A geomagnetic main magnetic field vector matching method based on orthogonal rotation compensation

Abstract

This application discloses a method, apparatus, medium, and device for geomagnetic main magnetic field vector matching based on orthogonal rotation compensation, relating to the field of aircraft navigation technology. The method acquires the aircraft's geomagnetic vector measurements and the inertial navigation system's reference attitude matrix and position sequence; extracts a matching reference map centered on the final reference position and constructs a candidate point sequence; and calculates the measurement difference matrix based on data from adjacent time points. D And map difference matrix A After centralization, an orthogonal Procrustes cost function is constructed to solve for the optimal matching position and orthogonal rotation matrix, thereby correcting the position and attitude of the inertial navigation system. This application weakens the impact of errors through differential and centralization, improves adaptability by combining translation and rotation search, and introduces an orthogonal correction matrix to compensate for attitude projection errors, thereby improving matching stability and navigation accuracy in high-altitude, weak-gradient geomagnetic environments.

Description

Technical Field

[0001] This application relates to the field of aircraft navigation and data processing technology, specifically to a method, device, electronic device, storage medium, and program for geomagnetic main magnetic field vector matching based on orthogonal rotation compensation. Background Technology

[0002] Geomagnetic navigation is a passive navigation technology that utilizes the spatial distribution characteristics of the Earth's magnetic field to achieve autonomous positioning. It features independence from external radio signals, good stealth, and strong anti-interference capabilities, making it valuable for long-range, autonomous, and anti-navigation scenarios for aircraft. For near-ground or low-altitude platforms, geomagnetic anomalies typically exhibit significant local gradient characteristics, which can be used for scalar or vector matching navigation. However, for aircraft, as flight altitude increases, crustal magnetic anomaly signals rapidly attenuate, local geomagnetic background gradients decrease significantly, and the spatial variation of the magnetic field tends to level off. The geomagnetic information that can be stably utilized mainly manifests as the main geomagnetic field and its slow-changing characteristics. Therefore, geomagnetic-assisted navigation for high-altitude aircraft is generally difficult to rely on the fine characteristics of geomagnetic anomalies and is more suitable for vector matching methods based on the main magnetic field model or database. This involves comparing the direction, magnitude, and combination characteristics of magnetic field vectors to help correct the accumulated errors of the inertial navigation system.

[0003] Existing geomagnetic vector matching methods typically rely on a reference attitude matrix provided by an inertial navigation system (INS). The geomagnetic vector measured by the aircraft's magnetometer is projected onto the navigation or geographic coordinate system, and then matched against candidate vectors in a geomagnetic master magnetic field database. However, when the aircraft operates at high speeds, over long distances, and with complex maneuvers, attitude errors in the INS accumulate over time and are directly introduced into the matching process during magnetic field vector projection. Because the gradient of the master magnetic field is small and changes slowly in the high-altitude region, the differences in master magnetic field vectors at different locations are limited. Even small errors in the attitude matrix can cause significant deviations in the direction and components of the projected magnetic field, distorting the magnetic field characteristics of the true location. This leads to problems such as position ambiguity, increased probability of mismatches, and unstable navigation corrections during the matching search. Therefore, it is necessary to propose a matching navigation method that utilizes the differential sequence of geomagnetic master magnetic field vectors and estimates and compensates for attitude projection errors to improve matching reliability and positioning accuracy in weak-gradient geomagnetic environments. Summary of the Invention

[0004] This application discloses a geomagnetic main magnetic field vector matching method, device, electronic device, storage medium and program based on orthogonal rotation compensation, which aims to solve the technical problems faced by aircraft when flying at high altitudes, such as small geomagnetic main magnetic field gradient, slow spatial change, weak candidate position identification, and geomagnetic vector projection deviation caused by attitude error of inertial navigation system, which leads to mismatch.

[0005] Technical solution To achieve the above objectives, the first aspect of this application provides a geomagnetic main magnetic field vector matching method based on orthogonal rotation compensation, comprising: Acquire the airframe geomagnetic vector measurements collected by the magnetic sensors on the aircraft, as well as the reference attitude matrix and reference position sequence output by the inertial navigation system; Centered on the reference position at the last moment of the reference position sequence, a matching reference map is extracted from the main magnetic field map, and grid points in the matching reference map are used as candidate matching points to construct a candidate point sequence. The measurement difference matrix is ​​obtained by performing differential calculations based on the reference attitude matrix at adjacent time points and the mechanical geomagnetic vector measurements. D Based on the map vectors at the corresponding positions of the candidate point sequences in the main magnetic field map, a difference calculation is performed to obtain the map difference matrix. A ; Perform translation and rotation searches on the candidate point sequence. For each candidate sequence obtained after translation and rotation, calculate the corresponding map difference matrix. A and the measurement difference matrix D And map difference matrix A Centralized processing is implemented; Based on the centered measurement difference matrix and map difference matrix, an orthogonal Procrustes cost function is constructed using the orthogonal rotation matrix as a variable. J Solving for the cost function J The goal is to achieve the minimum optimal matching position and the optimal orthogonal rotation matrix, where the optimal orthogonal rotation matrix represents the attitude error compensation matrix of the inertial navigation system. The position and attitude of the inertial navigation system are corrected using the optimal matching position and the optimal orthogonal rotation matrix, and the navigation results are output. Optionally, a measurement difference matrix is ​​obtained by performing differential calculations based on the reference attitude matrix and the machine-system geomagnetic vector measurements at adjacent time points. D ,include: Based on the geomagnetic vector measurements of the machine system at adjacent time points and the reference attitude matrix output by the inertial navigation system, the geomagnetic vector projection difference in the navigation system is calculated. The map difference matrix is ​​obtained by performing difference calculations on the map vectors at the corresponding positions of the candidate point sequences in the main magnetic field map. A ,include: Based on the map vectors of the candidate point sequence at the corresponding positions in the main magnetic field map, calculate the map vector difference between adjacent time points; Among them, differential calculation is used to eliminate geomagnetic diurnal variation error, magnetic field common deviation, and sensor constant error.

