Clock Error Research Articles

Improved Simulated Annealing Algorithm on the Design of Satellite Orbits for Common-View Laser Time Transfer

Laser Time Transfer (LTT) has proven to be able to improve remote time transfer accuracy compared to microwave technology. The impact of satellite clock errors and atmospheric delays during LTT will be further reduced in the common-view mode. The challenge is presented as an optimization problem that is limited by satellite trajectories. This paper introduces an improved simulated annealing algorithm designed to maximize the common-view possibility among various station pairs within regional Satellite Laser Ranging (SLR) networks by optimizing satellite orbit trajectories. The study proposes a system model that integrates LTT principles with satellite visibility considerations. The simulated annealing algorithm is improved with new annealing strategies that incorporate control strategies, and modify the cooling function. Comparative simulation analyses demonstrate the effectiveness of the algorithm, resulting in a significant reduction in computation time by over 10 times. The optimized orbits exhibit common-view windows between 3.337 and 8.955 times longer than existing orbits. Further simulations are conducted to optimize the orbits, and common-view models are established for 45 pairs among 10 stations. The optimizations result in common-view times ranging from 6.183 to 60.633 min in the Asia-Pacific region and from 5.583 to 61.75 min in the Europe-to-Asia region. This can provide valuable references for designing satellite constellations.

Ocean Bottom Seismometer Clock Correction using Ambient Seismic Noise

Ocean-bottom seismometers (OBSs) are equipped with seismic sensors that record acoustic and seismic events at the seafloor, which makes them suitable for investigating tectonic structures capable of generating earthquakes offshore. One critical parameter to obtain accurate earthquake locations is the absolute time of the incoming seismic signals recorded by the OBSs. It is, however, not possible to synchronize the internal clocks of the OBSs with a known reference time, given that GNSS signals are unable to reach the instrument at the sea bottom. To address this issue, here we introduce a new method to synchronize the clocks of large-scale OBS deployments. Our approach relies on the theoretical time-symmetry of time-lapse (averaged) crosscorrelations of ambient seismic noise. Deviations from symmetry are attributed to clock errors. This implies that the recovered clock errors will be obscured by lapse crosscorrelations' deviations from symmetry that are not due to clock errors. Non-uniform surface wave illumination patterns are arguably the most notable source which breaks the time symmetry. Using field data, we demonstrate that the adverse effects of non-uniform illumination patterns on the recovered clock errors can be mitigated by means of a weighted least-squares inversion that is based on station-station distances. In addition, our methodology permits the recovery of timing errors at the time of deployment of the OBSs. This error can be attributed to either: i) a wrong initial time synchronization of the OBS or ii) a timing error induced by changing temperature and pressure conditions while the OBS is sunk to the ocean floor. The methodology is implemented in an open-source Python package named OCloC, and we applied it to the OBS recordings acquired in the context of the IMAGE project in and around Reykjanes, Iceland. As expected, most OBSs suffered from clock drift. Surprisingly, we found incurred timing errors at the time of deployment for most of the OBSs.

Satellite Navigation Message Authentication in GNSS: Research on Message Scheduler for SBAS L1.

SBAS is mainly used in civil aviation and navigation, and will be applied to autonomous driving in the future. Given the open signal format of the Satellite Based Augmentation System (SBAS), which exposes security threats such as spoofing attacks, the utilization of SBAS navigation message authentication technology can improve the SBAS anti-spoofing ability from the system side. SBAS message authentication technology has become the future direction of SBAS system development. However, during the initial design of SBAS on L1, message authentication technology was not considered, and the addition of authentication messages will lead to further strain on existing message bandwidth resources. Therefore, in response to the issue of insufficient bandwidth resources after adding authentication messages to SBAS L1, a study on message scheduler for SBAS L1 authentication was conducted. A fixed time sequence dynamic message scheduler for incorporating authentication messages was proposed. This scheduler reduces the frequency of broadcasting clock error parameters to mitigate the impact of adding authentication messages. Furthermore, an optimized fixed time sequence dynamic message scheduler based on SBAS clock error messages was introduced. The results show that the message scheduler can not only improve the flexibility of SBAS message broadcasting, but also shorten the update interval of various types of messages under the premise of meeting the maximum update interval requirement. With minimal impact on the maximum message update interval, it improves the integrity, authenticity, and availability of messages. This approach can increase the effective message ratio in SBAS to over 91%, and the optimal solution reduces the initial user positioning time to 26 s.

