Positioning system using muons

Abstract

Provided is a positioning system capable of performing positioning stably with high accuracy by using lightweight equipment. This positioning system includes a reference detector, a reception detector, a communication means for performing communication between the reference detector and the reception detector, and a calculation unit. The reference detector and the reception detector are each configured to detect a zenith angle and an azimuth angle of incident muons. The calculation unit is configured to calculate a relative position of the reception detector relative to the reference detector on the basis of at least the zenith angle and the azimuth angle. The reference detector and the reception detector each include an internal clock in which time points at which the muons are incident are continuously recorded. The calculation unit is further configured to synchronize the internal clocks of the reference detector and the reception detector on the basis of the continuously recorded time information.

Description

Muon-based positioning system

[0001] The present invention relates to a positioning system using muons, and more particularly to a positioning system that uses cosmic ray muons and is capable of stable, highly accurate positioning using lightweight equipment even inside buildings or underground, where positioning is difficult using conventional global positioning systems (GPS).

[0002] One positioning technology available is the Global Positioning System (GPS), which is based on satellite communications. However, because GPS requires radio wave communication with satellites, there is a problem in that the accuracy of positioning is significantly reduced inside buildings due to diffuse reflections from obstacles such as windows. Furthermore, GPS positioning is considered impossible underground because radio waves cannot reach the area.

[0003] In recent years, a muometric positioning system (MuPS) utilizing cosmic ray muons (also known as muons) has been proposed (Non-Patent Document 1). Cosmic ray muons are one of the elementary particles formed when the Earth's atmosphere reacts with cosmic rays accelerated by high-energy events such as supernova explosions in the galaxy. Cosmic ray muons have strong penetrating power and can penetrate any man-made structure at nearly the speed of light in a vacuum. Furthermore, because the intensity of muons is constant regardless of the angle of arrival and the number of muons arriving per unit time is almost constant, the distance between the ground-based reference detector and the underground receiving detector can be determined by measuring the muon's time of flight between the ground-based reference detector and the underground receiving detector.

[0004] In laboratory-scale experiments, the reference detector and the receiving detector were connected by wires, which significantly limited the degree of freedom of navigation. Therefore, a new wireless muPS system called the Muometric Wireless Navigation System (MuWNS) was proposed, which functions without requiring a wired configuration between the reference detector and the receiving detector (Non-Patent Document 2).

[0005] Tanaka, HKM Muometric positioning system (μPS) with cosmic muons as a new underwater and underground positioning technique. Scientific Reports volume 10, Article number: 18896 (2020)Tanaka, HKM Wireless muometric navigation system. Sci Rep 12, 10114 (2022)

[0006] However, in the initially proposed MuWNS, extremely precise timing accuracy (e.g., <300 ps) is required to identify the TOF (Time of Flight) of the same muon event (i.e., whether the muon passing through the reference detector and the receiving detector is the same muon, and the time of flight of the muon between the reference detector and the receiving detector), and this requires expensive components such as atomic clocks. Nevertheless, the navigation accuracy is only 2 m to 14 m, which is far from the level required for practical navigation applications.

[0007] The present invention was completed in consideration of the above problems, and in one embodiment, it is an object of the present invention to provide a positioning system that is capable of stable, highly accurate positioning using lightweight equipment.

[0008] As a result of extensive research, the inventors have discovered that a more flexible and stable long-term positioning is possible based on a principle that is fundamentally different from the principle of measuring the distance between a reference detector and a receiving detector, which is the basis of conventional navigation technology. More specifically, rather than relying on extremely precise timing to identify the same muon event, the same muon event can be identified by measuring the muon direction vector, i.e., the muon incident angle, with both the reference detector and the receiving detector while synchronizing the internal clocks of the reference detector and the receiving detector, thereby enabling stable positioning at low cost. Furthermore, centimeter-level positioning accuracy is possible, a significant improvement over conventional technology.

