A muon navigation positioning method based on relativistic energy characteristics recognition

Abstract

A muon navigation and positioning method based on relativistic energy feature identification comprises the following steps: Step 1): Constructing an energy model for the muon navigation and positioning system and calculating the average energy loss of muons received from the base station; Step 2): Calculating the range of the muons; Step 3): Calculating the receiver position based on the distance to the base station; Step 4): Constructing a muon signal acquisition system; Step 5): Calculating the position change of the muon receiver; Step 6): Calculating the actual position of the receiver. This invention constructs an energy loss model and corrects the velocity of the muons using the energy information of the receiver and the base station, thereby obtaining distance and direction information. This enables navigation and positioning using the relativistic energy of muons. The muon navigation and positioning method provided by this invention has muon energy identification capability and autonomous positioning capability, and can well meet the requirements of navigation and positioning in extreme environments.

Description

Technical Field

[0001] This invention relates to the fields of radiation detection and navigation and positioning, specifically to a muon navigation and positioning method based on relativistic energy characteristic identification for scenarios where positioning using satellite technology is difficult, such as deep sea, deep earth, and polar scenarios. Background Technology

[0002] The vast universe contains numerous high-energy cosmic rays. These rays collide with atoms in Earth's atmosphere, producing many secondary particles. Among them is a particle that interacts very weakly with other matter—the muon (also called a 'muon'). Muons carry either a positive or negative charge and belong to the lepton family. Traveling at near the speed of light, muons, due to relativistic effects, can reach the horizontal plane before decaying. They are a major component of cosmic rays reaching the horizontal plane, and muons can even be found deep underground. The average energy of muons observed at the horizontal plane is 3-4 GeV, while their flux against the atmospheric background is generally considered to be 1 cm⁻¹. -2 ·min -1 .

[0003] Cosmic ray muons undergo electromagnetic energy loss and multiple Coulomb scattering primarily when passing through materials. These two effects form the basis of muon transmission imaging and muon scattering imaging techniques. Transmission imaging is mainly used in geological exploration, while scattering imaging is primarily used for nuclear material detection. There are three common muon detection schemes: nuclear emulsion, scintillation counters, and gas detectors. Using a multilayer air-gap resistive plate chamber as the transmission detection device offers advantages such as simple structure, ease of fabrication into a large-area position-sensitive detector, high temporal and spatial resolution, almost no muon energy loss, and the ability to reconstruct muon energy and orientation information.

[0004] Current navigation and positioning systems using traditional satellites are highly sensitive to environmental conditions, making them unusable in mountainous areas, oceans, and underground. Furthermore, they are susceptible to information transmitted from external sources, lacking good stealth capabilities. In contrast, cosmic ray muons are widely distributed throughout the atmosphere, eliminating regional limitations on the Earth's surface and providing a comprehensive source for detection. Currently, when other sensors are interfered with and unable to provide proper navigation and positioning, high-precision and highly stable inertial navigation systems serve as the last line of defense. However, with further research into cosmic ray muons, these weakly interacting particles, widely present in the atmospheric background, exhibit autonomy similar to inertial systems under appropriate conditions. Therefore, the use of cosmic ray muons holds promise for broader and more precise applications. Summary of the Invention

[0005] To meet the demands of extreme environments such as the deep sea, deep earth, and polar regions, the purpose of this invention is to build a novel combined positioning system based on relativistic muon energy feature identification and to propose a muon navigation and positioning method based on relativistic energy feature identification. This invention combines an inertial navigation system to adjust the attitude of the receiver and the base station. Since muons have not yet been used in the positioning field, this is a pioneering advancement compared to the current application areas of muons.

[0006] The muon energy detector used in this invention employs a scintillator detector and a multi-layer parallel plate gas detector as references for muon detection, energy detection, and direction identification. The energy receiver used in this invention employs a multi-layer parallel plate gas detector for energy detection and direction identification within the receiving system.

