Method of processing velocity increase of measuring results of quantum frequency standard parameters for information transfer velocity increase in satellite communication systems Anna Grevtseva Vadim Davydov Vasiliy Rud Peter the Great Saint Petersburg Peter the Great Saint Petersburg All-Russian Research Institute of Polytechnic University Polytechnic University Phytopathology Saint-Petersburg, Russia Saint-Petersburg, Russia Moscow, Russia annagrevtseva@mail.ru All-Russian Research Institute of rudvas.spb@gmail.com Phytopatholog Moscow, Russia davydov_vadim66@mail.ru Abstract—The new method for frequency characteristics [4. 19, 26-28, 30 - 34]. And also to improve the frequency calculating of the quantum frequency standard on the adjustment systems, since of the frequency drift in a satellite rubidium atoms – 87 is considered. The implementation of this communication system will have a negative impact on the method in the developed software is presented. The processing quality and speed of information transfer. of the experimental results with using a developed software is In real-time regime of the results tracking requires the realized. The proposed method allows to adjust the standard frequency tuning on during its deviates to the nominal value increase of data processing velocity. The increasing of the over shorter interval of time than before. During this time large array processing velocity of the experimental data is interval, the information transfer rate does not deteriorate. one of the urgent tasks in this area. One of the possible The results of experimental investigations of the metrological solutions to this problem is presented in our work. characteristics are presented. II. THE FREQUENCY CHARACTERISTICS OF THE Keywords—quantum frequency standard, velocity processing, STANDARD AND THE METHOD OF THEIR CALCULATION information transfer, Allan deviation, root mean deviation, The following methods are used to assess the stability of frequency drift frequency standards: the standard deviation of the frequency I. INTRODUCTION (classical variance) is calculated and the Allan deviation is calculated [1, 5, 19, 27, 28, 30]. The standard deviation S of Currently, one of the urgent tasks in modern the group containing N measurement results is calculated by communication and navigation systems is to increase the the formula: synchronization accuracy of the time scales between various ∑𝑁 (𝑥𝑖 −𝑥̅ )2 devices [1-9]. This is necessary for obtaining of the reliable 𝑆 = √ 𝑖=1 , (1) results during the investigations conducting of the Earth's N−1 surface, the upper atmosphere, the transmission and where 𝑥𝑖 is result of frequency measurement on step i, 𝑥̅ is processing of large amounts of information at high speed [7- the arithmetic mean value. 17]. Depending on the required accuracy of the This characteristic is used to assess the stability of synchronization of time scales, different models of frequency standards, but its use can be difficult if there is a frequency standards are used in the systems. The most correlation between fluctuating values. In addition, as a optimal solution to this problem is the using of quantum result of various investigations, it was found that with many frequency standards (QFS). Among the quantum frequency measurements, the use of standard deviation becomes standards for various navigation systems the most popular ineffective in assessing the stability of frequency standards. were rubidium QFS, as them have small size and low cost Therefore, Allan proposed the original solution, the essence compared to other types of QFS. These key advantages of which was as follows. The during a calculating the allow to use the rubidium standards in composed of the deviation, it is necessary to use the difference between two small-sized rubidium watches, which are widely used at adjacent frequency measurements, and not the measurement base stations of the mobile communications and on board of of the frequency deviation from the mean value, as in the the communication satellites [4, 18-21]. Such systems classical case. This method is called Allan deviation: should are working the autonomously for a long time. ∑𝑁−1 𝛿0𝑖 2 Therefore, for information processing in them are used the 𝜎𝑦 (𝜏) = √ 𝑖=1 (2) 2(𝑁−1) various optical systems [20-26]. where 𝛿0𝑖 is relative frequency variation in the i-th One of the most important characteristics of any measurement: standard is the stability of its operation. The stability is 𝑓 −𝑓 determined the quality of the QFS [1, 2, 4, 5, 19-21, 26-30]. 𝛿0𝑖 = 𝑖+1 𝑖 (3) 𝑓𝑟𝑎𝑡 To produce high-quality rubidium frequency standards 𝑓𝑖 − value of frequency measure at i-th measurement, (RFS), prototypes of the standard undergo various tests. The frat = 5 MHz − rated frequency value, N − number of during implementation of these tests, it is necessary in real measurements. time to control the change in the frequency characteristics of the test sample, in order to identify instabilities in its work Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0) Data Science Currently, Allan deviation is the most convenient and One of the outputs of the test sample of the rubidium more reliable measure to determine the stability of the frequency standard is connected to the measuring device, frequency in the time domain. Its analogue in Russian which is used as a frequency counter Pendulum CNT-91. At standards is the mean square relative random variation σ the same time, a signal from the reference standard is sent to (SRRV), which differs from the Allan deviation by a the frequency counter. The hydrogen standard is used as a 𝜎 constant 𝜎𝑦 (𝜏) = . reference in the experiment. The frequency counter in this √2 For calculating of these frequency characteristics was case acts as a comparator, comparing the signal of the been developed the following method. The total data stream studied standard with a more stable signal of the reference which is coming from the measuring device is divided into standard. The obtained data from the frequency counter is fed to a computer, where they are analyzed and further time series. After that the corresponding