uses small sub-matrices approximations to replace extremely high-dimensional matrices, reducing computational time in the update stage of the UKF. The latter reduces energy consumption by setting response intervals at the receiving end, eliminating the need for timestamp exchange during the synchronization process. Therefore, this algorithm can achieve long-term synchronization without requiring excessive computational and communication overhead. The results show that the proposed method, while maintaining accuracy unchanged, reduced the running time by 20% to 90% as the number of observations increased, thus verifying the effectiveness of the algorithm.

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

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

An improved clock synchronization model for typical IoT applications

In today’s scenario, the Internet of Things (IoT) has transformed people’s lives by enabling data exchange among pervasive devices in various applications. However, clock synchronization is essential to ensure seamless transmission and synchronization among IoT entities involved in processing and communication. This paper proposes a clock synchronization algorithm based on linear-quadratic regression (LQR) to address synchronization-errors in IoT applications. The algorithm uses a linear model of skew and offsets to estimate clock parameters, and performance is evaluated in terms of R-square error (RSE) and Root Mean Square Error (RMSE). Our proposed algorithm outperformed traditional algorithms with an R-Square Error of 0.71% and RMSE of 0.379%. This paper also evaluated the stability of the proposed model using the correlation coefficient, which indicated a high correlation among the variables at 86%. The results below demonstrate the proposed algorithm’s effectiveness and goodness of fit in addressing clock synchronization errors for IoT applications.

Frequency-Offset Information Aided Self Time Synchronization Scheme for High-Dynamic Multi-UAV Networks

Due to the unique merits of unmanned aerial vehicle (UAV) systems, they have already been harnessed for military, public, and civil applications. Time synchronization is a significant premise of formatting and applying UAV networks. However, the irregular high-speed mobile UAVs pose new challenges to time synchronization, especially when external time references are unavailable in some rigid scenarios. Therefore, in these harsh cases, self-time-synchronization (STS) without any external assistance should be concerned to overcome the relative velocity between UAVs caused by irregular high-speed motion. In this paper, a realistic timestamps model for the multi-UAV networks is established, and then a dynamic topology-based maximum likelihood estimator will be developed to carry out the STS. Furthermore, by introducing the information on frequency offset, a new estimator with the closed-form expression is proposed based on a two-way message exchange framework. After that, a tracking algorithm with the assistance of estimation results will be introduced to compensate for the time-varying change of the clock parameters for the dynamic topology UAV networks. To evaluate the performance of the estimator, both the estimation error and Cramér-Rao lower bound are analyzed. Numerical results show that the proposed algorithm exhibits its superiority in STS performance and computational complexity compared to the existing two-way message exchange algorithm using timestamps only.

Design of Light, Small, and High-precision Digital Servo Clock for LEO Constellation

Modern low earth orbit (LEO) satellite systems have placed increasingly stringent requirements on spaceborne time-frequency systems in the fields of constellation autonomous management, distributed synthetic aperture radar (SAR) imaging, and navigation time service. Admittedly, the original high-stability constant-temperature crystal oscillator and high-stability temperature-compensated crystal oscillator can no longer comply with the indicator requirements of clock source frequency characteristics and clock synchronization accuracy. Likewise, traditional satellites use atomic clocks (rubidium atomic clocks and cesium atomic clocks). On account of their inherent characteristics, the ground receiving system needs to observe and count the clock parameter characteristics for a long time after the satellite enters orbit and frequently modify the future working state parameters. The features of being expensive and bulky increase the operation and maintenance costs of the ground system and the complexity of engineering implementation. In this paper, a kind of light and small high-precision digital servo clock based on the deep coupling of the global navigation satellite system (GNSS) is designed for the LEO satellite constellation. The tame clock is deeply coupled with the GNSS navigation receiver, and the high precision time-frequency difference between the local clock frequency source and GNSS is obtained by using the carrier and pseudo-range measurement information of visible satellite and carrier phase measurement information of the receiver. It not only utilizes the short-term high stability of OCXO but also employs the long-term time-frequency maintenance ability of GNSS so that the tamed OCXO is locked in GNSS for a long time, which can achieve frequency calibration of local clock sources and long-term output to various space-borne systems. The system is small in size and low in power consumption, with output frequency stability better than 3E-13 (10000 s), accuracy better than ±2E-13, and timing accuracy better than ±10 ns, which is comparable to the key technical indexes of spaceborne miniaturized rubidium clocks, in line with the current demand of miniaturization, low power consumption, and low cost of LEO constellations.

