Rubidium Atomic Frequency Standard Research Articles

Status quo and improvements of timekeeping in GNSSs

A time offset of 1 microsecond could lead to 300-meter positioning offset for a global navigational satellite system (GNSS). Therefore, appropriately evaluating and improving the clock performance onboard GNSS satellites are critical. The research methods and conclusions of papers written in distinct periods about their contemporary satellites clocks are chronologically synthesized. The satellites clocks among the same and different GNSSs are compared, with the time primarily centered around the launching and development of BeiDou-2 and BeiDou-3. It is found that passive hydrogen maser (PHM) and rubidium atomic frequency standard (RAFS) have a better performance than cesium (Cs) clocks, and PHM are among the best clock onboard satellites so more attention may be given to its development. Two major factors affecting timekeeping precision are the selection of clock manufacturers and clock types. The European manufacturing technique is pioneering, but the RAFS and PHM independently developed by China in recent years indicate a good performance. To improve navigation service, an accurate evaluation of satellites performance should be conducted, and the results can be used to assign the weight of satellite differently in computing navigation information.

Analysis of the Long-Term Characteristics of BDS On-Orbit Satellite Atomic Clock: Since BDS-3 Was Officially Commissioned

Satellite atomic clocks are the key elements for position, navigation, and timing services of the Global navigation satellite system (GNSS); it is necessary to research the characteristics of BDS-3 on-orbit satellite atomic clocks for their further optimization. In this study, clock offset data with a duration of 620 days since BDS-3 was officially commissioned were applied to long-term characteristic analysis. To begin with, the precision clock offset data of Deutsches geoforschungs zentrum (GFZ) processed by a MAD-based method were used as reliable test data. Herein, the working principle and main characteristics of satellite atomic clocks are analyzed and discussed, and thus, a comprehensive long-term characteristic analysis scheme is designed. On this basis, the performance indicators—mainly including physical parameters, periodic characteristics, frequency drift rate, frequency accuracy, frequency stability—were calculated and analyzed respectively, revealing the long-term characteristics of the BDS in orbit satellite atomic clocks during the test period. The results of experimental data testify that the performance of BDS-3 satellite atomic clocks is significantly superior to that of BDS-2, especially in terms of drift rate and frequency stability, and the performance of passive hydrogen maser (PHM) is generally superior to that of rubidium atomic frequency standards (RAFS). Within about half a year since BDS-3 was officially commissioned, the frequency stability of BDS-3 satellite atomic clock gradually improved and then reached the order of 10−15, reflecting the effectiveness of system maintenance and inter-satellite link. Furthermore, some novel conclusions are drawn, such as the long-term period term of the fitting residual and drift rate, which may be caused by the earth’s revolution.

Rubidium frequency standard with pulsed optical pumping and frequency instability of 2.5 × 10−13τ − 1/2

The work is dedicated to the further development of a compact quantum frequency standard based on a rubidium gas cell with a mixture of buffer gases. The results of frequency measurements and analysis of short-term frequency instability obtained on a laboratory prototype of a microwave rubidium atomic frequency standard (RAFS) with pulsed optical pumping (POP) are presented. The main in magnitude contributions to the overall frequency instability of the RAFS with POP are estimated. Short-term frequency instability expressed in terms of the Allan deviation and measured at averaging times τ up to several tens of seconds, σy (τ) = 2.5×10−13 τ −1/2, coincides satisfactorily with the calculated value of σy (τ) = 2.1×10−13 τ −1/2.

A Novel Method for Rubidium Bulb Bonding and Key Characterization for Future Space Clocks.

RF-discharge lamp is a key component in space- and ground-based compact and portable atomic clocks, such as rubidium atomic frequency standards (RAFSs). Precise thermal, structural design, and control of a rubidium (Rb) bulb is of crucial importance for long-term reliable operation of the onboard clocks. An important aspect is the potting material that is used to mount the Rb bulb. Potting material directly determines the thermal contact between liquid Rb pool inside glass bulb enclosure and the heating element, which is the only path to control the Rb bulb's temperature. Failure or degradation of thermal contact of the Rb bulb with its metallic base will lead to Rb clock degradation or failure. Considering this, we have successfully designed, simulated, implemented, characterized, and tested the use of indium metal as a replacement to epoxy for the Rb bulb bonding that can be implemented in future space Rb atomic clocks. Its thermal advantage over other routine space-qualified epoxies and flexibility for multiple bonding and unbonding mechanisms make it ideal for such applications. The usefulness of key properties of indium for various other space and ground applications is discussed.