[0009] The present invention has been completed based on the above findings, and is exemplified below.

[0010] [1] A positioning system including a reference detector, a receiving detector, communication means for communicating between the reference detector and the receiving detector, and a calculation unit, wherein the reference detector and the receiving detector are each configured to detect a zenith angle and an azimuth angle of an incident muon, the calculation unit is configured to calculate a relative position of the receiving detector with respect to the reference detector based on at least the zenith angle and the azimuth angle, the reference detector and the receiving detector each include an internal clock configured to continuously record a time point when a muon is incident, and the calculation unit is further configured to synchronize the internal clocks of the reference detector and the receiving detector based on the continuously recorded time information. [2] The calculation unit is configured to calculate a width T w The internal clock of the reference detector or the receiving detector is shifted by 0.1 to 1 s, and among the incident muons detected by the reference detector and the receiving detector, T w [3] The system according to [1], wherein the calculation unit counts incidents of muons within a time difference of 2T, and regards the time shift that results in the highest count number as the time difference between the reference detector and the receiving detector, thereby establishing synchronization of the internal clocks of the reference detector and the receiving detector. w[4] The system according to [2], wherein the calculation unit is configured to count incident muons by changing the time shift in increments of . [4] The system according to [2] or [3], wherein the calculation unit is configured to count 10 to 100 incident muons to establish synchronization between the internal clocks of the reference detector and the receiving detector. [5] The system according to any one of [1] to [4], wherein the calculation unit is configured to continuously calculate the position of the receiving detector, and is further configured to obtain N consecutive calculated values ​​(N is an integer greater than or equal to 3), calculate an average thereof, delete the calculated value farthest from the average among the N calculated values, average the remaining N-1 calculated values, and output the result as the position of the receiving detector. [6] The system according to any one of [1] to [5], wherein the reference detector is a multi-wire proportional chamber (MWPC).

[0011] According to the present invention, it is possible to provide a positioning system that is capable of performing stable, highly accurate positioning using lightweight equipment.

[0012] 1 shows the relationship between the muon impact position (x3, y3, z2) at the receiving detector ("Receiver") and the muon impact position (x1, y1, z1) at the reference detector ("Reference") when the vertical position of the receiving detector (i.e., the vertical distance D between the receiving detector and the reference detector) is known. In the figure, "Mu" means muon. This figure shows the relationship between the muon impact position (x3, y3, z2) at the receiving detector ("Receiver") and the muon impact position (x1, y1, z1) at the reference detector ("Reference") when the vertical position of the receiving detector is unknown. This figure shows the results of tracking the position of the receiving detector when the reference detector is placed on the ceiling of a building and the receiving detector is placed on a horizontal floor and the receiving detector is moved along a cross-shaped route with a total length of approximately 5 meters. This figure shows the results of averaging the calculated receiving detector positions for the test shown in FIG. 2. This figure shows how CTC lock is maintained over a period of more than one hour. 1 shows a typical "time correlation" plot of a time sequence as a function of the time shift Δt between the timestamp of the receiving detector and the timestamp of the reference detector, and FIG. 2 shows a schematic diagram of the configuration of a positioning system according to an embodiment of the present invention, and FIG. 3 shows the configuration of an example of the positioning system of the present invention.

[0013] Next, embodiments of the present invention will be described in detail with reference to the drawings. It should be understood that the present invention is not limited to the following embodiments, and that appropriate design changes and improvements may be made based on the ordinary knowledge of those skilled in the art without departing from the spirit of the present invention.

