Cosmic-ray arrival time (CAT) indoor navigation in the World Geodetic System

Cosmic-ray arrival time (CAT) indoor navigation in the World Geodetic System | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Cosmic-ray arrival time (CAT) indoor navigation in the World Geodetic System Hiroyuki K.M. Tanaka This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3998301/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Indoor positioning system (IPS) technologies have a wide range of applications; however, three major limitations associated with currently used IPS technologies are: (1) weak penetration strength of signals to penetrate building materials, inhibiting seamless connection of outdoor coordinates to indoor coordinates; hence these technologies rely on local coordinates, making them incompatible with the world geodetic system (WGS84) and universal traceability, (2) active source signals that require beacons to transmit navigation signals. In contrast, the muometric positioning system utilizes naturally abundant cosmic-ray muons signals to compensate for some of these setbacks. However, its main practical challenges are: (1) the low signal rate (~1 per 10 days for laptop-sized receivers horizontally located 50 m apart from each other) and (2) the requirement for large reference detectors (> 4 m2) above the receiver to track cosmic ray precipitation. In this work, an alternative concept called CAT navigation, which relies on the extended air shower time structure for higher rate positioning (without requiring reference detectors) is first proposed and demonstrated; it located receivers placed on the ground floors of multiple buildings (within WGS84) in conditions where other IPS methods are difficult to apply. The resultant positioning accuracy was 3-4 m (at 50 m apart), which is reasonably accurate for GPS -IPS seamless bridging, and with a laptop sized receiver the averaged positioning signal update rate was (683 s)-1 which can be improved to (170 s)-1 with a future upgrade of the data gathering electronics. By integrating CAT receivers into GPS equipped smartphones, it is anticipated that this GPS -CAT hybrid method will seamlessly connect multi-users’ coordinates from outdoor to indoor environments. Physical sciences/Engineering/Civil engineering Earth and environmental sciences/Environmental social sciences/Energy and society Earth and environmental sciences/Environmental social sciences/Socioeconomic scenarios Earth and environmental sciences/Environmental social sciences/Sustainability Earth and environmental sciences/Environmental social sciences Earth and environmental sciences/Solid earth sciences Physical sciences/Engineering Physical sciences/Physics Physical sciences/Physics/Particle physics Physical sciences/Physics/Particle physics/Experimental particle physics Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Introduction As rapidly developing digital technology continues to shape and expand growth opportunities in many aspects of our society, it particularly influences human living spaces, improving the comfort, energy efficiency (and sustainability), and safety of our communities. The concepts of smart cities 1 , smart buildings 2 , and smart homes 3 are increasingly being studied. These studies mainly focus on environmental, energy, and safety issues 4,5,6,7 . One of the most important ways to enhance the potential of these developments is to integrate new technologies with the Internet of Things (IoT) and machine learning (ML) 2,8 . Along with these technological developments, indoor positioning system (IPS) technology has been drawing attention for its potential to benefit various aspects of IoT applications. IPS can be used for many indoor applications such as for autonomous mobile robot operation, for navigation aids for people (including individuals with disabilities), for tourist information dissemination at museums and airports, for context-aware intelligent services applied to personal networks, and for locating patients and medical personnel in hospitals. IPS technology could also be an essential component for acquiring location information in modern wireless sensor networks, for example, remote health monitoring systems. Other effective application examples of IPS include generating digital twins, and assisting designers and labor managers in the building construction and maintenance industry. Several recent research proposals have emphasized how IPS technology, integrated with Building Information Models (BIM), could drastically improve the cooperation and communication between various design and construction teams (e.g., in architectural, mechanical, electrical, and plumbing departments) to boost quality and work efficiency 9 . BIM is an innovation in architectural design to semi-automatically produce buildings from a complete virtual 3D building mechanical, electrical, and plumbing (MEP) digital model that includes attributing data such as cost, finish, and management information. It is a data efficient and groundbreaking approach which is currently becoming an industry standard. This integrated BIM 3D model not only supports the entire life cycle of a building (from design to construction to maintenance management) but also makes it possible to streamline the workflow. Generally, BIM integration within outdoor environments needs to be seamless and accurate, however the currently available IPS solutions used in tandem with BIM have restrictions when it comes to universal traceability of key aspects (such as labor in tunnels and buildings, and the location of construction resources such as vehicles and materials 10,11,12,13 ), which hinder the implementation of comprehensive and universal management of buildings and underground in urban regions. The ideal scenario would be to have GPS-IPS seamless bridging technology that could easily track (at an accuracy level of 2 to 3 m 9 ) the position of elements (potentially in every space within a city) in order to link this data to the virtual 3D city models within the universal WGS84 framework in real time. While this required level of positioning accuracy (2-3 m) is attainable with the established IPS technologies, there are limitations to the situations where it can be used. Obviously, GPS cannot be directly used in most indoor environments. Common indoor positioning technologies such as RFID 14 , ultra-wideband (UWB) 15 , visual analysis 16 , WLAN 17 , and ultrasound 18 have already been developed and used in many occasions. However, the signals used for these IPS technologies (RF, visible light, and acoustic signals) cannot directly propagate through typical building materials such as concrete and steel walls. Therefore, it is necessary to install new infrastructure (such as transmitters) throughout the building which significantly adds to the cost and maintenance for the device, installation, and associated infrastructure arrangements (e.g. electricity). Moreover, when using currently available IPS technologies, the users can acquire only the local coordinates which can hinder the traceability of the tracking. Discovering a more flexible and cost effective IPS which could seamlessly connect (with global coordinates) to GPS would not only unlock the full potential of BIM, but also would have far-reaching benefits for several other applications essential to our society. Muometric positioning system (muPS) 19,20,21,22,23,24,25,26 is a relatively new technology that uses a new signal for IPS, an elementary particle called the muon, which can penetrate through almost all matter (including concrete slabs and rock) in cities in a straight trajectory. All muons detected on the surface of the Earth are produced when primary cosmic rays (relativistic high-energy particles which are accelerated by high-energy events within the galaxy) travel within the solar system and then interact with the Earth's atmosphere. The main advantage of muPS, including the time of flight (TOF) method (Muometric Wireless Navigation System: MuWNS) 20,21,23 and the Vector method (Vector Muometric Wireless Navigation System: MuWNS-V) 22,25 , is its capability to be unaffected by obstacles surrounding or within indoor environments which often block the signals of other IPS technologies. On the other hand, there is also a drawback. Being a finite resource, naturally occurring muon flux may not be sufficiently strong for certain applications. Also, the strength of the cosmic ray muon flux tends to be dependent on its angle: the vertical flux is generally strongest and as the angle of the flux becomes increasingly horizontal, the flux decreases in proportion to cos 2 q . For example, the flux decreases to half at 45º from the zenith and to ~3% of the vertical direction at 80º from the zenith. This flux limitation affects the geometric configurations of the conventional muPS setup, and thus far the strategy with muPS has been to install a large reference detector at a location far enough above the receiver in order to capture as many cosmic rays as possible from the highest possible elevation angle. For this reason, the reference and receiver detectors used for MuWNS and MuWNS-V must be (nearly) vertically aligned. For example, when positioning 50 m away from the reference (for muons at a q =45º) a reference detector would have to be positioned 50m above the ground. Even with this configuration, the reduction of the muon flux is suppressed by 1/2, but this configuration would be impractical in most cases. However, if the reference is installed 5 m above the ground, muons in a q =85º from the zenith must be detected, so in this case the flux in the vertical direction would decrease to less than 1%. Another challenge is that as the distance between the reference and the receiver increases, the number of events is reduced in proportion to the square of the distance. The open-sky muon rate arriving from the vertical direction is approximately 70 Hzm -2 sr -127 , but even if the sensitive area of both the reference and receiver is 1 m 2 , this muon rate is reduced to 0.028 Hz when separated from the receiver by 50 m vertically. If the reference is placed 5m above the ground, this will further decrease to below 0.0003 Hz. To compensate for this, in a prior MuWNS experiment 21 , large reference detectors (with a total area of 4 m 2 ) had to be installed on the 6th floor above the ground to navigate a receiver detector with an area of 1 m 2 which was located on the basement floor. The high costs for installation and operation of these large detectors hinder its flexibility and widespread use. Moreover, even with this configuration, it took 16 minutes to successfully track one point from the receiver. There are different pros and cons associated with both MuWNS and MuWNS-V. MuWNS doesn’t require a tracker, but extremely precise and stable local clocks are needed. On the other hand, MuWNS-V doesn’t require extremely precise and stable clocks, but instead requires a tracker for at least the reference detector; its angular resolution directly links to the positional resolution, therefore a value in the order of ~10 mrad is usually required 22,25 . Since trackers consist of multiple layers of position sensitive detectors, the operational costs of MuWNS-V are usually higher than regular MuWNS. However, the TOF method which MuWNS uses requires clock adjustment at the ns level, which also causes a drop in muPS positioning accuracy; for example, with a time-synchronization accuracy of 100 ns, positioning accuracy drops to 30 m. Currently, as with RF based techniques, there is no technique to synchronize clocks located beyond a concrete slab at 10 ns accuracy wirelessly. Therefore, extremely stable (and costly) local clocks are needed for MuWNS. To improve the flexibility and potential applications of the muPS technique, we need to remove (A) trackers, (B) extremely accurate and stable local clocks, and (C) inconvenient reference detectors from the system while we could also enhance (D) the signal update rate to improve the practicality of muPS; with this new scheme, the galactic-cosmic-ray-based positioning system (GCPS) would be more adjustable and cost effective since positioning could be done solely with multiple receivers on the ground in tandem with GPS measurements (or as a backup of GPS). In this paper, we propose a new technique called CAT navigation as a method to upgrade muPS for wider applications in IPS. This approach takes advantage of the characteristics of the extended air showers (EAS) time structure; the EAS particles almost simultaneously reach detectors as far as 50 meters away from each other at a rate of roughly once every 2 seconds per square meter 28 , which is a much higher