Stable Clock Research Articles

Network Time Protocol based Black Box Timing Accuracy Analysis for Internet of Things Devices

With large-scale Cyber-Physical Systems (Internet of Things) deployments, the low-cost networked devices are becoming ubiquitous. Time stamping of events is a basic requirement and it is crucial for distributed/isolated systems/devices to work in unison. The system clocks of these devices are not very stable and their behaviour is affected by ageing and environmental conditions. A clock’s timing behaviour is generally analysed independently by comparison to a highly stable standard reference clock using specialized instruments. Network Time Protocol (NTP) is widely used for time synchronization over computer networks. As the NTP server clock is more stable in comparison to a client’s system clock, the variation in the end device’s clock offset values with respect to the NTP server clock over a long time can be considered for analysing the behaviour of the end device’s clock. This paper presents a method for analysing clock behaviour based on NTP messages. A computer programme is developed, which utilizes an open-source NTP client library to exchange NTP messages and records end device’s system clock’s offset variations over time for a given periodicity to analyse the behaviour. This black box analysis approach does not require any direct access to the end device’s clock circuit. The solution may be useful for analysing clock behaviour for long-term stability under actual environmental conditions, for deciding time synchronization periodicity to optimize the number of synchronization packet exchanges, and for pre-deployment timing stability assessment of devices for deployment scenarios having intermittent/non-availability of periodic time synchronization.

A Study of Outliers in GNSS Clock Products

Time is an extremely important element in the field of GNSS positioning. In precise positioning with a single-centimetre accuracy, satellite clock corrections are used. In this article, the longest available data set of satellite clock corrections of four GNSS systems from 2014 to 2021 was analysed. This study covers the determination of the quality (outliers number and magnitude), availability, stability, and determination of the specificity and nature of the clock correction for each satellite system. One problem with the two newest satellite systems (Galileo and BeiDou) is the lack of availability of satellite signals in the early years of the analysis. These data were available only in the later years of the period covered by the analysis, as most of the satellites have only been in orbit since 2018–2019. Interestingly, the percentage of outlying observations was highest in Galileo and lowest in BeiDou. Phase and frequency plots showed a significant number of outlying observations. On the other hand, after eliminating outlying observations, each system showed a characteristic graph waveform. The most consistent and stable satellite clock corrections are provided by the GPS and GLONASS systems. The main problems discussed in this paper are the determination of the number and magnitude of outliers in clock products of four GNSS systems (GPS, GLONASS, Galileo, Beidou) and the study on the long-term stability of GNSS clocks analysis, which covers the years 2014–2021.

Design and Analysis of Ultra-low Power Voltage Controlled Oscillator in Nanoscale Technologies

In latest wired and wireless communication equipment, VCO (voltage-controlled oscillator) is the major building block and particularly used as the stable high frequency clock generator. VCO performance is measured through frequency range, power supply used, area occupied, power consumption, delay, and phase noise. VCO is the cascaded of odd number of inverter stages in a ring format, hence it is also articulated as a ring oscillator. Today’s portable communication devices are battery operated. Hence, low power and area efficient designs play a key role in battery life enhancement and device size reduction. Device scaling improves the effective silicon area utilization, but it leads to more leakages. Therefore, low power techniques along with the technology scaling is the best way of low power designs. In this article, discussed various low power schemes. The ring oscillator designs are carried out in various nano meter scaled technologies such as 180nm, 90nm,65nm and 45nm. A 5-stage ring oscillator is implemented in each technology along with low power schemes, simulated in Cadence virtuoso, and noted power, delay, and area. Observed that the proposed ring oscillator with sleepy keeper technique generated a stable frequency of oscillations in the range of 1GHz-2GHz. A control voltage of 1.8V to 0.4V is applied and targeted the power less than 30mW and delay in 0.25p sec.

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.

A step to the decentralized real-time timekeeping network

The composite time scale (CTS) provides an accurate and stable time-frequency reference for modern science and technology. Conventional CTS always features a centralized network topology, which means that the CTS is accompanied by a local master clock. This largely restricts the stability and reliability of the CTS. We simulate the restriction and analyze the influence of the master clock on the CTS. It proves that the CTS’s long-term stability is also positively related to that of the master clock, until the region dominated by the frequency drift of the H-maser (averaging time longer than ∼105 s). Aiming at this restriction, a real-time clock network is utilized. Based on the network, a real-time CTS referenced by a stable remote master clock is achieved. The experiment comparing two real-time CTSs referenced by a local and a remote master clock respectively reveals that under open-loop steering, the stability of the CTS is improved by referencing to a remote and more stable master clock instead of a local and less stable master clock. In this way, with the help of the proposed scheme, the CTS can be referenced to the most stable master clock within the network in real time, no matter whether it is local or remote, making democratic polycentric timekeeping possible.