[0006] Optionally, for the measurement difference matrix D And map difference matrixA Centralized processing includes: Calculate the measurement difference matrix separately D And map difference matrix A The mean vector for each row; Using measurement difference matrix D Subtracting its corresponding mean vector yields the centered measurement difference matrix. D c Using map difference matrix A Subtracting its corresponding mean vector yields the centered map difference matrix. A c .

[0007] Optionally, the orthogonal Procrustes cost function is constructed based on the centered measurement difference matrix and map difference matrix, using the orthogonal rotation matrix as a variable. J Solving for the cost function J The optimal orthogonal rotation matrix that achieves the minimum includes: Constructing the cost function , where δ C Represents an orthogonal rotation matrix. Denotes the Frobenius norm of a matrix; Let matrix ,matrix M Map difference matrix A c With measurement difference matrix D c The cross-correlation matrix between the matrices, for the matrix M Perform singular value decomposition to obtain M=UΣV ,in U It is a left singular vector matrix. S It is a singular value matrix. V Let T be a right singular vector matrix, and let T denote the matrix transpose. Based on the results of the singular value decomposition, the orthogonal rotation matrix δ is calculated. C The global optimal solution is expressed as follows: ,in, O For the reflection calibration matrix, Ensure , This is the determinant value of the matrix.

[0008] Optionally, a translation and rotation search is performed on the candidate point sequence, including: The reference position sequence is shifted to the matching candidate point to obtain the shifted candidate sequence; Define the rotation angle range and angle step size. Within the rotation angle range, rotate the candidate sequence successively according to the angle step size, and calculate the map difference matrix corresponding to the sequence after each rotation. A and cost function J , cost function J The matching candidate point and rotation angle corresponding to the historical minimum are determined as the optimal matching position and the optimal heading error angle.

[0009] Optionally, the position and attitude of the inertial navigation system are corrected using the optimal matching position and the optimal orthogonal rotation matrix, including: The optimal matching position is used as the true position to correct the reference position error of the inertial navigation system; The optimal orthogonal rotation matrix is ​​used as the attitude error compensation matrix to correct the reference attitude matrix of the inertial navigation system, thereby eliminating the geomagnetic vector projection deviation caused by attitude error.

[0010] This application discloses a method, apparatus, electronic device, storage medium, and program for geomagnetic main magnetic field vector matching based on orthogonal rotation compensation. The method includes acquiring airframe geomagnetic vector measurements collected by magnetic sensors on the aircraft, as well as a reference attitude matrix and reference position sequence output by the inertial navigation system; extracting a matching reference map from the main magnetic field map with the reference position at the last moment of the reference position sequence as the center, and constructing a candidate point sequence using grid points in the matching reference map as matching candidate points; and performing differential calculations based on the reference attitude matrix and airframe geomagnetic vector measurements at adjacent moments to obtain a measurement difference matrix. D Based on the map vectors at the corresponding positions of the candidate point sequences in the main magnetic field map, a difference calculation is performed to obtain the map difference matrix. A Perform translation and rotation searches on the candidate point sequence. For each candidate sequence obtained after translation and rotation, calculate the corresponding map difference matrix. A and the measurement difference matrix D And map difference matrix A Centralization is performed; based on the centralized measurement difference matrix and map difference matrix, an orthogonal Procrustes cost function is constructed using the orthogonal rotation matrix as a variable. J Solving for the cost function J The goal is to achieve the minimum optimal matching position and the optimal orthogonal rotation matrix, where the optimal orthogonal rotation matrix represents the attitude error compensation matrix of the inertial navigation system. The position and attitude of the inertial navigation system are corrected using the optimal matching position and the optimal orthogonal rotation matrix, and the navigation results are output.