rate than is possible with than other muPS methods using single muon detection. Furthermore, since CAT navigation doesn’t require tracking cosmic-ray precipitation, there is no need to install reference detectors above the receivers. In the following sections, the principle of CAT navigation and the demonstration results are described along with the discussion about possible operational forms and limitations. Results Principle. CAT navigation measures the fluctuation width of the displacements in EAS particle arrival times between two arbitrary points located within the shower disk in order to calculate the distance between these two points, and then subsequently the two-dimensional coordinates ( x , y ) of these points are derived. Its principle is essentially the inverse of the CTS 28,29,30 concept. The time difference in EAS particle arrival times between two arbitrary points (Point A and Point B) fluctuates around the average value of the time displacements. This fluctuation width, time displacement SD (standard deviation), increases as the distance between these points increases. This phenomenon has already been observed in prior CTS works, and it has been reported that time displacement SD is degraded as the distance between these points increases 30 . The CAT positioning procedure is described as follows. Supposing that an EAS event occurs in which particles nearly simultaneously arrive at three points A ( x 0 , y 0 ), B ( x 1 , y 1 ), and C ( x 2 , y 2 ) which is a total of n times at the time t i ( i = 1, 2, ... n ) during the time interval T , the distance between A-B and the distance between A-C would be respectively: D AB = [( x 1 - x 0 ) 2 +( y 1 - y 0 ) 2 ] 1/2 , (1-1) D AC = [( x 2 - x 0 ) 2 +( y 2 - y 0 ) 2 ] 1/2 . (1-2) On the other hand, since the fluctuation widths of the arrival time difference (time displacement SD) between A-B ( s AB ) and A-C ( s AC ) (CTS time fluctuations) are a function of D , D AB and D AC can be respectively expressed as: D AB = f ( s AB ), (2-1) D AC = f ( s AC ). (2-2) s AB and s AC are given from the measurements. Therefore, if the positions of B and C are known, the position of A can be derived by substituting Eqs. (2-1) and (2-2) with Eqs. (1-1) and (1-2). Figure 1 illustrates the basic principle of CAT navigation. In this paper, the first goal is to experimentally determine the parameters of f ( s ) in Eq. (2). In principle, a minimum of two detectors are required to take a coincidence and to identify an EAS event. However, since it is expected that the coincidence rate decreases as the distance between these two detectors increases, the relative fraction of the accidental coincidence (i.e., random timestamps) generated by open-sky muons increases. For example, when using two 100-cm 2 detectors to take a dual coincidence with a coincidence time window of 100 ns, the average time interval at which an accidental coincidence occurs is 0.5´1 2 ´10 7 = 5,000,000 s (~2 months); if the size of the detectors increases to 1 m 2 , this average time interval is reduced to 500 s. However, even with 1-m 2 detectors, by taking a triple coincidence measurement with a redundant detector, random timestamp generation errors will be reduced to a rate of once in 0.33´(10 -2 ) 3 ´(10 7 ) 2 = 33,000,000 s (~1 year); hence this type of error will become negligible. On the other hand, the results from prior EAS MC simulation studies 28 indicated that adding a redundant detector reduces the event rate by a factor of ~2. Therefore, there is a trade-off between the accidental rate and the positioning signal update rate. The decision of whether to use a redundant detector needs to be optimized based on the size of the receiver we use. In the current demonstration, considering that the detector size was relatively large (i.e., the open-sky muon rate is high), three detectors to identify an EAS event were used, and to reduce the generation of random timestamps. In the following subsections, we will discuss (1) f ( s ), the distance dependence of SD of CTS time fluctuations measured with the CTS experimental setup, and (2) the CAT navigation accuracy when paired with oven-controlled crystal oscillators (OCXO). CAT reference data taking. CAT reference data were taken to determine the parameters of f ( s ). The experimental setup was the following: one detector (Receiver A), consisting of a 1500-cm 2 plastic scintillator (ELJEN200), and a photomultiplier tube (PMT; Hamamatsu R7724), and other four 1-m 2 detectors (Receivers B-E) with the same configuration as Receiver A. All of the detectors were installed indoors on the ground floor of a building. Then, the triple coincidence was taken between Receivers A-B-C, Receivers B-C-D, and Receivers B-C-E to measure the time displacement SD. The distance between Receiver A and Receiver B was 10 m, the distance between Receiver A and Receiver C was 50 m, the distance between Receiver B and Receiver D was 35 m, and the distance between Receiver B and Receiver E was 180 m. All of the detectors except for Receiver E were wired with an RG coaxial cable to get rid of the local clock drift effect. (The positioning results using an independent local clock will be described in a later section.) For Receiver E, cabling was not possible since multiple third-party buildings were located in between Receiver B and Receiver E, so GPS-time-synchronized results acquired in the prior works were utilized 30 . The electronic circuit that is used for data collection was the same as previous experiments which have already been described in many references 20,21,28,29 , so its properties are only briefly mentioned here. The electronic circuit consists of a discriminator, 4-channel TDC, OCXO, and CPLD, and the PMT signals output from Detectors A-E are first digitized by the discriminator and input to each stop channel of the TDC. In parallel, the 10MHz TTL pulse output from the OCXO is fed to the TDC start channel, and the difference ( D t ) between the output timing of the OCXO's 10MHz pulse and the PMT signal is measured. A cosmic-ray arrival timestamp (CAT stamp) is generated by adding D t to (the number of OCXO 10MHz pulses) ´ (100ns). CAT stamp lists generated from these detectors are used for finding coincidence events in a given time window, and the temporal displacements between the coincided CAT stamps (called single signals) were subsequently calculated. The averaged triple coincidence rate for the combination including the 50-m baseline (the distance between detectors) was (68 s) -1 , and the triple coincidence rate for the combination including the 180-m baseline was (360 s) -1 . According to the EAS-MC results based on the prior work 28 , the average triple coincidence time intervals are respectively 3-4s and 40-50s for the 50-m and 180-m baselines with 1-m 2 detectors. This discrepancy comes from two factors: (A) the efficiency of Receivers B-E is about 50% 30 , and (B) the area of Receiver B is 1,500 cm 2 . Therefore, the detection rate has dropped to ~1/20 and ~1/8, respectively in comparison to the estimation. In this work, a positioning accuracy of 2 to 3 m 9 was targeted. The distance dependence of the CTS time fluctuations measured with this setup will be described in the next subsection. Distance dependence of the CTS time fluctuations. The distance dependence of the time displacement SD measured with the current setup was almost linear, but a better fit is made with the following quadratic function (Figure 2). s = 0.00171 D 2 + 0.49178237 D + 4.8652112, or (3-1) D = [-0.49178237 - {0.49178237 2 - 0.00684 ´ (4.8652112 - s )} 1/2 ]/0.00342 (3-2) The fitting errors are shown in Table 1. Accuracy of CAT positioning and the positioning information update rate. The accuracy of CAT positioning depends on the granularity of the time displacement SD. Therefore, a certain number of EAS events are required. From this section onwards, the triple coincidence event rate will be referred to as the single signal update rate, and the rate at which a cluster (single signal cluster) containing a certain number of single signals is generated is called the positioning signal update rate. Here, the cluster size refers to the number of single signals in the single signal cluster. As the cluster size increases, the SD granularity improves, but the positioning signal update rate is degraded. Figures 3A-3C show time-series graphs of the time displacement SD determined within each cluster by dividing the single signals obtained for D = 50 m into clusters of different sizes. As the cluster size increases, the temporal fluctuations in SD are reduced, but the positioning signal update rate decreases. Figures 3D-3F show positioning signals obtained by converting SD shown in Figures 3A-3C into the distance D using Eq. (3-2). The resultant distancing errors are respectively 9.4 m, 6.1 m and 3.8 m for a cluster size of 10, 20 and 50. In order to achieve the targeted accuracy, a cluster size of at least 50 is required. However, when considering the time required for the positioning signal update, a cluster size of 10 is ideal, and as is explained later, positioning errors can be improved by rejecting imaginary solutions of Eq. (1). Therefore, a cluster size of 10 is employed in the following discussions. Positioning with local clocks. In the previous subsections, all the detectors were connected via wires, so the CTS time fluctuations only originated from the EAS time structure. However, in an actual CAT operation scenario, positioning is wirelessly performed using independent local clocks. Consequently, time fluctuations due to clock drift are added to the EAS time structure. In conventional muPS that utilizes the muon’s time of flight, distances are determined on an event-by-event basis, so if the clock drifts while acquiring four tracks, this clock drift directly affects positioning accuracy. For example, a drift of 10 ns leads to a positioning error of 3 m. Moreover, this time offset generally changes non-linearly. On the other hand, CAT navigation uses SD as positioning information. Therefore, a time offset between clocks does not affect positioning accuracy. Furthermore, clock drifts can be linearly approximated since its single signal update rate is much higher than conventional muPS. By tracing the time series of a single signal with a straight line and subtracting this fitted straight line from each data point, it is possible to cancel out this drift effect. In summary, the positioning procedure using the clock is as follows. (1) Record CAT stamps in each receiver using the local clock associated with each detector. (2) The generated CAT stamps are sent to the central processing unit via Wi-Fi. (3) The cross-detector time displacements are computed from these CAT stamps at the central processing unit. (4) If the time displacements are smaller than the given time window, it is regarded as a single signal, and it is added to the single signal cluster at the central processing unit. (5) Once a certain number of single signals have been accumulated, a linear function is fitted to the time-sequential cross-detector time displacement data points to remove the local clock’s relative drift effect. (6) The time displacement SD of the data points is calculated at the central processing unit. (7) The distance between the detectors is derived with Eq. (3-2) at the central processing unit. (8) The position of the receiver is derived with Eq. (1) at the central processing unit. (9) The receiver’s position information is sent back to the receiver via Wi-Fi. In this demonstration, the above procedure was implemented in tandem with OCXOs (wireless) and cables (wired), so that the OCXO effect can be separated from the EAS time structure effect. Figure 4 shows an example of the time displacement data between the detectors, and the fitted linear function for D = 50 m. Tables 2 and 3 respectively show the SD of the time displacement data points after subtraction of the fitted function and deriving the distance with Eq. (3-2). 