[0014] (1. Vector MuPs) First, the principle of positioning using the muon's direction vector (hereinafter referred to as "Vector MuPs") will be explained. Unlike MuWNS, in Vector MuPS, the position of the receiving detector ("Receiver") is determined by the angle of the incident muon. If the vertical position (z = D) is known or given by an external source, one muon trajectory is sufficient to accurately identify the muon collision position (x3, y3, z2) on the receiving detector, i.e., the intersection point (see formula (1) below). (x3, y3, z2) = (x1 + (z2 - z1) tan θ, y1 ​​+ (z2 - z1) tan θ tan φ, (z2 - z1)) = (x1 + D tan θ, y1 ​​+ D tan θ tan φ, D) (1)

[0015] where (x, y, z) is the impact position of the muon on the reference detector ("Reference"), and θ and φ are the zenith and azimuthal angles of the incident muon (FIG. 1A). Note that θ and φ are in the polar coordinate system.

[0016] If the vertical position of the receiving detector is unknown, then (x, y, z) and (x, y, z) are additionally defined as the intersection points of the second muon trajectory and the reference detector, and the second muon trajectory and the receiving detector, respectively. If (x, y, z) and (x, y, z) are closer than the required position resolution, the three-dimensional position of the receiving detector can be derived from the two muon trajectories. This is because it is reasonable to approximate the position where these two trajectories are closest to each other as the position of the receiving detector (Figure 1B).

[0017] For orbit A and orbit B, vector a (a x , a y , a z ) and b(b x , b y , b z ), and two parameters s and t are introduced to determine the three-dimensional positions (x p , y p , z p ) and (x q , y q , z q) are defined respectively (the following formulas (2-1) and (2-2)). (x p , y p , z p ) = (x1 + sa x , y1+sa y , z1+sa z ) (2-1) (x q , y q , z q ) = (x2 + tb x , y2 + tb y , z1+tb z ) (2-2)

[0018] Next, d 2 If we define d as the distance between the closest points on trajectory A and trajectory B, it can be calculated as follows: 2 = (x p -x q ) 2 +(y p -y q ) 2 +(z p -z q ) 2 (3)

[0019] Since (x1, y1, z1), (x2, y2, z1), vector a and vector b are known, there are only two unknown parameters (t and s) in equations (2-1) and (2-2). 2 For , t and s can be found using the following binomial equations (3-1) and (3-2). 2 / ∂s=0 (3-1) ∂d 2 / ∂t=0 (3-2)

[0020] Here, the distance [(x4 - x3) 2 + (y4 - y3) 2 ] 1 / 2 is shorter than the required position resolution, the position where these two muon orbits are closest can be approximated as the position of the receiving detector (Equation (4) below). Therefore, by introducing the concept of vectors, Equations (3-1) and (3-2) show that two muon orbits are sufficient to identify the position of the receiving detector. (x p, y p , z p ) ~ (x q , y q , z q ) ~ (x3, y3, z2) ~ (x4, y4, z2) (4)

[0021] When the position of the receiving detector is defined in this manner, the maximum position error (z) in the z direction is: z = (W 2 +W2 2 ) 1 / 2 tanθ * (5)

[0022] where θ * is the angle between these two muon orbits, and W1 and W2 are the lengths of the long and short sides of the receiving detector, respectively.

[0023] In MuWNS, x, y, z, and t must be derived by solving the following four-term equation: L 2 i = (x i -x p ) 2 +(y i -y p ) 2 +(z i -z p ) 2 +ct 2 (6) where L is the distance between the reference detector and the receiving detector, i is the reference detector number (as there can be multiple reference detectors), and c is the speed of light in a vacuum.

[0024] Therefore, MuWNS requires at least four muon orbits for three-dimensional positioning and at least three for two-dimensional positioning. On the other hand, vector MuPS can reduce this number to two or one. Because cosmic ray muons are limited, reducing this number can significantly speed up the positioning process. Therefore, for three-dimensional or two-dimensional positioning, the positioning frequency (positioning time resolution) is simply doubled or tripled, respectively. This enables stable and highly accurate positioning. Note that the results calculated based on the above principle represent the relative position of the receiving detector with respect to the reference detector. Since the reference detector is usually placed in a known location, the location of the receiving detector can be identified. The contents of Non-Patent Documents 1 and 2 are incorporated herein by reference.

