Clock Parameters Research Articles

Rapid fault detection and recovery of in-orbit navigation satellite

Its an effective means to ensure maximum availability of satellite navigation systems by rapid fault detecting, recovering and satellite rejoining. In this paper, methods of in-orbit satellite failures rapid detection, fast clock error determination and orbit determination after fault recovery were studied. Then, rapid satellite fault recovery mechanism and processes were established, so as to ensure the constellation reforming capability with enough satellites in a short time, while service capability of navigation users was recovered. The test results indicate that satellite fault detecting time decreases to a level of 5 min compared with a level of 30 min before. Moreover, satellites clock parameters were quickly calculated and injection messages were generated as soon as possible. All methods above effectively decreased the satellite unavailable time, and reduced the waste of satellites resources and life caused by satellite failures.

Aging studies on micro-fabricated alkali buffer-gas cells for miniature atomic clocks

We report an aging study on micro-fabricated alkali vapor cells using neon as a buffer gas. An experimental atomic clock setup is used to measure the cell's intrinsic frequency, by recording the clock frequency shift at different light intensities and extrapolating to zero intensity. We find a drift of the cell's intrinsic frequency of (−5.2 ± 0.6) × 10−11/day and quantify deterministic variations in sources of clock frequency shifts due to the major physical effects to identify the most probable cause of the drift. The measured drift is one order of magnitude stronger than the total frequency variations expected from clock parameter variations and corresponds to a slow reduction of buffer gas pressure inside the cell, which is compatible with the hypothesis of loss of Ne gas from the cell due to its permeation through the cell windows. A negative drift on the intrinsic cell frequency is reproducible for another cell of the same type. Based on the Ne permeation model and the measured cell frequency drift, we determine the permeation constant of Ne through borosilicate glass as (5.7 ± 0.7) × 10−22 m2 s−1 Pa−1 at 81 °C. We propose this method based on frequency metrology in an alkali vapor cell atomic clock setup based on coherent population trapping for measuring permeation constants of inert gases.

A cycle slip fixing method with GPS + GLONASS observations in real-time kinematic PPP

A key limitation of precise point positioning (PPP) is the long convergence time, which requires about 30 min under normal conditions. Frequent cycle slips or data gaps in real-time operation force repeated re-convergence. Repairing cycle slips with GPS data alone in severely blocked environments is difficult. Adding GLONASS data can supply redundant observations, but adds the difficulty of having to deal with differing wavelengths. We propose a single-difference between epoch (SDBE) method to integrate GPS and GLONASS for cycle slip fixing. The inter-system bias can be eliminated by SDBE, thus only one receiver clock parameter is needed for both systems. The inter-frequency bias of GLONASS satellites also cancels in the SDBE, so cycle slips are preserved as integers, and the LAMBDA method is adopted to search for cycle slips. Data from 7 days of 20 globally distributed IGS sites were selected to test the proposed cycle slip fixing procedure with artificial blocking of the signal; cycle slips were introduced for all un-blocked satellites at each epoch. For a 30-s sampling interval, the average success rate of fixing can be improved from 73 to 98 % by adding GLONASS. Even for a 180-s sampling interval, GPS + GLONASS can achieve a success rate of 81 %. A real-time kinematic PPP experiment was also performed, and the results show that using GPS + GLONASS can achieve continuous high-accuracy real-time PPP without re-convergence.

Joint Ranging and Clock Parameter Estimation by Wireless Round Trip Time Measurements

In this paper we develop a new technique for estimating fine clock errors and range between two nodes simultaneously by two-way time-of-arrival measurements us- ing impulse-radio ultra-wideband signals. Estimators for clock parameters and the range are proposed that are robust with respect to outliers. They are analyzed numerically and by means of experimental measurement campaigns. The technique and derived estimators achieve accuracies below 1Hz for frequency estimation, below 1 ns for phase estimation and 20 cm for range estimation, at 4m distance using 100MHz clocks at both nodes. Therefore, we show that the proposed joint approach is practical and can simultaneously provide clock synchronization and positioning in an experimental system.

