Fifth Generation (5G) Mobile/Cellular Radio Access Network (RAN)1 systems, industrial automation and control systems2as well as land3 and ocean4 observation networks all require real-time connectivity with precise time synchronization in order to provide robust reference timing information to devices located in these networks on a common time base with a jitter level of less than 1 microsecond1. These requirements are typically met through wired technologies such as Time Sensitive Networking (TSN)5. TSN provides guaranteed real-time data delivery based on IEEE-802.1 with precise time synchronization. Additionally, recent advances have been made in fiber optic time and frequency techniques which allow near perfect compensation for time delay or phase fluctuations when used bi-directionally on the same optical fibers to allow for time synchronization with an accuracy ranging from 10 ps to less than 1 ns depending on the link length and the technology used6,7,8,9,10. While wireless technologies offer various advantages for network communication11.12, accuracy is one of the most important concerns. For example, since seismological and volcanological observations with an array of seismometers require the seismic wave sampling rate to be greater than 1 kHz, in this case wireless time synchronization accuracy of less than 10 microseconds would be required.3. Wireless devices can achieve perfect time alignment with Coordinated Universal Time (UTC) using Global Positioning System (GPS)/Global Navigation Satellite System (GNSS) receivers. Currently, a 2 ns level of accuracy is achievable with GPS-based time transfer links13 and even 1 ns accuracy can be achieved with a new state-of-the-art method for calibrating receivers14. Additionally, two-way satellite time and frequency transfer (TWSTFT) links with geostationary satellites could improve this accuracy to sub-nanosecond levels.15. However, this solution does not work when GPS signals are not available or when GPS signals are only partially available (e.g. polar, inland, mountainous areas, underground or underwater environments) or when GPS network nodes malfunction (e.g. reception of signals from different GPS satellites or time lag of GPS satellites). Also, if we equip all nodes in the network with GPS receivers, the total power consumption increases and therefore the battery drains faster. Reliable battery performance, specifically maintaining longer performance times between battery charging sessions, is a critical issue for field measurements in particular.
Requirements for effective wireless synchronicity for industrial use have been summarized by several researchers16.17. The possible approaches have been classified into three categories. Class (I): remote control and monitoring, Class (II): mobile robotics and process control, and Class (III): closed-loop motion control. For classes (I), (II) and (III), synchronicities with accuracies of less than 1 s, 1 ms, 1 µs respectively are required. In order to meet these requirements, there have been various WLAN-based research approaches addressing wireless time synchronization techniques, including the Reference Broadcast Infrastructure Synchronization Protocol method, which has achieved an accuracy from 200 ns to 3 µs.18the adaptive synchronization method in multi-hop time-slotted-channel-hopping (TSCH) networks, which achieved an accuracy of 76 µs19the temperature-assisted clock synchronization method, which achieved an accuracy of 15 µs20and a time synchronization method based on the second-order linear consensus algorithm, which realizes an accuracy of 1 µs21. Other techniques include the dynamic stochastic time synchronization method, which achieved an accuracy of about 8 µs with a Kalman filter (KF) estimator22and the 6.29 µs fine-grained grating time synchronization with a linear regression (LR) estimator23. There are advantages and disadvantages for all of these techniques. Since all of these aforementioned techniques use electromagnetic waves for communications, relatively small sized devices can be facilitated. However, in order to avoid communication failures due to noise and collisions, usually the automatic repeat request (ARQ) mechanism and communication latency must be included in these techniques; thus degrading the quality of synchronization. On the other hand, since the presently proposed technique uses multiple natural particles arriving around the world at the same time, such communication failure and message collisions do not occur. However, a larger device size, compared to those used in WLAN techniques, would likely be required due to the limited flux of cosmic rays.
In underwater environments, the situation is harsher because WLAN techniques cannot be used in water. If we compare radio networks for general computing or sensor networks to short-range acoustic networks, we see that the propagation delay is much greater due to a large difference between the speed of light ( a few hundred thousand km/s) and the speed of sound in water (1500 m/s)24. Recently, a high time-resolution (ns-scale) wireless sensor network has been designed, consisting of sensor nodes that are synchronized to within 1 ns using periodic high-intensity optical pulses from bursts of light-emitting diodes (LEDs) .25. However, in this scheme, an empty space is required between the nodes, and therefore it is difficult to practically use this technique in an environment such as inside commercial buildings, underwater or in an underground complex. One possibility to solve this problem is to use an atomic clock to provide backup timing signals when the GPS signal is lost. For example, a commercially available cesium oscillator provides stable timing information with a drift level of only 100 ns in 14 days. However, the extremely high hardware cost of the atomic clock (over $300k) limits its large-scale use.26. Another possibility to temporarily solve this problem is the “holdover”.27. Synchronization standards have defined the term “holdover” to mean when the network continues to operate reliably even when the synchronization input (eg, GPS/GNSS signals) has been interrupted or becomes temporarily unavailable. To this end, the Oven Controlled Crystal Oscillator (OCXO) has been industrialized to provide a reliable and accurate efficiency measurement capability; this can be used during times when the GPS/GNSS receiver is not picking up a signal. However, the drift level of the OCXO is much higher than the atomic clock and is generally limited to 0.5 microseconds per hour27, which means that the synchronization can deviate by more than 1 microsecond in 24 hours. If a non-GPS timing input could be provided frequently to OCXO, devices on the network could be synchronized more accurately and consistently.
The muon component of an extended air shower (EAS) was used to estimate the energy and mass of its primary cosmic rays28.29. An EAS can be measured by sampling multiple showers of secondary particles at ground level with 2-dimensional scattered detector arrays such as KASCADE30GREX/COVER_PLATEX31and AKENO32. Since the primary cosmic rays arrive at a speed close to the speed of light, the resulting secondary particles generated in the atmosphere tend to travel generally in the same direction as the primaries and arrive at ground level almost at the same time (this time structure is referred to below as EAS time structure); however, the shower particles spread slightly laterally as they move towards the ground surface, generating a specific and recognizable spatial extent of shower particles at ground level (this spatial extent will be referred to hereafter as the EAS disk) . Muons, one of the shower particles, are generally produced near the tropopause; however, they scatter much less than electromagnetic (EM) particles and therefore their trajectories towards the Earth’s surface are generally straight. On the contrary, EM particles reach the ground level after undergoing multiple diffusion processes. As a result, their path lengths are longer than the path lengths of muons, and therefore each has a longer time of flight (TOF). As a result, the muonic components arrive earlier at ground level than the EM components. The temporal structure of the EAS disk has been extensively studied for muons with energies greater than 10 PeV, and the mean arrival time and disk thickness (standard deviation of the particle arrival time distribution) have been measured as a function of the distance from the axis of the shower, and it was found that inside an EAS disk area measuring less than 200 m from the axis of the shower, these muons arrive in the 50 ns time range33.
Cosmic ray muons are highly penetrating particles, and muography takes advantage of the characteristics of muons, in particular their penetrating nature and universality, for a wide variety of applications, including visualization of the internal structure of volcanoes.34.35ocean36railway tunnels37natural caves38and cultural heritage39 global. Likewise, using its universality and relativistic nature, cosmic muons can be used for underwater or underground navigations.40. This paper proposes a novel wireless time synchronization technique that takes advantage of the characteristics of EAS particles, the predictable nature of their arrival at the Earth’s surface (in conjunction with OCXO), to provide stable and accurate time synchronization. without GPS signal input; the results of this proposal showed the ability of CTS to achieve perpetual time synchronization levels below 100 ns. This technique is applicable everywhere on Earth where muons can arrive, including underground and underwater regions.