An online evolutionary aeromagnetic compensation method and system

Abstract

This invention discloses an online evolving aeromagnetic compensation method and system. The method includes the following steps: performing a calibration flight and acquiring calibration flight data; initializing a compensation model based on the calibration flight data; performing a mission flight and acquiring mission flight data; updating the compensation model using the data at the current moment in the mission flight data and the target matrix in the previous compensation model through the Woodbury equation; using the updated compensation model to compensate for aircraft interference; and continuing to perform the steps of performing mission flights and acquiring mission flight data until the mission flight ends. This invention can evolve the magnetic compensation model parameters during mission flight based on the previous compensation model and the updated flight data, effectively reducing the impact of changes in magnetic interference during mission flight.

Description

Technical Field

[0001] This invention relates to the field of aeromagnetic compensation technology, and in particular to an online evolving aeromagnetic compensation method and system. Background Technology

[0002] Aeromagnetic compensation is widely used in fields such as airborne geophysical exploration and magnetic anomaly detection, with the primary purpose of eliminating interfering magnetic fields generated by aircraft. The most classic aeromagnetic compensation model is described by Tolles Lawson (TL), which consists of 18 linear equations representing the permanent field, induced field, and eddy current field. Therefore, a key issue in aeromagnetic compensation technology is the estimation of the compensation coefficients, described as a linear regression problem. To accurately solve this problem, existing research has proposed many techniques, such as ridge regression, truncated singular value decomposition, partial least squares regression, principal component analysis, Levenberg-Marquard neural networks, deep autoencoders, and generalized regression neural networks. These studies mainly address the problems of multicollinearity or overfitting of linear models, thereby improving the level of interference reduction in aeromagnetic compensation technology.

[0003] Despite significant improvements in compensation performance, traditional compensation methods still require refinement because the characteristics of the interfering magnetic field on an aircraft platform are not constant but vary with time and space. On one hand, the interfering magnetic field is related to the operational status of the aircraft platform, which is constantly changing. On the other hand, the interfering magnetic field is related to the Earth's magnetic field, which varies spatially during flight. This renders compensation models built during calibration flights unsuitable for specific missions. Furthermore, updating the parameter matrix of traditional interference models requires another calibration flight and offline post-processing. However, in some emergency situations, such as underwater target magnetic detection and tracking, repeating a calibration flight is nearly impossible. Summary of the Invention

[0004] The technical problem to be solved by this invention is: In view of the technical problems existing in the prior art, this invention provides an online evolutionary aeromagnetic compensation method and system, which can evolve the magnetic compensation model parameters during mission flight based on the previous compensation model and the updated flight data, and can effectively reduce the impact of magnetic interference changes during mission flight.

[0005] To solve the above-mentioned technical problems, the technical solution proposed by this invention is as follows:

[0006] An online evolutionary aeromagnetic compensation method includes the following steps:

[0007] S1) Perform calibration flight and acquire calibration flight data, and initialize the compensation model based on the calibration flight data;

[0008] S2) Perform mission flight and acquire mission flight data. Update the compensation model using the data at the current moment in the mission flight data and the target matrix in the previous compensation model through the Woodbury equation.

[0009] S3) Use the updated compensation model to perform aircraft interference compensation, and continue to execute the steps of conducting mission flight and acquiring mission flight data until the mission flight ends.

[0010] Furthermore, in step S1, when initializing the compensation model based on the calibration flight data, the following steps are included: using the calibration flight data as the dataset for solving the compensation model, and using the least squares and ridge regression methods to solve the coefficient matrix of the TL model to obtain the initial compensation model.

[0011] Furthermore, in step S2, when updating the compensation model using the current data from the mission flight data and the target matrix from the previous compensation model through the Woodbury equation, the following steps are included:

[0012] Get the previous compensation model The inverse calculation matrix A in the middle T_1 ;

[0013] Construct an evolutionary compensation model and define matrix A in the evolutionary compensation model. T_2 To describe A T_1 The update matrix;

[0014] Based on the Woodbury equation, and using A T_1 The inverse matrix and the observation matrix X at the current time. T_2 Find A T_1 Update matrix A T_2 The inverse matrix;

[0015] A T_2 The inverse matrix is ​​input into the evolutionary compensation model to obtain the current compensation model.

