Shielding environment muon navigation method

Abstract

The invention discloses a shielded environment muon navigation method. The method comprises the following steps: deploying a reference detector array and a receiving detector; collecting a plurality of pieces of muon track information by using an accidental coincidence event detected by the reference detector array and the receiving detector; performing non-repeated pairwise combination on all the collected muon track information to form a plurality of combination pairs, establishing equation sets about muon track distances, then integrating all the equation sets, and establishing overdetermined equation sets about all the muon track distances; distributing weights of overdetermined equations according to the position resolution and the angle resolution of the reference detector corresponding to the collected muon trajectory information, and establishing weighted overdetermined equations about all muon trajectory distances; and based on the solution of the weighted overdetermined equation set, obtaining the final position coordinates of the receiving detector, thereby carrying out the positioning and navigation of the navigation terminal. According to the invention, the positioning precision of the vector muon navigation system can be effectively improved.

Description

Technical Field

[0001] The present invention relates to the field of navigation technology, and in particular to a muon navigation method in a shielded environment. Background Art

[0002] Obscured environments are areas where satellite navigation signals are blocked, such as indoors, in caves, in forests, and underwater. In obscured environments, users cannot use satellite signals to locate and navigate their targets. Navigation technologies for obscured environments include Zigbee, radio frequency identification, lidar, Wi-Fi fingerprinting, ultra-wideband, Bluetooth low energy, and sonar positioning. However, the signal carriers used by these technologies are subject to interference from the propagation medium and obstructions, thereby reducing positioning accuracy.

[0003] Vector muon navigation is a new navigation technology that uses the position and angle information of cosmic ray muons to locate in obscured environments. Its signal carrier is the high-energy particle muon, which has the characteristics of high penetrability and near-light speed. The interference from the propagation medium and obstructions is far less than that of electromagnetic signals, which can effectively improve the positioning accuracy in obscured environments.

[0004] The reference detectors of the existing vector muon navigation system need to be deployed in the same plane, which severely limits the flexibility of actual deployment. In addition, only two sets of muon trajectory information are used for single positioning, and the positioning error is greatly affected by the position resolution and angular resolution of the muon detectors. Summary of the Invention

[0005] The purpose of the present invention is to provide a muon navigation method in a shielded environment to reduce the errors of a vector muon navigation system caused by factors such as position resolution and angular resolution, so as to improve the positioning accuracy of the vector muon navigation system.

[0006] In order to achieve the above tasks, the present invention adopts the following technical solutions:

[0007] A muon navigation method in a shielded environment, comprising:

[0008] Deploy a reference detector array and a receiving detector; wherein the receiving detector is arranged on the navigation terminal inside the shielded area, and multiple reference detectors with known positions are deployed above the outside of the shielded area;

[0009] Collect multiple muon trajectory information using accidental coincidence events detected by the reference detector array and the receiving detector;

[0010] All collected muon trajectory information is combined into pairs without duplication to form multiple combination pairs;

[0011] For each combination of muon trajectory information, a set of equations about the distance of muon trajectories is established, and then all the equations are integrated to establish an overdetermined set of equations about the distance of all muon trajectories;

[0012] Assign weights to the overdetermined equations according to the position resolution and angular resolution of the reference detector corresponding to each muon trajectory information collected, and establish a weighted overdetermined equation system for the distances of all muon trajectories;

[0013] The weighted overdetermined equations are used to solve all muon trajectory distances, which are then multiplied by the corresponding guidance vector of the muon arrival direction. The distances are then added to the position coordinates on the corresponding reference detector and averaged to obtain the final receiving detector position coordinates, thereby locating and navigating the navigation terminal.

[0014] Furthermore, the reference detector has a layered structure, so that the zenith angle and azimuth information of the incident muon can be obtained according to the coordinates of the detection points in different layers; the vertical distance between the reference detector and the receiving detector in the shielded area is within a preset range; the reference detector and the receiving detector are both used to detect the muon trajectory information, including the zenith angle, azimuth angle and coordinates of the muon.