characteristics are processed. calculated. A time series is a sequence of observations of a To process the frequency values, special software was parameter in successive equal time intervals t. Individual observations make up the level of the series and are denoted developed, which implemented the above calculation methods: standard deviation, Allan deviation and SRRV. by 𝑥𝑡 , where t = 1, ..., n. In the study of the time series, During the calculations, the interaction of two data several components are distinguished: streams was used: the first stream was used to obtain the 𝑥𝑡 = 𝑢𝑡 + 𝑦𝑡 + 𝑐𝑡 + 𝑒𝑡 , 𝑡 = 1, … , 𝑛, (4) primary frequency values from the device, and in the second where 𝑢𝑡 is a smoothly changing component that describes stream, the required values were directly calculated. This the net influence of long-term factors (for example, linear processing algorithm proposed by us in the implementation frequency drift with time); 𝑦𝑡 – seasonal component of calculations using (1), (2) and (3) in the developed reflecting the frequency of processes over a not very long program allowed us to assess the stability of standards in period (day, week, month, etc.); 𝑐𝑡 is a cyclic component real time and significantly accelerated the processing of that reflects the recurrence of processes over long periods of experimental results. The calculation of standard deviation, time over one year; 𝑒𝑡 is a random component that reflects Allan deviation and SRRV in the program during the the influence of random factors that cannot be taken into experiment for two days is presented on fig. 2-4. account and recorded (for example, the influence of external noise). The first three components are deterministic components. The random component is formed as a result of a superposition of a large number of external factors that each individually have a minor effect on the change in the values of the investigated parameter. Analysis and research of the time series allow us to build models for predicting parameter values for the future, if the sequence of observations in the past is known. Currently, time series are the most intensively developing, promising area of mathematical statistics. The using this approach, it is possible to reduce the time of the experiment and predict the behavior of the frequency characteristics of the standard based on the analysis of the data obtained. In our work Fig. 2. The fragment of the program a during the calculating SRRV. during of the measurement results processing, we used the time series recommended by the state standard: 1, 2, 5, 10, 100 ... s. The value of the characteristic at each point in the time series is updated and filled in as data is received from the measuring device in real time. Thus, according to the data obtained, it is possible to investigate the standard stability and predict its future work. III. CONDUCTING AN EXPERIMENT AND PROCESSING MEASUREMENT RESULTS An experimental setup was used to assess the stability and quality of the standard. Its structural diagram is presented on fig. 1. Fig. 3. The fragment of the program a during the calculating Allan deviation. Fig. 1. Block diagram of the experimental setup. VI International Conference on "Information Technology and Nanotechnology" (ITNT-2020) 16 Data Science the influence of long-term factors, such as linear drift of the standard frequency, light shifts, and temperatures. TABLE I. COMPARISON OF EXPERIMENTAL DATA WITH TECHNICAL REQUIREMENTS FOR THE STANDARD MODEL UNDER STUDY Measu SRRV Stability rement SRRV(CNT- SRRV (VCH- (technical time, τ, 91) 315) requirements), s no more than Satisfac 1 1.66*10-11 1.08*10-11 1.5·10-11 torily Satisfac 100 3.18*10-12 3.73*10-12 1.0·10-11 torily Satisfac 1000 1.12*10-12 1.29*10-12 5.0·10-12 torily IV. CONCLUSION The results of experimental investigations have shown that rubidium QFS is achieved the maximum stability of the measurement time τ ≈ 1000 s. The using of the method Fig. 4. The fragment of the program a during the calculating standard proposed by us and the developed software for its deviation. implementation allows to increase the processing velocity of measurement results in several times. This makes it possible The stability of the rubidium standard is influenced by to reduce the frequency adjustment time of during its various factors. One of them is frequency drift. Long-term deviates from the nominal value and maintain the quality frequency instability is determined by the drift and and velocity of information transfer. frequency drift of the reference transition. During the In addition, the using of the method of dividing data into operation of the RFS, the composition and partial pressures time series allowed us to analyze the change in the of the filling components of the optical elements slowly characteristics of the standard in the long-term field. It is change (diffusion inside the cell walls, gas leakage from the extremely important for implement of the reliable standard outside, etc.), which leads to a shift in the frequency of the operation in the satellite information transmission systems. reference transition. The values of these parameters can change under the influence of changes in ambient ACKNOWLEDGMENT temperature and atmospheric pressure, which also leads to This research work was supported by the Academic periodic departures of the frequency of the reference Excellence Project 5-100 proposed by Peter the Great St. transition. Because of this, it is necessary to correctly Petersburg Polytechnic University. evaluate the stability of the investigated standard. Comparing the standard deviation and Allan deviation, REFERENCES we note that the use of standard deviation as a measure of [1] F. Riehle, “Frequency standard. Basic and applications,” Wiley- VCH Verlag CmbH Co. KGaA: New-York, 2008. frequency stability is not recommended. Since this value [2] A.I. Efimov, L.A. Lykanina, L.N. Samoznaev, I.V. Chashey and does not converge for some types of noise commonly found M.K. Bred, “Intensity of fluctuations in the frequency of radio in frequency sources. 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