[0007] The specific technical solution of the present invention is as follows:

[0008] A muon navigation and positioning method based on relativistic energy feature recognition, the specific steps of which are as follows:

[0009] Step 1): Construct an energy model for the muon navigation and positioning system, and calculate the average energy loss of muons received from the base station, as follows:

[0010] An energy model for the muon navigation and positioning system is constructed, and the energy loss during muon propagation is corrected according to the Bethe-Bloch equation. The average energy loss rate is as follows:

[0011]

[0012] E represents the muon energy, Θ=∫ρ(θ)dθ represents the integral of the muon through the matter density with respect to the penetration length, a represents the energy loss rate due to ionization, and bE represents the energy loss rate due to bremsstrahlung, electron pair production, and nuclear interactions.

[0013] The average energy loss of muon penetration received from the reference station is calculated as shown in equation (22):

[0014]

[0015] Step 2): Using the energy model established in Step 1), the range of the muon is calculated using the following formula based on the energy change in equation (22):

[0016]

[0017] Step 3): Calculate t i Energy of muons in constant motion

[0018]

[0019] In equation (24) Indicates t i The energy of the muon at time d, m0 represents the rest mass of the muon, d n The distance between the n-layer detector plates represents the distance between the muons, and c represents the speed of light in a vacuum. α represents the moment when the muon passes through the nth layer of the detector plate, and α represents the angle at which this muon passes through the multi-layer gas detector plate.

[0020] At the reference station t i The energy of muons is measured at all times. After a period of time, in t i+1 The energy measured at each moment is By detecting a certain number of muons, the detected distance is corrected using statistical probability, and a distance formula based on relativistic energy (25) is constructed. Since the latitude and longitude coordinates of the reference station are known, the receiver position is calculated based on the distance to the reference station.

[0021]

[0022] In the formula Let v(t) represent the position of the receiver, v(t) represent the velocity of the muon at time t during transmission, and ΔP(E) represent the position error caused by energy detection error.

[0023] Step 4): Based on the energy model built in Step 1), and based on the detection principle in Step 3), build a muon signal acquisition system;

[0024] Step 5): Based on the muon signal acquisition system in Step 4), the initial direction and energy of the muon event are first determined by the reference station. The attitude of the receiver is corrected using an inertial navigation system or a level to make the receiver attitude the same as that of the reference station. The angle between the incident muons is calculated using the reference station signal in Step 3). The muons passing through the reference station and the receiver are identified by this angle. The energy of the muons in the receiver is calculated, and it is observed whether the energy of the receiver is less than that of the muons in the reference station. Finally, the attitude is corrected by the inertial navigation system. At the same time, the energy lost during transmission is corrected by the models in Steps 1), 2), and 3), and the velocity change of the muons is calculated. The final position change of the muon receiver is shown in Equation (25):

[0025]

[0026] In the formula, Δx i ,Δy i ,Δh i This represents the projection of the line segment between the base station and the receiver in the northeast-north-sky coordinate system.

[0027] Step 6): Perform coordinate transformation according to Step 5), Δx i,Δy i ,Δh i The projection of the line segment between the base station and the receiver into the northeast-northeast coordinate system is given; the corrected distance is obtained according to equation (26), and the position of the base station is known. The actual location of the receiver The solution can be obtained using formula (27); since The coordinates representing the longitude, latitude, and altitude of the reference station and the receiver are used. Therefore, in the northeast-northeast coordinate system, the distance from the reference station to the receiver is projected as shown in equation (27):

[0028]

[0029] R in the formula N ,R M This represents the radius of the Earth's longitude circle and the radius of the Earth's latitude circle. If the base station can receive satellite signals, it receives the satellite signals through a satellite guide plate to obtain the longitude and latitude coordinates. At the same time, it uses a satellite clock for time correction. Based on the incident trajectory of the muon, the angle between the receiver and the northeast celestial coordinate system is calculated, and thus the actual position of the receiver can be determined. It enables positioning based on muon energy detection; if the base station is established in a scenario without satellites, the latitude and longitude coordinates of the base station are obtained by measuring and aligning the system through mapping and inertial navigation.