Multiple Ambiguity Datum Precise Point Positioning Technique Using Multi-Constellation GNSS: GPS, GLONASS, Galileo and BeiDou

Precise Point Positioning (PPP) is traditionally based on dual-frequency observations of GPS or GPS/GLONASS satellite navigation systems. Recently, new GNSS constellations, such as the European Galileo and the Chinese BeiDou are developing rapidly. With the new IGS project known as IGS MGEX which produces highly accurate GNSS orbital and clock products, multi-constellations PPP becomes feasible. On the other hand, the un-differenced ionosphere-free is commonly used as standard precise point positioning technique. However, the existence of receiver and satellite biases, which are absorbed by the ambiguities, significantly affected the convergence time. Between-satellite-single-difference (BSSD) ionosphere free PPP technique is traditionally used to cancel out the receiver related biases from both code and phase measurements. This paper introduces multiple ambiguity datum (MAD) PPP technique which can be applied to separate the code and phase measurements removing the receiver and satellite code biases affecting the GNSS receiver phase clock and ambiguities parameters. The mathematical model for the three GNSS PPP techniques is developed by considering the current full GNSS constellations. In addition, the current limitations of the GNSS PPP techniques are discussed. Static post-processing results for a number of IGS MGEX GNSS stations are presented to investigate the contribution of the newly GNSS system observations and the newly developed GNSS PPP techniques and its limitations. The results indicate that the additional Galileo and BeiDou observations have a marginal effect on the positioning accuracy and convergence time compared with the existence combined GPS/GLONASS PPP. However, reference to GPS PPP, the contribution of BeiDou observations can be considered geographically dependent. In addition, the results show that the BSSD PPP models slightly enhance the convergence time compared with other PPP techniques. However, both the standard un-differenced and the developed multiple ambiguity datum techniques present comparable positioning accuracy and convergence time due to the lack of code and phase-based satellite clock products and the mathematical correlation between the positioning and ambiguity parameters.

Satellite Orbit Determination Using Short Arcs of GPS Data

This work is concerned with short arcs orbit determination using GPS signals. A special case of truncated arcs assuming that GPS data is only available when the satellite carrying the GPS receiver passes over a ground tracking station is presented. The behaviour of an Extended Kalman filter (EKF) in real time satellite orbit determination using short arcs of data is analysed. The algorithm is a simplified and compact model with low computational cost, and uses the EKF to estimate the state vector, composed of position and velocity components, and GPS receiver clock parameters. The algorithm may use different step-sizes between the GPS signal measurements. Its force model in the motion equations considered the perturbations as being due to the geopotential up to the 10thorder and degree of the spherical harmonics. The algorithm has been formerly qualified using raw single frequency pseudorange GPS measurements of the Topex/Poseidon (T/P) satellite, and used as reference in this work. However, the GPS data are truncated as if they had been collected by a single ground tracking station. In other words, the data are obtained only when the satellite T/P is within the viewing area of the station. The research results are presented showing the degradation of performance when compared to a full arc orbit determination.

A simplified and unified model of multi-GNSS precise point positioning

Additional observations from other GNSS s can augment GPS precise point positioning (PPP) for improved positioning accuracy, reliability and availability. Traditional multi-GNSS PPP model requires the estimation of inter-system bias (ISB) parameter. Based on the scaled sensitivity matrix (SSM) method, a quantitative approach for assessing parameter assimilation, we theoretically prove that the ISB parameter is not correlated with coordinate parameters and it can be assimilated into clock and ambiguity parameters. Thus, removing ISB from multi-GNSS PPP model does not affect coordinate estimation. Based on this analysis, we develop a simplified and unified model for multi-GNSS PPP, where ISB parameter does not need to be estimated and observations from different GNSS systems are treated in a unified way. To verify the new model, we implement the algorithm to the self-developed software to process 1year GPS/GLONASS data of 53 IGS (International GNSS Service) worldwide stations and 1month GPS/BDS data of 15 IGS MGEX (Multi-GNSS Experiment) stations. Two types of GPS/GLONASS and GPS/BDS combined PPP solution are performed, one is based on traditional model and the other implements the new model. RMSs of coordinate differences between the two type of solutions are few μm for daily static PPP and less than 0.02mm for GPS/GLONASS kinematic PPP in the North, East and Up components, respectively. Considering the millimeter-level precision of current GNSS PPP solutions, these statistics demonstrate equivalent performance of the two solution types.