Improving the start-up characteristics of the rubidium atomic clock

Considering the importance of start-up characteristics of the rubidium atomic clock in engineering applications, the objective of this paper is to optimize the start-up characteristics of the rubidium atomic clock by studying the theory of the rubidium atomic frequency standards, especially the light pumping process, and the effect of light intensity on frequency accuracy. Our analysis demonstrated that frequency accuracy is proportional to the light intensity, and hence, we propose a method for actively optimizing the start-up characteristics of the rubidium atomic clock by utilizing the fluctuations in light intensity. Additionally, some related experiments using the proposed method indicate that the light intensity–frequency coefficient of the rubidium atomic clock is improved from 1.84 × 10−9 to 4.21 × 10−10 V−1 within 30 min after the rubidium atomic clock is locked, and also, the lockout time is less than 5 min with a wide working temperature range (0–50 °C), indicating a significant improvement in the start-up characteristics of the rubidium atomic clock.

Precise calorimetric rubidium mass estimation and its application to the rubidium atomic frequency standard (RAFS)

Precise calorimetric rubidium mass estimation and its application to the rubidium atomic frequency standard (RAFS)

A Physics Package with Shot-noise Limited Frequency Stability Better Than 1×10-13τ-1/2 for Rubidium Atomic Frequency Standards

A Physics Package with Shot-noise Limited Frequency Stability Better Than 1×10-13τ-1/2 for Rubidium Atomic Frequency Standards

BeiDou-3 broadcast clock estimation by integration of observations of regional tracking stations and inter-satellite links

The BeiDou navigation satellite system (BDS) tracks medium earth orbit (MEO) satellites using only regional tracking stations in China. As a result, the broadcast clock accuracy of the MEO satellites decreases rapidly during the invisible arcs because of the lack of available observations. The inter-satellite link (ISL) technology of the third generation of BDS (BDS-3) can be used to extend the visible arcs of MEO satellites and to measure the relative inter-satellite clock in nearly real time. We propose a broadcast clock approach for BDS-3 by integrating observations from regional tracking stations and ISLs. The clock error between satellites is obtained through centralized estimation based on ISLs. The Ka-band hardware delay is calibrated by taking the double difference between ISL-centralized clock and the Multi-satellite Precise Orbit Determination clock. The deviation between the ISL-centralized clock and the BeiDou time is obtained using only one Two-way Satellite Time Comparison station or anchor station. To validate the algorithms, we analyze clock estimation and prediction accuracy, hardware delay stability, and time synchronization accuracy. The results show that the frequency stability of the BDS-3 onboard passive hydrogen maser (PHM) and rubidium atomic frequency standard (RAFS) is competitive to those of the GPS IIF RAFS and Galileo FOC PHM and better than those of GPS IIR RAFS. The root-mean-square error of the 2-h clock prediction is better than 0.25 ns, and the validation result relative to the post-processed precise clock product is better than 0.4 ns. The time synchronization accuracy of better than 1 ns can be obtained based on only one TSTC station or an anchor station, and the standard deviation of Ka-band hardware delay is about 0.12 ns. It is believed that the ISL and the proposed algorithms will bring a significant upgrade in the estimation of BDS-3 broadcast clock; the broadcast clock accuracy will be greatly improved, and reliance on the ground segment will also be reduced significantly.

Time and frequency characterization of GLONASS and Galileo on-board clocks

As the core component of navigational satellites, the on-board atomic clock is of key importance for guaranteeing the stable operation of global satellite navigation systems (GNSSs). As GNSSs are modernized, the clocks of several satellites have been changed to support long-term in-orbit operation. Analysis of the performance of on-board clocks is therefore crucial for supporting the positioning, navigation and timing of the satellite navigation system. Most studies involving stability analysis have not paid much attention to performance variation as a consequence of clocks being changed. This motivated our study, in which we analyzed the time domain characterization of on-board clocks from January 2016 to October 2018 to detect the variation. With respect to frequency domain characterization, conventional methods for noise analysis are easily affected by frequent fluctuations and local discontinuities as the averaging time increases. Hence, we propose the lag 1 autocorrelation function method based on overlapping samples to identify the noise of satellite clocks. We find that the time domain stability of the Galileo clock is of the magnitude of 10–13, 10–14 and 10–15 at averaging times of 100 s, 1000 s and 1 d, respectively, which is one order of magnitude better than that of the Russian global navigation satellite system (GLONASS). Moreover, the stability of the passive hydrogen masers on board Galileo shows a certain improvement due to the frequency modulation. The overall performance of the GLONASS cesium atomic clock and the Galileo rubidium atomic frequency standard is stable without any obvious aging in recent years. In terms of the frequency domain characterization, GLONASS clocks are mainly affected by flicker phase modulation noise, white frequency modulation noise and flicker frequency modulation noise, whereas the Galileo clocks are mainly affected by three kinds of frequency modulation noise.