[0016] Furthermore, A T_2 The expression for the inverse matrix is ​​as follows:

[0017]

[0018] in, This indicates that the matrix A is inverted. T_1 The inverse matrix, X T_2 This represents the observation matrix at the current moment in the mission flight data, where I represents the identity matrix.

[0019] Furthermore, the expression for the evolutionary compensation model is as follows:

[0020]

[0021]

[0022] Among them, X T_1 X represents the observation matrix of the previous moment in the mission flight data. T_2 This represents the observation matrix at the current moment in the mission flight data. This represents the transpose of the observation matrix from the previous time step in the mission flight data. H represents the transpose of the observation matrix at the current moment in the mission flight data. mT_1 H represents the measured magnetic field at the previous moment in the mission flight data. mT_2 Let λ represent the measured magnetic field at the current moment in the mission flight data, λ represent the regularization coefficient, I represent the identity matrix, and A represent the magnetic field. T_1 This represents the inverse calculation matrix in the previous compensation model.

[0023] Furthermore, the current compensation model The expression is as follows:

[0024]

[0025] in, Let X represent the previous compensation model. T_2 This represents the observation matrix at the current moment in the mission flight data. H represents the transpose of the observation matrix at the current moment in the mission flight data. mT_2 This represents the measured magnetic field at the current moment in the mission flight data, where I represents the identity matrix. Let denote the inverse matrix of the matrix calculated in the previous compensation model.

[0026] Furthermore, during the calibration flight in step S1, the maneuver sequence is set in the order of roll, pitch, and yaw in all four flight headings: east, south, west, and north.

[0027] Furthermore, during mission flight in step S2, random maneuvers are included.

[0028] The present invention also proposes an online evolutionary aeromagnetic compensation system, including a computer device, said computer device being programmed or configured to perform any of the online evolutionary aeromagnetic compensation methods described herein.

[0029] The present invention also proposes a storage medium storing a computer program programmed or configured to perform any of the online evolutionary aeromagnetic compensation methods described herein.

[0030] Compared with the prior art, the advantages of the present invention are as follows:

[0031] (1) The compensation model established in this invention can evolve with the data obtained during mission flight. Therefore, this compensation model is more capable of handling constantly changing disturbances;

[0032] (2) When updating the compensation model, the present invention updates the correlation matrix in the model based on the Woodbury equation, without the need for another calibration flight. Attached Figure Description

[0033] Figure 1 This is a flowchart of the method according to Embodiment 1 of the present invention.

[0034] Figure 2 This is a schematic diagram of the evolution process of the compensation model in Embodiment 1 of the present invention.

[0035] Figure 3 This is a schematic diagram of the calibration flight route in Embodiment 1 of the present invention.

[0036] Figure 4 The aircraft in Embodiment 1 of the present invention is from the reference coordinate system.

[0037] Figure 5 This is a schematic diagram of the flight route for the mission in Embodiment 1 of the present invention. Detailed Implementation

[0038] The present invention will be further described below with reference to the accompanying drawings and specific preferred embodiments, but this does not limit the scope of protection of the present invention.

[0039] Example 1

[0040] When using aeromagnetic compensation to reduce magnetic interference, considering that aircraft interference is not constant, the compensation model initially obtained through calibration flights may not be applicable to aircraft after a period of flight. Therefore, this embodiment proposes an online evolving aeromagnetic compensation method, such as... Figure 1 As shown, it includes the following steps:

[0041] S1) Perform calibration flight and acquire calibration flight data, and initialize the compensation model based on the calibration flight data;

[0042] S2) Perform mission flight and acquire mission flight data. Update the compensation model using the data at the current moment in the mission flight data and the target matrix in the previous compensation model through the Woodbury equation.

