An adaptive modeling-based aeromagnetic compensation method

Abstract

The present application belongs to the field of airborne magnetic force detection, and particularly relates to an airborne magnetic compensation method based on adaptive modeling, which comprises the following steps: obtaining a data set of calibration flight in four directions; calculating VIF values of variables in T-L equation, repeatedly excluding variables with maximum VIF until the multicollinearity among the remaining variables is less than a set threshold; performing t test on the remaining variables, and repeatedly removing variables with small significance; obtaining four-direction models constructed by finally assigned variables; calculating four sets of compensation coefficients corresponding to the four-direction models; automatically assigning the direction models and compensation coefficients corresponding to the four-direction data sets of compensation flight; and performing magnetic interference compensation according to the corresponding direction models and compensation coefficients to obtain compensated magnetic interference. According to variable data characteristics of different directions, the present application adaptively assigns model variables for each direction, optimizes and improves the compensation model, and solves the model ill-conditioning problem caused by multicollinearity.

Description

Technical Field

[0001] This invention belongs to the field of airborne magnetic detection, specifically an airborne magnetic compensation method based on adaptive modeling. Background Technology

[0002] Airborne magnetics exploration, as an important geophysical exploration method, has significant applications in geological structure and mineral resource exploration. Unmanned aerial vehicles (UAVs) equipped with fluxgate magnetometers and optically pumped magnetometers measure the geomagnetic field strength during flight, enabling rapid, high-precision geological structure surveys and studies unaffected by terrain. However, during data acquisition, the magnetic sensors record not only the necessary aeromagnetic data but also magnetic interference generated by the aircraft itself. To ensure the quality of the aeromagnetic data, aeromagnetic compensation technology is employed to eliminate magnetic interference generated by the aircraft.

[0003] The earliest work on magnetic compensation was the mathematical model (TL model) established by Tolles and Lawson, which relates magnetic interference to aircraft attitude. Leliak designed a compensation model based on this model to solve for compensation coefficients and eliminate magnetic interference. In 1980, Leliak treated magnetic compensation as a linear regression problem and proposed the ridge regression method to solve the multicollinearity problem in the TL equations. Because the TL model is composed of cosine functions and their derivatives in three directions, the variables in the model are not independent, inevitably leading to multicollinearity. The ill-conditioned nature of the model results in low accuracy of the calculated compensation coefficients, and the same set of compensation coefficients has significantly different compensation effects in different headings, thus affecting the accuracy of aeromagnetic compensation. Summary of the Invention

[0004] The technical problem to be solved by this invention is to provide an aeromagnetic compensation method based on adaptive modeling, which solves the ill-conditioned problem of multicollinearity in the model caused by the influence of aircraft heading, and the problem of multicollinearity among model variables affecting the compensation accuracy.

[0005] This invention is implemented as follows:

[0006] An aeromagnetic compensation method based on adaptive modeling, the method comprising:

[0007] Step S1: Automatically identify the heading of the calibration flight data and obtain a dataset of the four headings of the calibration flight;

[0008] Step S2: Calculate the VIF value of each variable in the TL equation, and repeatedly eliminate the variable with the largest VIF until the multicollinearity among the remaining variables is less than the set threshold.

[0009] Step S3: Perform a t-test on the remaining variables after completing step S2, and repeatedly eliminate variables with low significance until the final assigned variables are variables with high significance and small contribution to multicollinearity.

[0010] Step S4: Perform steps S2 and S3 on the datasets of the four headings of the calibration flight respectively to obtain the four heading models constructed by the final assigned variables;

[0011] Step S5: Calculate the four sets of compensation coefficients corresponding to the four heading models;

[0012] Step S6: Automatically identify the heading of the compensated flight data and obtain the four heading datasets for the compensated flight;

[0013] Step S7: Automatically assign the heading model and compensation coefficients corresponding to the four heading datasets of the compensated flight;

[0014] Step S8: Perform magnetic interference compensation based on the corresponding heading model and compensation coefficient to obtain the compensated magnetic interference.

[0015] Furthermore, for the i-th variable, the VIF is calculated as follows:

[0016]

[0017] Among them, R i 2 The independent variable X i The coefficient of determination R between the residual independent variables in the linear regression model and 2 value.