[0015] Furthermore, in the muon trajectory information obtained by the reference detector and the receiving detector:

[0016] The coordinates of all muon positions collected by the reference detector array are: The position coordinates of all muons received by the receiving detector are: The corresponding guidance vectors of the muon arrival direction are V1, V2, ... V n ,...,V N , the corresponding muon trajectory distances are D1, D2, ... D n ,...D N , the corresponding muon zenith angles are θ1, θ2, ... θ n ,...,θ N , the muon azimuth is The angular resolution and position resolution of the reference detector corresponding to the nth and mth groups of muon trajectory information are and and n,m=1,2,...,N;

[0017] Among them, in the nth muon trajectory information, the corresponding guidance vector of the muon arrival direction is expressed as and The distance between the muon trajectories is expressed as D n .

[0018] Furthermore, the method for determining the correspondence between the muon trajectory information and the reference detector is:

[0019] Accidental coincidence events are used to select muon trajectory information that meets the requirements, and the coordinate points of the muon trajectory information on the reference detector are recorded. The coordinate points are compared with the detectable coordinate ranges of different reference detectors. If they are within the detection coordinate range, it can be considered that the muon has been detected by the reference detector, thereby obtaining the angular resolution and position resolution of the reference detector corresponding to the muon trajectory information.

[0020] Furthermore, based on the combination pair (n, m) consisting of the nth and mth groups of muon trajectory information, the corresponding muon trajectory distance (D n ,D m ), the quadratic equation system can be expressed as:

[0021]

[0022] Furthermore, the distances D1, D2, D3, ..., D of N muon trajectories are established. N The overdetermined system of equations can be expressed as follows:

[0023] AD = b;

[0024] Where A is the coefficient matrix of the overdetermined equations, D is the vector of muon trajectory distances to be solved for the overdetermined equations, and b is the constant vector of the overdetermined equations;

[0025]

[0026] Among them A (1,2) ,A (1,3) ,...,A (1,N) ,A (2,3) ,A (2,4) ,...,A (2,N) ,A (3,4) ,...,A (N-1,N) are the coefficient sub-matrices corresponding to all combination pairs respectively;

[0027] D=[D1 D2...D N ] T ;

[0028]

[0029] Among them, b (n,m) Represents the constant subvector corresponding to the combination pair (n, m) consisting of the nth and mth groups of muon trajectory information.

[0030] Furthermore, the coefficient submatrix expression of the combination pair (n, m) composed of the nth and mth groups of muon trajectory information is:

[0031]

[0032] a 21 ,a 22 ,…a 2n ,…a 2m ,…a 2N Represents matrix A (n,m) The expressions for the 1st, 2nd, ..., nth, ...mth, ...Nth elements in the second row are:

[0033]

[0034] Among them, V n 、V m represents the guidance vector of the arrival direction of the muon corresponding to the nth and mth groups of muon trajectory information, a ij Indicates that in A (n,m) Except a 1n 、a 2m 、a 1m 、a 2n All but four elements;

[0035]

[0036] Furthermore, the weight matrix of the equation group corresponding to the combination pair (n, m) consisting of the nth and mth groups of muon trajectory information is set to:

[0037]

[0038] Among them, w (n,m) is the weight submatrix corresponding to the combination pair (n,m);

[0039] The weighted overdetermined system of equations can be expressed as:

[0040] WAD=Wb;

[0041] Among them, W is the weight matrix composed of the weight sub-matrices of all combination pairs.

[0042] Furthermore, the weighted overdetermined equations are solved to calculate the distances of all muon trajectories, which can be expressed as:

[0043]

[0044] in, is the weighted least squares solution corresponding to the distances of N groups of muon trajectories; the superscript T represents the matrix transpose, and the superscript -1 represents the matrix inversion.

[0045] Furthermore, the muon trajectory distance is multiplied by the corresponding guidance vector of the muon arrival direction, and then accumulated and averaged with the position coordinates on the corresponding reference detector to obtain the final receiving detector position coordinates, including:

[0046] The N sets of calculated positioning coordinates corresponding to the N sets of muon trajectory distances can be expressed as:

[0047]

[0048] in, are the weighted least squares coordinates of the muons corresponding to the 1st, 2nd, ..., Nth muon trajectory distances, and I is the N×N identity matrix.

[0049] The N groups of calculated positioning coordinates are averaged to obtain the final receiving detector position coordinate P WLS :

[0050]

[0051] Among them, P WLS is the final weighted least squares position coordinate, Indicates The nth weighted least squares coefficient in .