[0025] (2. Positioning Accuracy) Positioning accuracy is determined by the angular resolution (δθ, δφ) of the reference detector and the receiving detector. Assuming that the angular resolutions of the reference detector and the receiving detector are the same, and that the zenith angle resolution δθ and the azimuth angle resolution δφ are also the same (δθ = δφ), the positioning accuracy (δx) at (x, y, D) can be expressed as follows: δx = δθ [(x - x1) 2 +(y-y1) 2 +D 2 ] (7-1) δx=δθL (7-2)

[0026] An angular resolution of ≤10 mrad for determining θ and φ can be easily achieved with currently available muon detectors, making it possible to achieve centimeter-level positioning accuracy for L ≤ 10 m. For example, the angular resolution reported in Olah, L., Tanaka, HKM, Ohminato, T. et al. High-definition and low-noise muography of the Sakurajima volcano with gaseous tracking detectors. Sci Rep 8, 3207 (2018) is 2.7 mrad.

[0027] To improve positioning accuracy, it is preferable that the positioning system be able to identify identical muon events. That is, because cosmic ray muons rain down from all angles, there may be muons that are incident only on the reference detector and not on the receiving detector, or that are incident only on the receiving detector and not on the reference detector. Even if such muons are detected by the reference detector or the receiving detector, they cannot represent an accurate position and will become noise (also called "background").

[0028] Figure 2 shows the results of tracking the position of the reference detector placed on the ceiling of a building and the receiving detector placed on a horizontal floor as it was moved along a cross-shaped route with a total length of approximately 5 meters. The graph on the left plots the results of calculating the positions of all muons detected by the receiving detector, while the graph on the right plots the results of calculating the positions only when muons with the same direction vector were detected between the reference detector and the receiving detector. In this test, if the angular difference between the direction vectors detected by the reference detector and the receiving detector is within 80 mrad (4.6 degrees), they are considered to have the same direction vector.

[0029] As can be seen from Figure 2, most of the noise has disappeared in the graph on the right, and the route of the receiving detector has almost the same shape. Therefore, by identifying the same muon event (i.e., the muon that passed through the reference detector and the receiving detector is the same muon), noise can be eliminated and a more accurate position can be calculated.

[0030] However, unless the identity of the muon itself can be proven, it is not possible to identify exactly the same muon event, so the above method is essentially statistical, and in order to further improve positioning accuracy, it is possible to further average multiple measurement values.

[0031] Specifically, one possible approach is to obtain N consecutive calculated values ​​(N is an integer equal to or greater than 3), calculate their average, delete the calculated value farthest from the average value among the N calculated values, average the remaining N-1 calculated values, and output the result as the position of the receiving detector. Figure 3 shows the results of averaging the calculated position values ​​of the receiving detector. In the graph on the left, N=4, and in the graph on the right, N=8. It can be seen that averaging a larger number of values ​​improves positioning accuracy.

[0032] (3. Cosmic Time Calibration) A positioning system according to an embodiment of the present invention can identify the same muon event by measuring the direction vector of the muon with both the reference detector and the receiving detector, and therefore can significantly improve positioning accuracy without using expensive components such as atomic clocks. The reason for this is as follows.

[0033] Cosmic ray muons are not frequently injected, so when the reference detector and the receiving detector detect the injection of a muon with the same direction vector at almost the same time, it is highly likely that this is the same muon event. Therefore, it is possible to identify the same muon even without an accurate clock or high-speed wireless communication to reliably and continuously maintain time synchronization between the reference detector and the receiving detector. For example, the width of the allowable time difference between the reference detector and the receiving detector, i.e., the time window (T W) may be about 0.1 ms. This is a much looser time window compared to MuWNS, which requires picosecond-level time accuracy. The time window can be set appropriately depending on the required accuracy, and can be any time, for example, 0.2 ms or less, more preferably 0.1 ms or less, even more preferably 0.05 ms or less, and even more preferably 0.01 ms or less. The lower limit of the time window is not particularly limited, but can typically be 0.0001 ms or more, or 0.001 ms or more, or 0.01 ms or more. In some embodiments, the time window can be any time between 0.0001 ms and 0.2 ms, any time between 0.001 ms and 0.1 ms, or any time between 0.01 ms and 0.05 ms.