[0043] S3) Use the updated compensation model to perform aircraft interference compensation, and continue to execute the steps of conducting mission flight and acquiring mission flight data until the mission flight ends.

[0044] Through the above steps, the evolution process of the aeromagnetic compensation model is as follows: Figure 2As shown, for ease of explanation, timestamps T_0, T_1, and T_2 are used to represent calibration flight, mission flight I, and mission flight II, where T_1 is the previous time step of T_2. The compensation model is initialized through calibration flight, while mission flight I provides updated data to evolve the compensation model. The evolved compensation model is then applied to mission flight II. This embodiment's method only requires the previous compensation model and the updated data to continuously update the compensation model, making the evolved compensation model more capable of handling constantly changing interference and effectively reducing the impact of magnetic interference variations.

[0045] Each step is explained in detail below.

[0046] In step S1 of this embodiment, the flight path during calibration flight is as follows: Figure 3 As shown, the calibration flight included four flight paths: east, south, west, and north. The maneuver sequence for each path was set as roll, then pitch, and finally yaw, with a maximum angle of 5 degrees and a maneuver frequency of 0.125 Hz. The flight speed was 70 m / s. Each flight path was 30 km long, with a flight altitude of 350 meters and a sampling frequency of 10 Hz. The calibration flight data collected during the calibration flight was used to initialize the compensation model.

[0047] In step S1 of this embodiment, the initialization of the compensation model is achieved by solving the physical model of aircraft interference using the least squares and ridge regression method. Calibration flight data collected during calibration flight is used as the dataset for the solution. The physical model of aircraft interference is the TL model, meaning that in the aircraft reference coordinate system, magnetic interference can be described as a superposition of a fixed magnetic field, an induced magnetic field, and an eddy current magnetic field. For example... Figure 4 As shown, an aircraft reference coordinate system can be established to describe the TL model. The magnetometer is located at the origin O, the aircraft's nose points to the x-axis, the left wing points to the y-axis, and the z-axis is perpendicular. m H represents the total magnetic field measured using a scalar magnetometer. mx H my H mz These are the three components of the measured magnetic field given by the vector magnetometer. According to the TL model, the magnetic interference of an aircraft can be described as a fixed magnetic field, an induced magnetic field, and an eddy current magnetic field, which can be written in the form of an algebraic sum of the interference coefficient and the observation matrix, as shown in the following equation:

[0048]

[0049] In the formula, u i It represents the projection relationship between the total field and the component fields. i ' is the corresponding time derivative. p ij ,a ij ,b ijThese are the coefficients of the fixed magnetic field, the induced magnetic field, and the eddy current magnetic field.

[0050] The TL model describes the above three disturbances as the product of the coefficient matrix to be solved and the observation matrix. The matrix form of equation (1) is expressed as:

[0051] H m =Xθ (2)

[0052] Where X is R n×18 The observation matrix represents the direction cosines under different conditions, where θ is R 18×1 The coefficient matrix represents the estimated coefficients.

[0053] Equation (2) transforms the aeromagnetic compensation problem into a linear estimation problem of the coefficients to be solved. The purpose of aeromagnetic compensation is to estimate the coefficient matrix and eliminate magnetic interference from the measured magnetic field, which can be viewed as a linear regression model. As shown in the following equation, the coefficient matrix can be estimated using the least squares and ridge regression methods, and the regression parameters are determined by the regularization coefficient λ using K-ford cross-validation:

[0054]

[0055] in, X represents the estimated parameters after calibration flight, and X represents the observation matrix obtained during calibration flight. T H represents the transpose of the observation matrix X. m Let I represent the measurement signal obtained during the calibration flight, λ represent the identity matrix, and λ represent the regularization coefficient determined by K-ford cross-validation.

[0056] Therefore, in step S1 of this embodiment, when initializing the compensation model based on the calibration flight data, the following steps are included: using the calibration flight data as the dataset for solving the compensation model, solving the coefficient matrix of the TL model using the least squares and ridge regression methods, and obtaining the initial compensation model.

