The Statistics of Computer Clocks and the Design of Synchronization Algorithms.

In this study, I used standard statistical tools (such as the various forms of the two-sample Allan variance) to characterize the clocks in computers, and I show how the results of this study are used to design algorithms to synchronize the computer clocks. These synchronization algorithms can be used to synchronize the time of a computer to a local reference clock or to a remote server. The algorithms by themselves are not intended to be a simple replacement for software that implements the Network Time Protocol (NTP) or any other similar application. Instead, they describe the statistical principles that should be used to design an algorithm to synchronize any computer clock by using data from any external reference received in any format. These algorithms have been used to synchronize the clocks of the computers that support the Internet Time Service operated by the National Institute of Standards and Technology (NIST), and I illustrate the performance of the algorithm with real-time data from these servers. In addition to presenting the design principles of the algorithm, I illustrate the principles with two specific examples: synchronizing a computer clock to a local reference signal, and the design of a synchronization process that is based on time-difference data received from a remote server over the public Internet. The message exchange between the local system and the remote server in this configuration is realized in NTP format, but that is not a fundamental requirement.

Demonstration of a Timescale Based on a Stable Optical Carrier.

We report on the first timescale based entirely on optical technology. Existing timescales, including those incorporating optical frequency standards, rely exclusively on microwave local oscillators owing to the lack of an optical oscillator with the required frequency predictability and stability for reliable steering. We combine a cryogenic silicon cavity exhibiting improved long-term stability and an accurate ^{87}Sr lattice clock to form a timescale that outperforms them all. Our timescale accumulates an estimated time error of only 48±94 ps over 34 days of operation. Our analysis indicates that this timescale is capable of reaching a stability below 1×10^{-17} after a few months of averaging, making timekeeping at the 10^{-18} level a realistic prospect.

Optical-Clock-Based Time Scale.

A time scale is a procedure for accurately and continuously marking the passage of time. It is exemplified by Coordinated Universal Time (UTC) and provides the backbone for critical navigation tools such as the Global Positioning System. Present time scales employ microwave atomic clocks, whose attributes can be combined and averaged in a manner such that the composite is more stable, accurate, and reliable than the output of any individual clock. Over the past decade, clocks operating at optical frequencies have been introduced that are orders of magnitude more stable than any microwave clock. However, in spite of their great potential, these optical clocks cannot be operated continuously, which makes their use in a time scale problematic. We report the development of a hybrid microwave-optical time scale, which only requires the optical clock to run intermittently while relying upon the ensemble of microwave clocks to serve as the flywheel oscillator. The benefit of using a clock ensemble as the flywheel oscillator instead of a single clock can be understood by the Dick-effect limit. This time scale demonstrates for the first time subnanosecond accuracy over a few months, attaining a fractional frequency stability of 1.45 × 10-16 at 30 days and reaching the 10-17 decade at 50 days, with respect to UTC. This time scale significantly improves the accuracy in timekeeping and could change the existing time-scale architectures.

Incorporating an Optical Clock Into a Time Scale.

This paper discusses the results of a simulation of a time scale based on continuously operating commercial hydrogen masers and an optical frequency standard that does not operate continuously as a clock. The simulation compares the performance of this time scale with one that is based on the same commercial devices but incorporates a continuously operating cesium fountain instead of the optical standard. The results are independent of the detailed characteristics of the optical frequency standard; the only requirement is that the optical device be much more stable than the masers in the ensemble. We discuss two methods for realizing the results of this simulation in an operational time scale.

A Historical Perspective on the Development of the Allan Variances and Their Strengths and Weaknesses.

Over the past 50 years, variances have been developed for characterizing the instabilities of precision clocks and oscillators. These instabilities are often modeled as nonstationary processes, and the variances have been shown to be well-behaved and to be unbiased, efficient descriptors of these types of processes. This paper presents a historical overview of the development of these variances. The time-domain and frequency-domain formulations are presented and their development is described. The strengths and weaknesses of these characterization metrics are discussed. These variances are also shown to be useful in other applications, such as in telecommunication.

An Algorithm for Synchronizing a Clock When the Data Are Received Over a Network With an Unstable Delay.

A method is presented for synchronizing the time of a clock to a remote time standard when the channel connecting the two has significant delay variation that can be described only statistically. The method compares the Allan deviation of the channel fluctuations to the free-running stability of the local clock, and computes the optimum interval between requests based on one of the three selectable requirements: 1) choosing the highest possible accuracy; 2) choosing the best tradeoff of cost versus accuracy; or 3) minimizing the number of requests to realize a specific accuracy. Once the interval between requests is chosen, the final step is to steer the local clock based on the received data. A typical adjustment algorithm, which supports both the statistical considerations based on the Allan deviation comparison and the timely detection of errors, is included as an example.

Usage Analysis of the NIST Internet Time Service.

The Internet Time Service (ITS) at the National Institute of Standards and Technology (NIST) currently receives over 16 billion time requests per day. ITS servers derive their system time from the NIST atomic-referenced time scale and distribute it freely to the public. Here we explore ITS usage patterns discovered by analysis of inbound network traffic. For example, over a period of four weeks, just two of the ≈ 20 ITS servers received requests from 316 million unique Internet Protocol (IPv4) addresses, which is at least 8.5 % of the entire Internet. We offer recommendations for networked device/software manufacturers, and providers and consumers of network time services.