Characterizing the fault performance of real-time precise satellite orbit and clock correction products

The a priori fault probability of the real-time precise satellite orbit and clock correction products is the critical parameter for integrity monitoring of precise point positioning (PPP). The traditional fault probability evaluation methods use the worst-case instantaneous user ranging error (IURE) as the conservative test statistic. However, the systematic biases of IURE contained in the worst-case IURE barely affect the PPP accuracy, which will undermine the statistical distribution of test statistic and reduce the sensitivity of fault detection. The fault probability will be estimated over-conservatively for the traditional methods. By clarifying the sources of the systematic biases, a new test statistic is constructed by deliberately removing the systematic biases of IURE originated from satellite orbit and clock errors. One-year Global Positioning System correction products evaluation results have demonstrated that the constructed test statistic follows the Gaussian distribution with the decreased uncertainty and the improved fault detection sensitivity. The real-world data experiments have shown that the a priori probabilities of the satellite fault and the constellation fault are at the order of 10−4 and 10−5 levels, respectively.

The convergence mechanism of Low Earth Orbit enhanced GNSS (LeGNSS) Precise Point Positioning (PPP)

ABSTRACT The recruitment of the Low Earth Orbit (LEO) constellation is recognized as an effective way to augment Global Navigation Satellite System (GNSS) Precise Point Positioning (PPP) in the near future. Its potential to accelerate PPP convergence has been proved with simulated data. However, the mechanism of how the geometric change of LEO accelerates the convergence of GNSS PPP has not been studied from a theoretical perspective, which hampers the understanding and exploitation of the enhancement of LEO. In this article, the convergence mechanism of LEO enhanced GNSS PPP is investigated in terms of theoretical analysis and simulated verification. To show the characteristics of the ambiguities during convergence, eigenvalue decomposition is used to divide the ambiguities into orthogonal components, named geometric-related component, clock-error-related component, and independent component. The results show that the precision of geometric-related components of ambiguities, which correlates with position parameters, is low at a single epoch, while the precision can be greatly improved with the fast geometric change of LEO. On the other hand, the precision of clock-error-related components of ambiguities, which correlates with clock errors, cannot be improved by fast geometric change of LEO constellation due to its irrelevance to geometry, which causes the precision of each ambiguity to be low. Further investigations show that single-differenced ambiguities could overcome this drawback and are beneficial to ambiguity resolution.

Galileo high accuracy service performance and anomaly mitigation capabilities

Precise point positioning (PPP) and real-time kinematic techniques are interesting in several sectors, especially for autonomous applications. These users have high accuracy needs coupled with stringent requirements on continuity, availability, integrity, and convergence time, whose satisfaction can be challenging in harsh environments. Galileo launched on January 2023 the initial high accuracy service (HAS), a European free-of-charge PPP service with a worldwide coverage transmitted on E6 signals and provided through an internet connection. This paper characterizes the Galileo HAS product performance, including orbital errors, clock errors, code biases, and overall signal in space error (SISE), with live signals transmitted since HAS service declaration. The paper also presents the behavior of HAS SIS in the case of four satellite anomalies between September 2021 and August 2022, occurring for Galileo and GPS. Finally, the paper presents the results of HAS performance in both static open sky and road scenarios, showing a few-decimeter accuracy even in environments with degraded visibility. The paper shows the improvements in terms of robustness to satellite anomaly thanks to the Galileo HAS characteristics.

The Implementation of Precise Point Positioning (PPP): A Comprehensive Review.

High-precision positioning from Global Navigation Satellite Systems (GNSS) has garnered increased interest due to growing demand in various applications, like autonomous car navigation and precision agriculture. Precise Point Positioning (PPP) offers a distinct advantage over differential techniques by enabling precise position determination of a GNSS rover receiver through the use of external corrections sourced from either the Internet or dedicated correction satellites. However, PPP's implementation has been challenging due to the need to mitigate numerous GNSS error sources, many of which are eliminated in differential techniques such as Real-Time Kinematics (RTK) or overlooked in Standard Point Positioning (SPP). This paper extensively reviews PPP's error sources, such as ionospheric delays, tropospheric delays, satellite orbit and clock errors, phase and code biases, and site displacement effects. Additionally, this article examines various PPP models and correction sources that can be employed to address these errors. A detailed discussion is provided on implementing the standard dual-frequency (DF)-PPP to achieve centimeter- or millimeter-level positioning accuracy. This paper includes experimental examples of PPP implementation results using static data from the International GNSS Service (IGS) station network and a kinematic road test based on the actual trajectory to showcase DF-PPP development for practical applications. By providing a fusion of theoretical insights with practical demonstrations, this comprehensive review offers readers a pragmatic perspective on the evolving field of Precise Point Positioning.