[0034] Herein, the establishment of time synchronization between the reference detector and the receiving detector by relying on the detection of muons is referred to as "Cosmic Timing Calibration (CTC)." The basic concept of CTC is described in Tanaka, H.K.M. "Cosmic time calibrator for wireless sensor network." Scientific Reports, volume 13, Article number: 5951 (2023), the contents of which are incorporated herein by reference.

[0035] Considering the fact that the receiving detector can be moved anywhere and that muons passing through both the reference detector and the receiving detector may be the only means of connecting the two, time synchronization between the two is necessary. Since the reference detector and the receiving detector are assumed to be located at separate locations, it is assumed that timing information is based on the internal clocks of the reference detector and the receiving detector, respectively. In a positioning system according to one embodiment of the present invention, the internal clocks of the reference detector and the receiving detector are configured to continuously record the time points when muons are incident, i.e., muon events.

[0036] Precise time synchronization can be achieved using the CTC mentioned above. Continuous calculations can be used not only to measure position but also to adjust the internal clock. This allows synchronization to be continuously maintained; that is, the reference detector and the receiving detector are "locked" to each other. Because the level of random background is low enough, once this CTC lock is acquired, it is highly unlikely to be lost.

[0037] Figure 4 shows how CTC lock is maintained over a period of more than an hour. In this test, the data update rate was 0.31 Hz, i.e., successive calculations were taken approximately every 3 seconds. The time window (T W After obtaining eight updates within a time period of ≈0.1 ms, the internal clock of the receiving detector was adjusted (offline) to match the internal clock of the reference detector. However, in another embodiment of the present invention, the internal clock of the reference detector can also be adjusted to match the internal clock of the receiving detector. The vertical scale indicates the time difference between the trigger timestamps of the receiving detector and the reference detector. The accumulation of dots near zero corresponds to updates, while the scattered dots represent random background. To maintain synchronization of the two completely independent internal clocks, a rolling average of eight updates was used. The time difference between updates varied only 0.01 to 0.02 ms on a minute-by-minute basis. It can be seen that even with this internal clock and low update frequency, CTC lock is securely maintained. Therefore, time synchronization is possible via commonly used communication technologies without the need for particularly precise clocks. In this way, stable, highly accurate positioning is possible even with lightweight equipment in the receiving detector.

[0038] It should be noted that smart algorithms such as machine learning can be used to optimize the time window values ​​and utilize receiver detector position constraints (e.g., eliminating impossible position ranges) to more effectively maintain CTC lock.

[0039] It has been demonstrated that once CTC lock is established, time synchronization can be maintained by acquiring and following all subsequent updates. Next, we describe how to establish CTC lock on the first (few) updates.

[0040] In the first step, both the receiving detector and the reference detector acquire data for several minutes. The amount of data is not particularly limited, but typically records 10 to 100 muon incidents, i.e., 10 to 100 updates. Next, the receiving detector shares a timestamp with the reference detector via communication means, resulting in a time sequence T Rec,1 …T Rec,N Similarly, the time sequence of the reference detector is T Ref,1 …T Ref,M (N and M are both 10 4 ~10 5 (It can be an integer of order 0.) For all combinations (n, m), the time difference t diff = (T Rec,n -T Ref,m ) can be evaluated (n and m denote integers up to N and M, respectively).