[0057] In step S2 of this embodiment, the route during mission flight is as follows: Figure 5 As shown. During the mission flight, the altitude was 200 meters, the speed was 70 m / s, and the flight path length was 60 kilometers. The course of this mission flight was northeast and southwest, but it was not limited to this route. During the mission flight, these maneuvers were random, meaning they were performed randomly during the mission flight.

[0058] Step S2 of this embodiment evolves the compensation model based on the updated data obtained at the current moment during mission flight and the compensation model at previous moments. Step S2 involves updating the compensation model using the current moment's data from the mission flight data and the target matrix from the previous compensation model via the Woodbury equation, including:

[0059] Get the previous compensation model The inverse calculation matrix A in the middle T_1 The above compensation model is used as the initial compensation model. For example, at time T_1 of mission flight I, the measurement data at time T_1 is input into the previous compensation model to obtain the corresponding compensation model. Describe it using the following formula:

[0060]

[0061] Among them, X T_1 This represents the observation matrix at time T_1 in the mission flight data. X represents the observation matrix at time T_1 in the mission flight data. T_1 The transpose matrix, H mT_1 This represents the measured magnetic field at time T_1 in the mission flight data, and I represents the identity matrix.

[0062] To obtain the expression simply, we introduce matrix A. T_1 This represents the required inverse calculation part as shown in the equation, where the inverse calculation matrix A is... T_1 Describe it using the following formula:

[0063]

[0064] Among them, X T_1 This represents the observation matrix at time T_1 in the mission flight data. X represents the observation matrix at time T_1 in the mission flight data. T_1 The transpose of λ is given by λ, where I represents the identity matrix and λ represents the regularization coefficient determined by K-ford cross-validation.

[0065] A T_1 It is an R 18×18 Matrix. And X T_1 Comparison, A T_1 By compressing X T_1 The information in the matrix is ​​used to reduce its dimensionality, which saves storage and computational resources and ensures the practicality of the evolution. Therefore, the compensation model at time T_1 of mission flight I can be rewritten as follows:

[0066]

[0067] Among them, A T_1 This represents the inverse calculation matrix in the compensation model at time T_1. X represents the observation matrix at time T_1 in the mission flight data. T_1 The transpose matrix, H mT_1This represents the measured magnetic field at time T_1 in the mission flight data.

[0068] Next, we construct an evolutionary compensation model. At time T_2 of mission flight II, considering the data updated between T_1 and T_2, the evolutionary compensation model should satisfy the following equation:

[0069]

[0070] Among them, X T_1 X represents the observation matrix at time T_1 in the mission flight data. T_2 H represents the observation matrix at time T_2 in the mission flight data. mT_1 H represents the measured magnetic field at time T_1 in the mission flight data. mT_2 This represents the measured magnetic field at time T_2 in the mission flight data. This represents the evolutionary compensation model corresponding to time T_2.

[0071] Further derivation from equation (7) yields:

[0072]

[0073] Among them, X T_1 X represents the observation matrix at time T_1 in the mission flight data. T_2 This represents the observation matrix at time T_2 in the mission flight data. X represents the observation matrix at time T_1. T_1 The transpose of the matrix, X represents the observation matrix at time T_2. T_2 The transpose matrix, H mT_1 H represents the measured magnetic field at time T_1 in the mission flight data. mT_2 Let I represent the measured magnetic field at time T_2 in the mission flight data, I represent the identity matrix, and λ represent the regularization coefficient determined by K-ford cross-validation.

[0074] In the compensation model of evolution in equation (8), matrix A is defined. T_2 To describe A T_1 The update matrix is:

[0075]

[0076] Among them, X T_1 X represents the observation matrix at time T_1 in the mission flight data. T_2 This represents the observation matrix at time T_2 in the mission flight data. X represents the observation matrix at time T_1. T_1 The transpose of the matrix, X represents the observation matrix at time T_2.T_2 The transpose of A T_1 Let I represent the inverse calculation matrix in the compensation model at time T_1, where I represents the identity matrix and λ represents the regularization coefficient determined by K-ford cross-validation.