Wavelength-Division Multiplexed Fiber-Connected Sensor Network for SLource Localization

A fiber-connected source localization sensor network based on optical wavelength-division multiplexing technology is proposed and demonstrated. Thanks to the wavelength-division multiplexed architecture, the signals from the emitter received by different sensors can be identified by different optical carriers, and no clock synchronization or parameter estimation is required at the sensor nodes, which greatly simplifies the entire system. Also, since the received signals are separated in the wavelength domain, the proposed system is suitable for both pulsed and nonpulsed signal source localization, independent of the format of the emitted signal. A proof-of-concept experiment for two-dimensional localization of a wireless fidelity signal is demonstrated. Spatial resolution of less than 17 cm is achieved.

Algebraic Solution for Joint Localization and Synchronization of Multiple Sensor Nodes in the Presence of Beacon Uncertainties

This paper addresses the problem of joint localization and synchronization of multiple sensor nodes simultaneously using the time stamp information from message exchanges between the sensor nodes and beacons and among the sensor nodes. Through parameter transformation and multi-stage processing, two computationally efficient algebraic solutions are developed for this challenging non-linear estimation problem. One is without message exchanges among the sensor nodes and the other is with the exchanges. Theoretical analysis shows that the performance of the proposed solutions is able to reach the CRLB accuracy for the sensor node positions, as well as the clock parameters over the mild error region. Simulation results support very well the theoretical performance of the proposed solutions.

Enhancing the kinematic precise orbit determination of low earth orbiters using GPS receiver clock modelling

Clock error estimation has been the focus of a great deal of research because of the extensive usage of clocks in GPS positioning applications. The receiver clock error in the spacecraft orbit determination is commonly estimated on an epoch-by-epoch basis, along with the spacecraft’s position. However, due to the high correlation between the spacecraft orbit altitude and the receiver clock parameters, estimates of the radial component are degraded in the kinematic approach. Using clocks with high stability, the predictable behaviour of the receiver oscillator can be exploited to improve the positioning accuracy, especially for the radial component. This paper introduces two GPS receiver clock models to describe the deterministic and stochastic property of the receiver clock, both of which can improve the accuracy of kinematic orbit determination for spacecraft in low earth orbit. In particular, the clock parameters are estimated as time offset and frequency offset in the two-state model. The frequency drift is also estimated as an unknown parameter in the three-state model. Additionally, residual non-deterministic random errors such as frequency white noise, frequency random walk noise and frequency random run noise are modelled. Test results indicate that the positioning accuracy could be improved significantly using one day of GRACE flight data. In particular, the error of the radial component was reduced by over 40.0% in the real-time scenario.

Galileo orbit and clock quality of the IGS Multi-GNSS Experiment

The Multi-GNSS Experiment (MGEX) of the International GNSS Service (IGS) aims at the data collection and analysis of all available satellite navigation systems. In particular the new global and regional satellite navigation systems are of interest, i.e., the European Galileo, the Chinese BeiDou, the Japanese QZSS as well as satellite based augmentation systems. This article analyzes the orbit and clock quality of the Galileo products of four MGEX analysis centers for a common time period of 20weeks. Orbit comparisons of the individual analysis centers have a consistency at the 5–30cm level. Day boundary discontinuities range from 4 to 28cm whereas 2-day orbit fit RMS values vary between 1 and 7cm. The accuracy evaluated by satellite laser ranging residuals is on the one decimeter level with a systematic bias of about −5cm for all analysis centers. In addition, systematic errors on the decimeter level related to solar radiation pressure mismodeling are present in all orbit products. Due to the correlation of radial orbit errors with the clock parameters, these errors are also visible as a bump in the Allan deviation of the Galileo satellite clocks at the orbital frequency.

Galileo orbit determination using combined GNSS and SLR observations

The first two Galileo In-Orbit Validation satellites were launched in October 2011 and started continuous signal transmission on all frequencies in early 2012. Both satellites are equipped with two different types of clocks, namely rubidium clocks and hydrogen masers. Based on two test periods, the quality of the Galileo orbit determination based on Global Navigation Satellite System (GNSS) and Satellite Laser Ranging (SLR) observations is assessed. The estimated satellite clock parameters are used as quality indicator for the orbits: A bump at orbital periods in the Allan deviation indicates systematic errors in the GNSS-only orbit determination. These errors almost vanish if SLR observations are considered in addition. As the internal consistency is degraded by the combination, the offset of the SLR reflector is shifted by +5 cm, resulting in an improved orbit consistency as well as accuracy. Another approach to reduce the systematic errors of the GNSS-only orbit determination employs constraints for the clock estimates with respect to a linear model. In general, one decimeter orbit accuracy could be achieved.