[0030] Preferably, in step 1), the calculation process for the energy loss rate due to ionization is as follows:

[0031] Assuming the muon energy is E and the initial velocity is v, the energy loss through the medium due to ionization and excitation processes is as follows:

[0032]

[0033] z represents the charge of the incident particle, expressed as electron charge |e|; Z and A represent the atomic number and atomic weight of the substance passing through, with A in g / mol and m... e Indicates electron mass, N represents the square of the classical electron radius. a δ is Avogadro's constant; I is the average excitation energy, which is related to the molecular state of the substance; δ is the density effect correction parameter.

[0034] The distribution of ionization energy loss is as follows:

[0035]

[0036] Where λ represents the deviation from the most probable energy loss;

[0037]

[0038] Where ΔE represents the actual energy loss in a medium of thickness x;

[0039] The energy loss corresponding to the point of maximum probability in the energy loss distribution, i.e., the most probable energy loss Δp, is:

[0040]

[0041] j is taken as 0.200, ξ = (K / 2)z 2 (Z / A)(x / β 2 MeV, where x is in g / cm³ 2 For cases where the absorption layer is very thick, i.e. The energy loss distribution is approximated by a Gaussian distribution.

[0042] Preferably, in step 1), the calculation process for energy loss caused by bremsstrahlung, electron pair generation, and nuclear interactions is as follows:

[0043] a) The average energy loss rate caused by bremsstrahlung is:

[0044]

[0045] α is the fine structure constant, and z, m, and E are the charge, mass, and energy of the incident particle, respectively.

[0046] b) The average energy loss rate caused by the direct generation of electron pairs is:

[0047]

[0048] c) The average energy loss rate caused by photonucleation is:

[0049]

[0050] Preferably, in the muon signal acquisition system of step 4), the energy signal is acquired by FPGA and then processed and calculated by DSP; if the base station can receive satellite signals, it receives satellite signals through the satellite guidance board and receives satellite clock information, and finally transmits it to the host computer for position calculation and clock calibration of the base station.

[0051] Compared with the prior art, the advantages and positive effects of this invention are as follows:

[0052] As can be seen from the above technical solution, compared with the prior art, this invention discloses a muon navigation and positioning method based on relativistic energy characteristic identification. Muons are widely present in the atmospheric background, and information about muons can be obtained on the Earth's surface through muon detectors. This method has a high degree of autonomy, can avoid transmitting signals to the outside world, and belongs to a highly autonomous positioning system.

[0053] Because energy loss is minimal in low-Z matter, an energy loss model can be constructed based on this. By using energy information from the receiver and reference station, the velocity of the muon can be corrected, thereby obtaining distance and direction information, enabling navigation and positioning using the relativistic energy of the muon. Therefore, the muon navigation and positioning method provided by this invention has muon energy identification capability and autonomous positioning capability, and can well meet the requirements of navigation and positioning in extreme environments. Attached Figure Description

[0054] Figure 1 The radiation energy loss coefficient of muons in an iron absorber

[0055] Figure 2 A schematic diagram of a multilayer muon detector structure based on relativistic effects.

[0056] Figure 3 Signal flow diagram for a muon navigation and positioning system Detailed Implementation

[0057] To meet the demands of extreme environments such as the deep sea, deep earth, and polar regions, the purpose of this invention is to build a novel combined positioning system based on relativistic muon energy feature identification and to propose a muon navigation and positioning method based on relativistic energy feature identification. This invention combines an inertial navigation system to adjust the attitude of the receiver and the base station. Currently, existing technologies have not yet used muons in the positioning field, and this invention represents a pioneering advancement compared to current muon application areas.

[0058] The muon energy detector used in this invention employs a scintillator detector and a multi-layer parallel plate gas detector as references for muon detection, energy detection, and direction identification. The energy receiver used in this invention employs a multi-layer parallel plate gas detector for energy detection and direction identification within the receiving system.

[0059] 1. System Model Building:

[0060] The muon positioning system determines the energy and direction of the muon based on its energy. A detailed model of the muon energy is needed, which first requires knowing the energy loss of the muon as it passes through the medium. Assuming the muon energy is E and the initial velocity is v, according to the Bethe-Bloch equations, the energy loss through the medium is:

[0061]

[0062] The meanings of the parameters are as follows: z represents the charge of the incident particle, in units of electron charge |e|. Z and A represent the atomic number and atomic weight of the substance passing through, with A in g / mol and m... e Indicates electron mass, N represents the square of the classical electron radius. aδ is Avogadro's constant; I is the average excitation energy, which is related to the molecular state of the substance; δ is the density effect correction parameter.

