**5.2 Tools and methods for synchronization of the time and frequency scale standards**

One of the main tasks of the coordinated time software is a support and development of a group standard time and frequency which forms a single group time scale with the possibility of prompt access to it. In order to form a unified group scale there can be used various methods of synchronization of standard time and frequency which are remote from each other by the distances of hundreds and thousands of kilometers. Currently the most accurate and commonly used methods are:


Equipment complex for duplex comparisons of time scales over TWSTFT channels (Twoway Satellite Time and Frequency Transfer) ensures synchronization of time scales with an error that does not exceed ± 2 ns for any geographically distributed time and frequency standards. High precision of this method is explained by the fact that asymmetry of bidirectional channel delay is much less than delay factor for signal propagation in one direction. According to the data given by (Ryzhkov and others, 2007), in duplex method there is no direct correlation between an error and a measuring channel length.

The highest degree of precision in terms of comparison of time scales up to 1 ns is achieved by TQC method, as time scales are compared in close vicinity by means of direct wire connection. Precision of synchronization in TQC method is caused mostly by instability characteristics of transportable clocks and influence of relativistic effect, which appears because the clocks being compared are located in different coordinate frames, that move in parallel with each other with variable speed and which are different in gravity field potential values. That is why it is also necessary to take into account corrections for relativistic effect in any other methods of synchronization of scales of spaced-apart clocks. Synchronization of time scales by means of TQC, by one- or two-way radio transmission methods, as well as methods of taking into account corrections for relativistic effect and other natural factors which influence precision of measurements, are described in details in the book (Oduan & Gino, 2002).

Synchronization of clocks in compliance with GNSS signals is based on receiving by aerials of spaced locations of the same navigation signals from radiating aerials located in outer space. GNSS satellites radiate exact time signals by means of atomic clock that is synchronized with system time of central synchronizer.

Receiver clock is also synchronized with system time, and as a result it is possible to calculate distance from satellite to receiving aerial according to a measured difference between radiation time and time of receiving signals from the satellite. In order to determine three spatial coordinates of a consumer, delay factors for radio signal propagation from at least three satellites at the same time are measured; it enables to receive a single-valued solution of photographic intersection. In order to determine difference between onboard clock scale and ground borne clock scale, it is necessary to measure additionally a delay factor from one more satellite. Then system of four equations that has 4 indeterminants (three coordinates and difference between scales) and a single-valued solution can be set up. In practical work many redundant measurements from ground-station network by GNSS spacecrafts constellations are carried out. Number of redundant equations achieves hundreds and thousands. These equations are solved with an ordinary least square method and its versions. Uncertainties of measurements at any distances can be reduced to several nanoseconds by averaging for more than one day. Precision of synchronization in this case is influenced most of all by uncertainties of coordinate assignment of receiving aerials and equipment delays in the receiver. That is why coordinates of receiving aerials of non-requesting measuring stations (NMS) and coordinates of spacecrafts (SC) should be known with an error that does not exceed several dozens of centimetres in the same coordinate system. For measurement of delays navigation signals' simulators, which form signals similar to those that are radiated from the spacecraft, are used. In practical work task of synchronization is reduced to calibration of difference between delays of receivers by means of transportation of a standard receiver. Precision of synchronization is also greatly influenced by instability of clock scales located on board a spacecraft and NMS clock scales. Consequently, desynchronization of clock scales occurs which can be partially taken into account by means of an appropriate mathematical model, which would enable to calculate values of compensating corrections. Precision of calculation of these corrections is influenced by:


According to researches described in the work (Unoshev, 1983), the highest precision of synchronization of spaced-apart clocks А and В is achieved by application of quasisynchronous receiving method in locations А and В of signals from one SCi (method in common view (СV)). This method enables to minimize the listed errors thanks to choice of optimum viewing conditions and application of processing algorithm. Principle of method can be explained by means of analysis of equation of signal propagation delay measurement in the way from SC to consumer equipment (CE) in location А. Let us represent the delay equation as follows:

$$
\tau\_{iA} = \frac{\left| \overline{r\_{iA}} \right|}{\nu} + \Delta T\_A - \Delta T\_i + \delta\_{\text{LiA}} + \delta\_{\text{TiA}} \tag{10}
$$

where

374 Modern Metrology Concerns

because the clocks being compared are located in different coordinate frames, that move in parallel with each other with variable speed and which are different in gravity field potential values. That is why it is also necessary to take into account corrections for relativistic effect in any other methods of synchronization of scales of spaced-apart clocks. Synchronization of time scales by means of TQC, by one- or two-way radio transmission methods, as well as methods of taking into account corrections for relativistic effect and other natural factors which influence precision of measurements, are described in details in