10 independent runs are shown as an example. It can be seen that there is a large deviation in the value in Run #6 for D = 180m. This error is caused by the nonlinear clock drift (see a green dashed line in Figure 5) since the time scale required for positioning signal update was longer for D = 180m. Figure 5 shows the OCXO drift. The run numbers shown in Figure 5 correspond to the run numbers shown in Tables 2 and 3. Besides this irregularity, the error (1SD) due to the clock drift had a value of 3-4 meters regardless of the length of D . At the end of this section, the 2-dimensional wireless positioning results with OCXO will be shown. The geometric configuration and positioning results within the framework of WGS84 are shown in Figure 6A. If an imaginary solution was derived in Eq. 1, that dataset was discarded. Since imaginary solutions indicate that the circular functions in Eq. (1) do not intersect, low quality positioning signals are automatically discarded in this process. Additionally, regarding the conjugate solutions, the values closer to the initial position were taken. The resultant positioning accuracy in this geometric configuration was 3.4 m (SD) in the x direction and 4.8 m (SD) in the y direction. This x - y asymmetry comes from this geometric configuration. Figures 6B and 6C show the x - and y -direction slices of the current positioning results. The slices in the y direction are symmetrical in positive and negative directions, but the slices in the x direction are asymmetrical. This asymmetry comes from the current solution selection criteria. The current results were obtained with 1-m 2 detectors and a 1,500-cm 2 detector. A 1-m 2 detector weighs more than 10 kg and cannot be used as a portable receiver, whereas a 1,500-cm 2 detector weighs less than 2 kg and is the size of a large laptop (e.g. the size of Dell Alienware m18 is 410.3×319.9×25.1mm 3 and 4.23 kg) so it is more portable. Additionally, by improving the buffer capacity of the data acquisition electronic circuit, efficiency can be improved to nearly 100%. With this improvement, it is expected that the time scale required for positioning signal update can be improved to 170 seconds (for a cluster size of 10) for a range of 50 m. Discussion Operation. The following two possibilities can be considered as operational methods: (A) placing a large detector outside targeted buildings (e.g., roads). (B) dispersing a large number of portable detectors amongst individuals in a city to virtually function as a large detector. Regarding (A), since CAT navigation does not require a vertical relationship between the reference and the receiver, as is the case with conventional muPS technologies, a large detector can be installed relatively easily. One example would be to bury a detector unit underneath road at a given position identified in WGS84. For example, if two 3 ´ 3 m 2 reference detectors are buried, the positioning signal update rate at one laptop-sized receiver (1,500 cm 2 ) located 50 m away will be ~0.5 Hz (for a cluster size of 10). This solution would be more appropriate for remote locations with low population density. However, even though these detectors do not have to be placed above the receiver, preparation of such infrastructure is rather inflexible and costly in comparison to Option (B) which does not require additional infrastructure. With Option (B), a large number of CAT navigation users carrying smartphone-sized portable detectors cooperatively determine the locations of each user by measuring the distance existing between each user. If some users are located outside a building, and some users are located inside the building, the outside users can acquire the location data with GPS, and the indoor users can use this data (the outside users’ location data) to determine their location inside the building; thus, their inside coordinates are also defined in WGS84. As previously mentioned, in the case of a portable receiver, the sensitive area is small, so it is possible to keep the accidental rate reasonably low even in the dual coincidence mode. The positioning procedure for Option (B) will be described below more in detail. If the users are located outdoors, the exact location for a single signal event can be measured with GPS. Therefore, the outdoor user's location averaged over the time required for making a single signal cluster can be calculated. Here, let us assume that many users (User B, User C, …) are in the vicinity (≤ 50 m) of User A’s position and a coincidence event between User A and User B occurs at time t 1 , and a coincidence between User A and User C occurs at time t 2 , and so on. At the same time, the positions of users (User B, User C, ...) are determined with GPS. Since f ( s ) in Eq. (3) is approximately linear, the time displacement SD measured in the interval [ t 1 , t n ] reflects the RMS distance averaged over the distances of A-B, A-C, and all other nearby pairs. Therefore, by solving the equation below, the position of A ( x 0 , y 0 ) can be derived. More specifically, if the positions of the users (User B, User C, ...) are ( x 1 , y 1 , t 1 ), ( x 2 , y 2 , t 2 ), . . ., the distances between A-B, A-C, and all other nearby pairs are [( x 1 - x 0 ) 2 +( y 1 - y 0 ) 2 ] 1/2 , [( x 2 - x 0 ) 2 +( y 2 - y 0 ) 2 ] 1/2 , and so on (Figure 7A). If we divide the single signal events stored in a single signal cluster into n = n 1 + n 2 to form subclusters (Subcluster 1 and Subcluster 2), ( x 0 , y 0 ) can be derived from the following equations: where D 1 2 = ( x 1 - x 0 ) 2 +( y 1 - y 0 ) 2 , (5-1) D 2 2 = ( x 2 - x 0 ) 2 +( y 2 - y 0 ) 2 , (5-2) ( x 1 , y 1 ), ( x 1 , y 1 ), … are given from GPS data, and s 1 and s 2 respectively indicate the time displacements SD calculated for Subcluster 1 and Subcluster 2. The error associated with this linear approximation is less than 30 cm within a range of 50 m. In conclusion, the positioning procedure in Method B is as follows. (1) Record the CAT stamps in each detector using a local clock associated with each detector. (2) Send the generated CAT stamps and the position data (if the GPS signal is available) to the central processing unit via Wi-Fi. (3) Compute the cross-detector temporal displacements from these timestamps at the central processing unit. (4) If the time displacements are smaller than the given time window, accumulate this data to the single signal cluster at the central processing unit. (5) Once a certain number of the time displacements is accumulated, fit the time sequential time displacement data points with a linear function, and subtract this fitted linear function from the time displacements. (6) Calculate the SD of the data points at the central processing unit. (7) Split the single signal cluster into subclusters. (7) Calculate Eq. (4) to derive the position of the indoor users at the central processing unit. (8) Send the position of the indoor users back to the indoor receivers. We are currently developing a device called the CosmoSmartPhone that can be attached to a smartphone and can record the arrival time of cosmic rays. Most recent smartphones are equipped with a high-precision clock and a TDC for laser distance measurements which can be used for CAT stamping. One main advantage of CAT navigation is that it does not require a tracker detector, so navigation setup can be achieved with a fast-speed single radiation counter. Therefore, in principle, a CosmoSmartPhone can be created by simply adding an SiPM and a small scintillator at a cost of less than $50 USD. Each CosmoSmartPhone is equipped with a ~200 cm 2 plastic scintillator. An example of the Method-B model case will be discussed by assuming that a substantial number of CosmoSmartPhones have been dispersed throughout a large segment of the population in a given urban area. A human flow visualization experiment conducted on a typical city street in Shinjuku, Tokyo (Mosaic Street in the Shinjuku Mylord district) revealed that a flux of 30 to 60 people per minute were present on average in this district during afternoon hours 31 . Assuming an average moving speed of 0.5 ms -1 per individual, this number indicates that there are always 100-200 people within ±50 m of Mosaic Street. In this scenario, if all the individuals on or near Mosiac Street own CosmoSmartPhone, the total outdoor receiver “detector” size would virtually increase to 2-4 m 2 . By utilizing dual coincidence CAT stamps between users, the positioning signals could be updated every 5-10 minutes at each user’s receiver (a single signal cluster size of 10 at a range up to 50 m). If the targeted positioning accuracy is ±3 m, and if there are 10 people within an area of 3 m in radius, since the size of the indoor receiver virtually increases as well, this update rate will be reduced to 30 s - 60 s. Since most smartphones are equipped with a GPS receiver, adding CosmoSmartPhone capabilities would make it possible to seamlessly navigate from outdoors to indoors. However, the single point positioning accuracy of GPS in urban areas often exceeds 100 m 32,33 . Collaboration with Centimeter Level Augmentation Service (CLAS) 34 might be a good solution to achieve reasonable accuracy in indoor positioning. Figure 7B shows an example of an application of this technique for 3D city modelling. Recently, indoor positioning systems (IPS) based on digital twins (DT) have also been proposed 35 . DT is a real-virtual interaction technology that provides efficient, real-time, and intelligent services to the physical world through interaction between physical and digital spaces (taking full advantage of the information in virtual objects) 36, 37 . Considerable research has been conducted on using DT to apply to all services required during the entire lifecycle of industrial products 38 , and BIM is one of these examples. The location of the measurement points is planned in the digital space, then the measurement points are installed in the physical space, and after collecting the measurement data, a neural network-based positioning error reduction method is used to improve the positioning data in the physical space 35 . For this aspect, it is important to define all of the national properties including buildings, as well as natural and cultural heritage sites (architecture, ruins, caves, etc) within the framework of WGS84. BIM was introduced previously in this paper as an example, but collaboration between DT and muPS for other applications might also be fruitful. Limitation. CAT navigation is expected to significantly upgrade the positioning signal update rate compared to conventional MuWNS. However, it is still far below the GPS signal update rate (1 Hz). In order to essentially solve this problem, the detector size must be enlarged, but in practice, this would degrade the flexibility of this technology. This is the first limitation of this technology. Furthermore, in order to derive the receiver's position information, the SD is needed from multiple events. Therefore, the position the user receives is usually not the same as the positionat the moment when the user receives the position information, but the averaged position over the time required to generate a single signal cluster. Therefore, this system works best when users carrying receivers move slowly or stay in place for a certain amount of time (several tens of seconds or more) to record sufficient amounts of event data. This is the second limitation of this technology. One possible solution to overcome this limitation would be to use CAT signals for calibration of an inertial measurement unit (IMU). CAT positioning data would help to improve adjustments to position tracking for moving IMU. Since the arrival time of each single signal event is accurately recorded, CAT navigation signals can be used for the IMU’s drift correction by using the same principle as Eq. (4). Many recent smartphone navigation systems incorporate IMU which is a component that is frequently used to calibrate navigation for a limited time when GPS signals are very weak and cannot otherwise be used. Likewise, CAT navigation in tandem with IMU measurements could be used as an improved GPS backup. Another characteristic of CAT navigation (differing from other muPS techniques) is that the vertical coordinate ( z ) cannot be measured. However, this is rather a good feature for the following reasons. In fabricated indoor/underground environments, the z coordinate is usually pre-defined (as, for example, Floor 3). Therefore, in many cases, the most practical useful information for users in most cases is the horizontal ( x-y ) location. CAT navigation handles the vertical data as being a reflected by the time offset in the time displacement data and therefore this doesn’t affect the time displacement SD. (Therefore, if the users have a very precisely globally synchronized local clock, they can derive their vertical location from this time offset). Moreover, by using this strategy the number of points required for positioning can be reduced overall. In conclusion, as a new cosmic-ray IPS concept, CAT navigation was proposed and demonstrated for the first time. The measured positioning accuracy was 3-4 m for 50-m range measurements which is reasonably accurate for DT applications. Moreover, the positioning signal update rate was significantly upgraded in comparison to other muPS techniques. In this work, due to the buffer size of the electronics, the particle detection efficiency for a 1-m 2 detector was reduced to 50%. This buffer size is currently being improved and is expected to reach 100% efficiency in the near future. On the other hand, it was found that the CAT positioning signal update rate is still lower than other positioning technologies; however, an effective and practical solution to this is to use it in tandem with IMU. Another significant benefit of CAT navigation is that the system doesn’t require a reference detector above the receivers. This feature significantly improves the flexibility of the cosmic-ray-based positioning system. It is anticipated that CAT navigation as a new type of the galactic cosmic-ray positioning system (GCPS) or global navigation cosmic-ray system (GNCS) will realize seamless connection between GPS and IPS. Declarations Contributions H.K.M.T. wrote the text. H.K.M.T. prepared the figures. H.K.M.T. reviewed the manuscript. Corresponding author Correspondence to Hiroyuki K. M. Tanaka. Ethics declarations Competing interests The authors declare no competing interests. Data Availability The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request. References Sengan, S. et al. Enhancing cyber–physical systems with hybrid smart city cyber security architecture for secure public data-smart network. Sustain. Cities. Soc. 112 , 724–737 (2020). Jia, M. et al. Adopting Internet of Things for the development of smart buildings: A review of enabling technologies and applications. Autom. Constr. 