[0011] To address the challenges faced by aircraft during high-altitude flight, such as small geomagnetic gradients, slow spatial changes, and weak discernibility of candidate positions, this method combines candidate path translation search, track rotation search, and orthogonal registration of vector difference sequences to jointly solve for the optimal matching position and attitude projection error correction matrix. This method reduces the impact of common magnetic field bias, sensor constant errors, and main magnetic field model baseline bias on the matching results by differencing and centering the measured geomagnetic vector sequence and candidate map vector sequence. Constructing a candidate point sequence within the matching region and performing translation and rotation searches on the candidate path improves the algorithm's adaptability to inertial navigation position and track orientation errors. Introducing an orthogonal correction matrix δ into the cost function further enhances the algorithm's effectiveness. C This invention can estimate and compensate for magnetic vector projection deviations caused by reference attitude matrix errors, reducing the risk of mismatches due to attitude projection errors in traditional vector matching methods. Compared with methods that directly utilize inertial navigation reference attitude for geomagnetic vector matching, this invention exhibits better matching stability and robustness under weak gradient conditions in the high-altitude main magnetic field. It can enhance the ability of geomagnetic navigation to correct accumulated errors in inertial navigation, and improve the autonomous navigation accuracy and anti-interference performance of long-endurance, long-distance aircraft. Attached Figure Description

[0012] Figure 1 This is a schematic diagram of the East-North-Sky coordinate system; Figure 2 A schematic diagram illustrating the relationship between the local horizontal coordinate system and the carrier coordinate system; Figure 3 A schematic diagram illustrating a geomagnetic main magnetic field vector matching method based on orthogonal rotation compensation provided in an embodiment of this application; Figure 4 A flowchart illustrating a method for a geomagnetic main magnetic field vector matching device based on orthogonal rotation compensation, provided in an embodiment of this application. Detailed Implementation

[0013] Target data: refers to the airframe geomagnetic vector measurements collected by the magnetic sensors on the aircraft and the reference attitude matrix and reference position sequence output by the inertial navigation system, which serve as the input data objects for the matching solution in this application.

[0014] Eigenvector / Eigenmatrix: refers to the measurement difference matrix D And map difference matrix A , used to characterize the changes in geomagnetic vectors at adjacent times, is the core feature representation for orthogonal Procrustes matching solutions.

[0015] Constraint information: refers to the orthogonal rotation matrix constraint in the orthogonal Procrustes cost function, which is used to characterize the orthogonality of the attitude error compensation matrix and ensure the physical rigid body rotation transformation.

[0016] Edge devices / terminals: These refer to navigation calculation devices mounted on aircraft, including magnetic sensors and inertial navigation systems, used to perform data acquisition and matching calculations.

[0017] Business object / control object: refers to the inertial navigation system, which uses the optimal matching position and optimal orthogonal rotation matrix obtained in this application to correct its reference position and reference attitude in order to output high-precision navigation results.

[0018] Key Existing Technology Description Existing geomagnetic vector matching methods typically rely on a reference attitude matrix provided by an inertial navigation system. The geomagnetic vector measured by the aircraft's magnetometer is projected onto the navigation or geographic coordinate system, and then matched against candidate vectors in a geomagnetic main magnetic field database. However, when the aircraft operates at high speeds, over long ranges, and undergoes complex maneuvers, attitude errors in the inertial navigation system accumulate over time and are directly introduced into the matching process during magnetic field vector projection. Because the gradient of the main magnetic field is small and changes slowly in the high-altitude region, the differences in the main magnetic field vector at different locations are limited. Even small errors in the attitude matrix can cause significant deviations in the direction and components of the projected magnetic field, distorting the magnetic field characteristics of the true location. This leads to problems such as position ambiguity, increased probability of mismatches, and unstable navigation corrections during the matching search.

[0019] refer to Figure 3 and Figure 4 The first embodiment of this application provides a geomagnetic main magnetic field vector matching method based on orthogonal rotation compensation to solve the technical problems mentioned in the background art, such as small geomagnetic main magnetic field gradient, slow spatial change, weak candidate position identification, and geomagnetic vector projection deviation caused by attitude error of inertial navigation system, which leads to mismatch. This method can be executed by a processor, which can be set in a terminal or server. The execution process of the geomagnetic main magnetic field vector matching method based on orthogonal rotation compensation can be as follows: Step S101: Obtain the airframe geomagnetic vector measurement value collected by the magnetic sensor on the aircraft, as well as the reference attitude matrix and reference position sequence output by the inertial navigation system.

[0020] Step S102: Taking the reference position at the last moment of the reference position sequence as the center, extract the matching reference map from the main magnetic field map, and construct the candidate point sequence by using the grid points in the matching reference map as matching candidate points.

[0021] Step S103: Based on the reference attitude matrix and the measured values ​​of the machine system geomagnetic vector at adjacent time points, differential calculation is performed to obtain the measurement difference matrix. DBased on the map vectors at the corresponding positions of the candidate point sequences in the main magnetic field map, a difference calculation is performed to obtain the map difference matrix. A .

[0022] Step S104: Perform translation and rotation search on the candidate point sequence. For each candidate sequence obtained after translation and rotation, calculate the corresponding map difference matrix. A and the measurement difference matrix D And map difference matrix A Centralized processing is implemented.

[0023] Step S105: Based on the centered measurement difference matrix and map difference matrix, construct an orthogonal Procrustes cost function with the orthogonal rotation matrix as the variable. J Solving for the cost function J The goal is to achieve the minimum optimal matching position and the optimal orthogonal rotation matrix, where the optimal orthogonal rotation matrix represents the attitude error compensation matrix of the inertial navigation system.