[0041] In the next step, the time sequence in which the muon incident was detected is calculated as -T W <(t diff −Δt) < T W Δt represents the unknown time shift between the clocks (the time difference between the internal clocks of the receiving detector and the reference detector). Since Δt is unknown, for example, 2T W The subsequent calculations are performed by changing the time increments. Normally, Δt is expected to be in the range of 0.1 to 1 s. W <(t diff −Δt) < T W The time difference between the time when the muon incident on the receiving detector and the time when the muon incident on the reference detector is detected is T wThis means that the time difference between the receiving detector and the reference detector is within Δt, in which case the same muon event is considered to be detected and counted as one. When the Δt between the receiving detector and the reference detector becomes true Δt, a peak corresponding to the true Δt value is expected, since all real identical muon events will be counted. In that case, the true updates (true muon events) will add up, but at time shifts other than Δt, only random (background) combinations will be obtained. Figure 5 shows a typical "time correlation" plot of a time sequence. Data was acquired for 2 minutes with an update frequency of 0.6 Hz. The vertical axis shows the time difference between any combination of muon events within the time window T W The counts shown are for cases where the error is less than T. The counts showing a sharp peak correspond to actual muon events. All other counts are from random background. In this case, the actual time difference between the clocks was about 110 ms. W Using this information, which has an accuracy of 1 / 2, the clocks of the receiving detector and the reference detector can be adjusted. After that, CTC lock synchronization can be maintained for an arbitrarily long period of time. Note that the direction vector of the incident muon does not need to be taken into account in the CTC lock procedure.

[0042] (4. Positioning System) FIG. 6 shows a schematic diagram of the configuration of a positioning system according to one embodiment of the present invention. The positioning system 1 of this embodiment includes a reference detector 11, a receiving detector 12, a communication means 13 for communicating between the reference detector 11 and the receiving detector 12, and a calculation unit 14. The specific configuration of the reference detector 11 and the receiving detector 12 is not limited as long as they have the function of detecting muons. For example, a multi-wire proportional chamber (MWPC) or a scintillator can be used. However, from the viewpoint of positioning accuracy, it is preferable to use a MWPC. In particular, it is preferable to use a MWPC as the reference detector 11. The MWPC can be configured, for example, with multiple wires arranged at equal intervals on a flat surface. The contents of JP 2017-198482 A are incorporated herein by reference. Furthermore, it is preferable that the MWPC has a structure in which two or more wire chambers are stacked. This is because higher angular resolution can be achieved. In the embodiment of FIG. 6 , the reference detector 11 is shown as a two-layer MWPC. Meanwhile, the receiver-detector 12 can be any detector, such as a scintillator, a GEM (Gas Electron Multiplier), a MWPC, or a GRPC (Glass Resistive Plate Chamber). However, since a small volume is often preferable, a detector already installed in a mobile information communication device such as a mobile phone or tablet terminal can be used, eliminating the need for a new component as the receiver-detector. For example, the receiver-detector 12 can be configured as a complementary metal-oxide-semiconductor (CMOS), which is already used in cameras on common mobile phones. Although the embodiment of FIG. 6 includes one receiver-detector 12, the positioning system 1 may include multiple receiver-detectors 12.

[0043] A communication means 13 exists between the reference detector 11 and the receiving detector 12. The communication means 13 can be a wired or wireless connection, but a wireless connection is preferred for convenient positioning in locations such as underground. The wireless connection can be any wireless asynchronous communication channel, such as a wireless local area network (LAN) such as Wi-Fi, Bluetooth (registered trademark), ultrasonic, infrared, or optical-based data transfer. Even in this case, as mentioned above, cosmic ray muons are not frequently incident, so it is possible to synchronize the reference detector 11 and the receiving detector 12. Furthermore, location information can be encrypted using Cosmic Coding and Transfer (COSMOCAT) technology to enhance security. For more information on COSMOCAT technology, see Tanaka, H.K.M. "Cosmic coding and transfer storage (COSMOCATS) for invincible key storage." Sci Rep 13, 8746 (2023). The entire contents of said publication are incorporated herein by reference.