101 , 111–126 (2019). Sung, W. & Hsiao, S. 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Muometric positioning system (muPS) utilizing direction vectors of cosmic-ray muons for wireless indoor navigation at a centimeter-level accuracy. Sci. Rep. 13 , 15272 (2023). Li, H. et al. A muon high-resolution pseudorange measurement method: Application to muon navigation in confined spaces. Chin. J. Aeronaut. in press (2023). https://doi.org/10.1016/j.cja.2023.12.022 Bai, Y. et al. Toward Autonomous Multi-UAV Wireless Network: A Survey of Reinforcement Learning-Based Approaches. IEEE Commun. Surv. 25 , 3038-3067 (2023). Varga, D, & Tanaka, H.K.M. Developments of a centimeter-level precise muometric wireless navigation system (MuWNS-V) and its first demonstration using directional information from tracking detectors (2023). Retrieved from https://arxiv.org/abs/2308.10108. Awaji, B.H., Kamruzzaman, M.M., Althuniabt, A. et al. Novel multiple access protocols against Q-learning-based tunnel monitoring using flying ad hoc networks. 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Adaptive estimation of measurement noise to improve the performance of GNSS single point positioning in dense urban environment. Acta Geod. Geophys. 48 , 149–161 (2013). Tominaga, T., & Kubo, N. Adaptive estimation of measurement noise to improve the performance of GNSS single point positioning in dense urban environment. J. IPNTJ 8 , 1–8 (2017). Hsu, L.T. et al . 3D building model-based pedestrian positioning method using GPS/GLONASS/QZSS and its reliability calculation. GPS Solut. 20 , 413–428 (2016). Li, S. et al. Mould Algorithm: A New Method for Stochastic Optimization. Future Gener. Comput. Syst. 111 , 300–323 (2020). Tao, F. et al. Digital twin and its potential application exploration. Comput. Intergr. Manuf. Syst. 24 , 1–18 (2018). Tao, F. et al. Digital twin-driven product design, manufacturing and service with big data. Int. J. Adv. Manuf. Tech. 94 , 3563–3576 (2018). Jones, D.M. et al. Characterising the Digital Twin: A systematic literature review. CIRP J. Manuf. Sci. Tec. 29 , 36–52 (2020). Tables Tables 1 to 3 are available in the Supplementary Files section. Additional Declarations No competing interests reported. Supplementary Files Tables.docx Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3998301","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":278101165,"identity":"ced8c588-67f5-45de-8dcb-15b2e7900d96","order_by":0,"name":"Hiroyuki K.M. Tanaka","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2klEQVRIiWNgGAWjYBACAwbmAyASBJhhggn4tbCxJUC0sBGvhQdiBbIW/MBcvufj44oChsQG+ebDxjwVDPL8DQzPHuDTYtnGu9nwjAFQCxtbcjLPGQbDGQcY0g3wOuwY7zbJBqCW/cd4jA/ztjEwbmBgSJPAr4Xn+c8GsC0QLfbEaGFjhGlJBmpJJEJLmjHQYRLGDWxpyYZzzkgkzzhMyC+HDz/82PDHRraB+fBhiTcVNrb97T1pD/BpgQKIS5h4QAxmnjQidEAB4w8wxX6MeC2jYBSMglEwEgAAcEw+XDN0tzwAAAAASUVORK5CYII=","orcid":"","institution":"University of Tokyo","correspondingAuthor":true,"prefix":"","firstName":"Hiroyuki","middleName":"K.M.","lastName":"Tanaka","suffix":""}],"badges":[],"createdAt":"2024-02-29 02:53:30","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3998301/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3998301/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":52538188,"identity":"4a232e38-bca7-4726-8280-49f8c31c2de0","added_by":"auto","created_at":"2024-03-12 16:55:11","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":253320,"visible":true,"origin":"","legend":"\u003cp\u003ePrinciple of CAT navigation. If the coordinate (\u003cem\u003ex\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e, \u003cem\u003ey\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e) is determined within the framework of the WGS84 with GPS/GNSS, indoor/underwater/underground coordinates (\u003cem\u003ex\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e, \u003cem\u003ey\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e), (\u003cem\u003ex\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e, \u003cem\u003ey\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e), (\u003cem\u003ex\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e, \u003cem\u003ey\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e), …, (\u003cem\u003ex\u003c/em\u003e\u003csub\u003en\u003c/sub\u003e, \u003cem\u003ey\u003c/em\u003e\u003csub\u003en\u003c/sub\u003e) are also determined in WGS84.\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-3998301/v1/e5a89a02451c98e210b44208.png"},{"id":52537758,"identity":"55c4afeb-500b-4011-9596-ca30e2bf8d2c","added_by":"auto","created_at":"2024-03-12 16:47:11","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":62424,"visible":true,"origin":"","legend":"\u003cp\u003eDistance dependence of the time displacement SD (\u003cem\u003es\u003c/em\u003e). The radius of the filled circles is 1 m. The dashed curve indicates the fitted quadratic function (Eq. 3-1).\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-3998301/v1/6a26da5713b26522d764824c.png"},{"id":52537761,"identity":"918e9dc7-2320-42ab-a973-bd36bd3688f6","added_by":"auto","created_at":"2024-03-12 16:47:11","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":344660,"visible":true,"origin":"","legend":"\u003cp\u003eTime-series graph of the time displacement SD determined within a cluster size of 10 (A), 20 (B), and 50 (C). The distance values obtained by converting SD are also plotted for a cluster size of 10 (D), 20 (E), and 50 (F).\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-3998301/v1/f5ddf87debd86fa716caa32e.png"},{"id":52537765,"identity":"e0c68355-354c-4dbf-95e9-2fcaecf81e62","added_by":"auto","created_at":"2024-03-12 16:47:11","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":210226,"visible":true,"origin":"","legend":"\u003cp\u003eCross-detector time displacements for \u003cem\u003eD\u003c/em\u003e = 50 m (filled circles), and the fitting results (dashed lines) with linear functions. The plots for Run#1 (A) to Run#9 (I) are shown as an example.\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-3998301/v1/388b1f7231fa06665573601c.png"},{"id":52537763,"identity":"787e320b-e14c-4ccb-994c-a61afd73124c","added_by":"auto","created_at":"2024-03-12 16:47:11","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":170766,"visible":true,"origin":"","legend":"\u003cp\u003eDrift of OCXO. The OCXO data points (filled circles) are plotted only when the single signal for \u003cem\u003eD\u003c/em\u003e = 180 m is updated. The dashed lines indicate the fitting results with a quadratic function (green dashed lines) and with linear functions (other dashed lines). The plots for Run#1 to Run#10 are shown as an example.\u003c/p\u003e","description":"","filename":"image5.png","url":"https://assets-eu.researchsquare.com/files/rs-3998301/v1/8511aaf5b92e25240561218d.png"},{"id":52537762,"identity":"14993420-04b9-4058-8cea-9f6d26cb660d","added_by":"auto","created_at":"2024-03-12 16:47:11","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":387314,"visible":true,"origin":"","legend":"\u003cp\u003eCAT positioning results (small blue filled circles). The positioning geometry configuration (A) is shown along with the \u003cem\u003ex\u003c/em\u003e-direction (B) and \u003cem\u003ey\u003c/em\u003e-direction (C) slices of the current positioning results. Large blue filled circles indicate the positions of Receiver B and Receiver C defined in WGS84. A red arrow indicates the geometrical location of Receiver A to be positioned. Small blue filled circles are the positioning results for a single signal cluster size of 10. The position of Receiver A is also defined in WGS84. The numbers on the upper side and the right side respectively indicate the latitude and the longitude. Gray-colored boxes and yellow-colored objects respectively indicate buildings and the road.\u003c/p\u003e","description":"","filename":"image6.png","url":"https://assets-eu.researchsquare.com/files/rs-3998301/v1/7e179871853f05590b9ef9d0.png"},{"id":52537764,"identity":"521a6aad-d7bc-4ca0-bd60-b4fb9fa6b3b0","added_by":"auto","created_at":"2024-03-12 16:47:11","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":444245,"visible":true,"origin":"","legend":"\u003cp\u003eConcept of CAT positioning with multiple receivers (A). A box indicates a top view of a building, and blue and red filled circles respectively indicate the receiver inside the building and the receivers outside the building. \u0026nbsp;An example of a use case of multiple-receiver CAT positioning for 3D city modelling is shown (B). According to a recent human flow visualization experiment conducted in Shinjuku, Tokyo, 100 people are constantly present within a range of 50 m of this particular Shinjuku street. Therefore, in this scenario, people near this street with CosmoSmartPhones would act as a virtual 2-m\u003csup\u003e2\u003c/sup\u003e detector within a range of 50 m.\u003c/p\u003e","description":"","filename":"image7.png","url":"https://assets-eu.researchsquare.com/files/rs-3998301/v1/8df74ce6aa9fe50819772c54.png"},{"id":55735569,"identity":"b91205d1-f29b-4fc9-9382-55c69b850ce2","added_by":"auto","created_at":"2024-05-02 12:16:26","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2147763,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3998301/v1/60465c79-c606-456b-94ac-586e269e6a1f.pdf"},{"id":52537760,"identity":"0c2d88b0-966e-4c8c-b040-2232cf74b41c","added_by":"auto","created_at":"2024-03-12 16:47:11","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":22242,"visible":true,"origin":"","legend":"","description":"","filename":"Tables.docx","url":"https://assets-eu.researchsquare.com/files/rs-3998301/v1/e629bb4170c9a55ce96786bd.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Cosmic-ray arrival time (CAT) indoor navigation in the World Geodetic System","fulltext":[{"header":"Introduction","content":"\u003cp\u003eAs rapidly developing digital technology continues to shape and expand growth opportunities in many aspects of our society, it particularly influences human living spaces, improving the comfort, energy efficiency (and sustainability), and safety of our communities. The concepts of smart cities\u003csup\u003e1\u003c/sup\u003e, smart buildings\u003csup\u003e2\u003c/sup\u003e, and smart homes\u003csup\u003e3\u003c/sup\u003e are increasingly being studied. These studies mainly focus on environmental, energy, and safety issues\u003csup\u003e4,5,6,7\u003c/sup\u003e. \u0026nbsp;One of the most important ways to enhance the potential of these developments is to integrate new technologies with the Internet of Things (IoT) and machine learning (ML)\u003csup\u003e2,8\u003c/sup\u003e. Along with these technological developments, indoor positioning system (IPS) technology has been drawing attention for its potential to benefit various aspects of IoT applications. IPS can be used for many indoor applications such as for autonomous mobile robot operation, for navigation aids for people (including individuals with disabilities), for tourist information dissemination at museums and airports, for context-aware intelligent services applied to personal networks, and for locating patients and medical personnel in hospitals. IPS technology could also be an essential component for acquiring location information in modern wireless sensor networks, for example, remote health monitoring systems. \u0026nbsp;Other effective application examples of IPS include generating digital twins, and assisting designers and labor managers in the building construction and maintenance industry.