Stochastic modeling of the receiver clock parameter in Galileo-only and multi-GNSS PPP solutions

In Precise Point Positioning (PPP), the receiver clock parameter is typically estimated independently in each observation epoch, which increases the noise of the estimated station coordinates and troposphere parameters due to correlations. Applying stochastic modeling to the receiver clock parameter stabilizes PPP solutions and reduces clock noise for the time transfer. However, the receiver clock modeling is possible only for the GNSS receivers connected to the utmost stable atomic clocks. We propose receiver clock modeling that involves the Markov stochastic process in the form of a random walk. We test different levels of random walk constraints for GNSS stations equipped with different types of clocks for Galileo-only and multi-GNSS solutions in kinematic and static PPP. In multi-GNSS solutions, the common clock parameter is derived with inter-system biases (ISBs). This raises the question of the constraints that should be imposed on the common clock only or also on the ISBs. We found that similar results can be achieved by imposing constraints on the common clock parameter and estimating ISB as a constant parameter and when constraining the common clock parameter and ISBs with a ratio of 1:100. Other ratios of clock-to-ISB constraints, such as 1:1 and 1:10, give inferior results. In the kinematic PPP, stochastic clock modeling has a marginal impact on the North and East coordinate components, whereas the Up component is substantially improved for GNSS receivers equipped with hydrogen masers. In the static PPP, the clock modeling improves the time transfer, due to the reduced noise of the clocks.

Clock Rigidity and Joint Position-Clock Estimation in Ultrawideband Sensor Networks

Joint position and clock estimation is crucial in many wireless sensor network applications, especially in distance-based estimation with time-of-arrival (TOA) measurements. In this work, we study the graph properties under which an ultra-wideband (UWB) sensor network is localizable and clock synchronizable with one round TOA-based timestamp measurements. A novel clock rigidity theory is proposed and its topological condition is proved to have close relationship to bearing rigidity. Based on clock rigidity, a graphical approach for analyzing the joint position and clock problem is investigated. It is shown that a position-clock framework with certain graph properties can be uniquely determined up to some trivial variations corresponding to both position and clock parameters. Simulation results are presented to demonstrate how clock rigidity theory is exercised in clock estimation and joint position-clock estimation.

LEO Satellite Clock Modeling and Its Benefits for LEO Kinematic POD

High-accuracy Low Earth Orbit (LEO) satellite clock and orbital products are preconditions to realize LEO augmentation for high-accuracy GNSS-based positioning on the ground. There is a high correlation between the orbit and clock parameters in the kinematic Precise Orbit Determination (POD) process. While future LEO satellites are planned to be equipped with better clocks, the benefits of modeling high-stability LEO satellite clocks are not yet thoroughly investigated, particularly when mid- to long-term systematic effects induced by the complex LEO relativistic effects and the external environment remain in the clocks. Through clock modeling, this study attempts to reduce not only the short-term noise of radial kinematic orbits, but also mis-modeled effects caused by, e.g., real-time GNSS orbital and clock errors. To explore the benefits of clock modeling, the clocks need to be first detrended by the mid- to long-term systematic effects. While over-detrending limits the orbital improvements, weak detrending would also hamper strong clock modeling and easily lead to performance degradations. A balance between the strengths of the detrending and the model thus needs to be investigated for different clock types. In this study, the Piece-Wise Linear (PWL) model of different time lengths and a 2.5-state filter with different strengths (h values) are tested using real data from GRACE FO-1 with an Ultra-Stable Oscillator (USO) on board. Using the CNES real-time GPS products, it was found that when detrending the clocks with a smoothing window of 300 to 500 s, one could generally expect an improvement larger than 10% in the estimation of radial orbits when applying a PWL model with a length from 300 to 1200 s. Improvements of this size can also be expected when using the 2.5-state model with h−1 (for Flicker Frequency Noise) from 10−28 to 10−30.

