Aeromagnetic airborne electronic interference feature selection method based on model interpretation force

Abstract

The invention discloses an aeromagnetic airborne electronic interference feature selection method based on model interpretation force, and relates to the technical field of aeromagnetic field detection, and the method comprises the steps: firstly constructing a latent variable space through a partial least square method, so as to eliminate the multicollinearity among multi-dimensional electrical features; quantifying the actual contribution degree of each feature to the interference magnetic field based on a variable importance projection index; secondly, based on double criteria of variable importance projection and Pearson's correlation coefficients between features, through an iterative screening strategy, selecting out an optimal feature combination which is high in contribution degree and is not redundant to one another; and finally, constructing an extended Tools-Lawson compensation model based on the feature combination to carry out interference compensation. According to the method, the model is introduced to explain the real contribution of the mechanical characteristics, and the redundancy is eliminated in combination with the correlation constraint, so that the core interference source is accurately screened from the high-dimensional electrical characteristics, and the compensation effect of the airborne electronic equipment interference in the aviation magnetic survey is remarkably improved.

Description

Technical Field

[0001] This invention belongs to the field of airborne magnetic field detection technology, specifically relating to a method for selecting airborne electronic interference features based on model interpretation. Background Technology

[0002] Geomagnetic navigation, with its excellent passive and autonomous nature, is an important navigation technology under satellite rejection conditions. It is generally used as an auxiliary means to correct deviations in inertial navigation, and its correction effectiveness largely depends on the accuracy of geomagnetic measurements. If the current Earth's magnetic field of the carrier cannot be accurately measured, geomagnetic navigation will lose its attitude correction capability and may even introduce additional errors, further reducing navigation accuracy. However, the Earth's magnetic field is susceptible to interference and difficult to obtain directly and accurately, necessitating effective compensation.

[0003] For airborne magnetic sensors, the main types of interfering magnetic fields in the aviation field are: 1) a fixed magnetic field caused by the aircraft's own materials and structure, which does not change or changes extremely slowly over time; 2) an induced magnetic field generated by the magnetization of the aircraft's soft magnetic materials under the influence of the Earth's magnetic field, which changes with the strength of the geomagnetic field; 3) eddy current magnetic fields generated by the aircraft cutting through the Earth's magnetic field lines during its movement; and 4) OBE (Onboard Electronics) interference caused by electromagnetic effects when airborne electronic equipment is operating. Traditional TL models can compensate for fixed magnetic fields, induced magnetic fields, and eddy current magnetic fields, but their compensation effect for OBE interference is limited. Therefore, it is necessary to extend the OBE interference to the TL model for compensation.

[0004] Due to the numerous airborne electronic devices and their varying contributions to OBE interference, it is necessary to select key interference sources. Traditional selection methods, based on the correlation between the electrical characteristics of the equipment and the magnetic field, only consider the statistical correlation between the two, rather than the actual contribution. Even a current with a very small amplitude, if strongly correlated with OBE interference, often produces relatively small actual interference. Furthermore, currents within the same circuit exhibit strong correlations, resulting in high correlation levels between these currents and OBE interference. If selection is based solely on the magnitude of correlation, multiple indicators from the same interference source are easily selected simultaneously, leading to severe redundancy in information for that circuit, while valuable information from other circuits may be overlooked due to insufficient representativeness. Summary of the Invention

[0005] To address the aforementioned problems in the existing technology, this invention provides a method for selecting airborne electronic interference features based on model interpretation. The technical problem to be solved by this invention is achieved through the following technical solution: This invention provides a method for selecting airborne electronic interference features based on model explanatory power, including: Step 1: Based on the electrical characteristic data and OBE interference magnetic field data, construct the latent variable space using the partial least squares method to eliminate multicollinearity among multiple electrical characteristics; Step 2: Based on the constructed latent variable space, calculate the contribution of each electrical feature to the OBE interference magnetic field based on the variable importance projection index; Step 3: Based on the preset dual criteria of variable importance projection index and Pearson correlation coefficient between features, select the optimal feature combination from all electrical features.