[0063] The above equation describes the energy loss caused by ionization and excitation processes. When a particle passes through a thin layer of material, the distribution of ionization energy loss is not symmetrical, but rather closer to the Landau distribution. The approximate form of the Landau distribution is as follows:

[0064]

[0065] Where λ represents the deviation from the most probable energy loss.

[0066]

[0067] Where ΔE represents the actual energy loss in a medium of thickness x, and the most probable energy loss Δp is the energy loss corresponding to the point of maximum probability in the energy loss distribution, i.e.:

[0068]

[0069] j is usually taken as 0.200, and ξ = (K / 2)z 2 (Z / A)(x / β 2 MeV, where x is in g / cm³ 2 Because the measured energy loss distribution is usually wider than the result given by the Landau distribution, especially for thin absorbing layers. For very thick absorbing layers, i.e. At this point, the tail of the Landau distribution contracts, and the energy loss distribution can be approximated by the Gaussian distribution.

[0070] Besides the ionization and excitation energy losses described by the Bethe-Bloch equations, energy is also lost through the Coulomb field interactions of atomic nuclei in matter. Especially at high particle energies, radiation energy begins to play a significant role. During radiation, the energy lost is proportional to the particle's energy; for high-energy muons, the energy loss primarily comes from radiation energy loss. This mainly includes the following forms:

[0071] 1. Bremsstrahlung

[0072] When a charged muon is decelerated by a Coulomb field, there is a probability that it will emit some of its kinetic energy as photons. This is bremsstrahlung, and the average energy loss rate caused by this radiation is:

[0073]

[0074] α is the fine structure constant, and z, m, and E are the charge, mass, and energy of the incident particle, respectively. Bremsstrahlung energy loss is proportional to the energy of the incident particle, while ionization energy loss, after reaching minimum ionization, is proportional to the logarithm of the energy. Therefore, the final radiation energy loss will exceed the ionization energy loss.

[0075] 2. Electron pairs directly produce radiation.

[0076] Under the influence of the Coulomb field of the nucleus, high-energy incident particles can interact with nuclear matter and generate electron-positron pairs (μ+nucleus→μ+e) through virtual photons. + +e - +nucleus). The average energy loss rate caused by the direct production of electron pairs can usually be parameterized as:

[0077]

[0078] The parameter b(Z,A,E) changes slowly with energy at high energies. For example, the energy lost by a 100 GeV muon in iron through direct electron pairing is:

[0079]

[0080] Compared to bremsstrahlung, direct electron pairs have a higher probability of producing low-energy transfers, so high-energy transfers still mainly come from bremsstrahlung.

[0081] 3. Photonucleation

[0082] Charged particles can lose some energy through inelastic scattering with the atomic nuclei of absorbing matter via virtual gauge particles. This is known as photonucleation, a secondary form of radiative energy loss, and the energy loss is proportional to the particle's energy.

[0083]

[0084] Based on the above energy loss portion, the present invention provides the following total average energy loss rate for muons:

[0085]

[0086] Where a(Z,A,E) represents the energy loss caused by ionization and excitation, and b(Z,A,E) represents the total contribution of bremsstrahlung, direct generation of electron pairs, and photonucleation.

[0087] 2. Locating the target using a constructed muon energy detection model:

[0088] Due to the random fluctuations in the energy loss process, the range of a muon in matter is difficult to describe with a single expression. Therefore, the range of a muon is generally calculated using the following formula:

[0089]

[0090] The range variation of low-energy muons is extremely complex, and low-energy muons can almost never pass through both the reference station and the receiver simultaneously. Therefore, this invention only considers the range of high-energy relativistic muons. When the muon energy is sufficiently high, the slow changes in coefficients a and b are ignored and treated as constants, then:

[0091]

[0092] E is the incident energy of the muon. This is the critical energy. When the muon energy is 1 TeV, its range in an iron absorber can reach 265m. For common underground experiments, taking standard rock with Z=11 and A=22, when the muon energy is greater than 10 GeV, the muon range formula is:

[0093]

[0094] in The unit of E is MeV.