[0024] Step S106: Correct the position and attitude of the inertial navigation system using the optimal matching position and the optimal orthogonal rotation matrix, and output the navigation results.

[0025] In one embodiment of this application, a measurement difference matrix is ​​obtained by performing differential calculation based on the reference attitude matrix at adjacent time points and the measured values ​​of the machine system's geomagnetic vector. D ,include: The geomagnetic vector projection difference in the navigation system is calculated based on the geomagnetic vector measurements of the machine system at adjacent time points and the reference attitude matrix output by the inertial navigation system.

[0026] The map difference matrix is ​​obtained by performing difference calculations on the map vectors at the corresponding positions of the candidate point sequences in the main magnetic field map. A ,include: Based on the map vectors of the candidate point sequence at the corresponding positions in the main magnetic field map, the map vector difference between adjacent time points is calculated.

[0027] Among them, differential calculation is used to eliminate geomagnetic diurnal variation error, magnetic field common deviation, and sensor constant error.

[0028] In an optional embodiment of this application, the measurement difference matrix D And map difference matrix A Centralized processing includes: Calculate the measurement difference matrix separately D And map difference matrix A The mean vector for each row.

[0029] Using measurement difference matrix DSubtracting its corresponding mean vector yields the centered measurement difference matrix. D c Using map difference matrix A Subtracting its corresponding mean vector yields the centered map difference matrix. A c .

[0030] Furthermore, based on the centralized measurement difference matrix and map difference matrix, an orthogonal Procrustes cost function is constructed using the orthogonal rotation matrix as a variable. J Solving for the cost function J The optimal orthogonal rotation matrix that achieves the minimum includes: Constructing the cost function , where δ C Represents an orthogonal rotation matrix. Denotes the Frobenius norm of a matrix; Let matrix ,matrix M Map difference matrix A c With measurement difference matrix D c The cross-correlation matrix between the matrices, for the matrix M Perform singular value decomposition to obtain M=UΣV ,in U It is a left singular vector matrix. S It is a singular value matrix. V Let T be a right singular vector matrix, and let T denote the matrix transpose. Based on the results of the singular value decomposition, the orthogonal rotation matrix δ is calculated. C The global optimal solution is expressed as follows: ,in, O For the reflection calibration matrix, Ensure , This is the determinant value of the matrix.

[0031] For example, a translation and rotation search of the candidate point sequence includes: The reference position sequence is shifted to the matching candidate point to obtain the shifted candidate sequence.

[0032] Define the rotation angle range and angle step size. Within the rotation angle range, rotate the candidate sequence successively according to the angle step size, and calculate the map difference matrix corresponding to the sequence after each rotation. A and cost function J , cost function J The matching candidate point and rotation angle corresponding to the historical minimum are determined as the optimal matching position and the optimal heading error angle.

[0033] In one embodiment of this application, the position and attitude of an inertial navigation system are corrected using the optimal matching position and the optimal orthogonal rotation matrix, including: The optimal matching position is used as the true position to correct the reference position error of the inertial navigation system.

[0034] The optimal orthogonal rotation matrix is ​​used as the attitude error compensation matrix to correct the reference attitude matrix of the inertial navigation system, thereby eliminating the geomagnetic vector projection deviation caused by attitude error.

[0035] Furthermore, this application relates to the following coordinate system definitions and transformations: like Figure 1 As shown, for the local horizontal coordinate system (East-North-Sky): Aircraft navigation coordinate systems are typically described using an East-North-Sky coordinate system, denoted as . n The East-North-Sky coordinate system is usually represented as: (a) The origin of the coordinate system is the location of the carrier.

[0036] (b) x The axis points due east.

[0037] (c) y The axis points due north.

[0038] (d) z The axes are perpendicular to the ground plane where the carrier is located and point to the sky. The three axes form a right-handed rectangular coordinate system.

[0039] Carrier coordinate system: In most applications, the sensitive axes of gyroscopes and accelerometers coincide with their carrier axes, which together form the carrier coordinate system (denoted as ). b The coordinate axes of the carrier coordinate system are defined in this method as follows: (a) The origin is the center of mass of the aircraft.

[0040] (b) y The axis runs along the longitudinal axis of the aircraft and points towards the nose of the aircraft.

[0041] (c) x The axis lies within the longitudinal symmetry plane of the aircraft and is perpendicular to... y The axis points to the right.

[0042] (d) z shaft and x axis, y The axes form a right-handed rectangular coordinate system.