[0077] Based on the Woodbury equation, matrix A T_2 The inverse operation does not require direct inversion, but can be performed based on the known A. T_1 The inverse matrix and the observation matrix X at time T_2 T_2 We obtain it using A. T_1 The inverse matrix and the observation matrix X at the current time. T_2 Find A T_1 Update matrix A T_2 The inverse matrix is ​​shown below:

[0078]

[0079] Among them, X T_2 This represents the observation matrix at time T_2 in the mission flight data. X represents the observation matrix at time T_2 in the mission flight data. T_2 The transpose of A T_1 Let I represent the inverse calculation matrix in the compensation model at time T_1, and let I represent the identity matrix. This step is the theoretical basis of the evolutionary aeromagnetic compensation method in this embodiment, which means that the parameter matrix of the evolutionary compensation model can be used. X T_2 H mT_2 The solution eliminates the need to store past measurement data, enabling the evolution of aeromagnetic compensation methods.

[0080] Based on the relationship between equations (8) and (9), A in equation (10) T_2 The inverse matrix is ​​input to the evolutionary compensation model of equation (8), and the evolutionary compensation model of equation (8) can be rewritten as follows:

[0081]

[0082] in, Let X represent the compensation model at time T_1. T_1 X represents the observation matrix at time T_1 in the mission flight data. T_2 This represents the observation matrix at time T_2 in the mission flight data. X represents the observation matrix at time T_1. T_1 The transpose of the matrix, X represents the observation matrix at time T_2. T_2 The transpose matrix, H mT_1 H represents the measured magnetic field at time T_1 in the mission flight data. mT_2Let λ represent the measured magnetic field at time T_2 in the mission flight data, λ represent the regularization coefficient, I represent the identity matrix, and A represent the magnetic field at time T_2. T_1 This represents the inverse calculation matrix in the compensation model at time T_1.

[0083] The compensation model at time T_2 is obtained through equation (11). When the next compensation model update is needed, the compensation model obtained in this update will be used. As a new compensation model The compensation model obtained in this update The corresponding matrix A T_2 As the previous compensation model Inverse calculation of matrix A T_1 And repeat the derivation process from equation (7) to equation (11) to obtain the compensation model for the next update.

[0084] In step S2 of this embodiment, the inversion calculation matrix A is introduced. T_1 Compress the observation matrix X at time T_1 T_1 The information in the model allows for the compensation model at time T_1 to be used with A. T_1 The inverse matrix description. Based on the Woodbury equation, A can be used. T_1 The inverse matrix and the updated observation matrix X at time T_2 T_2 A at time T_2 can be obtained directly. T_2 The inverse matrix of A. Using A T_2 The inverse matrix of the compensation model and the relationship between the inverse matrix can be used to directly obtain the updated compensation model at time T_2.

[0085] As can be seen, step S2 in this embodiment only requires the compensation model from the previous time step (i.e., time step T_1). And the inverse of the matrix is ​​calculated. The observation matrix X in the mission flight data at the current time (i.e., time T_2) T_2 and measuring magnetic field H mT_2 This allows us to obtain the compensation model for the current time step (i.e., time T_2). It does not require storing the observation matrix and measurement data such as the measured magnetic field from the previous time step (i.e., time T_1) in the mission flight data.

[0086] To quantitatively analyze the compensation results, we used the standard deviation (STD) of the magnetic signal before and after compensation. When the interference parameter changes by 5%, traditional compensation can reduce the magnetic interference from 0.9410 nT (uncompensated) to 0.0756 nT (compensated). The method in this embodiment can reduce it from 0.9410 nT (uncompensated) to 0.0201 nT (compensated). When the parameter changes by 10%, traditional compensation can reduce the magnetic interference from 0.9766 nT to 0.0885 nT. The method in this embodiment can reduce it to 0.0206 nT. When the parameter changes by 15%, traditional compensation can reduce the magnetic interference from 1.0317 nT to 0.1077 nT. The method in this embodiment can reduce it to 0.0209 nT. By comparing the results under different interference parameters, it can be concluded that the more drastic the change in magnetic interference, the lower the STD value maintained by the method in this embodiment, demonstrating better performance compared to traditional compensation methods.