[0052] A terminal device comprises a processor, a memory and a computer program stored in the memory; when the processor executes the computer program, the shielded environment muon navigation method is implemented.

[0053] A computer-readable storage medium stores a computer program; when the computer program is executed by a processor, the shielded environment muon navigation method is implemented.

[0054] Compared with the prior art, the present invention has the following technical features:

[0055] 1. Compared with the existing vector muon navigation system, the present invention uses the least squares method to solve the trajectory information of more than two muons in a single positioning, which can effectively reduce the positioning error caused by the position resolution and angular resolution of the detector. For systems with large amounts of data, the positioning accuracy of the system can be significantly improved when the trajectory information of the muons is increased.

[0056] 2. Based on the multi-muon trajectory least squares positioning scheme, the present invention performs weighted processing on the residual term of the least squares positioning equation according to the position resolution and angular resolution of the reference detector, which can weaken the distortion error caused by the low-resolution detector and effectively balance the difference between the angular dimension and the position dimension.

[0057] 3. This invention expands upon the existing vector muon navigation system model, enabling the deployment of reference detectors at varying altitudes, thus increasing the deployment flexibility of the vector muon navigation system. In practical engineering applications, the elevation parameters of the detector array can be optimized based on site spatial characteristics such as terrain undulation and obstacle distribution, achieving coupled adaptation of the vector muon navigation network to the physical environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 is the muon navigation system model;

[0059] Figure 2 Comparison chart of horizontal positioning accuracy and vertical positioning accuracy of the navigation method of the present invention and existing positioning algorithms. DETAILED DESCRIPTION

[0060] The weighted least squares algorithm is an effective method for dealing with overdetermined systems of equations. When the number of equations exceeds the number of unknowns, it can minimize the sum of squared residuals of the weighted system, yielding an approximate solution to the unknowns. Its advantages can be effectively applied to vector muon navigation systems: First, in a single positioning pass, information from more than two muon trajectories can be utilized, increasing the amount of information required for the single positioning solution. Second, weights can be assigned to the corresponding solution equations based on the positional and angular resolutions of the reference detectors, mitigating the problem of large positioning accuracy errors caused by low-resolution reference detectors. Furthermore, consideration should be given to situations where the reference detectors are not coplanar, thus increasing flexibility in deployment. Therefore, this paper proposes a muon navigation technology solution for shielded environments based on a weighted least squares algorithm, aiming to reduce the positioning error of the vector muon navigation system and increase the flexibility of reference detector deployment. Regarding positioning algorithm optimization, a weighted overdetermined equation positioning model based on multiple muon trajectories is constructed, utilizing information from multiple muon trajectories for positioning calculations. The residual terms of the least squares method are weighted according to the positional and angular resolutions of the reference detectors. Regarding reference detector array configuration optimization, an extended vector muon navigation system model is proposed, improving the configuration dimensionality of the traditional two-dimensional layout. This paper reduces the positioning error of the vector muon navigation system, effectively weakens the distortion error of low-resolution detectors, and enhances the flexibility of reference detector deployment. This allows for precise positioning of the vector muon navigation system in a three-dimensional reference detector layout.

[0061] A muon navigation method in a shielded environment of the present invention comprises the following steps:

[0062] Step 1: Deploy the reference detector array and the receiving detector.

[0063] Above the outside of the shielded area where the receiving detector is located, multiple reference detectors with known coordinates are deployed to form a reference detector array; the reference detectors can detect the incident muons and can display the impact position of the muons on the reference detectors. Since the coordinates of the reference detectors themselves are known, when the reference detector detects a muon, the coordinates of the muon can be obtained; in terms of shape, the reference detectors are a layered structure, so that the zenith angle and azimuth angle information of the incident muon can be obtained according to the coordinates of the detection points in different layers; in terms of size, the size of each layer is 1 meter × 1 meter or above; in terms of deployment rules, the vertical distance from the receiving detector in the shielded area should not be too long, for example, it can be controlled within 50 meters, and at least 4 reference detectors are deployed. The reference detectors need to be deployed above the shielded area and parallel to the horizontal plane, and there is no requirement for the deployment direction; the zenith angle, azimuth angle, coordinates, etc. detected by the reference detectors are the muon trajectory information collected in step 2.