[0043] about n System and b Coordinate transformation relationships between systems: refer to Figure 2 From the East-North-Sky coordinate system ( n From the coordinate system to the carrier coordinate system b The transformation between systems is commonly achieved using a transformation matrix called the attitude matrix. Attitude matrix mid-pitch angle Roll angle and heading angle Among them, heading angle Normally, north-southeast is taken as positive. Attitude matrix This can be obtained by three rotations: First, around n Department z Axis rotation Degree (or circle) z Axis rotation Its rotation (degrees) can be represented by an elementary rotation matrix as follows: Secondly, around the new n Department x Axis rotation An angle can be represented using an elementary rotation matrix. Finally, around the new n Department y Axis rotation The degree can be represented by an elementary rotation matrix as follows: Align the axes of the two coordinate systems sequentially to obtain the attitude matrix. for: (1) The pose matrix is ​​obtained by unfolding: (2) Furthermore, the principle of geomagnetic vector matching based on orthogonal Procrustes is as follows: by n Using the system as a navigation reference coordinate system, let the actual magnetic field vector at a certain point be in... n The projection under the system is B n Measurement vector in b The projection under the system is .but: (3) In the formula, This is a soft magnetic coefficient matrix that includes the soft magnetic error calibration residuals. For hard magnetic error calibration residuals in b The projection under the system. Due to the time-varying characteristics of geomagnetic diurnal and monthly variations, there is a difference between the map vector and the measurement vector, and this difference can be considered constant in a short period of time, so: (4) In the formula, the map vector is , This represents the map vector error caused by the time-varying characteristics of the Earth's magnetic field.

[0044] Substituting equation (4) into equation (3), we have: (5) After deformation, we get: (6) In the formula, express The inverse matrix introduces the time stamp. , record i Time for , i 1 moment is and calculate i and i 1 moment Substitute the difference into (6): (7) In the formula, and They represent i Time and i The true pose matrix at time 1 and They represent i Time and i The measurement vector value at time 1. and They represent i Time and i Hard magnetic error calibration residual at time 1 Indicates in i Time and i The magnetic field changes caused by the diurnal variation of the geomagnetic field between moments 1 and 2 can be considered to be very small at adjacent moments, therefore: (8) Considering the attitude error that exists in the calculation of actual navigation systems, attitude matrix error is introduced. : (9) In the formula, express i The attitude error matrix caused by navigation system errors at any given moment. n ′ represents the navigation calculation coordinate system with errors. express iThe inertial navigation system provides a reference attitude matrix with errors at all times. i The attitude error matrix at time 1 can be similarly expressed as follows: Equation (9) and Substitute (8): (10) Furthermore, it can be assumed that the attitude error matrix caused by inertial navigation calculation errors remains unchanged over a short period of time. replace and Therefore, equation (10) can be written as: (11) because The residual error matrix after calibration, therefore It can be linearly represented as: (12) Substituting into (11), we get: (13) in, and Zhongdu contains In a difference structure, this can be considered a higher-order small quantity, while The meaning is the difference projection term of the hard magnetic residual in the navigation system caused by attitude changes. Since the hard magnetic residual is a small quantity, when the attitude change amplitude between adjacent time steps is small, The difference structure can also be regarded as higher-order minors. Therefore, after ignoring these higher-order terms, equation (13) can be written as: (14) Equation (14) indicates that the difference structure composed of the attitude matrix provided by the inertial navigation system and the measurement values ​​of the magnetic sensor differs from the difference at the corresponding position read from the vector map by only one orthogonal matrix. It is important to note here that even when the amplitude of the attitude change is small, Difference structures cannot be considered as higher-order small quantities because... and These are measurement results at different positions. Even if the attitude matrix is ​​the same, positional differences will cause different measurement differences. Therefore, this difference structure cannot be regarded as a higher-order small quantity. In equation (14), It is an orthogonal matrix, therefore as well as The resulting difference sequence can be used to solve... ,and It includes measurement information at the actual location, and It contains location information on the map. Therefore, as long as a geomagnetic vector reference map is available... f A unique location on a map can be determined by the fact that any two sequences on the map have different internal structures. Therefore, for the orthogonal Procrustes problem... J : (15) In the formula, Let represent the Frobenius norm of the matrix. L Under a given measurement, in equation (15): (16) In the formula, T represents the matrix transpose. It represents the set of real numbers.

[0045] when When the global optimum is obtained, the corresponding map difference matrix is... A With measurement difference matrix D The paths on the map can be considered to overlap.

[0046] For orthogonal Procrustes problems, the optimal solution is obtained using the Singular Value Decomposition (SVD) method. It must be the globally optimal solution. Therefore, this method proposes using the SVD method to solve it. For equation (15), we have: (17) In the formula, tr represents the trace of the matrix, let , M This is the cross-correlation matrix between the map difference matrix and the measurement difference matrix. M The singular value decomposition can be expressed as ,in U It is a left singular vector matrix. S It is a singular value matrix. V Let be a right singular vector matrix. Under the special orthogonality constraint, the unique maximum solution of equation (17) is the Kabsch / Umeyama solution, therefore: (18) In equation (18), for The global optimal solution. O The purpose of this is to ensure the reflection calibration matrix. determinant value , O The expression is as follows: (19) For example, the matching process is as follows: Matching begins with a vector, and the reference trajectory provided by the inertial navigation system is denoted as: (20) In the formula, k Represents the first in the sequence k The point, and the first k The measurement time at each point is recorded as t k , Indicates that the inertial navigation system is in t k The reference position for the output at any given time, abbreviated as P { t k} Indicates reference latitude, Indicates reference longitude. L Let represent the maximum length of the matching sequence, and let be the sampling time of the last point in the sequence. t L Let the matching candidate point sequence be... Q : (twenty one) In the formula, Indicates the first i The latitude and longitude of each matching candidate point are denoted as . Q { i}. Reference trajectory P Translate to matching candidate point Q { i It can be obtained from the following formula: (twenty two) In the formula, Indicates will P Move to matching candidate point Q { i The sequence following} is abbreviated as S i . Operator representation of point coordinates x With sets y The coordinates of each column in the sequence are added together to form a new sequence. express P Translate to Q { i The corresponding after} t k The latitude and longitude of a moment, abbreviated as: .