Distributed Clock Parameters Tracking in Wireless Sensor Network

Clock parameters (skew and offset) in sensor network are inherently time-varying due to imperfect oscillator circuits. This paper develops a distributed Kalman filter for clock parameters tracking. The proposed algorithm only requires each node to exchange limited information with its direct neighbors, thus is energy efficient, scalable with network size, and is robust to changes in network connectivity. A low-complexity distributed algorithm based on Coordinate-Descent with Bootstrap (CD-BS) is also proposed to provide rapid initialization to the tracking algorithm. Simulation results show that the performance of the proposed distributed tracking algorithm maintains long-term clock parameters accuracy close to the Bayesian Cramer-Rao Lower Bound.

Time Comparison Experiments Between the Qzs-1 and its Time Management Station

The National Institute of Information and Communications Technology (NICT) developed the time management system of the first Quasi-Zenith Satellite (QZS-1) in order to monitor the onboard clock as a part of the satellite navigation system. While an onboard clock is usually estimated together with the orbit of the satellite, the system described here enables the direct measurement of an onboard clock by comparing it with a ground clock by making use of a two-way time and frequency transfer which removes most of the propagation errors. Our system achieves a measurement precision of about 25 picoseconds which is an order of magnitude better than the precision of the clock parameters obtained from the combined orbit and clock estimation. Copyright © 2013 Institute of Navigation

Joint Node Localization and Time-Varying Clock Synchronization in Wireless Sensor Networks

The problems of node localization and clock synchronization in wireless sensor networks are naturally tied from a statistical signal processing perspective. In this work, we consider the joint estimation of an unknown node's location and clock parameters by incorporating the effect of imperfections in node oscillators, which render a time varying nature to the clock parameters. The data exchange mechanism is based on a two-way message exchange with anchor nodes. In order to alleviate the computational complexity associated with the optimal maximum a-posteriori estimator, two iterative approaches are proposed as simpler alternatives. The first approach utilizes an Expectation-Maximization (EM) based algorithm which iteratively estimates the clock parameters and the location of the unknown node. The EM algorithm is further simplified by a non-linear processing of the data to obtain a closed form solution of the location estimation problem using least squares (LS). The performance of the estimation algorithms is benchmarked by deriving the Hybrid Cramer-Rao lower bound (HCRB) on the mean square error (MSE) of the estimators. The theoretical findings are corroborated by simulation studies which reveal that the LS estimator closely matches the performance of the EM algorithm for small time of arrival measurement noise, and is well suited for implementation in low cost sensor networks.

A new seismogeodetic approach applied to GPS and accelerometer observations of the 2012 Brawley seismic swarm: Implications for earthquake early warning

The 26 August 2012 Brawley seismic swarm of hundreds of events ranging from M1.4 to M5.5 in the Salton Trough, California provides a unique data set to investigate a new seismogeodetic approach that combines Global Positioning System (GPS) and accelerometer observations to estimate displacement and velocity waveforms. First in simulated real‐time mode, we analyzed 1–5 Hz GPS data collected by 17 stations fully encircling the swarm zone at near‐source distances up to about 40 km using precise point positioning with ambiguity resolution (PPP‐AR). We used a reference network of North American GPS stations well outside the region of deformation to estimate fractional‐cycle biases and satellite clock parameters, which were then combined with ultrarapid orbits from the International GNSS Service to estimate positions during the Brawley seismic swarm. Next, we estimated seismogeodetic displacements and velocities from GPS phase and pseudorange observations and 100–200 Hz accelerations collected at three pairs of GPS and seismic stations in close proximity using a new tightly coupled Kalman filter approach as an extension of the PPP‐AR process. We can clearly discern body waves in the velocity waveforms, including P‐wave arrivals not detectable with the GPS‐only approach for earthquake magnitudes as low as Mw 4.6 and significant static offsets for magnitudes as low as Mw 5.4. Our study shows that GPS networks upgraded with strong motion accelerometers can provide new information for improved understanding of the earthquake rupture process and be of critical value in creating a robust early warning system for any earthquake of societal significance.