[0064] A receiving detector is deployed on a navigation terminal in the shielded area, such as a vehicle or robot. The height of the receiving detector should not exceed 50 meters from the vertical height of any reference detector. It should be placed parallel to the horizontal plane where the shielded area is located, and should be placed as far as possible on the inner side of the area formed by multiple reference detectors in the horizontal direction. The size should be as small as possible, for example, it can be controlled within 0.25 meters × 0.25 meters; both the reference detector and the receiving detector can detect muon information such as the arrival time, zenith angle, azimuth, and coordinates of the muons.

[0065] Step 2: Collect multiple muon trajectory information using the reference detector array and the accidental coincidence events detected by the receiving detector.

[0066] An accidental coincidence event refers to the coincidence of two particles that have no regular connection in time. In this scheme, for a large number of independent muon incidence events, the muon signals detected by the reference detector array and the receiving detector respectively occur within a very short period of time. At this time, it can be considered that both have collected the same muon.

[0067] Assume that in step 1, the vector muon navigation system composed of a reference detector array and a receiving detector collects a total of N groups of muon trajectory information.

[0068] For the convenience of representation, let the zenith angle of the corresponding muon in the nth group of muon trajectory information collected be θ n , azimuth is The position coordinates on the reference detector are in express The coordinate components on the x, y, and z axes; in the nth muon trajectory information, the corresponding guidance vector of the muon arrival direction is expressed as Among them, an ,b n ,c n Indicates V n Components on the x, y, and z axes; in the nth muon trajectory information, the muon position coordinates to be solved obtained by the receiving detector are expressed as in, express Coordinate components on the x, y, and z axes; and The distance between the muon trajectories is expressed as D n .

[0069] Similarly, after the collection is completed, the coordinates of all muon positions collected by the reference detector array are: The position coordinates of all muons received by the receiving detector are: The corresponding guidance vectors of the muon arrival direction are V1, V2, ... V n ,...,V N , the corresponding muon trajectory distances are D1, D2, ... D n ,...D N , the corresponding muon zenith angles are θ1, θ2, ... θ n ,...,θ N , the muon azimuth is In addition, since the angle and position resolutions of the multiple reference detectors deployed are not necessarily the same, for the sake of rigor, the angle resolutions of the reference detectors corresponding to the N sets of muon trajectory information collected are The position resolution is Among them, the angular resolution and position resolution corresponding to the nth and mth groups of muon trajectory information are and and n,m=1,2,...,N.

[0070] The method to determine the correspondence between muon trajectory information and reference detector is:

[0071] Accidental coincidence events are used to select muon trajectory information that meets the requirements, and the coordinate points of the muon trajectory information on the reference detector are recorded. The coordinate points are compared with the detectable coordinate ranges of different reference detectors. If they are within the detection coordinate range, it can be considered that the muon has been detected by the reference detector, thereby obtaining the angular resolution and position resolution of the reference detector corresponding to the muon trajectory information. Since the same reference detector may detect different muons, the angular resolution and position resolution of the reference detectors corresponding to different muon trajectory information may also be the same.

[0072] In step 3, the N sets of collected muon trajectory information are combined in pairs without duplication. The resulting combination pairs can be expressed as (1,2), (1,3), ..., (1,N), (2,3), (2,4) ... (2,N), (3,4), ... (N-1,N); each pair of combinations here represents two different sets of muon trajectory information, and each set of muon trajectory information only participates in the formation of N-1 different combination pairs, ensuring the non-repetitiveness and comprehensiveness of the combination; for example, (n,m) represents the combination pair consisting of the nth and mth sets of muon trajectory information.

[0073] Each combination pair needs to meet the following conditions: the two muon trajectory information corresponding to the combination pair should be detected by both the reference detector and the receiving detector.

[0074] Step 4: Establish a set of equations about the muon trajectory distance for each combination pair of muon trajectory information.

[0075] Based on the combination pair (n, m) consisting of the nth and mth groups of muon trajectory information, the corresponding muon trajectory distance (D n ,D m ), the quadratic equation system can be expressed as:

[0076]

[0077] This system of equations can be obtained by Get, where L represents and The square of the distance between Represents L to D respectively n 、D m The partial derivative of and The square of the distance between n 、D m When the partial derivative is 0, and The distance between them reaches the minimum. Since the size of the receiving detector is small enough, it can be approximately considered that and The distance between them meets the minimum condition.