Cryo-CMOS modeling and a 600 MHz cryogenic clock generator for quantum computing applications

The development of large-scale quantum computing has boosted an urgent desire for the advancement of cryogenic CMOS (cryo-CMOS), which is a promising scalable solution for the control and read-out interface of quantum bits. In the current work, 180 nm CMOS transistors were characterized and modeled down to 4 K, and the impact of low-temperature transistor performance variations on circuit design was also analyzed. Based on the proposed cryogenic model, a 180 nm CMOS-based 450 to 850 MHz clock generator operating at 4 K for quantum computing applications was presented. At the output frequency of 600 MHz, it achieved < 4.8 ps RMS jitter with 30 mW power consumption (with test buffer), corresponding to a −211.6 dB jitter-power FOM, which is suitable for providing a stable clock signal for the control and readout electronics of scalable quantum computers.

Multi-GNSS precise point positioning with predicted orbits and clocks

Global Navigation Satellite Systems (GNSS) Real-time Precise Point Positioning (RT-PPP) strongly relies on the precise satellite orbits and clocks, especially the latter requires high update rate, e.g., five seconds, due to its limited prediction accuracy. Such a high-rate update frequency is a burden to both the data analysis and communicating, and interruption in communicating is almost unavoidable. For the new constellations such as Galileo and BDS-3 with high-stability hydrogen clocks onboard, it is possible to predict satellite clocks to a longer arc. Moreover, recent developments in multi-GNSS ultra-rapid precise orbit determination enables the half-hourly update, ensuring the availability with a prediction arc of 30–60 min. We investigate multi-GNSS RT-PPP using half-hourly predicted products and demonstrate that a 3-D accuracy of 2.9 and 11.3 cm can be achieved for static and simulated kinematic solutions, respectively. We present the different clock prediction accuracies of different types of satellites and propose a satellite-specific weighting strategy in PPP, which exploits the benefits of the satellites of good performance. The method is based on the prediction accuracy of both, satellites and clocks, and shows an improvement of 15 to 60% compared to those without satellite-specific weighting or with simplified weighting strategies. We also demonstrate that Galileo satellites contribute the most in the quad-constellation solution, thanks to the highly stable satellite clocks.

Evaluating Optical Clock Performance for GNSS Positioning.

Atomic clocks are highly precise timing devices used in numerous Positioning, Navigation, and Timing (PNT) applications on the ground and in outer space. In recent years, however, more precise timing solutions based on optical technology have been introduced as current technology capabilities advance. State-of-the-art optical clocks-predicted to be the next level of their predecessor atomic clocks-have achieved ultimate uncertainty of 1 × 10-18 and beyond, which exceeds the best atomic clock's performance by two orders of magnitude. Hence, the successful development of optical clocks has drawn significant attention in academia and industry to exploit many more opportunities. This paper first provides an overview of the emerging optical clock technology, its current development, and characteristics, followed by a clock stability analysis of some of the successfully developed optical clocks against current Global Navigation Satellite System (GNSS) satellite clocks to discuss the optical clock potentiality in GNSS positioning. The overlapping Allan Deviation (ADEV) method is applied to estimate the satellite clock stability from International GNSS Service (IGS) clock products, whereas the optical clock details are sourced from the existing literature. The findings are (a) the optical clocks are more stable than that of atomic clocks onboard GNSS satellites, though they may require further technological maturity to meet spacecraft payload requirements, and (b) in GNSS positioning, optical clocks could potentially offer less than a 1 mm range error (clock-related) in 30 s and at least 10 times better timing performance after 900 s in contrast to the Galileo satellite atomic clocks-which is determined in this study as the most stable GNSS atomic clock type used in satellite positioning.