Multi-GNSS PPP solutions with different handling of system-specific receiver clock parameters and inter-system biases

In the multi-GNSS solutions integrating GPS, GLONASS, Galileo, and BeiDou, the receiver clock may be treated twofold; the clock parameter may be estimated for each GNSS separately or the common clock can be estimated, e.g., for GPS, with inter-system biases (ISBs) for other systems. The latter strategy reduces the number of estimated independent clock parameters per epoch almost by a factor of four because the clock parameters are estimated epoch-wise, whereas ISBs are estimated as constant values for the entire day or month. Due to the discontinuities in reference satellite clocks, the estimated ISBs and receiver clock parameters have also to be reinitialized at day boundaries. This raises questions about whether only the common clock has to be reset or all ISB values and what is the impact of the reinitialization of clock parameters with covariance values when estimating system-specific clock parameters. We analyze the effects of different types of stochastic modeling applied to the parameters of clocks and ISBs. In this study, we test five different strategies to clock handling in multi-GNSS kinematic Precise Point Positioning derived continuously for one month. We found that two solutions can be considered equivalent: (1) estimating system-specific clocks and (2) estimating the common clock with ISB and resetting at day boundaries the common clock parameter and ISBs. Oppositely, resetting only the common clock parameter or assuming that the ISB keep their stabilities over long periods is insufficient to obtain superior results of station coordinates and reliable time transfer results.

Timestamp-Free Synchronization Under Delays With Arbitrary Distribution in Wireless Sensor Networks

Clock synchronization is a key technology in wireless sensor networks (WSNs). It is significant and challenging to track clock parameters under arbitrary delay distributions. This letter proposes an Adaptive Gaussian mixture extended Kalman particle filter (AGMEKPF), which is robust to arbitrarily distributed delays in practical WSNs and can jointly track clock skew and offset. It is combined with the timestamp-free synchronization, which is a clock synchronization protocol that can effectively reduce energy consumption without exchanging timestamps. Simulation results show that the proposed method outperforms similar methods in terms of accuracy and complexity.

Lithium affects the circadian clock in the choroid plexus – A new role for an old mechanism

Lithium is an effective mood stabilizer, but the mechanism of its therapeutic action is not well understood. We investigated the effect of lithium on the circadian clock located in the ventricle barrier complex containing the choroid plexus (CP), a part of the glymphatic system that influences gross brain function via the production of cerebrospinal fluid. The mPer2Luc mice were injected with lithium chloride (LiCl) or vehicle, and their effects on the clock gene Nr1d1 in CP were detected by RT qPCR. CP organotypic explants were prepared to monitor bioluminescence rhythms in real time and examine the responses of the CP clock to LiCl and inhibitors of glycogen synthase kinase-3 (CHIR-99021) and protein kinase C (chelerythrine). LiCl affected Nr1d1 expression levels in CP in vivo and dose-dependently delayed the phase and prolonged the period of the CP clock in vitro. LiCl and CHIR-99021 had different effects on 1] CP clock parameters (amplitude, period, phase), 2] dexamethasone-induced phase shifts of the CP clock, and 3] dynamics of PER2 degradation and de novo accumulation. LiCl-induced phase delays were significantly reduced by chelerythrine, suggesting the involvement of PKC activity. The effects on the CP clock may be involved in the therapeutic effects of lithium and hypothetically improve brain function in psychiatric patients by aligning the function of the CP clock-related glymphatic system with the sleep-wake cycle. Importantly, our data argue for personalized timing of lithium treatment in BD patients.

Security enhancement of quantum noise stream cipher system based on optical temporal scrambling

In order to enhance security of QNSC signal, an optical temporal scrambling scenario which can avoid leaking synchronous clock parameters in QNSC system is proposed and experimentally demonstrated. In the proposed scenario, it utilized a cascaded FPCs to disturb time signature of 12.5 Gbps QNSC with 1024(210) intensity levels. The results indicate that, optical temporal scrambler cascaded 36 FPCs can spread the QNSC signal, resulting in the neighboring 12.5 bits of QNSC signal may be overlapped, which makes the signal look like noise both in intensity level and in time domain. Then, the descrambling process can be implemented by a matched filter corresponding to the optical temporal descrambling. Furthermore, by analyzing the scrambled QNSC signals, the power penalty caused by transmission for 50.8 km is about 3.22 dB. As for its actual effect, it greatly enhanced the security of the QNSC signal due to the concealment of time features.