\u003c/p\u003e\n\u003cp\u003eSeveral recent research proposals have emphasized how IPS technology, integrated with Building Information Models (BIM), could drastically improve the cooperation and communication between various design and construction teams (e.g., in architectural, mechanical, electrical, and plumbing departments) to boost quality and work efficiency\u003csup\u003e9\u003c/sup\u003e. BIM is an innovation in architectural design to semi-automatically produce buildings from a complete virtual 3D building mechanical, electrical, and plumbing (MEP) digital model that includes attributing data such as cost, finish, and management information. It is a data efficient and groundbreaking approach which is currently becoming an industry standard. This integrated BIM 3D model not only supports the entire life cycle of a building (from design to construction to maintenance management) but also makes it possible to streamline the workflow. Generally, BIM integration within outdoor environments needs to be seamless and accurate, however the currently available IPS solutions used in tandem with BIM have restrictions when it comes to universal traceability of key aspects (such as labor in tunnels and buildings, and the location of construction resources such as vehicles and materials\u003csup\u003e10,11,12,13\u003c/sup\u003e), which hinder the implementation of comprehensive and universal management of buildings and underground in urban regions.\u003c/p\u003e\n\u003cp\u003eThe ideal scenario would be to have GPS-IPS seamless bridging technology that could easily track (at an accuracy level of 2 to 3 m\u003csup\u003e9\u003c/sup\u003e) the position of elements (potentially in every space within a city) in order to link this data to the virtual 3D city models within the universal WGS84 framework in real time. While this required level of positioning accuracy (2-3 m) is attainable with the established IPS technologies, there are limitations to the situations where it can be used. Obviously, GPS cannot be directly used in most indoor environments. Common indoor positioning technologies such as RFID\u003csup\u003e14\u003c/sup\u003e, ultra-wideband (UWB)\u003csup\u003e15\u003c/sup\u003e, visual analysis\u003csup\u003e16\u003c/sup\u003e, WLAN\u003csup\u003e17\u003c/sup\u003e, and ultrasound\u003csup\u003e18\u003c/sup\u003e have already been developed and used in many occasions. However, the signals used for these IPS technologies (RF, visible light, and acoustic signals) cannot directly propagate through typical building materials such as concrete and steel walls. Therefore, it is necessary to install new infrastructure (such as transmitters) throughout the building which significantly adds to the cost and maintenance for the device, installation, and associated infrastructure arrangements (e.g. electricity). Moreover, when using currently available IPS technologies, the users can acquire only the local coordinates which can hinder the traceability of the tracking. Discovering a more flexible and cost effective IPS which could seamlessly connect (with global coordinates) to GPS would not only unlock the full potential of BIM, but also would have far-reaching benefits for several other applications essential to our society.\u003c/p\u003e\n\u003cp\u003eMuometric positioning system (muPS)\u003csup\u003e19,20,21,22,23,24,25,26\u003c/sup\u003e is a relatively new technology that uses a new signal for IPS, an elementary particle called the muon, which can penetrate through almost all matter (including concrete slabs and rock) in cities in a straight trajectory. All muons detected on the surface of the Earth are produced when primary cosmic rays (relativistic high-energy particles which are accelerated by high-energy events within the galaxy) travel within the solar system and then interact with the Earth\u0026apos;s atmosphere. The main advantage of muPS, including the time of flight (TOF) method (Muometric Wireless Navigation System: MuWNS)\u003csup\u003e20,21,23\u003c/sup\u003e and the Vector method (Vector Muometric Wireless Navigation System: MuWNS-V)\u003csup\u003e22,25\u003c/sup\u003e, is its capability to be unaffected by obstacles surrounding or within indoor environments which often block the signals of other IPS technologies. On the other hand, there is also a drawback. Being a finite resource, naturally occurring muon flux may not be sufficiently strong for certain applications. Also, the strength of the cosmic ray muon flux tends to be dependent on its angle: the vertical flux is generally strongest and as the angle of the flux becomes increasingly horizontal, the flux decreases in proportion to cos\u003csup\u003e2\u003c/sup\u003e\u003cem\u003eq\u003c/em\u003e. \u0026nbsp;For example, the flux decreases to half at 45\u0026ordm; from the zenith and to ~3% of the vertical direction at 80\u0026ordm; from the zenith. This flux limitation affects the geometric configurations of the conventional muPS setup, and thus far the strategy with muPS has been to install a large reference detector at a location far enough above the receiver in order to capture as many cosmic rays as possible from the highest possible elevation angle. For this reason, the reference and receiver detectors used for MuWNS and MuWNS-V must be (nearly) vertically aligned. For example, when positioning 50 m away from the reference (for muons at a \u003cem\u003eq\u003c/em\u003e =45\u0026ordm;) a reference detector would have to be positioned 50m above the ground. Even with this configuration, the reduction of the muon flux is suppressed by 1/2, but this configuration would be impractical in most cases. However, if the reference is installed 5 m above the ground, muons in a\u003cem\u003e\u0026nbsp;\u003c/em\u003e\u003cem\u003eq\u003c/em\u003e =85\u0026ordm; from the zenith must be detected, so in this case the flux in the vertical direction would decrease to less than 1%. Another challenge is that as the distance between the reference and the receiver increases, the number of events is reduced in proportion to the square of the distance. The open-sky muon rate arriving from the vertical direction is approximately 70 Hzm\u003csup\u003e-2\u003c/sup\u003esr\u003csup\u003e-127\u003c/sup\u003e, but even if the sensitive area of both the reference and receiver is 1 m\u003csup\u003e2\u003c/sup\u003e, this muon rate is reduced to 0.028 Hz when separated from the receiver by 50 m vertically. If the reference is placed 5m above the ground, this will further decrease to below 0.0003 Hz. To compensate for this, in a prior MuWNS experiment\u003csup\u003e21\u003c/sup\u003e, large reference detectors (with a total area of 4 m\u003csup\u003e2\u003c/sup\u003e) had to be installed on the 6th floor above the ground to navigate a receiver detector with an area of 1 m\u003csup\u003e2\u003c/sup\u003e which was located on the basement floor. The high costs for installation and operation of these large detectors hinder its flexibility and widespread use. Moreover, even with this configuration, it took 16 minutes to successfully track one point from the receiver.\u003c/p\u003e\n\u003cp\u003eThere are different\u0026nbsp;pros and cons associated with both MuWNS and MuWNS-V. MuWNS doesn\u0026rsquo;t require a tracker, but extremely precise and stable local clocks are needed. On the other hand, MuWNS-V doesn\u0026rsquo;t require extremely precise and stable clocks, but instead requires a tracker for at least the reference detector; its angular resolution directly links to the positional resolution, therefore a value in the order of ~10 mrad is usually required\u003csup\u003e22,25\u003c/sup\u003e. Since trackers consist of multiple layers of position sensitive detectors, the operational costs of MuWNS-V are usually higher than regular MuWNS. \u0026nbsp;However, the TOF method which MuWNS uses requires clock adjustment at the ns level, which also causes a drop in muPS positioning accuracy; for example, with a time-synchronization accuracy of 100 ns, positioning accuracy drops to 30 m. Currently, as with RF based techniques, there is no technique to synchronize clocks located beyond a concrete slab at 10 ns accuracy wirelessly. Therefore, extremely stable (and costly) local clocks are needed for MuWNS. \u0026nbsp; To improve the flexibility and potential applications of the muPS technique, we need to remove (A) trackers, (B) extremely accurate and stable local clocks, and (C) inconvenient reference detectors from the system while we could also enhance (D) the signal update rate to improve the practicality of muPS; with this new scheme, the galactic-cosmic-ray-based positioning system (GCPS) would be more adjustable and cost effective since positioning could be done solely with multiple receivers on the ground in tandem with GPS measurements (or as a backup of GPS).\u003c/p\u003e\n\u003cp\u003eIn this paper, we propose a new technique called CAT navigation as a method\u0026nbsp;to upgrade muPS for wider applications in IPS. This approach takes advantage of the characteristics of the extended air showers (EAS) time structure; the EAS particles almost simultaneously reach detectors as far as 50 meters away from each other at a rate of roughly once every 2 seconds per square meter\u003csup\u003e28\u003c/sup\u003e, which is a much higher rate than is possible with than other muPS methods using single muon detection. Furthermore, since CAT navigation doesn\u0026rsquo;t require tracking cosmic-ray precipitation, there is no need to install reference detectors above the receivers. In the following sections, the principle of CAT navigation and the demonstration results are described along with the discussion about possible operational forms and limitations.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003e\u003cstrong\u003ePrinciple.\u003c/strong\u003e CAT navigation measures the fluctuation width of the displacements in EAS particle arrival times between two arbitrary points located within the shower disk in order to calculate the distance between these two points, and then subsequently the two-dimensional coordinates (\u003cem\u003ex\u003c/em\u003e, \u003cem\u003ey\u003c/em\u003e) of these points are derived. Its principle is essentially the inverse of the CTS\u003csup\u003e28,29,30\u0026nbsp;\u003c/sup\u003econcept. The time difference in EAS particle arrival times between two arbitrary points (Point A and Point B) fluctuates around the average value of the time displacements.\u0026nbsp;This fluctuation width, time displacement SD (standard deviation), increases as the distance between these points increases. This phenomenon has already been observed in prior CTS works, and it has been reported that time displacement SD is degraded as the distance between these points increases\u003csup\u003e30\u003c/sup\u003e. The CAT positioning procedure is described as follows.\u003c/p\u003e\n\u003cp\u003eSupposing that an EAS event occurs in which particles nearly simultaneously arrive at three points A (\u003cem\u003ex\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e, \u003cem\u003ey\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e), B (\u003cem\u003ex\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e, \u003cem\u003ey\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e), and C (\u003cem\u003ex\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e, \u003cem\u003ey\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e) which is a total of \u003cem\u003en\u003c/em\u003e times at the time \u003cem\u003et\u003csub\u003ei\u003c/sub\u003e\u003c/em\u003e (\u003cem\u003ei\u003c/em\u003e = 1, 2, ... \u003cem\u003en\u003c/em\u003e) during the time interval \u003cem\u003eT\u003c/em\u003e, the distance between A-B and the distance between A-C would be respectively:\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003eAB\u0026nbsp;\u003c/sub\u003e= [(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e-\u003cem\u003ex\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e)\u003csup\u003e2\u003c/sup\u003e+(\u003cem\u003ey\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e-\u003cem\u003ey\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e)\u003csup\u003e2\u003c/sup\u003e]\u003csup\u003e1/2\u003c/sup\u003e, \u003cem\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u003c/em\u003e(1-1)\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003eAC\u003c/sub\u003e = \u0026nbsp;[(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e-\u003cem\u003ex\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e)\u003csup\u003e2\u003c/sup\u003e+(\u003cem\u003ey\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e-\u003cem\u003ey\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e)\u003csup\u003e2\u003c/sup\u003e]\u003csup\u003e1/2\u003c/sup\u003e.