Stable frequency transfer for clock synchronization for telecom networks

A stable and reliable clock synchronization system that transfers reference clocks to nodes is essential for telecom networks. Mainly, the clock synchronization of telecom networks is carried out through satellite links. However, for the evolving ubiquitous wireless communications, especially in some harsh environments, such as underground and trenches, the satellite-based clock synchronization scheme bears inevitable obstacles, which may cause strategic risks for the telecom networks, since no control and manipulation can be imposed on the satellite systems. Therefore, to ensure the robust operation of telecom networks with performance guarantees, some auxiliary means are desirable to assist clock synchronization that is solely based on satellite links. In this article, we report a phase-stabilized frequency signal transmission on branching optical fiber for clock synchronization for telecom networks. Particularly, the phase fluctuation due to optical carriers separation link and fiber link is compensated by a feedback network, which employs a high-precision voltage-controlled oscillator in the phase-locked loop to drive the acousto-optic frequency shifter for fast phase correction. Furtherly, the factors that cause performance limitations of the frequency distribution system are analyzed. Eventually, the experiment results obtained show that a stabilized fiber-optic frequency transfer scheme can be used as a reliable method for clock synchronization with high accuracy.

Mercury isotope clocks predict coastal residency and migration timing of hammerhead sharks

Abstract The management of migratory taxa relies on the knowledge of their movements. Among them, ontogenetic habitat shift, from nurseries to adult habitats, is a behavioural trait shared across marine taxa allowing resource partitioning between life stages and reducing predation risk. As this movement is consistent over time, characterizing its timing is critical to implement efficient management plans, notably in coastal areas to mitigate the impact of fisheries on juvenile stocks. In the Mexican Pacific, habitat use of the smooth hammerhead shark (Sphyrna zygaena) is poorly described, while the species is heavily harvested. Given the large uncertainties associated with the timing of out‐migration from coastal nursery grounds to offshore waters prior to reproductive maturity, a more precise assessment of smooth hammerhead shark movements is needed. Photochemical degradation of mercury imparts mass‐independent isotope fractionation (Δ199Hg) which can be used to discriminate between neonate coastal shallow habitats and the offshore deep foraging patterns of late juveniles. Here, we present the application of muscle Δ199Hg as molecular clocks to predict the timing of ontogenetic habitat shifts by smooth hammerhead sharks, based on their isotopic compositions at the initial and arrival habitats and on muscle isotopic turnover rate. We observed decreases in Δ199Hg values with shark body length, reflecting increasing reliance on offshore mesopelagic prey with age. Coastal residency estimates indicated that smooth hammerhead sharks utilize coastal resources for 2 years prior to offshore migration, suggesting a prolonged residency in these ecosystems. Policy implications. This study demonstrates how mercury stable isotopes and isotopic clocks can be implemented as a complementary tool for stock management by predicting the timing of animal migration—a key aspect in the conservation of marine taxa. In the Mexican Pacific, fishing pressure on shark species occurs in coastal habitats depleting juvenile stocks. Consequently, management decision support tools are imperative for effectively maintaining early life stage population levels over time. The finding that smooth hammerhead sharks extensively rely on highly fished habitats for 2 years after parturition supports the relevance of establishing a size limit in coastal fisheries and demonstrates how the current temporal shark fishing closure could lack efficiency for the species.

Towards global time distribution via satellite-based sources of entangled photons

We propose a satellite-based scheme to perform clock synchronization between ground stations spread across the globe using quantum resources. We refer to this as a quantum clock synchronization (QCS) network. Through detailed numerical simulations, we assess the feasibility and capabilities of a near-term implementation of this scheme. We consider a small constellation of nanosatellites equipped only with modest resources. These include quantum devices such as spontaneous parametric down conversion (SPDC) sources, avalanche photo-detectors (APDs), and moderately stable on-board clocks such as chip scale atomic clocks (CSACs). In our simulations, the various performance parameters describing the hardware have been chosen such that they are either already commercially available, or require only moderate advances. We conclude that with such a scheme establishing a global network of ground based clocks synchronized to sub-nanosecond level (up to a few picoseconds) of precision, would be feasible. Such QCS satellite constellations would form the infrastructure for a future quantum network, able to serve as a globally accessible entanglement resource. At the same time, our clock synchronization protocol, provides the sub-nanosecond level synchronization required for many quantum networking protocols, and thus, can be seen as adding an extra layer of utility to quantum technologies in the space domain designed for other purposes.