[0047] Because inertial navigation systems have accumulated errors, if the geomagnetic navigation system is powered on late, the reference trajectory provided by the inertial navigation system may have a large error in direction. Therefore, drawing on the idea of ​​rotation matching, the optimal... At this time, the reference trajectory can be rotated successively in the plane and calculated. J ,Will S i Sequence rotation i The angle can be obtained from the following formula: (twenty three) In the formula, i Indicates the rotation angle. Let the origin of rotation be... Indicates to S i Rotation i The resulting sequence Represents the reference trajectory P Translate to candidate point Q { i After rotating i Angle correspondence t k The latitude and longitude of the moment.

[0048] Sequences obtained from translation and rotation transformations Calculate the map difference matrix : (twenty four) Simultaneously combined with the calculations of the inertial navigation system t k Reference attitude matrix at time step And the measurement vector of the magnetic sensor, calculate the measurement difference matrix. D As shown in equation (16). Due to the measurement difference matrix D Interference exists during the measurement process, therefore, it is advisable to first check the orthogonal Procrustes before performing the solution. and D Centralization: (25) In the formula, and D c They represent and D The result of centralization. and Represent matrices respectively sum matrix D A vector composed of the mean values ​​of each row. Iterate through all... And calculate using equation (15) J , J When the minimum is reached, the corresponding Q { i} is the optimal matching point Q *

[0049] The pseudocode of the program used in the method of this application is shown in Table 1.

[0050] Table 1. Pseudocode of the matching algorithm

[0051] This application addresses the challenges faced by aircraft during high-altitude flight, including small geomagnetic gradients, slow spatial changes, and weak discernibility of candidate positions. It combines candidate path translation search, track rotation search, and orthogonal registration of vector difference sequences to jointly solve for the optimal matching position and attitude projection error correction matrix. This method reduces the impact of common magnetic field bias, sensor constant errors, and main magnetic field model baseline bias on the matching results by differential and centering the measured geomagnetic vector sequence and candidate map vector sequence. Constructing a candidate point sequence within the matching region and performing translation and rotation searches on the candidate path improves the algorithm's adaptability to inertial navigation position and track orientation errors. An orthogonal correction matrix δ is introduced into the cost function. C This invention can estimate and compensate for magnetic vector projection deviations caused by reference attitude matrix errors, reducing the risk of mismatches due to attitude projection errors in traditional vector matching methods. Compared with methods that directly utilize inertial navigation reference attitude for geomagnetic vector matching, this invention exhibits better matching stability and robustness under weak gradient conditions in the high-altitude main magnetic field. It can enhance the ability of geomagnetic navigation to correct accumulated errors in inertial navigation, and improve the autonomous navigation accuracy and anti-interference performance of long-endurance, long-distance aircraft.

[0052] Another embodiment of this application also provides a geomagnetic main magnetic field vector matching system based on orthogonal rotation compensation. The system of this embodiment includes a three-axis magnetic sensor, an inertial navigation system, a main magnetic field map / model database, and a matching solution module. The magnetic sensor outputs the geomagnetic vector and total field strength scalar, and the inertial navigation system outputs reference attitude, velocity, and position information. The execution flow of this system is shown below.

[0053] 1. Parameter initialization: Set the size of the matching region. M × N Matching sequence length L Attitude error search angle range ± i m and angle step size d i And set a weighted matching criterion for vector difference and scalar difference.

[0054] 2. Data Acquisition and Sequence Construction: Continuous data acquisition according to the sampling period. L Calculate the magnetic vector, magnetic field scalar, and inertial navigation data at each sampling time. t The reference attitude matrix and reference position sequence.

[0055] 3. Baseline Map Extraction and Candidate Construction: Using the final time reference position P ( t L Centered on ), extract a size of from the main magnetic field map. M × N Matching baseline map f All grid points in the baseline map are used as candidate starting points, and a sequence of candidate points is constructed by combining them with the reference track. S i .

[0056] 4. Attitude error search and matching calculation: For each candidate sequence S i Within the angular range - i m to i m Inner step size d i Rotate gradually to obtain R ( i , S i Calculate the vector difference between the measurement sequence and the candidate sequence respectively. A ( i , S i The cost function is then centralized and constructed. J .

[0057] 5. Optimal Solution Output: After traversing all candidate points and all attitude error angles, output the valence function. J The minimum result is used as the optimal matching position and optimal attitude error estimate, and the inertial navigation position and attitude are corrected accordingly to output the final navigation result.