\u0026nbsp; \u003cem\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u003c/em\u003e(1-2)\u003c/p\u003e\n\u003cp\u003eOn the other hand, since the fluctuation widths of the arrival time difference (time displacement SD) between A-B (\u003cem\u003es\u003c/em\u003e\u003csub\u003eAB\u003c/sub\u003e) and A-C (\u003cem\u003es\u003c/em\u003e\u003csub\u003eAC\u003c/sub\u003e) (CTS time fluctuations) are a function of \u003cem\u003eD\u003c/em\u003e, \u003cem\u003eD\u003c/em\u003e\u003csub\u003eAB\u0026nbsp;\u003c/sub\u003eand \u003cem\u003eD\u003c/em\u003e\u003csub\u003eAC\u0026nbsp;\u003c/sub\u003ecan be respectively expressed as:\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003eAB\u0026nbsp;\u003c/sub\u003e= \u003cem\u003ef\u003c/em\u003e (\u003cem\u003es\u003c/em\u003e\u003csub\u003eAB\u003c/sub\u003e), \u003cem\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;\u003c/em\u003e(2-1)\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003eAC\u0026nbsp;\u003c/sub\u003e= \u003cem\u003ef\u003c/em\u003e (\u003cem\u003es\u003c/em\u003e\u003csub\u003eAC\u003c/sub\u003e). \u003cem\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;\u003c/em\u003e(2-2)\u003c/p\u003e\n\u003cp\u003e\u003cem\u003es\u003c/em\u003e\u003csub\u003eAB\u003c/sub\u003e and \u003cem\u003es\u003c/em\u003e\u003csub\u003eAC\u003c/sub\u003e are given from the measurements. Therefore, if the positions of B and C are known, the position of A can be derived by substituting Eqs. (2-1) and (2-2) with Eqs. (1-1) and (1-2). Figure 1 illustrates the basic principle of CAT navigation. In this paper, the first goal is to experimentally determine the parameters of \u003cem\u003ef\u003c/em\u003e (\u003cem\u003es\u003c/em\u003e) in Eq. (2).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIn principle, a minimum of two detectors are required to take a coincidence and to identify an EAS event. However, since it is expected that the coincidence rate decreases as the distance between these two detectors increases, the relative fraction of the accidental coincidence (i.e., random timestamps) generated by open-sky muons increases. For example, when using two 100-cm\u003csup\u003e2\u003c/sup\u003e detectors to take a dual coincidence with a coincidence time window of 100 ns, the average time interval at which an accidental coincidence occurs is 0.5\u0026acute;1\u003csup\u003e2\u003c/sup\u003e\u0026acute;10\u003csup\u003e7\u003c/sup\u003e = 5,000,000 s (~2 months); if the size of the detectors increases to 1 m\u003csup\u003e2\u003c/sup\u003e, this average time interval is reduced to 500 s. However, even with 1-m\u003csup\u003e2\u003c/sup\u003e detectors, by taking a triple coincidence measurement with a redundant detector, random timestamp generation errors will be reduced to a rate of once in 0.33\u0026acute;(10\u003csup\u003e-2\u003c/sup\u003e)\u003csup\u003e3\u003c/sup\u003e\u0026acute;(10\u003csup\u003e7\u003c/sup\u003e)\u003csup\u003e2\u003c/sup\u003e = 33,000,000 s (~1 year); hence this type of error will become negligible. On the other hand, the results from prior EAS MC simulation studies\u003csup\u003e28\u003c/sup\u003e indicated that adding a redundant detector reduces the event rate by a factor of ~2. Therefore, there is a trade-off between the accidental rate and the positioning signal update rate. The decision of whether to use a redundant detector needs to be optimized based on the size of the receiver we use. In the current demonstration, considering that the detector size was relatively large (i.e., the open-sky muon rate is high), three detectors to identify an EAS event were used, and to reduce the generation of random timestamps. In the following subsections, we will discuss (1) \u003cem\u003ef\u003c/em\u003e (\u003cem\u003es\u003c/em\u003e), the distance dependence of SD of CTS time fluctuations measured with the CTS experimental setup, and (2) the CAT navigation accuracy when paired with oven-controlled crystal oscillators (OCXO).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCAT reference data taking.\u0026nbsp;\u003c/strong\u003eCAT reference data were taken to determine the parameters of \u003cem\u003ef\u003c/em\u003e (\u003cem\u003es\u003c/em\u003e). The experimental setup was the following: one detector (Receiver A), consisting of a 1500-cm\u003csup\u003e2\u003c/sup\u003e plastic scintillator (ELJEN200), and a photomultiplier tube (PMT; Hamamatsu R7724), and other four 1-m\u003csup\u003e2\u003c/sup\u003e detectors (Receivers B-E) with the same configuration as Receiver A. All of the detectors were installed indoors on the ground floor of a building. Then, the triple coincidence was taken between Receivers A-B-C, Receivers B-C-D, and Receivers B-C-E to measure the time displacement SD. The distance between Receiver A and Receiver B was 10 m, the distance between Receiver A and Receiver C was 50 m, the distance between Receiver B and Receiver D was 35 m, and the distance between Receiver B and Receiver E was 180 m. All of the detectors except for Receiver E were wired with an RG coaxial cable to get rid of the local clock drift effect. (The positioning results using an independent local clock will be described in a later section.) For Receiver E, cabling was not possible since multiple third-party buildings were located in between Receiver B and Receiver E, so GPS-time-synchronized results acquired in the prior works were utilized\u003csup\u003e30\u003c/sup\u003e. The electronic circuit that is used for data collection was the same as previous experiments which have\u0026nbsp;already been described in many references\u003csup\u003e20,21,28,29\u003c/sup\u003e, so its properties are\u0026nbsp;only\u0026nbsp;briefly mentioned here. The electronic circuit consists of a discriminator, 4-channel TDC, OCXO, and CPLD, and the PMT signals output from Detectors A-E are first digitized by the discriminator and input to each stop channel of the TDC. In parallel, the 10MHz TTL pulse output from the OCXO is fed to the TDC start channel, and the difference (\u003cem\u003eD\u003c/em\u003e\u003cem\u003et\u003c/em\u003e) between the output timing of the OCXO\u0026apos;s 10MHz pulse and the PMT signal is measured. A cosmic-ray arrival timestamp (CAT stamp) is generated by adding \u003cem\u003eD\u003c/em\u003e\u003cem\u003et\u003c/em\u003e to (the number of OCXO 10MHz pulses) \u0026acute; (100ns). CAT stamp lists generated from these detectors are used for finding coincidence events in a given time window, and the temporal displacements between the coincided CAT stamps (called single signals) were subsequently calculated. The averaged triple coincidence rate for the combination including the 50-m baseline (the distance between detectors) was (68 s)\u003csup\u003e-1\u003c/sup\u003e, and the triple coincidence rate for the combination including the 180-m baseline was (360 s)\u003csup\u003e-1\u003c/sup\u003e. According to the EAS-MC results based on the prior work\u003csup\u003e28\u003c/sup\u003e, the average triple coincidence time intervals are respectively 3-4s and 40-50s for the 50-m and 180-m baselines with 1-m\u003csup\u003e2\u003c/sup\u003e detectors. This discrepancy comes from two factors: (A) the efficiency of Receivers B-E is about 50%\u003csup\u003e30\u003c/sup\u003e, and (B) the area of Receiver B is 1,500 cm\u003csup\u003e2\u003c/sup\u003e. Therefore, the detection rate has dropped to ~1/20 and ~1/8, respectively in comparison to the estimation. In this work, a positioning accuracy of 2 to 3 m\u003csup\u003e9\u003c/sup\u003e was targeted. The distance dependence of the CTS time fluctuations measured with this setup will be described in the next subsection.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDistance dependence of the CTS time fluctuations.\u0026nbsp;\u003c/strong\u003eThe distance dependence of the time displacement SD measured with the current setup was almost linear, but a better fit is made with the following quadratic function (Figure 2). \u0026nbsp;\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cem\u003es\u003c/em\u003e = 0.00171\u003cem\u003eD\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e + 0.49178237\u003cem\u003eD\u003c/em\u003e + 4.8652112, or \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;(3-1)\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eD\u003c/em\u003e = [-0.49178237 - {0.49178237\u003csup\u003e2\u0026nbsp;\u003c/sup\u003e- 0.00684\u0026nbsp;\u0026acute;\u0026nbsp;(4.8652112 -\u003cem\u003e\u0026nbsp;s\u003c/em\u003e)}\u003csup\u003e1/2\u003c/sup\u003e]/0.00342 \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;(3-2)\u003c/p\u003e\n\u003cp\u003eThe fitting errors are shown in Table 1.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAccuracy of CAT\u003c/strong\u003e \u003cstrong\u003epositioning and the positioning information update rate.\u0026nbsp;\u003c/strong\u003e The accuracy of CAT positioning depends on the granularity of the time displacement SD. Therefore, a certain number of EAS events are required. From this section onwards, the triple coincidence event rate will be referred to as the single signal update rate, and the rate at which a cluster (single signal cluster) containing a certain number of single signals is generated is called the positioning signal update rate. Here, the cluster size refers to the number of single signals in the single signal cluster. As the cluster size increases, the SD granularity improves, but the positioning signal update rate is degraded.\u003c/p\u003e\n\u003cp\u003eFigures 3A-3C show time-series graphs of the time displacement SD determined within each cluster by dividing the single signals obtained for \u003cem\u003eD\u003c/em\u003e = 50 m into clusters of different sizes. As the cluster size increases, the temporal fluctuations in SD are reduced, but the positioning signal update rate decreases. Figures 3D-3F show positioning signals obtained by converting SD shown in Figures 3A-3C into the distance \u003cem\u003eD\u003c/em\u003e using Eq. (3-2). The resultant distancing errors are respectively 9.4 m, 6.1 m and 3.8 m for a cluster size of 10, 20 and 50. In order to achieve the targeted accuracy, a cluster size of at least 50 is required. However, when considering the time required for the positioning signal update, a cluster size of 10 is ideal, and as is explained later, positioning errors can be improved by rejecting imaginary solutions of Eq. (1). Therefore, a cluster size of 10 is employed in the following discussions.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ePositioning with local clocks.\u0026nbsp;\u003c/strong\u003eIn the previous subsections, all the detectors were connected via wires, so the CTS time fluctuations only originated from the EAS time structure. However, in an actual CAT operation scenario, positioning is wirelessly performed using independent local clocks. Consequently, time fluctuations due to clock drift are added to the EAS time structure.\u003c/p\u003e\n\u003cp\u003eIn conventional muPS that utilizes the muon\u0026rsquo;s time of flight, distances are determined on an event-by-event basis, so if the clock drifts while acquiring four tracks, this clock drift directly affects positioning accuracy. For example, a drift of 10 ns leads to a positioning error of 3 m. Moreover, this time offset generally changes non-linearly. \u0026nbsp;On the other hand, CAT navigation uses SD as positioning information. Therefore, a time offset between clocks does not affect positioning accuracy. Furthermore, clock drifts can be linearly approximated since its single signal update rate is much higher than conventional muPS. By tracing the time series of a single signal with a straight line and subtracting this fitted straight line from each data point, it is possible to cancel out this drift effect. In summary, the positioning procedure using the clock is as follows.\u003c/p\u003e\n\u003cp\u003e(1) Record CAT stamps in each receiver using the local clock associated with each detector.\u003c/p\u003e\n\u003cp\u003e(2) The generated CAT stamps are sent to the central processing unit via Wi-Fi.\u003c/p\u003e\n\u003cp\u003e(3) The cross-detector time displacements are computed from these CAT stamps at the central processing unit.\u003c/p\u003e\n\u003cp\u003e(4) If the time displacements are smaller than the given time window, it is regarded as a single signal, and it is added to the single signal cluster at the central processing unit.