Synchronization of clocks in compliance with GNSS signals is based on receiving by aerials of spaced locations of the same navigation signals from radiating aerials located in outer space. GNSS satellites radiate exact time signals by means of atomic clock that is

Receiver clock is also synchronized with system time, and as a result it is possible to calculate distance from satellite to receiving aerial according to a measured difference between radiation time and time of receiving signals from the satellite. In order to determine three spatial coordinates of a consumer, delay factors for radio signal propagation from at least three satellites at the same time are measured; it enables to receive a single-valued solution of photographic intersection. In order to determine difference between onboard clock scale and ground borne clock scale, it is necessary to measure additionally a delay factor from one more satellite. Then system of four equations that has 4 indeterminants (three coordinates and difference between scales) and a single-valued solution can be set up. In practical work many redundant measurements from ground-station network by GNSS spacecrafts constellations are carried out. Number of redundant equations achieves hundreds and thousands. These equations are solved with an ordinary least square method and its versions. Uncertainties of measurements at any distances can be reduced to several nanoseconds by averaging for more than one day. Precision of synchronization in this case is influenced most of all by uncertainties of coordinate assignment of receiving aerials and equipment delays in the receiver. That is why coordinates of receiving aerials of non-requesting measuring stations (NMS) and coordinates of spacecrafts (SC) should be known with an error that does not exceed several dozens of centimetres in the same coordinate system. For measurement of delays navigation signals' simulators, which form signals similar to those that are radiated from the spacecraft, are used. In practical work task of synchronization is reduced to calibration of difference between delays of receivers by means of transportation of a standard receiver. Precision of synchronization is also greatly influenced by instability of clock scales located on board a spacecraft and NMS clock scales. Consequently, desynchronization of clock scales occurs which can be partially taken into account by means of an appropriate mathematical model, which would enable to calculate values of compensating corrections. Precision of

errors of an unpredictable deviation of standard clock scale in time intervals between

errors of measurements of points of standard clock scale and spaced-apart clock NMS

errors of an unpredictable deviation of NMS clock scale in time intervals between

the book (Oduan & Gino, 2002).

synchronized with system time of central synchronizer.

calculation of these corrections is influenced by:

synchronization sessions;

synchronization sessions.

scale;

$$\left| \overline{r\_{iA}} \right| = \sqrt{\left(\mathbf{x}\_A - \mathbf{x}\_i\right)^2 + \left(y\_A - y\_i\right)^2 + \left(z\_A - z\_i\right)^2} \tag{11}$$

is a geometric range from SCi, to CE in location А;

is average radio signal propagation speed from SC to NMS;

 *TT T A RA C* is difference between receiving equipment clock scales in location А and system scale *TC* ;

*TTT i iC* is difference between SCi clock scale and system scale *TC* ;

*UiA* is signal delay in ionosphere on the way SCi -A;

*TiA* is signal delay in troposphere on the way SCi -А.

Let us assume that in locations А and В time keepers are located. At these locations the reception of the same signal from some SCi is carried out at the time points *TA* and *TB* and differences between receiving equipment scales *TRA*, *TRB* and time keepers scales are measured:

$$
\Delta\_A = T\_{RA} - T\_{A\prime} \quad \Delta\_B = T\_{RB} - T\_B \tag{12}
$$

Then, after data exchange *<sup>A</sup>* и *<sup>B</sup>* in locations А and В one can find the second differences:

$$
\Delta\_{AB} = \Delta\_A - \Delta\_B = e\_\Sigma - \left(T\_A - T\_B\right). \tag{13}
$$

These differences contain information concerning discrepancy between keepers scales *TA* and *TB* and overall synchronization error *e* . The lowest level of synchronization error in the "CV" mode is achieved at the moment SC crosses "traverse plane" (TP) – a plane that crosses the midpoint of segment АВ transversely to it.

Now the various consumers set the increasingly higher requirements for time standards synchronization and frequency nominal coincidence. For example, a synchronization of the primary time standards with an accuracy of (100-10) ps and a frequency coincidence of 10-15 to 10-16 per day is required for an effective operation of the high-speed digital fibre optic communication lines, which transfer data at the rates of tens or hundreds tera-bits per second. Only the VLBI technology can fulfil such requirements at long distances 2000 km or more (Finkelshtein, А. (2007).