Analysis and optimization of rubidium spectrum lamp to eliminate frequency fluctuations of rubidium atomic frequency standard

Rubidium atomic frequency standard (RAFS) is the most widely used frequency standard in space. The light used to pump the atoms and detect the resonance signal is emitted by rubidium spectrum lamp, so the light intensity of rubidium spectrum lamp directly determines the performance of RAFS. This paper discussed on-board RAFS’ output frequency fluctuations caused by rubidium spectrum lamp. The reason of frequency fluctuations from rubidium lamps was described. To obtain stable lamp light intensity, analysis and optimization of the lamp was developed. Relevant experiments were carried out to verify the optimization. The study content of this paper is beneficial to improve the performance of a single temperature controlled space RAFS physics package.

Atomic Clock Performance Assessment of BeiDou-3 Basic System with the Noise Analysis of Orbit Determination and Time Synchronization

The basic system of the BeiDou global navigation satellite system (BDS-3) with 18 satellites has been deployed since December 2018. As the primary frequency standard, BDS-3 satellites include two clock types with the passive hydrogen maser (PHM) and the rubidium atomic frequency standard (RAFS). Based on the final precise orbit and clock product from Xi’an Research Institute of Surveying and Mapping (XRS), the atomic clock performance of BDS-3 satellites is evaluated, including the frequency accuracy, frequency drift rate, and frequency stability, and compared with GPS block IIF satellites with RAFS, Galileo satellites with PHM, and BDS-2 satellites. A data auto-editing procedure to preprocess clock data and assess the clock performance is developed, where the assessed results are derived at each continuous data arc and the outliers are excluded properly. The stability of XRS product noise is given by using some stations equipped with high-precision active hydrogen masers (AHM). The best stability is 8.93 × 10−15 and 1.85 × 10−15 for the averaging time of 10,000 s and 1 day, which is basically comparable to one-third of the in-orbit PHM frequency stability. The assessed results show the average frequency accuracy and drift rate of BDS-3 with RAFS are slightly worse while the stability is better than BDS-2 medium earth orbit (MEO) satellites. The 10,000 s stability is better but the 1-day stability is worse than GPS, which may be related to the performance of the BDS-3 RAFS clock. As for BDS-3 with PHM, the frequency accuracy is slightly worse than Galileo PHM satellites; the drift rate, when excluding C34 and C35, is basically comparable to Galileo and significantly better than GPS satellites; the stability is comparable to Galileo, where the 10,000 s stability is slightly worse than Galileo and better than GPS. The 1-day stability among BDS-3 PHM, GPS IIF RAFS, and Galileo PHM satellites is basically comparable.

Study on the Effect of Excitation Circuit of Spectral Lamp on the Temperature Coefficient of Physics Package of Rubidium Atomic Clock

As one of the important factors affecting the long-term frequency stability of Rubidium atomic frequency standards (RAFS), the temperature coefficient has a great influence on the performance of RAFS. The temperature coefficient of physics package has an important influence on the temperature coefficient of rubidium atomic clock. The instability of temperature is often the most important error term of RAFS. The variation of temperature to several degrees means a month’s aging. As an important part of rubidium atomic clock physics package, the Lamp Excitation Circuit directly affects the voltage adaptation area and temperature coefficient of Rubidium gas cell physics package. In order to satisfy the long-term frequency stability and adapt extraterrestrial environment, we propose the improvements of Lamp Excitation Circuit in physics package of Rubidium Atomic Clock, since minute current change of Lamp Excitation Circuit are mapped onto the clock’s long-term frequency stability, and the stabilization of the lamp excitation circuit has the potential to significantly improve the RAFS’ long-term frequency stability and temperature coefficient. We demonstrate that the temperature coefficient of physics package can be reduced obviously by improved Lamp Excitation Circuit. Suggesting that performance of the RAFS could be improved greatly further.

Optics integrated compact cavity for rubidium atomic frequency standards.