[0044] To achieve time synchronization between the reference detector 11 and the receiving detector 12, each of them includes an internal clock (not shown) configured to continuously record the time when a muon is incident.

[0045] The specific configuration of the calculation unit 14 is not limited as long as it has a calculation function. Typically, the calculation unit 14 has a processor (e.g., an electronic processor such as a CPU). The positioning system may also have a non-transitory storage medium (e.g., a HDD, an SSD, etc.) for storing programs for calculations. These programs can be loaded into memory (e.g., a RAM, etc.) and executed by the processor as appropriate. The calculation unit 14 may be mounted on the reference detector 11, the receiving detector 12, or any independent location. The calculation unit 14 may also be located in multiple distributed locations as multiple components. In the embodiment shown in FIG. 6 , the calculation unit 14 is mounted on the reference detector 11. If necessary, the calculation unit 14 can be connected to the reference detector 11 or the receiving detector 12 via a communication means to transmit and receive information. The communication means may be any wireless asynchronous communication channel, such as a wireless LAN (local area network) such as Wi-Fi, Bluetooth (registered trademark), ultrasonic, infrared, or optical-based data transfer.

[0046] The calculation unit 14 is further configured to synchronize the internal clocks of the reference detector 11 and the receiving detector 12 based on the continuously recorded time information. Furthermore, the calculation unit 14 determines a width T w is set, the time of the internal clock of the reference detector 11 or the receiving detector 12 is shifted, and among the incident muons detected by the reference detector and the receiving detector, T w The time shift that produces the highest count is regarded as the time difference between the reference detector 11 and the receiving detector 12, and the internal clocks of the reference detector 11 and the receiving detector 12 are synchronized. The specific method is as described above, and will not be described here.

[0047] The calculation unit 14 is configured to calculate the trajectories of the two incident muons based on the zenith angle and azimuth angle of each of the two muons, and to calculate the three-dimensional position at which the two muon trajectories are closest to each other as the position of the receiving detector 12. The specific calculation method is as described above, and therefore will not be described here.

[0048] The calculation unit 14 may also be configured to continuously calculate the position of the receiving detector 12, and may further be configured to obtain N consecutive calculated values ​​(N is an integer equal to or greater than 3), calculate their average value, delete the calculated value farthest from the average value among the N calculated values, average the remaining N-1 calculated values, and output the result as the position of the receiving detector 12. The specific calculation method is as described above, and therefore will not be described here.

[0049] As specific examples of the positioning system of the present invention, the "LowRes" and "HiRes" configurations shown in FIG. 7 were constructed. In the "LowRes" configuration, a small reference detector with an angular resolution of approximately 15 mrad is applied. On the other hand, the "HiRes" configuration was constructed using a larger-area MWPC, improving the angular resolution to 6-8 mrad. Furthermore, these two reference detectors were placed on two different floors of a building. Receiving detectors (A) to (D) were placed at the positions shown in FIG. 7, respectively.

[0050] The evaluation results of the positioning accuracy and update frequency for each of the above configurations are shown in Table 1. The positioning accuracy is a value predicted based on the angular resolution of the reference detector, and the actual angular resolution value obtained by actually performing positioning. The prediction and measurement of the update frequency will be described later.

[0051]

[0052] As can be seen from Table 1, in the "LowRes" configuration, the positioning accuracy is 3.90 cm (RMS, root mean square) when the reference detector is 2.4 m above the receiving detector. On the other hand, in the "HiRes" configuration, when the distance D (altitude difference) between the reference detector and the receiving detector is 3.3 m, the positioning accuracy is improved to about 3 cm (RMS).