Estimating GNSS satellite clock error to provide a new final product and real-time services

Estimating GNSS satellite clock error to provide a new final product and real-time services

A - 33 Clock Drawing Performance Differences in World Trade Center Responders at Midlife.

World Trade Center (WTC) responders demonstrate elevated risk for cognitive impairment (CI) consistent with Alzheimer's Disease and Related Dementias (ADRD). Neuropsychological test performance is valuable in early detection efforts and non-invasive longitudinal tracking of populations at risk of ADRD. We hypothesized that WTC-CI would be associated with a greater number of errors on the clock drawing task (CDT). The CDT was administered to responders with/without CI who participated in a case/control study. WTC-CI was diagnosed following NIA-AA guidelines for diagnosing early-onset ADRD (ages <66years). CDT performance was evaluated using subsets of clock errors derived from four existing variations in CDT evaluation measuring the number of errors. An ANOVA was conducted to compare mean differences in clock characteristics. From 99 participants, responders with CI (n = 50, Mage = 55.82) had more errors when compared to responders without CI (n = 49, Mage = 55.94) in the following CDT components: contour (p = 0.006), hands (p < 0.001), hands similarity (p = 0.005), moderate graphical errors (p = 0.042), left-side number crowding (p = 0.038), time incorrectness (p < 0.001), and extra marks on clock face (p = 0.006). In this study, we demonstrated that CDT performance decline is associated with WTC-CI. CDT can be used as a non-invasive investigative tool that can track cognitive performance longitudinally, which can better aid in the early detection, monitoring, and intervention strategies when dealing with the emergence of encephalopathy in high-risk ADRD populations, such as the WTC cohort. Future research should evaluate additional measures that can address other comorbid issues that can arise in such populations, such as post-traumatic stress disorder (PTSD).

Transformer Graph Convolutional Network for Relative Travel-Time Shift Prediction

Abstract Predicting surface-wave travel-time shifts is valuable for analyzing potential effects caused by changes in medium properties, station clock errors, instrument response errors, and other factors. Many current neural networks used in seismology are single-station models trained using single-station (pair) data. However, most seismic methods require knowledge of the spatial positions between multiple stations. Multiple stations contain rich interrelationships and spatial information that cannot be exploited by single-station models. We proposed a multistation neural network structure Transformer Graph Convolutional Network (TGCN) that utilizes temporal attention and spatial attention to capture spatiotemporal information for predicting relative travel-time shifts. Before that, we introduced a method that treats station pairs as nodes and constructs a graph with multiple station pairs. We collected original ambient noise waveforms from 2017 to 2019 in the Alaska region and 2010 to 2014 in the southern California region to obtain relative travel-time shift sequences of station pairs for model training and testing. To showcase the improvement of spatial information to the model, we compared TGCN with two other baseline single-station models—temporal convolutional network and long short-term memory. Our proposed method predicted travel-time values more accurately than the two baseline models, and it also exhibited slower decay in performance when predicting over larger intervals. We also found that the number of station pairs has an impact on the model. When there are a sufficient number of station pairs, the model can effectively utilize the rich spatial information and achieve higher accuracy. Our approach, which incorporates spatiotemporal information, provides outputs that are more efficient and accurate compared with the traditional single-station (pair) method that only considers temporal information, suggesting that spatial information does enhance the performance of the model.

GNSS performance enhancement using measurement estimation in harsh environment.

Global navigation satellite systems (GNSSs) are commonly used to measure the position and time globally. A GNSS is convenient owing to its ability to measure accurate position relatively without using assistive tools for navigation by comparing with other sensors. Based on these benefits, the applicable area is expanding to commercial and social uses (e.g., vehicle navigation, smart grids, and smartphone apps). In the future, various services and technologies (e.g., the use of autonomous vehicles, unmanned delivery, and industrial field robots), which make Internet of Things (IOT) more active, will be used in our society. Conversely, the performance of GNSS can degrade in harsh environments, such as urban areas, owing to the property of GNSS, which calculates position and time via satellite signal reception. However, buildings in a city can block navigation satellite signals and generate multi-path errors. The blocked signals exacerbate the dilution of precision (DOP), which indicates the accuracy of the navigation solution and increases the navigation solution error. This study proposes methods to improve navigation performance by leveraging various techniques (e.g., range differences, receiver clock error hold, and virtual satellites). The methods were validated in harsh environments where visible satellites were reduced. In the simulation, each proposed method improved the navigation performance by creating an environment similar to a normal situation, despite the receiver entering a harsh environment. The results confirmed that the navigation performance deteriorated compared to the normal situation where the number of visible satellites decreased. However, the navigation performance was recovered gradually by applying the proposed techniques. Using the proposed methods, navigation performance can be maintained continuously even in situations where satellite signals are blocked.