[0078] Step 5: Integrate the equations of the muon trajectory distance for each pair of combinations to establish the equations of the N muon trajectory distances D1, D2, D3, ..., D N The overdetermined equations can be expressed as:

[0079] AD = b;

[0080] Where A is the N(N-1)×N coefficient matrix of the overdetermined equations, D is the N×1 vector of muon trajectory distances to be solved for the overdetermined equations, and b is the N(N-1)×1 constant vector of the overdetermined equations. The detailed expression of A is:

[0081]

[0082] Among them A (1,2) ,A (1,3) ,...,A (1,N) ,A (2,3) ,A (2,4) ,...,A (2,N) ,A (3,4) ,...,A (N-1,N) are the coefficient submatrices corresponding to all the combination pairs (1,2), (1,3), ..., (1,N), (2,3), (2,4) ... (2,N), (3,4), ... (N-1,N); the general expression of each coefficient submatrix is:

[0083]

[0084] For convenience, let A (n,m) The coefficient submatrix representing the combination pair (n, m) consisting of the nth and mth groups of muon trajectory information; a 11 ,a 12 ,…a 1n ,…a 1m ,…a 1N Represents matrix A (n,m) The 1st, 2nd, ..., nth, ...mth, ...Nth elements in the first row, a 21 ,a 22 ,…a 2n ,…a 2m ,…a 2N Represents matrix A (n,m) The general expressions corresponding to the 1st, 2nd, ..., nth, ...mth, ...Nth elements in the second row are:

[0085]

[0086] Among them, V n 、V m represents the guidance vector of the arrival direction of the muon corresponding to the nth and mth groups of muon trajectory information, a ij Indicates that in A (n,m) Except a 1n 、a 2m 、a 1m 、a 2n All but four of the elements.

[0087] The detailed expression of D is:

[0088] D=[D1 D2...D N ] T ;

[0089] The specific expression of b is:

[0090]

[0091] Among them, b (1,2) ,b (1,3) ,...,b (1,N) ,b (2,3) ,b (2,4) ,...,b (2,N) ,b (3,4) ,...,b (N-1,N) are the N(N-1)×1 constant subvectors corresponding to all the combinations of muon trajectory information (1,2), (1,3), ..., (1,N), (2,3), (2,4) ... (2,N), (3,4), ... (N-1,N); for the convenience of representation, let b (n,m) The constant subvector corresponding to the combination pair (n, m) consisting of the nth and mth groups of muon trajectory information is expressed as follows:

[0092]

[0093] Step 6: assign weights of the overdetermined equations according to the position resolution and angular resolution of the reference detector corresponding to each collected muon trajectory information, and establish the N muon trajectory distances D1, D2, D3, ..., D N The weighted overdetermined system of equations.

[0094] Since the positioning accuracy is inversely proportional to the position resolution and angular resolution, the weight matrix of the equation group corresponding to the combination pair (n, m) composed of the nth and mth groups of muon trajectory information is set to:

[0095]

[0096] Among them, w (n,m) is the weight submatrix corresponding to the combination pair (n,m).

[0097] The weighted overdetermined system of equations can be expressed as:

[0098] WAD=Wb;

[0099] Where W is the N(N-1)×1 weight matrix composed of the weight sub-matrices of all combination pairs, which can be expressed as the combination of weight sub-matrices:

[0100]

[0101] Among them, w (1,2) ,w (1,3) ,...,w (1,N) ,w (2,3) ,w (2,4) ,...,w (2,N) ,w (3,4) ,...,w (N-1,N) These are the weight sub-matrices corresponding to all the combinations of muon trajectory information (1,2), (1,3), ..., (1,N), (2,3), (2,4) ... (2,N), (3,4), ... (N-1,N).

[0102] Step 7: Solve the N groups of muon trajectory distances based on the weighted overdetermined equations.

[0103] The distances between N groups of muon trajectories can be expressed using a weighted least squares solution:

[0104]

[0105] in, is the weighted least squares solution corresponding to the distances of N groups of muon trajectories; the superscript T represents the matrix transpose, and the superscript -1 represents the matrix inversion.