[0058] To achieve the above objectives, the second embodiment of this application also provides a geomagnetic main magnetic field vector matching device based on orthogonal rotation compensation to solve the same technical problem as the method embodiment. The device 1000 includes: The data acquisition module 1001 is used to acquire the airframe geomagnetic vector measurement value collected by the magnetic sensor on the aircraft, as well as the reference attitude matrix and reference position sequence output by the inertial navigation system.

[0059] The candidate construction module 1002 is used to extract a matching reference map from the main magnetic field map with the reference position at the last moment of the reference position sequence as the center, and construct a candidate point sequence with the grid points in the matching reference map as matching candidate points.

[0060] The differential calculation module 1003 is used to perform differential calculations based on the reference attitude matrix and the mechanical geomagnetic vector measurement values ​​at adjacent time points to obtain the measurement differential matrix. DBased on the map vectors at the corresponding positions of the candidate point sequences in the main magnetic field map, a difference calculation is performed to obtain the map difference matrix. A .

[0061] The search and centralization module 1004 is used to perform translation and rotation searches on the candidate point sequence. For each candidate sequence obtained after translation and rotation, the corresponding map difference matrix is ​​calculated. A and the measurement difference matrix D And map difference matrix A Centralized processing is implemented.

[0062] The joint solver module 1005 is used to construct an orthogonal Procrustes cost function based on the centered measurement difference matrix and map difference matrix, using the orthogonal rotation matrix as a variable. J Solving for the cost function J The goal is to achieve the minimum optimal matching position and the optimal orthogonal rotation matrix, where the optimal orthogonal rotation matrix represents the attitude error compensation matrix of the inertial navigation system.

[0063] The navigation correction module 1006 is used to correct the position and attitude of the inertial navigation system using the optimal matching position and the optimal orthogonal rotation matrix, and output the navigation results.

[0064] To achieve the above objectives, the third embodiment of this application also provides an electronic device, including a processor and a memory, wherein a computer program is stored in the memory, and when the computer program is executed by the processor, it implements the geomagnetic main magnetic field vector matching method based on orthogonal rotation compensation as provided in the previous embodiment.

[0065] To achieve the above objectives, the fourth embodiment of this application also provides a computer-readable storage medium storing a computer program thereon. When the computer program is executed by a processor, it implements the geomagnetic main magnetic field vector matching method based on orthogonal rotation compensation as provided in the previous embodiments.

[0066] To achieve the above objectives, the fifth embodiment of this application also provides a computer program product, including a computer program that, when executed by a processor, implements the geomagnetic main magnetic field vector matching method based on orthogonal rotation compensation as provided in the previous embodiments.

[0067] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working process of the system and device described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0068] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. The apparatus embodiments described above are merely illustrative. For example, the division of modules is only a logical functional division, and there may be other division methods in actual implementation. Furthermore, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Additionally, the coupling or direct coupling or communication connection shown or discussed may be through some communication interface; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0069] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0070] In addition, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0071] If a function is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0072] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features. These modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for matching the geomagnetic main magnetic field vector based on orthogonal rotation compensation, characterized in that, include: Acquire the airframe geomagnetic vector measurements collected by the magnetic sensors on the aircraft, as well as the reference attitude matrix and reference position sequence output by the inertial navigation system; Using the reference position at the last moment of the reference position sequence as the center, a matching reference map is extracted from the main magnetic field map, and the grid points in the matching reference map are used as matching candidate points to construct a candidate point sequence; Based on the reference attitude matrix and the measured geomagnetic vector values ​​of the machine system at adjacent time points, a difference calculation is performed to obtain the measurement difference matrix. D ; Based on the map vectors at the corresponding positions of the candidate point sequences in the main magnetic field map, a difference calculation is performed to obtain the map difference matrix. A ; The candidate point sequence is searched by translation and rotation. For each candidate sequence obtained after translation and rotation, the corresponding map difference matrix is ​​calculated. A and the measurement difference matrix D and the map difference matrix A Centralized processing is implemented; Based on the centered measurement difference matrix and map difference matrix, an orthogonal Procrustes cost function is constructed using the orthogonal rotation matrix as a variable. J Solving for the cost function J The goal is to achieve the minimum optimal matching position and the optimal orthogonal rotation matrix, wherein the optimal orthogonal rotation matrix represents the attitude error compensation matrix of the inertial navigation system. The position and attitude of the inertial navigation system are corrected using the optimal matching position and the optimal orthogonal rotation matrix, and the navigation results are output.

2. The geomagnetic main magnetic field vector matching method based on orthogonal rotation compensation as described in claim 1, characterized in that, The reference attitude matrix based on adjacent time points and the measured values ​​of the machine system's geomagnetic vector are used to perform differential calculations to obtain a measurement difference matrix. D ,include: Based on the geomagnetic vector measurements of the machine system at adjacent time points and the reference attitude matrix output by the inertial navigation system, the geomagnetic vector projection difference in the navigation system is calculated. The map difference matrix is ​​obtained by performing a difference calculation on the map vectors at the corresponding positions of the candidate point sequence in the main magnetic field map. A ,include: Based on the map vectors of the corresponding positions of the candidate point sequences in the main magnetic field map, calculate the map vector difference between adjacent time points; The differential calculation is used to eliminate geomagnetic diurnal variation errors, magnetic field common deviations, and sensor constant errors.