[0006] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention presents a model-interpretive airborne electronic interference feature selection method. It constructs a latent space through partial least squares regression to resolve multicollinearity of multidimensional electrical features. It quantifies feature contribution using variable importance projection and designs a dual-constraint criterion based on correlation coefficients, achieving accurate selection of key electrical features for airborne electronic interference (OBE). This invention avoids the problem of misselection of "strongly correlated but low-contribution" features when relying solely on Pearson correlation coefficients, by quantifying the actual contribution of features through model interpretability, ensuring that selected features possess genuine OBE interference explanatory power. The dual-constraint screening mechanism effectively eliminates redundant information from currents in the same loop, preventing excessive superposition of information from a single loop and ensuring balanced retention of effective interference information from different loops. The selection logic, which considers both contribution and correlation, ensures that feature selection is both physically reasonable and statistically relevant, improving the matching degree between features and OBE interference. The optimized core feature set significantly enhances the compensation accuracy and generalization ability of subsequent compensation models, adapting to complex application scenarios involving multiple operating conditions and multi-source interference in airborne electronic equipment.

[0007] The above description is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described in detail below with reference to the accompanying drawings. Attached Figure Description

[0008] Figure 1 This is a schematic diagram of a method for selecting airborne electronic interference features based on model interpretation provided in an embodiment of the present invention; Figure 2 These are schematic diagrams of electrical features selected using different methods, wherein (a) is Pearson, (b) is Spearman, (c) is Kendall, and (d) is the method of the present invention; Figure 3 It is the correlation coefficient matrix of electrical characteristics selected using the method of this invention; Figure 4These are training set compensation error maps for different feature selection methods provided in the embodiments of the present invention; Figure 5 This is a verification set compensation error diagram of different feature selection methods provided in the embodiments of the present invention; Figure 6 This is a test set 1 error compensation diagram of different feature selection methods provided in the embodiments of the present invention; Figure 7 This is a test set 2 error compensation diagram of different feature selection methods provided in the embodiments of the present invention; Figure 8 This is a test set 3 compensation error diagram of different feature selection methods provided in the embodiments of the present invention; Figure 9 This is a test set 4 compensation error diagram of different feature selection methods provided in the embodiments of the present invention. Detailed Implementation

[0009] To further illustrate the technical means and effects adopted by the present invention to achieve the intended purpose, the following describes in detail, with reference to the accompanying drawings and specific embodiments, a method for selecting airborne electronic interference features based on model interpretation power proposed in accordance with the present invention.

[0010] The foregoing and other technical contents, features, and effects of the present invention will be clearly presented in the following detailed description of specific embodiments in conjunction with the accompanying drawings. Through the description of the specific embodiments, a more in-depth and concrete understanding can be gained of the technical means and effects adopted by the present invention to achieve its intended purpose. However, the accompanying drawings are for reference and illustration only and are not intended to limit the technical solutions of the present invention.

[0011] This invention provides a method for selecting airborne electronic interference features based on model interpretation, the core of which lies in achieving accurate screening of interference features through multi-dimensional quantitative analysis. Please refer to [link to relevant documentation]. Figure 1 , Figure 1 This is a schematic diagram of a method for selecting airborne electronic interference features based on model explanatory power, provided by an embodiment of the present invention. Figure 1 As shown in this embodiment, the aeromagnetic airborne electronic interference feature selection method based on model interpretation includes the following steps: Step 1: Based on the electrical characteristic data and OBE interference magnetic field data, construct the latent variable space using the partial least squares method to eliminate multicollinearity among multiple electrical characteristics.

[0012] In an optional embodiment, step 1 includes: Step 1.1: Standardize and clean the electrical characteristic data and OBE interference magnetic field data to construct the initial feature matrix and response variable vector.