[0053] And the update frequency f Uis defined as the number of muons that can be seen passing through both the reference and receiving detectors divided by the measurement time. Based on cosmic ray muons, we can predict the update frequency as follows:

[0054] The muon flux Φ is related to the detected muon velocity R from a solid angle area ΔΩ according to the following equation (8) (see Olah, L., Tanaka, HKM, & Varga, D. (eds) Muography: Exploring Earth's Subsurface with Elementary Particles. Geophysical Monograph 270. American Geophysical Union, John Wiley & Sons, Inc.: Hoboken, NJ, USA, ISBN 9781119723028 (2022)): R / (ΔΩ) = Φ(Θ)S(Θ) (8) where all quantities, including the effective detector area S(Θ), depend on the direction vector Θ. Assuming that the receiving detector is placed below the reference detector, the update frequency f U can be estimated as follows: f U =Φ Rec S Rec ΔΩ Ref (9) where ΔΩ Ref is the field of view angle of the reference detector as seen from the position of the receiving detector ("Ref" means the reference detector and "Rec" means the receiving detector). This quantity can be approximated as the following equation (10): ΔΩ Ref ≒S Ref / D 2 (10) Since muons follow a straight trajectory, the direction vector Θ of both detectors is the same. Therefore, the update frequency can be estimated as follows: f U ≒Φ Rec S Rec S Ref / D 2 = (R Rec / ΔΩ) (R Ref / ΔΩ) / (Φ Ref D 2 ) (11)

[0055] In formula (11), fU The second formula is particularly convenient because it directly uses the measurable R / ΔΩ. The muon flux Φ in the reference detector Ref Here, we assume that the roof of the building is thin enough to Ref ≒100cos 2 (θ) m -2 s -1 If the receiver is underground and the flux Φ Rec (and R accordingly) Rec ) decays, this equation holds.

[0056] There is a difference between the estimated and measured values, and the estimated f U There may be an uncertainty of about 20% in the calculation, including all systematic errors.

[0057] The above descriptions of the embodiments are merely descriptions of some preferred embodiments of the present invention, and the configurations of the embodiments can be combined in any manner based on the ordinary knowledge of those skilled in the art, as long as they do not deviate from the spirit of the present invention.

[0058] 1 Positioning system 11 Reference detector 12 Receiving detector 13 Communication means 14 Calculation unit

Claims

1. A positioning system including a reference detector, a receiving detector, a communication means for communicating between the reference detector and the receiving detector, and a calculation unit, wherein the reference detector and the receiving detector are each configured to detect the zenith angle and azimuth angle of an incident muon, the calculation unit is configured to calculate a relative position of the receiving detector with respect to the reference detector based on at least the zenith angle and the azimuth angle, the reference detector and the receiving detector each include an internal clock configured to continuously record a time when a muon is incident, and the calculation unit is further configured to synchronize the internal clocks of the reference detector and the receiving detector based on the continuously recorded time information.

2. The calculation unit calculates a time lag between the reference detector and the receiving detector within a permissible width T w The internal clock of the reference detector or the receiving detector is shifted by 0.1 to 1 s, and among the muon incidents detected by the reference detector and the receiving detector, T w and counting muon incidences within a time difference of 0.01 to 0.15, and regarding the time shift resulting in the highest number of counts as the time difference between the reference detector and the receiving detector, thereby establishing synchronization of internal clocks of the reference detector and the receiving detector.

3. The calculation unit is 2T w The system of claim 2 , configured to count incident muons by varying the time shift in increments of 0.

5.

4. The system of claim 2 or 3, wherein the calculation unit is configured to count between 10 and 100 muon incidences to establish synchronization of the internal clocks of the reference detector and the receiving detector.

5. The system of claim 1 or 2, wherein the calculation unit is configured to continuously calculate the position of the receiving detector, and further configured to obtain N consecutive calculated values ​​(N is an integer equal to or greater than 3), calculate an average thereof, delete the calculated value furthest from the average among the N calculated values, average the remaining N-1 calculated values, and output the result as the position of the receiving detector.

6. The system of claim 1 or 2, wherein the reference detector is a multi-wire proportional chamber (MWPC).

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