A feasibility study of 5G positioning with current cellular network deployment

This research examines the feasibility of using synchronization signals broadcasted by currently deployed fifth generation (5G) cellular networks to determine the position of a static receiver. The main focus lies on the analysis of synchronization among the base stations of a real 5G network in Milan, Italy, as this has a major impact on the accuracy of localization based on time of arrival measurements. Understanding such properties, indeed, is fundamental to characterize the clock drifts and implement compensation strategies as well as to identify the direct communication beam. The paper shows how the clock errors, i.e., inaccurate synchronization, among 5G base stations exhibit a significant bias, which is detrimental for precise cellular positioning. By compensating the synchronization errors of devices’ clocks, we demonstrate that it is in principle possible to localize a static user with an accuracy of approximately 8–10 m in non-obstructed visibility conditions, for urban and rural scenarios, using the deployed 5G network operating at 3.68 GHz and relying on broadcast signals as defined by 5G Release 15 standard. This work has been funded by the European Space Agency (ESA) Navigation Innovation and Support Program (NAVISP) Element 2 pillar which aims at improving the competitiveness of the industry of the participating States in the global Positioning, Navigation and Timing (PNT) market.

Precise GNSS Time Synchronization With Experimental Validation in Vehicular Networks

Time synchronization utilizing the Global Navigation Satellite System (GNSS) is being increasingly investigated for vehicular networks. Due to GNSS signal blockages, the availability and accuracy of GNSS timing solutions in various road settings is a recognized challenge. With the recent improvement of Multi-GNSS technology and the increased capacity of consumer-grade receivers, the application of GNSS in vehicular environments has brightened up. This paper systematically analyzes the required time synchronization of vehicular networks and presents a GNSS-based time synchronization solution. It also experimentally demonstrates the availability and capabilities of GNSS time synchronization using commercial-grade GNSS receivers and off-the-shelf communication devices. Our experiments show that the timing accuracy of an individual vehicular node can be as good as ±2 microseconds, resulting in synchronization accuracy of sub-10 microseconds among nodes. A momentary complete outage of the GNSS time solution due to signal blockage on the road adds clock error, leading to synchronization inaccuracy of up to sub-20 microseconds. This level of inaccuracy still meets the desired requirement for most applications in vehicular communication.

Novel Approach to Autonomous Lunar Localization and Timing

The ability of a deep space spacecraft to estimate its position, velocity, and clock errors without external clock error estimation is investigated. A novel approach to onboard estimation of clock errors is proposed. The effects of clock bias and drift on spacecraft position and velocity errors are derived. These derived equations are leveraged to design a Kalman filter that processes optical measurements along with one-way ranging or two-way position updates from the ground. Simulations are performed to numerically validate the proposed approach and show good localization and timing estimation performance even with lengthy tracking data gaps.

Misinterpreted Seismic Evidence for Localized Rapid Changes of the Inner Core Boundary Surface

AbstractThe nature of the inner core (IC) temporal changes is of great importance in understanding the deep earth dynamics. The comment by Tian and Wen (2023, https://doi.org/10.1029/2023gl103173) on our previous paper (Yang &amp; Song, 2022, https://doi.org/10.1029/2022gl098393) provided a new observation as evidence against the IC rotation and proposed that our observations are instead from localized rapid changes at the IC surface. Here we argue the opposite to its conclusions. The comment misinterpreted our logic and many of our observations and arguments. Its one new waveform does not contradict with the “rotation” model. The original evidence for the “surface” model is demonstrated to be an artifact from station clock errors and instrument changes. Additionally, the surface model lacks a solid physical and quantitative basis to explain existing seismic evidence. We conclude that the rotation model is currently the best interpretation and the surface model is not a viable alternative.