Performance of the Precision Time Protocol for clock synchronisation in smart grid applications

ABSTRACTAccurate time stamping is essential for reliable operation of the automation and control systems used across a smart grid. This paper investigates the performance of the Precision Time Protocol (PTP) for time distribution over the telecommunication networks interconnecting such systems. Distributed clocks are arranged in a PTP master‐slave hierarchy and can be synchronised to an international time standard with sub‐microsecond accuracy. Using Hydro Québec's telecommunications facilities, we investigate the synchronisation error that is observed using some of the latest PTP clock prototypes over a widely spread network. As such, field trials are performed by deploying PTP master and slave clocks in distant sites of Hydro Québec's wide area network (WAN). A thorough analysis of these trial outcomes is further conducted using laboratory experiments that point out the impact of different parameters such as the PTP messages rate, as well as the link bandwidth and asymmetry. Our analysis leads to important criteria for optimal PTP system design in a WAN environment using appropriate clock and network parameter settings. Improving the PTP clocks internal features is also part of this optimal design, since it is necessary for maintaining the required synchronisation performance in power grid applications running under scarce communication network bandwidth conditions. Copyright © 2013 John Wiley & Sons, Ltd.

Stochastic modeling of high-stability ground clocks in GPS analysis

In current global positioning system (GPS) applications, receiver clocks are typically estimated epoch-wise in the data analyses even for clocks with high performance like Hydrogen-masers (H-maser). Applying an appropriate clock model for high-stability receiver clocks should, in view of the strong correlation between the station height and the clock parameters, significantly improve the positioning results. Recent experiments have shown that modeling the deterministic behavior of high-quality receiver clocks can improve the kinematic precise point positioning considerably. In this paper, well-behaving ground clocks are studied in detail applying constraints between subsequent and near-subsequent clock parameters. The influence of different weights for these relative clock constraints on the positioning quality, especially on the height, is investigated. For excellent clocks, an improvement of up to a factor of 3 can be obtained for the repeatability of the kinematic height estimates. This may be essential to detect small but sudden changes in the vertical component (e.g., caused by earthquakes). Troposphere zenith path delays (ZPD) are also heavily correlated with the receiver clock estimates and station heights. All these parameters are usually estimated simultaneously. We show that the use of relative clock constraints allows for a higher time resolution of the ZPD estimates (smaller than 2 h) without compromising the quality of the kinematic height estimates.

Orbit and clock analysis of Compass GEO and IGSO satellites

China is currently focussing on the establishment of its own global navigation satellite system called Compass or BeiDou. At present, the Compass constellation provides four usable satellites in geostationary Earth orbit (GEO) and five satellites in inclined geosynchronous orbit (IGSO). Based on a network of six Compass-capable receivers, orbit and clock parameters of these satellites were determined. The orbit consistency is on the 1–2 dm level for the IGSO satellites and on the several decimeter level for the GEO satellites. These values could be confirmed by an independent validation with satellite laser ranging. All Compass clocks show a similar performance but have a slightly lower stability compared to Galileo and the latest generation of GPS satellites. A Compass-only precise point positioning based on the products derived from the six-receiver network provides an accuracy of several centimeters compared to the GPS-only results.

Orbit and Clock Determination of QZS-1 Based on the CONGO Network

QZS-1 is the first satellite of the Japanese QuasiZenith Satellite System (QZSS) launched in September 2010. QZSS provides regional augmentation capabilities to users of the Global Positioning System (GPS) in Asia and the Pacific. Five stations of the Cooperative Network for GIOVE Observation (CONGO) are able to track the QZSS L1, L2, and L5 navigation signals. Together with the GPS observations of these stations, QZS-1 orbit and clock parameters were estimated. Various orbit parameterizations were tested and a sub-meter accuracy of the best orbits could be achieved. Differences of orbits obtained from various linear combinations are on the decimeter level and differential code biases are on the few nanosecond level. QZS-1 is equipped with a rubidium atomic clock that is similar to the ones of the GPS Block IIF satellites. At periods up to 100 s both clocks show a very similar performance. However, short periodic variations with a peak-to-peak amplitude of about 4 cm were detected in the QZS-1 clock estimates. Three time intervals with different periods of 13.6–15.5 minutes could be identified. Three way carrier phase analysis confirmed the presence of these variations. The origin of these periodicities is unknown.