\u003c/p\u003e\n\u003cp\u003e(5) Once a certain number of single signals have been accumulated, a linear function is fitted to the time-sequential cross-detector time displacement data points to remove the local clock\u0026rsquo;s relative drift effect. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003e(6) The\u0026nbsp;time displacement\u0026nbsp;SD of the data points is calculated at the central processing unit.\u003c/p\u003e\n\u003cp\u003e(7) The distance between the detectors is derived with Eq. (3-2) at the central processing unit.\u003c/p\u003e\n\u003cp\u003e(8) The position of the receiver is derived with Eq. (1) at the central processing unit.\u003c/p\u003e\n\u003cp\u003e(9) The receiver\u0026rsquo;s position information is sent back to the receiver via Wi-Fi.\u003c/p\u003e\n\u003cp\u003eIn this demonstration, the above procedure was implemented in tandem with OCXOs (wireless) and cables (wired), so that the OCXO effect can be separated from the EAS time structure effect. Figure 4 shows an example of the time displacement data between the detectors, and the fitted linear function for \u003cem\u003eD\u003c/em\u003e = 50 m. Tables 2 and 3 respectively show the SD of the time displacement data points after subtraction of the fitted function and deriving the distance with Eq. (3-2). 10 independent runs are shown as an example. It can be seen that there is a large deviation in the value in Run #6 for \u003cem\u003eD\u003c/em\u003e = 180m. This error is caused by the nonlinear clock drift (see a green dashed line in Figure 5) since the time scale required for positioning signal update was longer for \u003cem\u003eD\u003c/em\u003e = 180m. Figure 5 shows the OCXO drift. The run numbers shown in Figure 5 correspond to the run numbers shown in Tables 2 and 3. \u0026nbsp;Besides this irregularity, the error (1SD) due to the clock drift had a value of 3-4 meters regardless of the length of \u003cem\u003eD\u003c/em\u003e.\u003c/p\u003e\n\u003cp\u003eAt the end of this section, the 2-dimensional wireless positioning results with OCXO will be shown. The geometric configuration and positioning results within the framework of WGS84 are shown in Figure 6A. If an imaginary solution was derived in Eq. 1, that dataset was discarded. Since imaginary solutions indicate that the circular functions in Eq. (1) do not intersect, low quality positioning signals are automatically discarded in this process. Additionally, regarding the conjugate solutions, the values closer to the initial position were taken. The resultant positioning accuracy in this geometric configuration was 3.4 m (SD) in the \u003cem\u003ex\u003c/em\u003e direction and 4.8 m (SD) in the \u003cem\u003ey\u003c/em\u003e direction. This \u003cem\u003ex\u003c/em\u003e-\u003cem\u003ey\u003c/em\u003e asymmetry comes from this geometric configuration. Figures 6B and 6C show the \u003cem\u003ex\u003c/em\u003e- and \u003cem\u003ey\u003c/em\u003e-direction slices of the current positioning results. The slices in the \u003cem\u003ey\u003c/em\u003e direction are symmetrical in positive and negative directions, but the slices in the \u003cem\u003ex\u003c/em\u003e direction are asymmetrical. This asymmetry comes from the current solution selection criteria.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe current results were obtained with 1-m\u003csup\u003e2\u003c/sup\u003e detectors and a 1,500-cm\u003csup\u003e2\u003c/sup\u003e detector. A 1-m\u003csup\u003e2\u003c/sup\u003e detector weighs more than 10 kg and cannot be used as a portable receiver, whereas a 1,500-cm\u003csup\u003e2\u003c/sup\u003e detector weighs less than 2 kg and is the size of a large laptop (e.g. the size of Dell Alienware m18 is 410.3\u0026times;319.9\u0026times;25.1mm\u003csup\u003e3\u003c/sup\u003e and 4.23 kg) so it is more portable. Additionally, by improving the buffer capacity of the data acquisition electronic circuit, efficiency can be improved to nearly 100%. With this improvement, it is expected that the time scale required for positioning signal update can be improved to 170 seconds (for a cluster size of 10) for a range of 50 m.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003e\u003cstrong\u003eOperation.\u003c/strong\u003e The following two possibilities can be considered as operational methods: (A) placing a large detector outside targeted buildings (e.g., roads). (B) dispersing a large number of portable detectors amongst individuals in a city to virtually function as a large detector. Regarding (A), since CAT navigation does not require a vertical relationship between the reference and the receiver, as is the case with conventional muPS technologies, a large detector can be installed relatively easily. One example would be to bury a detector unit underneath road at a given position identified in WGS84. For example, if two 3 \u0026acute; 3 m\u003csup\u003e2\u003c/sup\u003e reference detectors are buried, the positioning signal update rate at one laptop-sized receiver (1,500 cm\u003csup\u003e2\u003c/sup\u003e) located 50 m away will be ~0.5 Hz (for a cluster size of 10). This solution would be more appropriate for remote locations with low population density. However, even though these detectors do not have to be placed above the receiver, preparation of such infrastructure is rather inflexible and costly in comparison to Option (B) which does not require additional infrastructure. With Option (B), a large number of CAT navigation users carrying smartphone-sized portable detectors cooperatively determine the locations of each user by measuring the distance existing between each user. \u0026nbsp;If some users are located outside a building, and some users are located inside the building, the outside users can acquire the location data with GPS, and the indoor users can use this data (the outside users\u0026rsquo; location data) to determine their location inside the building; thus, their inside coordinates are also defined in WGS84. As previously mentioned, in the case of a portable receiver, the sensitive area is small, so it is possible to keep the accidental rate reasonably low even in the dual coincidence mode. The positioning procedure for Option\u003cs\u003e\u0026nbsp;\u003c/s\u003e(B) will be described below more in detail.\u003c/p\u003e\n\u003cp\u003eIf the users are located outdoors, the exact location for a single signal event can be measured with GPS. Therefore, the outdoor user\u0026apos;s location averaged over the time required for making a single signal cluster can be calculated. Here, let us assume that many users (User B, User C, \u0026hellip;) are in the vicinity (\u0026le; 50 m) of User A\u0026rsquo;s position and a coincidence event between User A and User B occurs at time \u003cem\u003et\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e, and a coincidence between User A and User C occurs at time \u003cem\u003et\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e, and so on. At the same time, the positions of users (User B, User C, ...) are determined with GPS. Since \u003cem\u003ef\u0026nbsp;\u003c/em\u003e(\u003cem\u003es\u003c/em\u003e) in Eq. (3) is approximately linear, the time displacement SD measured in the interval [\u003cem\u003et\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e, \u003cem\u003et\u003csub\u003en\u003c/sub\u003e\u003c/em\u003e] reflects the RMS distance \u0026lt;\u003cem\u003eD\u003c/em\u003e\u0026gt; averaged over the distances of A-B, A-C, and all other nearby pairs. Therefore, by solving the equation below, the position of A (\u003cem\u003ex\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e, \u003cem\u003ey\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e) can be derived. More specifically, if the positions of the users (User B, User C, ...) are (\u003cem\u003ex\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e, \u003cem\u003ey\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e, \u003cem\u003et\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e), (\u003cem\u003ex\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e, \u003cem\u003ey\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e, \u003cem\u003et\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e), . . ., the distances between A-B, A-C, and all other nearby pairs are [(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e-\u003cem\u003e\u0026nbsp;x\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e)\u003csup\u003e2\u003c/sup\u003e+(\u003cem\u003ey\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e-\u003cem\u003e\u0026nbsp;y\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e)\u003csup\u003e2\u003c/sup\u003e]\u003csup\u003e1/2\u003c/sup\u003e, [(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e-\u003cem\u003e\u0026nbsp;x\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e)\u003csup\u003e2\u003c/sup\u003e+(\u003cem\u003ey\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e-\u003cem\u003e\u0026nbsp;y\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e)\u003csup\u003e2\u003c/sup\u003e]\u003csup\u003e1/2\u003c/sup\u003e, and so on (Figure 7A). If we divide the single signal events stored in a single signal cluster into \u003cem\u003en\u0026nbsp;\u003c/em\u003e= \u003cem\u003en\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e+\u003cem\u003en\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e to form subclusters (Subcluster 1 and Subcluster 2), (\u003cem\u003ex\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e, \u003cem\u003ey\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e) can be derived from the following equations: \u0026nbsp; \u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"417\" height=\"137\"\u003e\u003c/p\u003e\n\u003cp\u003ewhere\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003csup\u003e2\u0026nbsp;\u003c/sup\u003e= (\u003cem\u003ex\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e-\u003cem\u003e\u0026nbsp;x\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e)\u003csup\u003e2\u003c/sup\u003e+(\u003cem\u003ey\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e-\u003cem\u003e\u0026nbsp;y\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e)\u003csup\u003e2\u003c/sup\u003e, \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; (5-1)\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u003csup\u003e2\u0026nbsp;\u003c/sup\u003e= (\u003cem\u003ex\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e-\u003cem\u003e\u0026nbsp;x\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e)\u003csup\u003e2\u003c/sup\u003e+(\u003cem\u003ey\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e-\u003cem\u003e\u0026nbsp;y\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e)\u003csup\u003e2\u003c/sup\u003e, \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; (5-2)\u003c/p\u003e\n\u003cp\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e,\u003cem\u003e\u0026nbsp;y\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e), (\u003cem\u003ex\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e,\u003cem\u003e\u0026nbsp;y\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e), \u0026hellip; are given from\u0026nbsp;GPS data, and\u0026nbsp;s\u003csub\u003e1\u003c/sub\u003e and s\u003csub\u003e2\u003c/sub\u003e respectively indicate the time displacements SD calculated for Subcluster 1 and Subcluster 2. The error associated with this linear approximation is less than 30 cm within a range of 50 m.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIn conclusion, the positioning procedure in Method B is as follows.\u003c/p\u003e\n\u003cp\u003e(1) Record the CAT stamps in each detector using a local clock associated with each detector.\u003c/p\u003e\n\u003cp\u003e(2) Send the generated CAT stamps and the position data (if the GPS signal is available) to the central processing unit via Wi-Fi.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e(3) Compute the cross-detector temporal displacements from these timestamps at the central processing unit.\u003c/p\u003e\n\u003cp\u003e(4) If the time displacements are smaller than the given time window, accumulate this data to the single signal cluster at the central processing unit.\u003c/p\u003e\n\u003cp\u003e(5) Once a certain number of the time displacements is accumulated, fit the time sequential time displacement data points with a linear function, and subtract this fitted linear function from the time displacements.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e(6) Calculate the SD of the data points at the central processing unit.\u003c/p\u003e\n\u003cp\u003e(7) Split the single signal cluster into subclusters.\u003c/p\u003e\n\u003cp\u003e(7) Calculate Eq. (4) to derive the position of the indoor users at the central processing unit.