[0095] Since this invention uses radiation detection technology, the medium typically used is air, soil, and concrete. Air is a substance with a low atomic number Z, while concrete and soil can be considered homogeneous media. Based on the above model, the energy loss can be simplified to its average energy loss rate, which can be simplified to the following formula:

[0096]

[0097] E represents the muon energy, Θ=∫ρ(θ)dθ represents the integral of the muon's penetration through the matter density with respect to the penetration length, a represents the energy loss rate due to ionization, and bE represents the energy loss rate due to bremsstrahlung, electron pair production, nuclear interaction, etc. a and b are related to the muon energy and the type of matter penetrated. Therefore, the average energy loss of muon penetration received from the reference station is shown in equation (14):

[0098]

[0099] Θ1 and Θ2 represent the position coordinates of the base station and the receiver. The greater the difference between the two, the more energy is lost. In special areas such as the deep sea and polar regions, since the water and ice layers that are penetrated are low-Z materials, the materials can be considered to be homogeneous. Therefore, the length of the muon passing through the detector can be calculated.

[0100] According to previous research, the rest mass of a muon is 105.7 MeV, approximately 207 times the mass of an electron. Considering relativistic effects, the kinetic energy of a moving muon can be expressed as:

[0101]

[0102] In formula (15) Indicates ti The energy of the muon at time d, m0 represents the rest mass of the muon, d n The distance between the n-layer detector plates represents the distance between the muons, and c represents the speed of light in a vacuum. The value α represents the moment when the muon passes through the nth layer of the detector plate, and α represents the angle at which this muon passes through the multiple gas detector plates. At the reference station t... i The energy of muons is measured at all times. After a period of time, in t i+1 The energy measured at each moment is From formula (15), we can see that:

[0103]

[0104] In equation (16) δ t δ represents the energy error caused by high-precision clock drift. E This indicates the energy detection error caused by external factors such as photodetectors. Through multi-layer gas detector correction, the base station and receiver can obtain an accurate position Θ1 and Θ2 by detecting changes in muon energy (usually represented by latitude and longitude coordinates; if relative coordinates are needed, a projected coordinate system can be constructed to represent the relative position). By detecting a certain number of muons and correcting the detected distance using statistical probability, a distance formula based on relativistic energy (17) can be constructed. Since the latitude and longitude coordinates of the base station are known, the receiver position can be accurately calculated based on the distance to the base station.

[0105]

[0106] In the formula Let v(t) represent the position of the receiver, v(t) represent the velocity of the muon at time t during transmission, which is a quantity related to the transmission time, and ΔP(E) represent the position error caused by the energy detection error.

[0107] The velocity v(t) in formula (17) does not actually change linearly with time and needs to be corrected by the change in energy. The energy loss ΔE is calculated. Since the medium is a homogeneous low-Z medium, considering the energy lost during decay, the energy lost by the muon penetrating the medium changes linearly, thus yielding the corrected muon flight distance. Assuming the muon's velocity passing through the base station is approximately β1c, and its velocity passing through the receiver is approximately β2c, these approximate velocities can be corrected using the average detector spacing d1, d2 and the average time differences Δt1, Δt2 recorded by the multi-layer detectors. Assuming it passes through a homogeneous medium, and that the detector planes of the base station and receiver are calibrated and parallel to each other, with an incident angle of θ for the muon, then the flight velocity is...