A Study of GPS Carrier-Phase Time Transfer Noise Based on NIST GPS Receivers.

To do a better time comparison between high-precision clocks (such as a Cesium-fountain clock and Hydrogen-maser clock), we want to study and eventually lower the GPS carrier-phase time transfer noise. The GPS carrier-phase time transfer noise comes from four sources: GPS satellite, GPS signal path, ground receiving equipment (receiver and antenna), and data-processing algorithm. This paper focuses on the noise introduced by the ground receiving equipment. At NIST, we have installed seven GPS receivers. All receivers have the same reference time, i.e., UTC(NIST). Three of them are connected to the same antenna. The other four are connected to four different antennas. This architecture enables us to study the time-transfer noise from the ground receiving equipment. We study both long-term (> 100 days) noise and short-term (< 1 day) noise. For the long-term noise, the time-transfer result using one receiver can vary from that using another receiver by up to 1.8 ns, during 1.3 years. To achieve sub-nanosecond GPS timing accuracy, a careful monitoring of the time delays or a more frequent calibration is needed. For the short-term noise, we find that the common-clock difference between receivers using the same antenna is less noisy than that using two different antennas, at an averaging time of less than 0.5 hour. This indicates that the antenna and antenna cable contribute to the super-short-term noise of GPS carrier-phase time transfer significantly. In addition, the response to the GPS receiver's reference-time change is tested in this paper. The variation in the response can be up to ± 350 ps. Last, this paper gives the best carrier-phase time transfer result we can currently achieve with the available equipment at NIST. The best frequency stability is 4.0×10-16 at 3 hours, 1.1×10-16 at 1 day, 4.0×10-17 at 10 days, and 1.3×10-17 at 48 days.

Toward Continuous GPS Carrier-Phase Time Transfer: Eliminating the Time Discontinuity at an Anomaly.

The wide application of Global Positioning System (GPS) carrier-phase (CP) time transfer is limited by the problem of boundary discontinuity (BD). The discontinuity has two categories. One is "day boundary discontinuity," which has been studied extensively and can be solved by multiple methods [1-8]. The other category of discontinuity, called "anomaly boundary discontinuity (anomaly-BD)," comes from a GPS data anomaly. The anomaly can be a data gap (i.e., missing data), a GPS measurement error (i.e., bad data), or a cycle slip. Initial study of the anomaly-BD shows that we can fix the discontinuity if the anomaly lasts no more than 20 min, using the polynomial curve-fitting strategy to repair the anomaly [9]. However, sometimes, the data anomaly lasts longer than 20 min. Thus, a better curve-fitting strategy is in need. Besides, a cycle slip, as another type of data anomaly, can occur and lead to an anomaly-BD. To solve these problems, this paper proposes a new strategy, i.e., the satellite-clock-aided curve fitting strategy with the function of cycle slip detection. Basically, this new strategy applies the satellite clock correction to the GPS data. After that, we do the polynomial curve fitting for the code and phase data, as before. Our study shows that the phase-data residual is only ~3 mm for all GPS satellites. The new strategy also detects and finds the number of cycle slips by searching the minimum curve-fitting residual. Extensive examples show that this new strategy enables us to repair up to a 40-min GPS data anomaly, regardless of whether the anomaly is due to a data gap, a cycle slip, or a combination of the two. We also find that interference of the GPS signal, known as "jamming", can possibly lead to a time-transfer error, and that this new strategy can compensate for jamming outages. Thus, the new strategy can eliminate the impact of jamming on time transfer. As a whole, we greatly improve the robustness of the GPS CP time transfer.

Invited review article: The statistical modeling of atomic clocks and the design of time scales.

I will show how the statistical models that are used to describe the performance of atomic clocks are derived from their internal design. These statistical models form the basis for time scales, which are used to define international time scales such as International Atomic Time and Coordinated Universal Time. These international time scales are realized by ensembles of clocks at national laboratories such as the National Institute of Standards and Technology, and I will describe how ensembles of atomic clocks are characterized and managed.

A straightforward frequency-estimation technique for GPS carrier-phase time transfer.

Although Global Positioning System (GPS) carrier-phase time transfer (GPSCPTT) offers frequency stability approaching 10-15 at averaging times of 1 d, a discontinuity occurs in the time-transfer estimates between the end of one processing batch (1-3 d in length) and the beginning of the next. The average frequency over a multiday analysis period often has been computed by first estimating and removing these discontinuities, i.e., through concatenation. We present a new frequency-estimation technique in which frequencies are computed from the individual batches then averaged to obtain the mean frequency for a multiday period. This allows the frequency to be computed without the uncertainty associated with the removal of the discontinuities and requires fewer computational resources. The new technique was tested by comparing the fractional frequency-difference values it yields to those obtained using a GPSCPTT concatenation method and those obtained using two-way satellite time-and-frequency transfer (TWSTFT). The clocks studied were located in Braunschweig, Germany, and in Boulder, CO. The frequencies obtained from the GPSCPTT measurements using either method agreed with those obtained from TWSTFT at several parts in 1016. The frequency values obtained from the GPSCPTT data by use of the new method agreed with those obtained using the concatenation technique at 1-4 x 10(-16).