[0013] In this embodiment, electrical characteristic data can be represented as 31 of which are electrical characteristic dimensions. The number of sampling points; OBE interference magnetic field data can be expressed as It is obtained by measuring the total field and compensating for interference from the machine body.

[0014] After acquiring electrical characteristic data and OBE interference magnetic field data, the first step is to... and Z-score standardization was implemented to eliminate differences in units and numerical ranges among different features (such as current and voltage), ensuring that each feature contributes equally in subsequent modeling. Data cleaning was then performed, checking for missing and outlier values ​​in the dataset. Based on the data distribution characteristics and actual research needs, targeted methods such as interpolation completion or outlier removal were used to complete the data cleaning, ensuring the integrity and reliability of the dataset. Finally, an initial feature matrix was constructed based on the standardized and cleaned electrical feature data and the OBE interference magnetic field data. and the corresponding response variable vector This lays a solid data foundation for the subsequent construction of partial least squares models.

[0015] Step 1.2: Extract the latent variable with the largest covariance through iteration and construct a partial least squares regression model.

[0016] In this embodiment, step 1.2 includes: Step 1.2.1: Initialize the residual matrix, let , ,in, The initial characteristic matrix, This is the response variable vector.

[0017] Understandably, due to the response variable vector It is one-dimensional data, and its latent variable is itself.

[0018] Step 1.2.2: Perform the first... The next iteration, in which , For the preset number of iterations, the following sub-steps are executed in each iteration: Step a: Solve the optimization problem To obtain the weight vector ,in, This means maximizing the covariance matrix. For the first The residual matrix of the next iteration. Indicates the first The weight vector for the next iteration is a unit vector; For the first The response variable vector for the next iteration; Step b: Convert the current feature residual matrix Projected onto the weight vector In the direction, we obtain the first Latent variables of the next iteration , ; Step c: Solve for the feature residual matrix using least squares regression. for latent variables load vector and response variable vector for latent variables load vector ,in, , , Indicates transpose; Step d: From the current feature residual matrix and response variable vector Subtracting the current latent variables The explanation part yields the residual matrix for the next iteration. and response variable vector ,in, , .

[0019] In this embodiment, the weight vector The projection direction that best explains the target variable in the current residual feature space is defined. It can be understood that the loading vector quantifies the latent variables through projection from the original high-dimensional data space to the low-dimensional latent variable space and reverse reconstruction. Compared with the characteristic residual matrix of independent variables before the update as well as The linear mapping relationship between them enables the decomposition and interpretation of the model structure.

[0020] By iterating through the above process, the model can be progressively optimized by successively extracting the data variation directions that best explain the dependent variable. The number of iterations can be adjusted accordingly. A trade-off can be struck between model effectiveness and simplicity: when When large enough, the model will fit the effective signal in the data as closely as possible; and A smaller value helps prevent overfitting, ensuring the model has good generalization and robustness. In this embodiment, the preset number of iterations... It is 15.

[0021] Step 1.2.3: After iteration, based on the latent variables, weight vectors, and loading vectors obtained during the iteration process, a partial least squares regression model is constructed. The partial least squares regression model is expressed as: ; in, For a latent variable matrix, This is the weight matrix. The loading matrix is ​​the initial characteristic matrix. The load vector is the response variable vector. This represents the model residuals.

[0022] Step 1.3: Determine the optimal number of latent variables through cross-validation, construct the final PLS model based on the optimal number of latent variables, and obtain the weight matrix, load matrix and latent variable matrix.

[0023] It should be noted that the number of latent variables directly affects model performance, so the optimal number of latent variables must be determined before integrating and constructing a complete model.

[0024] In this embodiment, 10-fold cross-validation is used to determine the optimal number of latent variables. Specifically, the dataset is divided into a training set and a validation set. One to 15 latent variables are extracted sequentially, and a model is built. The root mean square error (RMSE) on the validation set is calculated. The number of latent variables corresponding to the minimum validation set error is selected as the optimal value, thereby avoiding overfitting and ensuring the model's generalization ability. In this embodiment, the optimal number of latent variables... =7.