[0108]

[0109] According to equation (15), the relationship between the muon flight velocity coefficient and energy can be obtained as follows:

[0110]

[0111] Therefore, we can know According to equation (16), the energy E of a high-energy muon in a homogeneous medium can be approximated as a linear change. Therefore, based on the energy change, the muon flight distance between the two receivers can be corrected through integration. The corrected flight distances according to equations (16) and (17) are as follows:

[0112]

[0113] In the formula, Δx i ,Δy i ,Δh i This represents the projection of the line segment between the base station and the receiver into the northeast-northeast coordinate system. The corrected distance can be obtained from equation (19), given the location of the base station. The actual location of the receiver The solution can be obtained using formula (20). Because... The coordinates representing the longitude, latitude, and altitude of the reference station and the receiver are used. Therefore, in the northeast-northeast coordinate system, the distance from the reference station to the receiver is projected as shown in equation (20):

[0114]

[0115] R in the formula N ,R M This represents the radius of the Earth's longitude circle and the radius of the Earth's latitude circle. Since reference stations are generally established in environments with satellite signal input, they receive satellite signals via a satellite guide plate to obtain longitude and latitude coordinates, and can also use a satellite clock for time correction. Based on the muon incident track, the angle with the northeast celestial coordinate system can be calculated, thus determining the receiver's actual position. This invention enables a positioning system based on muon energy detection. If the base station is located in a scenario without satellites, its latitude and longitude coordinates can be obtained through mapping and inertial navigation system alignment. Therefore, the fiber optic inertial navigation system integrated into this system not only provides attitude alignment but also, with the aid of a satellite guidance plate, can obtain the initial latitude and longitude of the base station. Since the receiver is typically located in a position where satellite signals cannot be received, this highlights the role of the system proposed in this invention.

[0116] 3. Signal flow of the μ-navigation and positioning system:

[0117] Studies have shown that muon energy has a significant impact on muon velocity. The average statistical lifetime of a muon is 2.2 μs, so muon energy is reflected in its velocity. Since the velocity of a muon is close to the speed of light, it produces significant relativistic effects. Therefore, muon energy plays a significant role in determining the distance a muon travels.

[0118] The energy changes of muons reflect the velocity changes of muons. In a uniform low-Z material environment, considering the velocity changes of muons can accurately correct the measured distance. The following will provide a more detailed description of the muon navigation and positioning method based on relativistic energy characteristic identification according to the present invention, with reference to the accompanying drawings.

[0119] Step 1: Construct an energy model for the muon navigation and positioning system. Correct for energy loss during muon propagation based on the Bethe-Bloch equation, considering the effects of bremsstrahlung, direct electron pair radiation, and photonuclear interactions. Therefore, the muon energy loss model can be simplified to its average energy loss rate as follows:

[0120]

[0121] E represents the muon energy, Θ=∫ρ(θ)dθ represents the integral of the muon's penetration through the matter density with respect to the penetration length, a represents the energy loss rate due to ionization, and bE represents the energy loss rate due to bremsstrahlung, electron pair production, nuclear interaction, etc. a and b are related to the muon energy and the type of matter penetrated. Therefore, the average energy loss of muon penetration received from the reference station is shown in equation (22):

[0122]

[0123] Step 2: By means of Figure 1 The variation of the radiation energy loss coefficient of muons in the iron absorber shows that, for low-Z materials and below 100 GeV, the radiation energy loss coefficient has a linear relationship with the logarithm of the energy. Using the average energy loss model built in step 1, the range of muons can be calculated using the following formula based on the energy change in equation (22):

[0124]

[0125] Step 3: The multilayer muon detector structures of the base station and receiver are as follows Figure 2 As shown, this detector is based on the principle of energy detection. By calculating the distance and time between the multi-layer plates, the energy of the muons passing through the detector can be obtained. The kinetic energy of the moving muons can be expressed as:

[0126]

[0127] In equation (24) Indicates ti The energy of the muon at time d, m0 represents the rest mass of the muon, d n The distance between the n-layer detector plates represents the distance between the muons, and c represents the speed of light in a vacuum. The value α represents the moment when the muon passes through the nth layer of the detector plate, and α represents the angle at which this muon passes through the multiple gas detector plates. At the reference station t... i The energy of muons is measured at all times. After a period of time, in t i+1 The energy measured at each moment is By detecting a certain number of muons and correcting the detected distance using statistical probability, a distance formula based on relativistic energy (25) can be constructed. Since the latitude and longitude coordinates of the reference station are known, the receiver position can be accurately calculated based on the distance to the reference station.