A VMD-PE-SG denoising method based on K–L divergence for satellite atomic clock

The time scale of the global navigation satellite system (GNSS) is the core element for its position, navigation and timing services. A highly stable atomic clock is essential to ensure the reliability of the GNSS time scale. This study proposed a novel hybrid denoising model combining variational mode decomposition (VMD), K–L divergence, permutation entropy (PE), and Savitzky–Golay (SG) filter for satellite atomic clocks. Firstly, the key parameter of VMD is solved efficiently by taking the minimum sum of K–L divergence of decomposed modes as the constraint condition, and the optimised parameters are applied to the decomposition process. On this basis, the PE algorithm is used to determine the modes decomposed by VMD into signal-dominant and noise-dominant components by searching for the mutation of PE value at two adjacent points. Finally, the noise-dominant components are denoised by the SG filter and then reconstructed with the signal-dominant components to form the denoised signal. The analysis of the simulated signal shows that the method can effectively remove noise from the simulated signal, and the resulting denoised signal is similar to the pure signal. Compared with commonly used ensemble empirical mode decomposition and wavelet denoising methods, the signal-noise ratio of the proposed method is improved by 21.2% and 28.9%, and the root mean square error is improved by 24.1% and 29.8%, respectively. The results of experimental data testify that the K–L VMD-PE-SG-based denoising method can significantly reduce the dominant noise within one day, thus effectively improving the short to medium-term frequency stability. Compared with the original signal, the stability of the smoothing time within 76 800 s is generally improved, and the degree of improvement depends on the type of atomic clock and the smoothing time.

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.

Hamiltonian engineering of spin-orbit-coupled fermions in a Wannier-Stark optical lattice clock.

Engineering a Hamiltonian system with tunable interactions provides opportunities to optimize performance for quantum sensing and explore emerging phenomena of many-body systems. An optical lattice clock based on partially delocalized Wannier-Stark states in a gravity-tilted shallow lattice supports superior quantum coherence and adjustable interactions via spin-orbit coupling, thus presenting a powerful spin model realization. The relative strength of the on-site and off-site interactions can be tuned to achieve a zero density shift at a “magic” lattice depth. This mechanism, together with a large number of atoms, enables the demonstration of the most stable atomic clock while minimizing a key systematic uncertainty related to atomic density. Interactions can also be maximized by driving off-site Wannier-Stark transitions, realizing a ferromagnetic to paramagnetic dynamical phase transition.

A quality control method based on improved IQR for estimating multi-GNSS real-time satellite clock offset

Real-time satellite clock offset plays a prominent role in the Global Navigation Satellite System (GNSS) community. However, the GNSS raw observations are impacted by outliers, resulting in the quality of observations becomes poorer, which will dramatically affect the performance of estimated multi-GNSS satellite clock offset in real-time. In this contribution, an improved Inter Quartile Range (IQR) method is proposed to improve the quality of multi-GNSS satellite clock offset estimation in real-time, in which the improvements include two aspects. Firstly, the empirical threshold C1 is determined to adapt multi-GNSS satellite clock offset estimation, if one residual is not between (Q1-C1∗IQR,Q3+C1∗IQR), the observation is deleted. More importantly, to guarantee the clock offset of each satellite can be estimated at each epoch, if one satellite corresponding to all observation of stations is deleted, the IQR is conducted again at the current epoch for these observations. Three schemes are designed: 50 stations are used to perform multi-GNSS satellite clock offset estimation in real-time, which are without quality control (S1), with the proposed quality control method in this contribution(S2), and with quality control method using 8.5 medians of residuals (S3). Compared to S1, the satellite clock offset accuracy of GPS, Galileo, BDS-3, and GLONASS for S2 can be significantly improved from 0.082 to 0.055 ns, 0.106 to 0.072 ns, 0.178 to 0.083 ns, and 0.146 to 0.100 ns, respectively. The improvement is 32.93%, 32.07%, 53.37%, and 31.51%, respectively. The clock offset performance of S2 is better than that of S3 in terms of stability and reliability for GPS, BDS-3, and GLONASS. Another 52 stations are applied to perform multi-GNSS kinematic real-time precise point positioning (RT-PPP). For the convergence time and positioning accuracy, the RT-PPP employing the satellite clock offset generated from S2 shows the best performance. The experiment shows that the proposed quality control method can obtain real-time, stable, high-precision, and reliable multi-GNSS real-time satellite clock offset.

