Muometric positioning system (muPS) utilizing direction vectors of cosmic-ray muons for wireless indoor navigation at a centimeter-level accuracy

Abstract

Since the development of many future technologies are becoming more and more dependent on indoor navigation, various alternative navigation techniques have been proposed with radio waves, acoustic, and laser beam signals. In 2020, muometric positioning system (muPS) was proposed as a new indoor navigation technique; in 2022, the first prototype of wireless muPS was demonstrated in underground environments. However, in this first physical demonstration, its navigation accuracy was limited to 2–14 m which is far from the level required for the practical indoor navigation applications. This positioning error was an intrinsic problem associated with the clock that was used for determining the time of flight (ToF) of the muons, and it was practically impossible to attain cm-level accuracy with this initial approach. This paper introduces the completely new positioning concept for muPS, Vector muPS, which works by determining direction vectors of incoming muons instead of utilizing ToF. It is relatively easier to attain a 10-mrad level angular resolution with muon trackers that have been used for muographic imagery. Therefore, Vector muPS retains the unique capacity to operate wirelessly in indoor environments and also has the capacity to achieve a cm-level accuracy. By utilizing an essentially different concept from what is used in other navigation techniques, (measuring the distance between the reference and the receiver), Vector muPS enables more flexible, and longer-term stable positioning. Anticipated applications and the future outlook of Vector muPS is also discussed.

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

“…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.…”

“…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 ight (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.…”

“…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.…”