[0087] Example 2

[0088] This embodiment proposes an online evolutionary aeromagnetic compensation system based on Embodiment 1, including a computer device, which is programmed or configured to execute the online evolutionary aeromagnetic compensation method described in Embodiment 1.

[0089] This embodiment also proposes a storage medium storing a computer program programmed or configured to execute the online evolutionary aeromagnetic compensation method described in Embodiment 1.

[0090] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the invention. Therefore, any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention should fall within the protection scope of the present invention.

Claims

1. An online evolutionary aeromagnetic compensation method, characterized in that, Includes the following steps: S1 performs calibration flight and acquires calibration flight data, and initializes the compensation model based on the calibration flight data; S2 performs mission flight and acquires mission flight data. It then updates the compensation model using the current data from the mission flight data and the target matrix from the previous compensation model, employing the Woodbury equation. This includes: Get the previous compensation model The inverse calculation matrix A in the middle T_1 ; Construct an evolutionary compensation model and define matrix A in the evolutionary compensation model. T_2 To describe A T_1 The update matrix; Based on the Woodbury equation, and using A T_1 The inverse matrix and the observation matrix X at the current time. T_2 Find A T_1 Update matrix A T_2 The inverse matrix; A T_2 The inverse matrix is ​​input into the evolutionary compensation model to obtain the current compensation model. ; S3 uses the updated compensation model to compensate for aircraft interference and continues to perform the steps of mission flight and acquiring mission flight data until the mission flight ends.

2. The online evolutionary aeromagnetic compensation method according to claim 1, characterized in that, Step S1, which initializes the compensation model based on the calibration flight data, includes: using the calibration flight data as the dataset for solving the compensation model, and solving the coefficient matrix of the TL model using the least squares and ridge regression methods to obtain the initial compensation model. .

3. The online evolutionary aeromagnetic compensation method according to claim 1, characterized in that, A T_2 The expression for the inverse matrix is ​​as follows: in, This indicates that the matrix A is inverted. T_1 The inverse matrix, This represents the observation matrix at the current moment in the mission flight data. Represents the identity matrix.

4. The online evolutionary aeromagnetic compensation method according to claim 1, characterized in that, The expression for the evolutionary compensation model is as follows: in, This represents the observation matrix of the previous moment in the mission flight data. This represents the observation matrix at the current moment in the mission flight data. This represents the transpose of the observation matrix from the previous time step in the mission flight data. This represents the transpose of the observation matrix at the current moment in the mission flight data. This represents the measured magnetic field at the previous moment in the mission flight data. This represents the measured magnetic field at the current moment in the mission flight data. Represents the regularization coefficient. Let A represent the identity matrix. T_1 This represents the inverse calculation matrix in the previous compensation model.

5. The online evolutionary aeromagnetic compensation method according to claim 1, characterized in that, The current compensation model The expression is as follows: in, This represents the previous compensation model. This represents the observation matrix at the current moment in the mission flight data. This represents the transpose of the observation matrix at the current moment in the mission flight data. This represents the measured magnetic field at the current moment in the mission flight data. Represents the identity matrix. This represents the inverse matrix of the inverse calculation matrix in the previous compensation model.

6. The online evolutionary aeromagnetic compensation method according to claim 1, characterized in that, When calibrating the flight in step S1, the maneuver sequence is set in the order of roll, pitch, and yaw in all four flight headings: east, south, west, and north.

7. The online evolutionary aeromagnetic compensation method according to claim 1, characterized in that, When performing mission flight in step S2, it includes: random maneuvering during mission flight.

8. An online evolutionary aeromagnetic compensation system, characterized in that, It includes a computer device that is programmed or configured to perform the online evolutionary aeromagnetic compensation method according to any one of claims 1 to 7.

9. A storage medium, characterized in that, The storage medium stores a computer program programmed or configured to execute the online evolutionary aeromagnetic compensation method according to any one of claims 1 to 7.

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