Characteristics of the IGS receiver clock performance from multi-GNSS PPP solutions

Global navigation satellite system (GNSS) receivers belonging to the International GNSS Service (IGS) are equipped with different types of clocks, such as internal crystal quartz clocks, rubidium and cesium atomic clocks, as well as hydrogen masers. These clocks are characterized by different phase and frequency accuracies and stabilities, resulting in different systematic clock time series patterns. We analyze the clock offsets between different GNSS systems, provide noise characteristics of the undifferenced and differenced clock parameters, and detect systematic patterns of the clocks. The time series of the receiver clocks are dominated by the diurnal, semidiurnal, and sometimes terdiurnal signals with amplitudes up to several meters. Hydrogen masers provide the highest clock stability, and the lowest is by internal clocks. However, there are also groups of very stable internal clocks that perform similarly to low-performing hydrogen masers and rubidium clocks. The interquartile ranges for epoch-differenced clock parameters fall between 3 and 250 mm for the best hydrogen masers and the worst internal clocks, respectively.

Multi-Objective Optimization and Tradespace Analysis of a Mechanical Clock Movement Design

Abstract Pendulum clocks were the prevalent time keeping standard for centuries to regulate commerce and public activities. These mechanical movements were the most accurate timekeepers globally until replaced by electric clocks. Although mainly used for decorative purposes today, the pendulum clock's working principles and mechanical behavior can serve to demonstrate fundamental science and engineering concepts. The tradeoff between a clock's quality factor, pendulum properties, and period can best be explored with multiple objective optimization and tradespace analysis methods. In this project, a Multi-Objective Genetic Algorithm (MOGA-II) and a Multi-Objective Simulated Annealing (MOSA) optimization approaches are applied to evaluate a Graham escapement street clock for pendulum mass and time accuracy with a range of the period. These clock designs vary the pendulum length, pendulum bob radius, and bob thickness. Horological concepts are used to calculate the overall performance and general utility. The numerical results show a 0.7% increase in the quality factor, and a 0.56% reduction in the mass, while maintaining the designed period by modifying the clock parameters. More importantly, these changes can provide material cost savings in a mass production scenario. Overall, the study highlights the tradeoff designer engineers have considered for decades which can now be visualized using computer tools for greater insight.

METHOD OF DETERMINING THE TIME PARAMETER OF THE GAS GENERATOR HYDROGEN STORAGE AND SUPPLY SYSTEMS

The method of determining the hourly parameter of the main element of the system for saving and supplying water, the gas generator, has been developed. The method is based on the approximation of a partial frequency response for the phase-frequency characteristic of the gas generator of the water saving system in terms of frequency. This approximation is used to construct a mathematical dependence, which is used in determining the time parameter of the gas generator. In the quality of the cob data, when the hourly parameter of the gas generator is determined, the phase-frequency characteristic of the gas generator and the allowable values of the parameters of the characteristics and the parameters of the hourly parameter of the gas generator and the approximation of the first dynamic characteristic are recorded. To determine the frequency parameters, tolerance criteria for accuracy are used, with the help of such gains of analytical reliability of these frequency parameters in the form of variances. It is shown that the phase-frequency characteristic of the gas generator of the system for saving and supplying water is mainly carried out from the variation of the transitional function. For this purpose, an array of experimental data, obsessions, as a result of vimiryuvan in a discrete moment and time, is scored by the Kotelnikov-Nyquist-Shannon theorem. For the implementation of the method, a sequence of procedures was induced to ensure the determination of the hourly parameter of the gas generator. Verification of the method is marked by the way of the completion of the test task. It is shown that the change in the hourly parameter of the gas generator of the system for saving and supplying water does not exceed 1.0%. Keywords: water supply saving system, gas generator, clock parameter, phase-frequency characteristic.