[0025] Based on the number of optimal latent variables obtained By integrating all extracted latent variable correlation matrices, the weight matrix and loading matrix are first integrated to obtain the initial feature matrix. The mapping to the latent variable matrix is ​​then used to calculate the regression coefficient matrix of the pair, and finally the prediction model based on the original features is derived. At the same time, the core parameters such as the latent variable matrix, loading matrix, and weight matrix are output, thus completing the construction of the latent variable space.

[0026] Step 2: Based on the constructed latent variable space, calculate the contribution of each electrical feature to the OBE interference magnetic field using the variable importance projection index.

[0027] In this embodiment, the variable importance projection index is used to measure the contribution of electrical features to the OBE interference magnetic field and is a key quantitative indicator for screening electrical features.

[0028] Specifically, the formula for calculating the projection of variable importance is: ; In the formula, For the first The projected importance values ​​of the variables for each electrical feature. The number of electrical features, All latent variables in the response variable vector Explain the sum of variances. For the first One latent variable The vector of response variables that can be explained The sum of variances, The number of latent variables. For the first The electrical characteristic in the first The weight vector of each latent variable The corresponding weight value.

[0029] In this embodiment, , Note that... The PLS (Partial Least Squares) model explains The variance, rather than The total variance. As a normalization factor, it can make the sum of squares and mean of VIP values ​​satisfy... This ensures that the importance of features in different dimensions can be directly compared.

[0030] Step 3: Based on the preset dual criteria of variable importance projection index and Pearson correlation coefficient between features, select the optimal feature combination from all electrical features.

[0031] In this embodiment, the dual criteria include: the projected value of the variable importance is greater than a preset contribution threshold, and the absolute value of the Pearson correlation coefficient between electrical features does not exceed a preset correlation threshold.

[0032] Optionally, the preset contribution threshold is 1, and the preset correlation threshold is 0.75.

[0033] Specifically, step 3 includes: Step 3.1: Calculate the Pearson correlation coefficient matrix between all pairs of electrical characteristics; Step 3.2: Perform iterative filtering to obtain the optimal feature combination, wherein the iterative filtering includes: Based on the variable importance projection values ​​of all electrical features, a candidate feature set is constructed. The candidate feature set contains all electrical features whose variable importance projection values ​​are greater than a preset contribution threshold. The electrical feature with the highest variable importance projection value is selected from the candidate feature set and added to the optimal combination; Based on the Pearson correlation coefficient matrix, determine the Pearson correlation coefficient between the remaining electrical features in the candidate feature set and the selected electrical features; remove electrical features whose absolute value of the Pearson correlation coefficient is greater than the preset correlation threshold from the candidate feature set; The process of selecting and eliminating the remaining electrical features in the candidate feature set is repeated until the candidate feature set is empty, at which point the iteration stops.

[0034] In an optional embodiment, the aeromagnetic airborne electronic interference feature selection method based on model interpretation of this embodiment further includes: Step 4: using the extended TL model to compensate for OBE interference based on the optimal feature combination.

[0035] The aeromagnetic airborne electronic interference feature selection method of this invention, based on model explanatory power, avoids the problem of "strong correlation, low contribution" feature misselection when relying solely on Pearson correlation coefficients, by quantifying the actual contribution of features through model explanatory power. This ensures that the selected features have true OBE interference explanatory power. The dual-constraint screening mechanism can effectively eliminate redundant information from the same loop current, avoid excessive superposition of single loop information, and ensure balanced retention of effective interference information from different loops. The selection logic that takes into account both contribution and correlation makes feature selection both physically reasonable and statistically relevant, improving the matching degree between features and OBE interference. The optimized core feature set can significantly enhance the compensation accuracy and generalization ability of subsequent compensation models, adapting to the complex application scenarios of multi-condition and multi-source interference of airborne electronic equipment.