Asynchronous One-Way Range Measurement Applied to Microspace Probes

This paper presents a one-way range measurement method using an asynchronous communication scheme that is derived from Global Navigation Satellite Systems (GNSS) such as that represented by the Global Positioning System (GPS). The method does not require a transponder aboard a spacecraft and functions without a phase delay measurement facility using a highly stable clock on the ground. Besides, the method enables not only the range measurement but also the clock synchronization as well. This paper presents how it works and shows how it is practically applied to small and low-cost microspace probes flying in cislunar space and near-Earth interplanetary field. Semi-real-time positioning feasibility in cislunar space is also discussed.

GNSS user requirements for reuse development process considering pandemic

Global Navigation Satellite System (GNSS) use the internal continuous reference times to evaluate a navigation solution, which includes U.S. GPS time, Russian GLONASS Time, the E.U. Galileo System Time, and Chinese Beidou time. GNSSs time are designed and configured to internally synchronize systems and evaluate navigation solution, and they are adjusted to synchronize their time into an external and stable reference clock. This paper analyzes and extracts requirements that are needed for designing components and design a component specification, which is based on the extracted components. From this study, common functions of GPS applications were constructed as a component. This method has advantages that can be assembled and reused. That is, it would develop a highly reliable method for software when common components are extracted from requirements for GNSS construction and component-based GNSS development process is achieved.

Temperature compensated ring oscillator based VCO

Frequency drift due to temperature variations is a crucial design consideration and cannot always be compensated by a phase-locked loop especially when low-gain, multiband oscillators are employed. A ring oscillator architecture with reduced frequency drift over temperature is presented in this paper. The oscillator is incorporated in a phase locked loop (PLL) to produce a stable clock within the required frequency range under process, voltage, and temperature variations. The output frequency of the oscillator is compensated through a proportional to absolute temperature (PTAT) current in order to eliminate the frequency drift. A proof-of-concept PLL has been designed and fabricated in a 180 nm CMOS technology operating with 3.3 V supply voltage and providing a 480 MHz frequency. Measurement results of the fabricated chip show a frequency variation of the VCO from −1.5 % to + 0.4 % from the center frequency across the temperature range from −40 °C to 120 °C meeting the requirements for most consumer market applications. The duty cycle distortion is less than 1% across the temperature range. The phase noise of the oscillator was measured at −107 dBc/Hz.

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.

Stability of CubeSat Clocks and Their Impacts on GNSS Radio Occultation

Global Navigation Satellite Systems’ radio occultation (GNSS-RO) provides the upper troposphere-lower stratosphere (UTLS) vertical atmospheric profiles that are complementing radiosonde and reanalysis data. Such data are employed in the numerical weather prediction (NWP) models used to forecast global weather as well as in climate change studies. Typically, GNSS-RO operates by remotely sensing the bending angles of an occulting GNSS signal measured by larger low Earth orbit (LEO) satellites. However, these satellites are faced with complexities in their design and costs. CubeSats, on the other hand, are emerging small and cheap satellites; the low prices of building them and the advancements in their components make them favorable for the GNSS-RO. In order to be compatible with GNSS-RO requirements, the clocks of the onboard receivers that are estimated through the precise orbit determination (POD) should have short-term stabilities. This is essential to correctly time tag the excess phase observations used in the derivation of the GNSS-RO UTLS atmospheric profiles. In this study, the stabilities of estimated clocks of a set of CubeSats launched for GNSS-RO in the Spire Global constellation are rigorously analysed and evaluated in comparison to the ultra-stable oscillators (USOs) onboard the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC-2) satellites. Methods for improving their clock stabilities are proposed and tested. The results (i) show improvement of the estimated clocks at the level of several microseconds, which increases their short-term stabilities, (ii) indicate that the quality of the frequency oscillator plays a dominant role in CubeSats’ clock instabilities, and (iii) show that CubeSats’ derived UTLS (i.e., tropopause) atmospheric profiles are comparable to those of COSMIC-2 products and in situ radiosonde observations, which provided external validation products. Different comparisons confirm that CubeSats, even those with unstable onboard clocks, provide high-quality RO profiles, comparable to those of COSMIC-2. The proposed remedies in POD and the advancements of the COTS components, such as chip-scale atomic clocks and better onboard processing units, also present a brighter future for real-time applications that require precise orbits and stable clocks.