[0128]

[0129] Step 4: Based on the above steps, a basic model for muon energy detection is built. Then, based on the detection principle in Step 3, a muon energy detection system can be constructed. (Using...) Figure 3 As shown in the flowchart of the muon navigation and positioning system, the energy signals used by the muon navigation and positioning system are acquired through an FPGA and then processed and calculated by a DSP. If the base station can receive satellite signals, it can receive satellite signals through a satellite guidance board, and can also receive satellite clock information. Finally, it transmits the information to the host computer for position calculation and clock calibration of the base station.

[0130] Step 5: Based on the signal acquisition system in Step 4, the initial direction and energy of the muon event are first determined by the reference station. To maximize the throughput of the reference station and receiver, the attitude of the receiver can be corrected using an inertial navigation system or a level to make the receiver attitude the same as that of the reference station. The angle between the incident muons is calculated using the reference station signal from the navigation and positioning system in Step 3. The muons passing through the reference station and receiver can be identified by this angle. To improve the navigation and positioning accuracy, the energy of the muons in the receiver is calculated, and it is observed whether the energy of the receiver is less than that of the muons in the reference station. Finally, the attitude is corrected by the inertial navigation system, and the energy lost during transmission is corrected by the models in Steps 1, 2 and 3, and the velocity change of the muons is calculated. The final position change of the muon receiver is shown in Equation (25):

[0131]

[0132] In the formula, Δx i ,Δy i ,Δh i This represents the projection of the line segment between the base station and the receiver in the northeast-northeast coordinate system.

[0133] Step 6: Perform coordinate transformation according to Step 5, Δx i ,Δy i ,Δh i The projection of the line segment between the base station and the receiver into the northeast-northeast coordinate system is given; the corrected distance is obtained according to equation (26), and the position of the base station is known. The actual location of the receiver The solution can be obtained using formula (27); since The coordinates representing the longitude, latitude, and altitude of the reference station and the receiver are used. Therefore, in the northeast-northeast coordinate system, the distance from the reference station to the receiver is projected as shown in equation (27):

[0134]

[0135] R in the formula N ,R M This represents the radius of the Earth's longitude circle and the radius of the Earth's latitude circle. If the base station can receive satellite signals, it receives the satellite signals through a satellite guide plate to obtain the longitude and latitude coordinates. At the same time, it uses a satellite clock for time correction. Based on the incident trajectory of the muon, the angle between the receiver and the northeast celestial coordinate system is calculated, and thus the actual position of the receiver can be determined. It enables positioning based on muon energy detection; if the base station is established in a scenario without satellites, the latitude and longitude coordinates of the base station are obtained by measuring and aligning the system through mapping and inertial navigation.