[0036] Furthermore, the effectiveness of the airborne electronic interference feature selection method based on model interpretation power of the present invention is illustrated through simulation experiments.

[0037] The dataset used in this experiment comes from the field aeromagnetic survey conducted by large UAVs in the experimental area, providing highly realistic and applicable measured data support for the research of OBE interference compensation algorithm in the field of aeromagnetic survey.

[0038] The test platform is equipped with 5 optically pumped magnetometers and 4 vector fluxgate magnetometers to construct a multi-source magnetic detection data acquisition system. Among them, the data from the optically pumped magnetometers deployed at the tail boom of the aircraft has undergone professional magnetic compensation processing, and the accuracy meets the technical requirements of the reference true value of airborne magnetic detection. Therefore, it is used as the benchmark data for evaluating the performance of the magnetic compensation algorithm. Considering that among the 4 vector fluxgate magnetometers, fluxgate magnetometer B has the closest spatial layout to the tail boom and is less affected by the interference of the aircraft itself, the magnetic signal collected by fluxgate magnetometer B is selected as the original magnetic data to be compensated.

[0039] To comprehensively capture the interference characteristics during the operation of the OBE system, the test platform was simultaneously configured with 14 current sensors and 17 voltage sensors. The electrical signals collected by these two types of sensors were uniformly classified into a set of electrical characteristic variables for OBE interference, totaling 31 electrical characteristic variables. The index of each variable is shown in Table 1.

[0040] Table 1

[0041] The data partitioning follows the principles of continuous segmentation and independent operating conditions to ensure the consistency of data distribution and the comprehensiveness of validation: 1) Training set: 18,000 consecutive sampling points from the 1003.03 flight path; 2) Validation set: 1,500 consecutive sampling points from the subsequent training set to ensure the continuity of data distribution between the training and validation sets, used for parameter tuning of the compensation model; 3) Test set: Independent segments of four different maneuvering conditions from the 1003.03 flight path (labeled Test 1 to Test 4, with specific maneuvering types as: Test 1 - straight flight at 400 m altitude, Test 2 - turning at 400 m altitude, Test 3 - straight flight at 800 m altitude, and Test 4 - turning at 800 m altitude), each segment containing 1,500 sampling points, used to verify the generalization performance of the compensation algorithm under different maneuvering conditions.

[0042] To verify the superiority of the airborne electronic interference feature selection method based on model interpretation proposed in this invention, four sets of comparative experiments were designed. The core objective was to evaluate the impact of different feature selection strategies on the magnetic compensation effect. The specific feature selection schemes for each set of experiments are as follows: 1) Group A: Using the Pearson correlation coefficient method, the linear correlation coefficients between each electrical feature variable and the original magnetic data to be compensated were calculated, and the top 5 electrical feature variables with the highest absolute values ​​of the correlation coefficients were selected (as determined by previous verification); 2) Group B: Using the Spearman rank correlation coefficient method, the rank correlation coefficients between each electrical feature variable and the original magnetic data to be compensated were calculated, and the top 5 electrical feature variables with the highest absolute values ​​of the rank correlation coefficients were selected; 3) Group C: Using the Kendall correlation coefficient method, the rank correlation coefficients between each electrical feature variable and the original magnetic data to be compensated were calculated, and the top 5 electrical feature variables with the highest absolute values ​​of the rank correlation coefficients were selected; 4) Group D: Using the feature selection method proposed in this invention, the top 5 electrical feature variables were selected.

[0043] Electrical characteristics selected by different methods, such as Figure 2 As shown, Figure 2 These are schematic diagrams of electrical features selected using different methods, where (a) is Pearson, (b) is Spearman, (c) is Kendall, and (d) is the method of this invention. The specific values ​​of the correlation coefficients or VIPs of each selected feature are shown in Table 2.