\u003c/p\u003e\n\u003cp\u003e(8) Send the position of the indoor users back to the indoor receivers. \u0026nbsp;\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eWe are currently developing a device called the CosmoSmartPhone that can be attached to a smartphone and can record the arrival time of cosmic rays. Most recent smartphones are equipped with a high-precision clock and a TDC for laser distance measurements which can be used for CAT stamping. One main advantage of CAT navigation is that it does not require a tracker detector, so navigation setup can be achieved with a fast-speed single radiation counter. Therefore, in principle, a CosmoSmartPhone can be created by simply adding an SiPM and a small scintillator at a cost of less than $50 USD. Each CosmoSmartPhone is equipped with a ~200 cm\u003csup\u003e2\u0026nbsp;\u003c/sup\u003eplastic scintillator. An example of the Method-B model case will be discussed by assuming that a substantial number of CosmoSmartPhones have been dispersed throughout a large segment of the population in a given urban area. A human flow visualization experiment conducted on a typical city street in Shinjuku, Tokyo (Mosaic Street in the Shinjuku Mylord district) revealed that a flux of 30 to 60 people per minute were present on average in this district during afternoon hours\u003csup\u003e31\u003c/sup\u003e. Assuming an average moving speed of 0.5 ms\u003csup\u003e-1\u0026nbsp;\u003c/sup\u003eper individual, this number indicates that there are always 100-200 people within\u0026nbsp;\u0026plusmn;50 m of Mosaic Street. In this scenario, if all the individuals on or near Mosiac Street own CosmoSmartPhone, the total outdoor receiver \u0026ldquo;detector\u0026rdquo; size would virtually increase to 2-4 m\u003csup\u003e2\u003c/sup\u003e. \u0026nbsp;By utilizing dual coincidence CAT stamps between users, the positioning signals could be updated every 5-10 minutes at each user\u0026rsquo;s receiver (a single signal cluster size of 10 at a range up to 50 m). If the targeted positioning accuracy is \u0026plusmn;3 m, and if there are 10 people within an area of 3 m in radius, since the size of the indoor receiver virtually increases as well, this update rate will be reduced to 30 s - 60 s. Since most smartphones are equipped with a GPS receiver, adding CosmoSmartPhone capabilities would make it possible to seamlessly navigate from outdoors to indoors. However, the single point positioning accuracy of GPS in urban areas often exceeds 100 m\u003csup\u003e32,33\u003c/sup\u003e. Collaboration with Centimeter Level Augmentation Service (CLAS)\u003csup\u003e34\u003c/sup\u003e might be a good solution to achieve reasonable accuracy in indoor positioning. Figure 7B shows an example of an application of this technique for 3D city modelling.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eRecently, indoor positioning systems (IPS) based on digital twins (DT) have also been proposed\u003csup\u003e35\u003c/sup\u003e. DT is a real-virtual interaction technology that provides efficient, real-time, and intelligent services to the physical world through interaction between physical and digital spaces (taking full advantage of the information in virtual objects)\u003csup\u003e36, 37\u003c/sup\u003e. Considerable research has been conducted on using DT to apply to all services required during the entire lifecycle of industrial products\u003csup\u003e38\u003c/sup\u003e, and BIM is one of these examples. The location of the measurement points is planned in the digital space, then the measurement points are installed in the physical space, and after collecting the measurement data, a neural network-based positioning error reduction method is used to improve the positioning data in the physical space\u003csup\u003e35\u003c/sup\u003e. For this aspect, it is important to define all of the national properties including buildings, as well as natural and cultural heritage sites (architecture, ruins, caves, etc) within the framework of WGS84. BIM was introduced previously in this paper as an example, but collaboration between DT and muPS for other applications might also be fruitful.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eLimitation.\u003c/strong\u003e CAT navigation is expected to significantly upgrade the positioning signal update rate compared to conventional MuWNS. However, it is still far below the GPS signal update rate (1 Hz). In order to essentially solve this problem, the detector size must be enlarged, but in practice, this would degrade the flexibility of this technology. This is the first limitation of this technology. Furthermore, in order to derive the receiver\u0026apos;s position information, the SD is needed from multiple events. Therefore, the position the user receives is usually not the same as the positionat the moment when the user receives the position information, but the averaged position over the time required to generate a single signal cluster. Therefore, this system works best when users carrying receivers move slowly or stay in place for a certain amount of time (several tens of seconds or more) to record sufficient amounts of event data. This is the second limitation of this technology. One possible solution to overcome this limitation would be to use CAT signals for calibration of an inertial measurement unit (IMU). CAT positioning data would help to improve adjustments to position tracking for moving IMU. Since the arrival time of each single signal event is accurately recorded, CAT navigation signals can be used for the IMU\u0026rsquo;s drift correction by using the same principle as Eq. (4). Many recent smartphone navigation systems incorporate IMU which is a component that is frequently used to calibrate navigation for a limited time when GPS signals are very weak and cannot otherwise be used. Likewise, CAT navigation in tandem with IMU measurements could be used as an improved GPS backup. Another characteristic of CAT navigation (differing from other muPS techniques) is that the vertical coordinate (\u003cem\u003ez\u003c/em\u003e) cannot be measured. However, this is rather a good feature for the following reasons. In fabricated indoor/underground environments, the \u003cem\u003ez\u003c/em\u003e coordinate is usually pre-defined (as, for example, Floor 3). Therefore, in many cases, the most practical useful information for users in most cases is the horizontal (\u003cem\u003ex-y\u003c/em\u003e) location. CAT navigation handles the vertical data as being a reflected by the time offset in the time displacement data and therefore this doesn\u0026rsquo;t affect the time displacement SD. (Therefore, if the users have a very precisely globally synchronized local clock, they can derive their vertical location from this time offset). Moreover, by using this strategy the number of points required for positioning can be reduced overall.\u003c/p\u003e\n\u003cp\u003eIn conclusion, as a new cosmic-ray IPS concept, CAT navigation was proposed and demonstrated for the first time. The measured positioning accuracy was 3-4 m for 50-m range measurements which is reasonably accurate for DT applications. Moreover, the positioning signal update rate was significantly upgraded in comparison to other muPS techniques. In this work, due to the buffer size of the electronics, the particle detection efficiency for a 1-m\u003csup\u003e2\u003c/sup\u003e detector was reduced to 50%. This buffer size is currently being improved and is expected to reach 100% efficiency in the near future. On the other hand, it was found that the CAT positioning signal update rate is still lower than other positioning technologies; however, an effective and practical solution to this is to use it in tandem with IMU. Another significant benefit of CAT navigation is that the system doesn\u0026rsquo;t require a reference detector above the receivers. This feature significantly improves the flexibility of the cosmic-ray-based positioning system. It is anticipated that CAT navigation as a new type of the galactic cosmic-ray positioning system (GCPS) or global navigation cosmic-ray system (GNCS) will realize seamless connection between GPS and IPS.\u0026nbsp;\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eContributions\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eH.K.M.T. wrote the text. H.K.M.T. prepared the figures. H.K.M.T. reviewed the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCorresponding author\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eCorrespondence to Hiroyuki K. M. Tanaka.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics declarations\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eSengan, S. \u003cem\u003eet al.\u003c/em\u003e Enhancing cyber\u0026ndash;physical systems with hybrid smart city cyber security architecture for secure public data-smart network. \u003cem\u003eSustain. Cities. 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Tec.\u003c/em\u003e \u003cstrong\u003e29\u003c/strong\u003e, 36\u0026ndash;52 (2020).\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Tables","content":"\u003cp\u003eTables 1 to 3 are available in the Supplementary Files section.\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-3998301/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3998301/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Indoor positioning system (IPS) technologies have a wide range of applications; however, three major limitations associated with currently used IPS technologies are: (1) weak penetration strength of signals to penetrate building materials, inhibiting seamless connection of outdoor coordinates to indoor coordinates; hence these technologies rely on local coordinates, making them incompatible with the world geodetic system (WGS84) and universal traceability, (2) active source signals that require beacons to transmit navigation signals. In contrast, the muometric positioning system utilizes naturally abundant cosmic-ray muons signals to compensate for some of these setbacks. However, its main practical challenges are: (1) the low signal rate (~1 per 10 days for laptop-sized receivers horizontally located 50 m apart from each other) and (2) the requirement for large reference detectors (\u003e 4 m2) above the receiver to track cosmic ray precipitation. In this work, an alternative concept called CAT navigation, which relies on the extended air shower time structure for higher rate positioning (without requiring reference detectors) is first proposed and demonstrated; it located receivers placed on the ground floors of multiple buildings (within WGS84) in conditions where other IPS methods are difficult to apply. The resultant positioning accuracy was 3-4 m (at 50 m apart), which is reasonably accurate for GPS -IPS seamless bridging, and with a laptop sized receiver the averaged positioning signal update rate was (683 s)-1 which can be improved to (170 s)-1 with a future upgrade of the data gathering electronics. By integrating CAT receivers into GPS equipped smartphones, it is anticipated that this GPS -CAT hybrid method will seamlessly connect multi-users’ coordinates from outdoor to indoor environments.","manuscriptTitle":"Cosmic-ray arrival time (CAT) indoor navigation in the World Geodetic System","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-03-12 16:47:06","doi":"10.21203/rs.3.rs-3998301/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"35b15560-9ff6-4af5-bdf7-8ecf846826dc","owner":[],"postedDate":"March 12th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":29291585,"name":"Physical sciences/Engineering/Civil engineering"},{"id":29291586,"name":"Earth and environmental sciences/Environmental social sciences/Energy and society"},{"id":29291587,"name":"Earth and environmental sciences/Environmental social sciences/Socioeconomic scenarios"},{"id":29291588,"name":"Earth and environmental sciences/Environmental social sciences/Sustainability"},{"id":29291589,"name":"Earth and environmental sciences/Environmental social sciences"},{"id":29291590,"name":"Earth and environmental sciences/Solid earth sciences"},{"id":29291591,"name":"Physical sciences/Engineering"},{"id":29291592,"name":"Physical sciences/Physics"},{"id":29291593,"name":"Physical sciences/Physics/Particle physics"},{"id":29291594,"name":"Physical sciences/Physics/Particle physics/Experimental particle physics"}],"tags":[],"updatedAt":"2024-05-02T12:15:45+00:00","versionOfRecord":[],"versionCreatedAt":"2024-03-12 16:47:06","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3998301","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3998301","identity":"rs-3998301","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}