Manipulations of Libet clock parameters affect intention timing awareness

W judgments are a widely used intention timing awareness estimate. These judgments are typically obtained by using the classic Libet-style paradigm whereby participants are asked to estimate the time they become aware of their intention to act by using the location of a rotating object on a clock face. There is an inconsistency in the Libet clock parameters used in previous studies, and it is unclear whether this variability impacts W judgments and other outcome measures, with implications for the construct validity of this measure and the generalisability of results across studies. Here, we present a four-experiment study that systematically manipulated the Libet clock speed, number of clock markings, length of the clock hand and type of clock radius in order to examine whether these parameter manipulations affect intention timing awareness estimates. Our results demonstrate W judgments can be significantly influenced by the clock speed and number of clock markings. The meaning and implications of these results are discussed.

Delay Compensated One-Way Time Synchronization in Distributed Wireless Sensor Networks

Wireless sensor networks require accurate time synchronization to perform collaborative tasks on multiple distributed sensor nodes. However, the performance is greatly affected by the unpredictability of message delays in the synchronization process, which causes cumulative error and challenges to clock parameter estimations. We propose a delay compensated consensus Kalman-based time synchronization (DCCKTS) protocol to estimate the fluctuated delay effectively. We propose an algorithm to update all parameters in a one-way message exchange while maintaining time synchronization accuracy and energy consumption. The performance of the proposed algorithm is compared with traditional algorithms. Simulation results demonstrate that the algorithm performs better than conventional algorithms under an unknown Gaussian delay model.

Quality monitoring of real-time GNSS precise positioning service system

ABSTRACT The Real-Time Global Navigation Satellite System (GNSS) Precise Positioning Service (RTPPS) is recognized as the most promising system by providing precise satellite orbit and clock corrections for users to achieve centimeter-level positioning with a stand-alone receiver in real-time. Although the products are available with high accuracy almost all the time, they may occasionally suffer from unexpected significant biases, which consequently degrades the positioning performance. Therefore, quality monitoring at the system-level has become more and more crucial for providing a reliable GNSS service. In this paper, we propose a method for the monitoring of real-time satellite orbit and clock products using a monitoring station network based on the Quality Control (QC) theory. The satellites with possible biases are first detected based on the outliers identified by Precise Point Positioning (PPP) in the monitoring station network. Then, the corresponding orbit and clock parameters with temporal constraints are introduced and estimated through the sequential Least Square (LS) estimator and the corresponding Instantaneous User Range Errors (IUREs) can be determined. A quality indicator is calculated based on the IUREs in the monitoring network and compared with a pre-defined threshold. The quality monitoring method is experimentally evaluated by monitoring the real-time orbit and clock products generated by GeoForschungsZentrum (GFZ), Potsdam. The results confirm that the problematic satellites can be detected accurately and effectively with missed detection rate and false alarm rate . Considering the quality alarms, the PPP results in terms of RMS of positioning differences with respect to the International GNSS Service (IGS) weekly solution in the north, east and up directions can be improved by 12%, 10% and 27%, respectively.

DNN-Assisted Particle-Based Bayesian Joint Synchronization and Localization

In this work, we propose a Deep neural network-assisted Particle Filter-based (DePF) approach to address the Mobile User (MU) joint synchronization and localization (sync&loc) problem in ultra-dense networks. In particular, DePF deploys an asymmetric time-stamp exchange mechanism between the MUs and the Access Points (APs), which, traditionally, provides us with information about the MUs’ clock offset and skew. However, information about the distance between an AP and an MU is also intrinsic to the propagation delay experienced by the exchanged time-stamps. In addition, to estimate the angle of arrival of the received synchronization packets, DePF draws on the multiple signal classification algorithm that is fed with the Channel Impulse Response (CIR) experienced by the sync packets. The CIR is also leveraged to determine the link condition, i.e. Line-of-Sight (LoS) or Non-LoS. Finally, to perform joint sync&loc, DePF capitalizes on particle Gaussian mixtures that allow for a hybrid particle-based and parametric Bayesian Recursive Filtering (BRF) fusion of the aforementioned pieces of information and, thus, jointly estimates the position and clock parameters of the MUs. The simulation results verify the superiority of the proposed algorithm over the state-of-the-art schemes, especially that of the extended Kalman filter- and linearized BRF-based joint sync&loc. In particular, only drawing on the synchronization time-stamp exchange and CIRs from a single AP, for 90% of the cases, the absolute position and clock offset estimation error remain below 1 meter and 2 nanoseconds, respectively.