[0106] Step 8: Multiply the N groups of muon trajectory distances obtained by the solution with the corresponding guidance vector of the muon arrival direction, and accumulate and average them with the position coordinates on the corresponding reference detector to obtain the final receiving detector position coordinates.

[0107] The N sets of calculated positioning coordinates corresponding to the N sets of muon trajectory distances can be expressed as:

[0108]

[0109] in, are the weighted least squares coordinates of the muons corresponding to the 1st, 2nd, ..., Nth muon trajectory distances, and I is the N×N identity matrix.

[0110] The N groups of calculated positioning coordinates are averaged to obtain the final receiving detector position coordinate P WLS , based on the coordinates, the positioning and navigation of the navigation terminal are realized.

[0111]

[0112] Among them, P WLS is the final weighted least squares position coordinate, Indicates The nth weighted least squares coefficient in .

[0113] Figure 1 This is the model of the muon navigation system proposed in this invention; the upper part shows multiple reference detectors deployed at different heights, which together form the reference detector array, and the lower part shows the receiving detectors in the shielded area. The reference detector array and the receiving detectors together collect N sets of muon trajectory information, and their corresponding position coordinates on the reference detector array are The position coordinates on the receiving detector array are The distances of muon trajectories are D1, D2, ..., D N ; The collected N groups of muon trajectory information are processed by weighted least squares algorithm to finally obtain the coordinate positioning result of the receiving detector.

[0114] In one embodiment of the present invention, five reference detectors with known coordinates are deployed, and the vertical distance between the deployment area and the shielded area is approximately 30 meters; the size of the square structure of each layer of the reference detectors is 1 meter by 1 meter, and the size of the receiving detector is 0.25 meter by 0.25 meter; the vector muon navigation system composed of five reference detectors and one receiving detector collects information on a total of four groups of muon trajectories.

[0115] The accuracy of this embodiment is compared with that of the existing positioning algorithm. Figure 2 As shown in the figure, the reference detector is divided into four specifications: (1) distance resolution is 0.005m, angular resolution is 0.005rad; (2) distance resolution is 0.005m, angular resolution is 0.01rad; (3) distance resolution is 0.01m, angular resolution is 0.005rad; (4) distance resolution is 0.01m, angular resolution is 0.01rad. Figure 2 It can be clearly seen that the weighted least squares algorithm proposed in the present invention improves the horizontal positioning accuracy and vertical positioning accuracy of the receiving detector compared with the existing vector muon navigation system positioning algorithm, and the effect is more significant in improving the vertical positioning accuracy.

[0116] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present application, and should all be included in the scope of protection of the present application.

Claims

1. A muon navigation method in a shielded environment, characterized in that: include: Deploy a reference detector array and a receiving detector; wherein the receiving detector is arranged on the navigation terminal inside the shielded area, and multiple reference detectors with known positions are deployed above the outside of the shielded area; Collect multiple muon trajectory information using accidental coincidence events detected by the reference detector array and the receiving detector; All collected muon trajectory information is combined into pairs without duplication to form multiple combination pairs; For each combination of muon trajectory information, a set of equations about the distance of muon trajectories is established, and then all the equations are integrated to establish an overdetermined set of equations about the distance of all muon trajectories; Assign weights to the overdetermined equations according to the position resolution and angular resolution of the reference detector corresponding to each muon trajectory information collected, and establish a weighted overdetermined equation system for the distances of all muon trajectories; The weighted overdetermined equations are used to solve all muon trajectory distances, which are then multiplied by the corresponding guidance vector of the muon arrival direction. The distances are then added to the position coordinates on the corresponding reference detector and averaged to obtain the final receiving detector position coordinates, thereby locating and navigating the navigation terminal.

2. The muon navigation method in a shielded environment according to claim 1, characterized in that: In the muon trajectory information obtained by the reference detector and the receiving detector: The coordinates of all muon positions collected by the reference detector array are: The position coordinates of all muons received by the receiving detector are: The corresponding guidance vectors of the muon arrival direction are V1, V2, ... V n ,...,V N , the corresponding muon trajectory distances are D1, D2, ... D n ,...D N , the corresponding muon zenith angles are θ1, θ2, ... θ n ,...,θ N , the muon azimuth is The angular resolution and position resolution of the reference detector corresponding to the nth and mth groups of muon trajectory information are and and n,m=1,2,...,N; Among them, in the nth muon trajectory information, the corresponding guidance vector of the muon arrival direction is expressed as and The distance between the muon trajectories is expressed as D n .