A compact magnetron cavity having integrated optics is designed and realized for a rubidium atomic clock that is being developed for the Indian Regional Navigation Satellite System. This cavity comprises a cylindrical dielectric cell with 25 mm diameter and 25 mm height. The cavity is designed to resonate at the rubidium hyperfine ground-state frequency of 6.8346 GHz with TE011-mode. A loop gap resonator structure is employed to obtain the required uniform mode along the quantization-axis in the cavity. The cutoff frequency of the cavity is designed in such a way that the influence of optics on the cavity mode is negligible and it is well within the tuning range of the cavity. The measured results of the realized cavity match up to 90% with the RF simulation results. The overall volume and mass of the realized cavity are about 86 cm3 and 120 g, respectively, making it suitable for portable space based applications.

Barometric Effect in Vapor-Cell Atomic Clocks.

Vapor-cell atomic clocks are compact and high-performance frequency references employed in various applications ranging from telecommunication to global positioning systems. Environmental sensitivities are often the main sources of long-term instabilities of the clock frequency. Among these sensitivities, the environmental pressure shift describes the clock frequency change with respect to the environmental pressure variations. We report here on our theoretical and experimental analysis of the environmental pressure shift on rubidium atomic frequency standards (RAFSs) operated under open atmosphere. By using an unsealed high-performance laser-pumped rubidium standard, we demonstrate that the deformation of the vapor-cell volume induced by the environmental pressure changes (i.e., barometric effect) is the dominant environmental pressure shift in a standard laboratory environment. An experimental barometric coefficient of /hPa is derived, in good agreement with theory and with previously reported measurements of frequency shifts of RAFS operated when transiting to vacuum.

Improved prediction of GPS satellite clock sub-daily variations based on daily repeat

High-precision estimates of GPS satellite clock errors reveal systematic sub-daily clock bias variations on the order of 1 ns. The low noise levels in the Rubidium Atomic Frequency Standards onboard GPS IIR, IIR-M, and IIF satellites provide visibility of these small, but systematic behaviors. Prior studies have reported on this phenomenon and sought to characterize the specific frequency components present and to identify potential causes of the observed periodic variations. Our research focuses on the repeatability of the clock variations and the potential for using observed variations directly to predict future clock behavior. Results are presented and compared to IGS Ultra-rapid and broadcast message predictions for all operating GPS satellite clocks for a 1-month period in July 2017. During this time, the accuracy of the proposed sub-daily variation prediction is better than 0.15 ns (RMS) for 8 out of 9 GPS Block IIF Rb clocks and under 0.3 ns (RMS) for most GPS IIR and IIR-M Rb clocks. This approach is complementary to existing techniques for estimating longer-term clock rates and drift and can be combined with them to improve the fidelity of predictive satellite clock models for real-time GPS position, navigation, and timing applications.

Spectral emission from the alkali inductively-coupled plasma: Theory and experiment

The weakly-ionized, alkali inductively-coupled plasma (ICP) has a long history as the light source for optical pumping. Today, its most significant application is perhaps in the rubidium atomic frequency standard (RAFS), arguably the workhorse of atomic timekeeping in space, where it is crucial to the RAFS’ functioning and performance (and routinely referred to as the RAFS’ “rf-discharge lamp”). In particular, the photon flux from the lamp determines the signal-to-noise ratio of the device, and variations in ICP brightness define the long-term frequency stability of the atomic clock as a consequence of the ac-Stark shift (i.e., the light-shift). Given the importance of Rb atomic clocks to diverse satellite navigation systems (e.g., GPS, Galileo, BeiDou) – and thereby the importance of alkali ICPs to these systems – it is somewhat surprising to find that the physical processes occurring within the discharge are not well understood. As a consequence, researchers do not understand how to improve the spectral emission from the lamp except at a trial-and-error level, nor do they fully understand the nonlinear mechanisms that result in ICP light instability. Here, we take a first step in developing an intuitive, semi-quantitative model of the alkali rf-discharge lamp, and we perform a series of experiments to validate the theory’s predictions.