Claims

1. A muon navigation and positioning method based on relativistic energy feature recognition, characterized in that, The specific steps are as follows: Step 1): Construct an energy model for the muon navigation and positioning system, and calculate the average energy loss of muons received from the base station, as follows: An energy model for the muon navigation and positioning system is constructed, and the energy loss during muon propagation is corrected according to the Bethe-Bloch equation. The average energy loss rate is as follows: (21) E Represents the energy of the muon. This represents the integral of the muon's penetration through the matter density with respect to the penetration length. a This indicates the rate of energy loss due to ionization. bE This represents the energy loss rate resulting from bremsstrahlung, electron pair production, and nuclear interactions. The average energy loss of muon penetration received from the reference station is calculated as shown in equation (22): (22) Step 2): Using the energy model built in Step 1), the range of the muon is calculated using the following formula based on the energy change in equation (22): (23) Step 3): Calculation t i Energy of muons in constant motion : (24) In equation (24) express t i The energy of the muon at time t, where m0 represents the rest mass of the muon. This represents the spacing between muons after passing through n layers of detector plates. c Represents the speed of light in a vacuum. This indicates the time when the muon passes through the nth detector plate. This indicates the angle at which the muon passes through the multi-layer gas detector plate; At the reference station t i The energy of muons is measured at all times. After a period of time, in t i+1 The energy measured at each moment is By detecting a certain number of muons, the detected distance is corrected using statistical probability, and a distance formula based on relativistic energy (25) is constructed. Since the latitude and longitude coordinates of the reference station are known, the receiver position is calculated based on the distance to the reference station. (25) In the formula Indicates the location of the receiver. This represents the velocity of the muon at time t during its transmission. This indicates the positional error caused by energy detection error; Step 4): Based on the energy model built in Step 1), and based on the detection principle in Step 3), build a muon signal acquisition system; Step 5): Based on the muon signal acquisition system in Step 4), the initial direction and energy of the muon event are first determined by the reference station. The attitude of the receiver is corrected using an inertial navigation system or a level to make the receiver attitude the same as that of the reference station. The angle between the incident muons is calculated using the reference station signal in Step 3). The muons passing through the reference station and the receiver are identified by this angle. The energy of the muons in the receiver is calculated, and it is observed whether the energy of the receiver is less than that of the muons in the reference station. Finally, the attitude is corrected by the inertial navigation system. At the same time, the energy lost during transmission is corrected by the models in Steps 1), 2), and 3), and the velocity change of the muons is calculated. The final position change of the muon receiver is shown in the following formula (26): (26) In the formula, This represents the projection of the line segment between the base station and the receiver in the northeast-north-sky coordinate system. Step 6): Perform coordinate transformation according to Step 5). The projection of the line segment between the base station and the receiver into the northeast-northeast coordinate system is given; the corrected distance is obtained according to equation (26), and the position of the base station is known. The actual location of the receiver The solution can be obtained using formula (27); since The coordinates representing the longitude, latitude, and altitude of the reference station and the receiver are used. Therefore, in the northeast-northeast coordinate system, the distance from the reference station to the receiver is projected as shown in equation (27): (27) In the formula This represents the radius of the Earth's longitude circle and the radius of the Earth's latitude circle. If the base station can receive satellite signals, it receives the satellite signals through a satellite guide plate to obtain the longitude and latitude coordinates. At the same time, it uses a satellite clock for time correction. Based on the incident trajectory of the muon, the angle between the receiver and the northeast celestial coordinate system is calculated, and thus the actual position of the receiver can be determined. This enables positioning based on muon energy detection; if the base station is established in a scenario without satellites, the latitude and longitude coordinates of the base station are obtained by measuring and aligning the mapping and inertial navigation systems.

2. The muon navigation and positioning method based on relativistic energy feature recognition according to claim 1, characterized in that, In step 1), the calculation process for the energy loss rate due to ionization is as follows: Assume the muon energy is E, and the initial velocity is... v Energy loss through the ionization and excitation processes of the medium: (1) z represents the charge of the incident particle, expressed as the electron charge. The units are: Z and A, representing the atomic number and atomic weight of the substance, respectively; A is in g / mol. Indicates electron mass, Represents the square of the classical electron radius. It is Avogadro's constant; I It is the average excitation energy, which is related to the molecular state of the substance; It is a density effect correction parameter; The distribution of ionization energy loss is as follows: (2) in This represents the deviation from the most probable energy loss; (3) in This represents the actual energy loss in a medium of thickness x; The energy loss corresponding to the point of maximum probability in the energy loss distribution is the most probable energy loss. for: (4) j Take 0.200, MeV, x The unit is g / cm³ 2 For cases where the absorption layer is very thick, i.e. The energy loss distribution is approximated by a Gaussian distribution.

3. A muon navigation and positioning method based on relativistic energy feature identification according to any one of claims 1-2, characterized in that, In step 1), the calculation process for energy loss due to bremsstrahlung, electron pair production, and nuclear interactions is as follows: a) The average energy loss rate caused by bremsstrahlung is: (5) It is the fine structure constant. z , m and E These represent the charge, mass, and energy of the incident particle, respectively. b) The average energy loss rate caused by the direct generation of electron pairs is: (6) c) The average energy loss rate caused by photonucleation is: (8)。 4. A muon navigation and positioning method based on relativistic energy feature recognition according to claim 3, characterized in that, In the muon signal acquisition system of step 4), the energy signal is acquired by FPGA and then processed and calculated by DSP; if the base station can receive satellite signals, it receives satellite signals through the satellite guidance board and receives satellite clock information, and finally transmits it to the host computer for position calculation and clock calibration of the base station.

Images