3. The muon navigation method in a shielded environment according to claim 1, characterized in that: The method to determine the correspondence between muon trajectory information and reference detector is: The accidental coincidence events are used to select the muon trajectory information that meets the requirements, and the coordinate points of the muon trajectory information on the reference detector are recorded. The coordinate points are compared with the detectable coordinate ranges of different reference detectors. If they are within the detection coordinate range, it can be considered that the muon has been detected by the reference detector, thereby obtaining the angular resolution and position resolution of the reference detector corresponding to the muon trajectory information.

4. The muon navigation method in a shielded environment according to claim 1, characterized in that: Based on the combination pair (n, m) consisting of the nth and mth groups of muon trajectory information, the corresponding muon trajectory distance (D n ,D m ), the quadratic equation system can be expressed as:

5. The muon navigation method in a shielded environment according to claim 1, characterized in that: Establish the distances D1, D2, D3, ..., D of N muon trajectories N The overdetermined system of equations can be expressed as follows: AD = b; Where A is the coefficient matrix of the overdetermined equations, D is the vector of muon trajectory distances to be solved for the overdetermined equations, and b is the constant vector of the overdetermined equations; Among them A (1,2) ,A (1,3) ,...,A (1,N) ,A (2,3) ,A (2,4) ,...,A (2,N) ,A (3,4) ,...,A (N-1,N) are the coefficient sub-matrices corresponding to all combination pairs respectively; D=[D1 D2 ... D N ] T ; Among them, b (n,m) Represents the constant subvector corresponding to the combination pair (n, m) consisting of the nth and mth groups of muon trajectory information.

6. The muon navigation method in a shielded environment according to claim 1, characterized in that: The coefficient submatrix expression of the combination pair (n, m) composed of the nth and mth groups of muon trajectory information is: a 21 ,a 22 ,…a 2n ,…a 2m ,…a 2N Represents matrix A (n,m) The expressions for the 1st, 2nd, ..., nth, ...mth, ...Nth elements in the second row are: Among them, V n 、V m represents the guidance vector of the arrival direction of the muon corresponding to the nth and mth groups of muon trajectory information, a ij Indicates that in A (n,m) Except a 1n 、a 2m 、a 1m 、a 2n All but four of the elements; 7. The muon navigation method in a shielded environment according to claim 1, characterized in that: The weight matrix of the equation group corresponding to the combination pair (n, m) consisting of the nth and mth groups of muon trajectory information is set to: Among them, w (n,m) is the weight submatrix corresponding to the combination pair (n,m); The weighted overdetermined system of equations can be expressed as: WAD=Wb; Among them, W is the weight matrix composed of the weight sub-matrices of all combination pairs.

8. The muon navigation method in a shielded environment according to claim 1, characterized in that: Solve the weighted overdetermined equations to calculate the distances of all muon trajectories, which can be expressed as: in, is the weighted least squares solution corresponding to the distances of N groups of muon trajectories; the superscript T represents the matrix transpose, and the superscript -1 represents the matrix inversion.

9. The muon navigation method in a shielded environment according to claim 1, characterized in that: The muon trajectory distance is multiplied by the corresponding guidance vector of the muon arrival direction, and then accumulated and averaged with the position coordinates on the corresponding reference detector to obtain the final receiving detector position coordinates, including: The N sets of calculated positioning coordinates corresponding to the N sets of muon trajectory distances can be expressed as: in, are the weighted least squares coordinates of the muons corresponding to the 1st, 2nd, ..., Nth muon trajectory distances, and I is the N×N identity matrix. The N groups of calculated positioning coordinates are averaged to obtain the final receiving detector position coordinate P WLS : Among them, P WLS is the final weighted least squares position coordinate, Indicates The nth weighted least squares coefficient in .

10. A terminal device comprising a processor, a memory, and a computer program stored in the memory; characterized in that: When the processor executes the computer program, the muon navigation method in a shielded environment according to any one of claims 1 to 9 is implemented.

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