3. The geomagnetic main magnetic field vector matching method based on orthogonal rotation compensation as described in claim 1, characterized in that, For the measurement difference matrix D and the map difference matrix A Centralized processing includes: Calculate the measurement difference matrix respectively D and the map difference matrix A The mean vector for each row; Using the measurement difference matrix D Subtracting its corresponding mean vector yields the centered measurement difference matrix. D c Using the map difference matrix A Subtracting its corresponding mean vector yields the centered map difference matrix. A c .

4. The geomagnetic main magnetic field vector matching method based on orthogonal rotation compensation as described in claim 3, characterized in that, The orthogonal Procrustes cost function is constructed based on the centered measurement difference matrix and map difference matrix, using the orthogonal rotation matrix as a variable. J Solving for the cost function J The optimal orthogonal rotation matrix that achieves the minimum includes: Constructing the cost function , where δ C Represents an orthogonal rotation matrix. Denotes the Frobenius norm of a matrix; Let matrix ,matrix M Map difference matrix A c With measurement difference matrix D c The cross-correlation matrix between the matrices, for the matrix M Perform singular value decomposition to obtain M = UΣV ,in U It is a left singular vector matrix. Σ It is a singular value matrix. V Let T be a right singular vector matrix, and let T denote the matrix transpose. Based on the results of the singular value decomposition, the orthogonal rotation matrix δ is calculated. C The global optimal solution is expressed as follows: ,in, O For the reflection calibration matrix, Ensure , This is the determinant value of the matrix.

5. The geomagnetic main magnetic field vector matching method based on orthogonal rotation compensation as described in claim 1, characterized in that, The search for the candidate point sequence by translation and rotation includes: The reference position sequence is shifted to the matching candidate point to obtain the shifted candidate sequence; Define a rotation angle range and an angle step size. Within the rotation angle range, rotate the candidate sequence successively according to the angle step size, and calculate the map difference matrix corresponding to the sequence after each rotation. A and cost function J , cost function J The matching candidate point and rotation angle corresponding to the historical minimum are determined as the optimal matching position and the optimal heading error angle.

6. The geomagnetic main magnetic field vector matching method based on orthogonal rotation compensation as described in claim 1, characterized in that, Correcting the position and attitude of the inertial navigation system using the optimal matching position and the optimal orthogonal rotation matrix includes: The optimal matching position is used as the true position to correct the reference position error of the inertial navigation system; The optimal orthogonal rotation matrix is ​​used as the attitude error compensation matrix to correct the reference attitude matrix of the inertial navigation system, thereby eliminating the geomagnetic vector projection deviation caused by attitude error.

7. A geomagnetic main magnetic field vector matching device based on orthogonal rotation compensation, characterized in that, include: The data acquisition module is used to acquire the airframe geomagnetic vector measurement values ​​collected by the magnetic sensors on the aircraft, as well as the reference attitude matrix and reference position sequence output by the inertial navigation system; The candidate construction module is used to extract a matching reference map from the main magnetic field map with the reference position at the last moment of the reference position sequence as the center, and construct a candidate point sequence with the grid points in the matching reference map as matching candidate points. The differential calculation module is used to perform differential calculations based on the reference attitude matrix and the machine-system geomagnetic vector measurement values ​​at adjacent time points to obtain the measurement differential matrix. D ; Based on the map vectors at the corresponding positions of the candidate point sequences in the main magnetic field map, a difference calculation is performed to obtain the map difference matrix. A ; The search and centering module is used to perform translation and rotation searches on the candidate point sequence. For each candidate sequence obtained after translation and rotation, the corresponding map difference matrix is ​​calculated. A and the measurement difference matrix D and the map difference matrix A Centralized processing is implemented; The joint solver module is used to construct an orthogonal Procrustes cost function based on the centered measurement difference matrix and map difference matrix, with the orthogonal rotation matrix as the variable. J Solving for the cost function J The goal is to achieve the minimum optimal matching position and the optimal orthogonal rotation matrix, wherein the optimal orthogonal rotation matrix represents the attitude error compensation matrix of the inertial navigation system. The navigation correction module is used to correct the position and attitude of the inertial navigation system using the optimal matching position and the optimal orthogonal rotation matrix, and output the navigation result.

8. An electronic device, characterized in that, It includes a processor and a memory, wherein the memory stores a computer program, and when the computer program is executed by the processor, it implements the geomagnetic main magnetic field vector matching method based on orthogonal rotation compensation as described in any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the geomagnetic main magnetic field vector matching method based on orthogonal rotation compensation as described in any one of claims 1 to 6.

10. A computer program product, characterized in that, The method includes a computer program that, when executed by a processor, implements the geomagnetic main magnetic field vector matching method based on orthogonal rotation compensation as described in any one of claims 1 to 6.

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