[0044] Table 2

[0045] Further analysis of the electrical features selected by the method of this invention yields the following correlation matrix: Figure 3 As shown, Figure 3 This is the correlation coefficient matrix of electrical characteristics selected using the method of this invention. Figure 3 It can be seen that the highest Pearson correlation coefficient among the selected features is 0.64. I 24 and I 28 The correlation coefficients among the remaining features are all low, effectively avoiding the problem of information redundancy caused by selecting highly correlated features.

[0046] For each group of electrical characteristic variables obtained from the four sets of comparative experiments, a magnetic compensation model based on the extended TL model was constructed: ; in, and These are the aeromagnetic measurement total field and the reference total field, respectively. Interference with the body For OBE interference, they are represented as follows: ; in, u i ( i = 1, 2, 3) are the triaxial cosine values ​​obtained from measurements. p , a and c These are the parameters to be estimated.

[0047] ; in, It is the rate of change of current. , and The first i A current in x , y , z The induced interference coefficient on the axis. At the current moment... u It can be calculated in real time, therefore it will I and u Treat the product of these two factors as a known quantity. Thus, the above equation degenerates into a linear model, which can be solved using the least squares method.

[0048] Finally, the RMSE between the compensated measured magnetic field and the reference data was used as the evaluation criterion to determine the improvement rate of compensation accuracy of each method, verifying the effectiveness of the proposed OBE interference feature selection method based on model interpretation in improving magnetic compensation accuracy and enhancing the generalization performance of the algorithm. Table 3 shows the RMSE (unit: nT) results after compensation of electrical features selected using different feature selection methods for different datasets.

[0049] Table 3

[0050] The compensation results of the training set are as follows Figure 4 As shown, Figure 4 These are training set compensation error maps for different feature selection methods provided in embodiments of the present invention, from... Figure 4 It can be seen that the compensation accuracy of the method of this invention is basically the same as that of the other methods.

[0051] The compensation results for the validation set and multiple test sets are as follows: Figures 5-9 As shown, where, Figure 5 This is a verification set compensation error diagram of different feature selection methods provided in the embodiments of the present invention; Figure 6 This is a test set 1 error compensation diagram of different feature selection methods provided in the embodiments of the present invention; Figure 7 This is a test set 2 error compensation diagram of different feature selection methods provided in the embodiments of the present invention; Figure 8 This is a test set 3 compensation error diagram of different feature selection methods provided in the embodiments of the present invention; Figure 9 This is a test set 4 compensation error diagram of different feature selection methods provided in the embodiments of the present invention. As can be seen from the figure, on both the validation set and the test set, the compensation result of the method of the present invention is significantly closer to the zero point of the Y-axis, proving that the generalization performance of the method of the present invention is superior to that of the traditional method.

[0052] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations are intended to cover non-exclusive inclusion, such that an article or device comprising a list of elements includes not only those elements but also other elements not expressly listed. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the article or device comprising said element. Terms such as "connected" or "linked" are not limited to physical or mechanical connections but can include electrical connections, whether direct or indirect. The orientations or positional relationships indicated by terms such as "upper," "lower," "left," and "right" are based on the orientations or positional relationships shown in the accompanying drawings and are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as limiting the invention.

[0053] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0054] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for selecting airborne electronic interference features based on model explanatory power, characterized in that, include: Step 1: Based on the electrical characteristic data and OBE interference magnetic field data, construct the latent variable space using the partial least squares method to eliminate multicollinearity among multiple electrical characteristics; Step 2: Based on the constructed latent variable space, calculate the contribution of each electrical feature to the OBE interference magnetic field based on the variable importance projection index; Step 3: Based on the preset dual criteria of variable importance projection index and Pearson correlation coefficient between features, select the optimal feature combination from all electrical features.