Analysis of the baud rate of the UART to affects the data

This article explores the impact of different baud rates on Universal Asynchronous Receiver/Transmitter (UART) asynchronous serial communication. It discusses the frame format and calculation method of baud rate error, as well as the main reasons for error, such as clock error, sampling error, line noise, data bit error, and software delay. To ensure reliable communication, it is essential to test and debug the actual baud rate and adjust it accordingly. The study found that higher expected baud rates resulted in higher baud rate errors, affecting transmission distance, speed, reliability, and system complexity. The appropriate baud rate should be selected based on specific application scenarios and requirements. Higher baud rates are needed for high-speed transmissions, while lower baud rates are required for long transmission distances or high reliability requirements. However, further research is needed to determine the impact of unallocated baud rates on data. Overall, this article provides valuable insights into the development of UART.

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.

Integrated positioning with double-differenced 5G and undifferenced/double-differenced GPS

As the demand for hybrid indoor and outdoor positioning has increased, the research trend in positioning technology has shifted to hybrid positioning technology suitable for complex indoor and outdoor environments. High-precision positioning technology combined with Global Navigation Satellite Systems (GNSS) and fifth-generation mobile communication technology (5G) has many applications in many industries. A double-differenced algorithm applicable to 5G was proposed to solve the impact of the 5G clock synchronization error on the positioning. Double-differenced observations were obtained by introducing reference terminals to eliminate the influence of clock errors on positioning accuracy between terminals and base stations and between base stations and base stations. Then, the dynamic positioning performance of different combined positioning models under different occluded environments was investigated by combining 5G double-differenced observations with undifferenced/double-differenced GPS observations and comparing the positioning results with GPS-only. The results showed that the combined positioning model can achieve more accurate positioning results than a single system in different positioning modes, and the advantages were more evident in the occluded environment. This study provides a reference for hybrid positioning techniques in complex indoor and outdoor environments and promotes further development of seamless indoor and outdoor positioning.

Modal analysis under jittering and kernel clock distribution: single-output identification

Smartphones have attracted attention in the structural health monitoring community due to their embedded multisensory platforms suitable for crowdsourcing innovation. Despite their advantages, smartphone sensors are originally designed for user utility rather than technical engineering applications (e.g. vibration analysis and modal identification). Sampling jitter is among those problems adversely influencing smartphone performance as a scientific device that can be used for characterising civil infrastructure dynamic characteristics. With inconsistencies in the sampling period due to jitter effects, the identified modal frequencies of a structure can deviate from the actual value, which is artificially introduced by smartphone clock errors. In this study, the authors formulate the statistical characteristics of the smartphone sampling period through kernel distribution and apply a digital reconstruction remedy to the sampling jitter problem. Through introductory simulations of a sine wave and physical implementations through shaking table tests equipped with smartphones, the efficiency of kernel distribution diagnosis and the signal-reconstruction remedy is presented. Following the simulation and laboratory applications, the proposed techniques are applied to vibration monitoring of a steel pedestrian bridge in terms of the auto power spectral density and short-time Fourier transform of single-output signals. The results show successful rehabilitation of accelerometer data from smartphones, removing jitter-induced errors to a significant extent and accordingly improving the identification accuracy currently in a single-output setting.

Effect of synchronization system errors on the reception noise immunity of amplitude-phase shift keyed signals

Objectives. An urgent task in the context of modern radio and television systems is to improve the quality and quantity of transmitted information. For example, the use of multiple amplitude-phase shift keyed (APSK) signals—16-APSK and 32-APSK—in digital satellite television systems of the Digital Video Broadcasting-Satellite2 (DVB-S2) standard made it possible to transmit 30% more data in the same frequency bands in comparison with the previous DVB-S standard. Such increases in information transmission rates impose more stringent requirements on hardware. An important role in the reception of APSK signals, as well as the signals of other coherent signal processing systems, is played by the stability of synchronization systems. The presence of operational errors can significantly reduce the quality of information reception. The aim of the present work was to analyze the effect of phase and clock synchronization errors on the reception noise immunity of APSK signals with a ring signal constellation structure.Methods. The study used statistical radio engineering methods informed by optimal signal reception theory.Results. The effect of phase and clock synchronization errors on the reception noise immunity of APSK signals having a signal constellation ring structure is analyzed. The dependencies of the bit error probability on the magnitude of the phase shift and the clock offset were characterized. The effect of synchronization errors on reception quality were compared with the known results for quadrature amplitude modulation (QAM) signals.Conclusions. At an acceptable energy loss of no more than 1 dB, the critical phase error can be considered as 2°-3°, while the critical clock error is 3-4%. A coherent receiver of APSK signals is more sensitive to the phase error of reference oscillations than a similar receiver of QAM signals, whereas clock errors have the same effect on the reception quality of these signals.