Precise orbit and clock determination for BeiDou-3 experimental satellites with yaw attitude analysis

Five new-generation BeiDou-3 experimental satellites, called BeiDou-3e, have been launched into inclined geosynchronous orbit (IGSO) and medium orbit (MEO) since March 2015. In addition to newly designed signals and intersatellite links, different satellite buses, updated rubidium atomic frequency standards (RAFSs), and new passive hydrogen masers (PHMs) have been used. Using 15 stations, mainly in the Asia–Pacific region, we determined orbits and clock for both the BeiDou-3e and the regional BeiDou-2 satellites using the Extend CODE (Center for Orbit Determination in Europe) Orbit Model (ECOM). The orbit consistency, indicated by 3D orbit boundary discontinuity, is 50–70 and 40–60 cm for BeiDou-3e IGSO and MEO satellites, respectively, and better than 15 cm in radial component. Satellite laser ranging (SLR) validation gives about 17 and 10 cm for BeiDou-3e IGSO and MEO satellites. The BeiDou-3e satellites orbits show slightly better performance than the BeiDou-2 satellites as indicated by SLR. However, errors depending on the sun elongation angle were identified in SLR residuals for the BeiDou-3e IGSO C32 satellite, while such errors did not exist for BeiDou-2 IGSO/MEO and BeiDou-3e MEO satellites. No orbit accuracy degeneration for BeiDou-3e IGSO and MEO satellites was observed when the elevation angle (β angle) of the sun above the orbital plane was between − 4° and + 4°. In that case, the BeiDou-2 IGSO and MEO satellites are in orbit normal (ON) mode. An analysis of the yaw attitude identified that BeiDou-3e satellites did not use the ON mode, but experienced midnight- and noon-point maneuvers when the β angle is approximately between − 3° and + 3°. Compared with BeiDou-2 satellites, the onboard clocks of the BeiDou-3e IGSO satellites showed dramatic improved performance. The stability of BeiDou-3e IGSO satellites can be compared to the latest type of RAFSs employed onboard the GPS IIF satellites as well as the PHMs used onboard the Galileo satellites.

Influence of the ac-Stark shift on GPS atomic clock timekeeping

The ac-Stark shift (or light shift) is a fundamental aspect of the field/atom interaction arising from virtual transitions between atomic states, and as Alfred Kastler noted, it is the real-photon counterpart of the Lamb shift. In the rubidium atomic frequency standards (RAFS) flying on Global Positioning System (GPS) satellites, it plays an important role as one of the major perturbations defining the RAFS' frequency: the rf-discharge lamp in the RAFS creates an atomic signal via optical pumping and simultaneously perturbs the atoms' ground-state hyperfine splitting via the light shift. Though the significance of the light shift has been known for decades, to date there has been no concrete evidence that it limits the performance of the high-quality RAFS flying on GPS satellites. Here, we show that the long-term frequency stability of GPS RAFS is primarily determined by the light shift as a consequence of stochastic jumps in lamplight intensity. Our results suggest three paths forward for improved GPS system timekeeping: (1) reduce the light-shift coefficient of the RAFS by careful control of the lamp's spectrum; (2) operate the lamp under conditions where lamplight jumps are not so pronounced; and (3) employ a light source for optical pumping that does not suffer pronounced light jumps (e.g., a diode laser).

A physics package for rubidium atomic frequency standard with a short-term stability of 2.4 × 10-13 τ-1/2.

In this article, a new type of physics package with high signal to noise ratio for a rubidium atomic frequency standard is reported. To enhance the clock transition signal, a slotted tube microwave cavity with a field orientation factor of 0.93 and an absorption cell with the diameter of 30 mm were utilized in design of the cavity-cell assembly. Based on the spectral analysis of the three commonly used rubidium spectral lamps, the spectral lamp filled with Xe gas was chosen as the optical pumping source for its small line shape distortion. To suppress the shot noise of the signal, a band pass interference filter was used to filter out Xe spectral lines from the pumping light. A desk system of the rubidium frequency standard with the physics package was realized, and the short-term stability of the system was predicted and tested. The measured result is 2.4 × 10-13 τ-1/2 up to 100 s averaging time, in good agreement with the predicted one.

Autonomous Rubidium Clock Weak Frequency Jump Detector for Onboard Navigation Satellite System

Frequency jumps are common in rubidium frequency sources. They affect the estimation of user position in navigational satellite systems. These jumps must be detected and corrected immediately as they have direct impact on the navigation system integrity. A novel weak frequency jump detector is proposed based on a Kalman filter with a multi-interval approach. This detector can be applied for both "sudden" and "slow" frequency transitions. In this detection method, noises of clock data are reduced by Kalman filtering, for accurate estimation of jump size with less latency. Analysis on in-orbit rubidium atomic frequency standard (RAFS) phase telemetry data shows that the detector can be used for fast detection and correction of weak frequency jumps. Furthermore, performance comparison of different existing frequency jump detection techniques with the proposed detector is discussed. A multialgorithm-based strategy is proposed depending on the jump size and latency for onboard navigation satellites having RAFS as the primary frequency source.