2. The method for selecting airborne electronic interference features based on model explanatory power according to claim 1, characterized in that, Step 1 includes: Step 1.1: Standardize and clean the electrical characteristic data and the OBE interference magnetic field data to construct an initial feature matrix and response variable vector; Step 1.2: Extract the latent variable with the largest covariance through iteration and construct a partial least squares regression model; Step 1.3: Determine the optimal number of latent variables through cross-validation, and construct the final PLS model based on the optimal number of latent variables to obtain the weight matrix, load matrix and latent variable matrix.

3. The method for selecting airborne electronic interference features based on model explanatory power according to claim 2, characterized in that, Step 1.2 includes: Step 1.2.1: Initialize the residual matrix, let , ,in, The initial characteristic matrix, For the response variable vector; Step 1.2.2: Perform the first... The next iteration, in which , For the preset number of iterations, the following sub-steps are executed in each iteration: Step a: Solve the optimization problem To obtain the weight vector ,in, This represents maximizing the covariance matrix. For the first The residual matrix of the next iteration. Indicates the first The weight vector for the next iteration is a unit vector. For the first The response variable vector for the next iteration; Step b: Convert the current feature residual matrix Projected onto the weight vector In the direction, we obtain the first Latent variables of the next iteration , ; Step c: Solve for the feature residual matrix using least squares regression. for latent variables load vector and response variable vector for latent variables load vector ,in, , , Indicates transpose; Step d: From the current feature residual matrix and response variable vector Subtracting the current latent variables The explanation part yields the residual matrix for the next iteration. and response variable vector ,in, , ; Step 1.2.3: After iteration, based on the latent variables, weight vectors, and loading vectors obtained during the iteration process, a partial least squares regression model is constructed. The partial least squares regression model is expressed as: ； in, For a latent variable matrix, This is the weight matrix. The loading matrix is ​​the initial characteristic matrix. The load vector is the response variable vector. This represents the model residuals.

4. The method for selecting airborne electronic interference features based on model explanatory power according to claim 1, characterized in that, The formula for calculating the variable importance projection is as follows: ； In the formula, For the first The projected importance values ​​of the variables for each electrical feature. The number of electrical features, All latent variables in the response variable vector Explain the sum of variances. For the first One latent variable The vector of response variables that can be explained The sum of variances, The number of latent variables. For the first The electrical characteristic in the first The weight vector of each latent variable The corresponding weight value.

5. The method for selecting airborne electronic interference features based on model explanatory power according to claim 1, characterized in that, The dual criteria include: the projected value of the variable importance is greater than a preset contribution threshold, and the absolute value of the Pearson correlation coefficient between electrical features does not exceed a preset correlation threshold.

6. The method for selecting airborne electronic interference features based on model interpretation as described in claim 5, characterized in that, The preset contribution threshold is 1, and the preset correlation threshold is 0.

75.

7. The method for selecting airborne electronic interference features based on model explanatory power according to claim 1, characterized in that, Step 3 includes: Step 3.1: Calculate the Pearson correlation coefficient matrix between all pairs of electrical characteristics; Step 3.2: Perform iterative filtering to obtain the optimal feature combination, wherein, The iterative filtering includes: A candidate feature set is constructed based on the variable importance projection values ​​of all electrical features. The candidate feature set includes all electrical features whose variable importance projection values ​​are greater than a preset contribution threshold. The electrical feature with the highest variable importance projection value is selected from the candidate feature set and added to the optimal combination; Based on the Pearson correlation coefficient matrix, determine the Pearson correlation coefficient between the remaining electrical features in the candidate feature set and the selected electrical features; remove electrical features whose absolute value of the Pearson correlation coefficient is greater than a preset correlation threshold from the candidate feature set; The remaining electrical features in the candidate feature set are repeatedly selected and eliminated until the candidate feature set is empty, at which point the iteration stops.

8. The method for selecting airborne electronic interference features based on model explanatory power according to claim 1, characterized in that, Also includes: Step 4: Based on the optimal feature combination, use the extended TL model to compensate for OBE interference.

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