[0018] Furthermore, the t-test specifically includes:

[0019] Null hypothesis H j0 :b j =0, alternative hypothesis H j1 :b j ≠0 where j = 1, 2, ..., a; b j is the j-th regression coefficient; a is the number of variables X in the TL model;

[0020] The t-statistic is:

[0021]

[0022] Where na-1 is the degree of freedom; n is the number of samples; It is the standard deviation of the j-th regression coefficient; It is the regression value of the j-th regression coefficient;

[0023] The rejection field is:

[0024] |T j |≥t α / 2 (na-1)

[0025] Where α is the significance level;

[0026] The p-value of the t-test statistic is the probability of significance of the t-statistic. If p >= α, the null hypothesis is accepted, and the explanatory variables have no significant effect on the dependent variable; if p < α, the null hypothesis is rejected, and the alternative hypothesis is accepted, indicating that the j-th regression coefficient b j The corresponding variable X i It has a significant impact.

[0027] Furthermore, the TL equation is:

[0028] XC = H t

[0029] Where C is a set of column vectors C i Composed of i = 1, 2, ..., 18; H t It is a column vector;

[0030]

[0031] X consists of 18 variables, cosα, cosβ, cosγ and cos'α, cos'β, cos'γ, where cos'α, cos'β, cos'γ are the derivatives of cosα, cosβ, and cosγ, respectively; and cosα, cosβ, cosγ are the direction cosines of the Earth's magnetic field in the three directions in the aircraft coordinate system.

[0032] Compared with the prior art, the beneficial effects of this invention are as follows:

[0033] Most existing methods treat the compensated flight as a whole to solve the TL equations to obtain compensation coefficients for aeromagnetic compensation. However, using the same set of compensation coefficients yields significantly different compensation effects in different headings, thus affecting the accuracy of aeromagnetic compensation. This invention considers the impact of flight heading and attitude changes on compensation accuracy. Based on the variable data characteristics of different headings, it adaptively allocates model variables for each heading, optimizing and improving the compensation model. This effectively solves the ill-conditioned problem caused by multicollinearity, further improving compensation accuracy and model robustness. During adaptive modeling, variables with high significance and low multicollinearity are automatically assigned to construct the optimal heading model, thereby obtaining high-precision compensation coefficients. Attached Figure Description

[0034] Figure 1 A flowchart of aeromagnetic compensation based on adaptive modeling is provided for embodiments of the present invention;

[0035] Figure 2 This is a diagram of magnetic interference data for calibration flight provided in an embodiment of the present invention;

[0036] Figure 3 This is a magnetic interference data diagram for compensated flight provided in an embodiment of the present invention;

[0037] Figure 4 This is a comparison diagram of magnetic interference before and after compensation according to the present invention, provided as an embodiment of the present invention. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0039] See Figure 1 As shown, an aeromagnetic compensation method based on adaptive modeling includes:

[0040] Step S1: During the calibration phase, automatically identify calibration flight data (X). cal H t,cal The headings of the calibrated flight are determined, and four heading datasets are obtained.

[0041] Step S2: Calculate the VIF values ​​of the variables in the TL equation, and repeatedly eliminate variables with the largest VIF until the multicollinearity of the remaining variables is small;

[0042] Step S3: Perform t-tests on the remaining variables after completing Step S2, and repeatedly eliminate variables with low significance until the final assigned variables are highly significant and contribute little to multicollinearity.

[0043] Step S4: Perform steps S2 and S3 on the four headings of the calibration flight respectively to obtain the four heading models constructed by the final allocation variables;

[0044] Step S5: Calculate the four compensation coefficients (X) corresponding to the four heading models. cal C cal =H t,cal );

[0045] Step S6: During the compensation phase, automatically identify the compensation flight data (X). com H t,com The heading is determined to obtain four heading datasets for compensated flight.

[0046] Step S7: Automatically assign the heading model and compensation coefficients corresponding to the compensated flight heading data;

[0047] Step S8: Perform magnetic interference compensation Compensated magnetic interference

[0048] Step S9: Evaluate the compensation system by comparing the standard deviation (STD) and improvement ratio (IR) of the magnetic interference before and after compensation, and plot the graph.

[0049] The aircraft's magnetic interference model includes three components: the constant interference generated by various parts of the aircraft (H... p ) Magnetic field, the induction generated by the magnetization of the geomagnetic field (H i ) Magnetic field and eddy current (H) generated by aircraft motion ec Magnetic field, represented as:

[0050] H p = c1cosα + c2cosβ + c3cosγ

[0051]

[0052]

[0053] Where c1, c2, ..., c 18 These are the compensation coefficients; cos'α, cos'β, cos'γ are the derivatives of cosα, cosβ, cosγ; T t Cosα, cosβ, and cosγ are the direction cosines of the Earth's magnetic field in the three directions within the aircraft coordinate system. These can be determined from the data of a three-axis fluxgate magnetometer. x ,T y ,T z The calculation yielded:

[0054]

[0055] The total interference field can be expressed as:

[0056] H t =H p +H i +H ec =c1x1+c2x2+c3x3+c4x4+c5x5+c6x6+c7x7+c8x8+c9x9+c 10 x 10 +c 11 x 11 +c 12 x 12 +c 13 x 13 +c 14 x 14 +c 15 x 15 +c 16 x 16 +c 17 x 17 +c 18 x 18

[0057] The equation for TL can be obtained by rearranging:

[0058] XC = Ht

[0059] Where C is a set of column vectors C i Composed of (i = 1, 2, ..., 18); H t It is a column vector;

[0060]

[0061] X consists of 18 variables: cosα, cosβ, cosγ, and cos'α, cos'β, cos'γ.

[0062] The least squares (LS) solution to the TL equation is:

[0063] C LS =(X T X) -1 X T H t

[0064] The ridge regression (RR) solution for the TL equation is:

[0065] C RR =(X T X+μI) -1 X T H t

[0066] Where μ is a positive constant; I is the identity matrix.

[0067] The variables in the TL model can be obtained not only from a three-axis fluxgate magnetometer but also from aircraft attitude angle calculations. Let φ and θ represent the magnetic tilt angle and heading angle, respectively, and λ, ψ, and η represent the pitch angle, roll angle, and yaw angle, respectively. cosα, cosβ, and cosγ can be represented as follows:

[0068] For pitch angle:

[0069] cosα=cosφsinθ

[0070] cosβ=cosφcosθcosλ+sinφsinλ

[0071] cosγ=sinφcosλ-cosφcosθsinλ

[0072] For roll angle:

[0073] cosα=cosφsinθcosψ+sinφsinψ

[0074] cosβ=cosφcosθ

[0075] cosγ=sinφcosψ–cosφsinθsinψ

[0076] For yaw angle:

[0077] cosα=cosφsinθcosη-cosφcosθsinη

[0078] cosβ=cosφcosθcosη+cosφsinθsinη

[0079] cosγ=sinφ

[0080] For level flight:

[0081] cosα=cosφsinθ

[0082] cosβ=cosφcosθ

[0083] cosγ=sinφ

[0084] Since the value of θ is different in different directions (usually 0° for north, 90° for east, 180° for south, and 270° for west), the expressions for the variables of the TL model relative to the aircraft attitude angle in different headings are obtained based on the above formula (the expressions for south heading and north heading are similar, and the expressions for west heading and east heading are similar), as shown in Table 1:

[0085] Table 1

[0086]

[0087] All variables in the TL model are composed of combinations of three attitude angles, and some variables can be represented by other variables. Furthermore, the relationship between aircraft attitude angles and variables differs across different headings. This suggests a severe linear correlation among the variables, leading to multicollinearity in the TL model. This increases the variance of the parameter estimates, affecting the accuracy and stability of the compensation parameter estimates. Moreover, the inconsistent correlations between variables when the aircraft maneuvers in different headings indicate that the variable components influencing multicollinearity are different. In other words, the ill-conditioned nature of the TL model is related to both heading and variables.

[0088] Therefore, the heading of the compensated flight is considered separately, and four heading models are constructed through adaptive variable allocation to eliminate multicollinearity caused by the flight heading. During adaptive variable allocation, variables with higher significance and lower multicollinearity are automatically assigned based on VIF values ​​and t-tests to construct the optimal heading model, thereby obtaining high-precision compensation coefficients.

[0089] VIF stands for Variance Inflation Factor. VIF quantifies the severity of multicollinearity in a regression model. A larger VIF indicates a greater likelihood of collinearity among variables, meaning the model coefficients are highly collinear. For the i-th variable, VIF is defined as:

[0090]

[0091] Where R i 2 The independent variable X i The R² value of the coefficient of determination between the remaining independent variables in the linear regression model and the model.

[0092] The t-test can be used to test the significance of regression coefficients and whether the explanatory variables corresponding to the regression coefficients have a significant impact on the explained variable. In other words, the t-test examines the variable X in a TL model. i Magnetic interference H t Does it have a significant effect? ​​Null hypothesis H j0 :b j =0, alternative hypothesis H j1 :b j ≠0 where j = 1, 2, ..., a; b j is the j-th regression coefficient; a is the number of variables X in the TL model (a = 18).

[0093] The t-statistic is:

[0094]

[0095] Where na-1 is the degree of freedom; n is the number of samples; It is the standard deviation of the j-th regression coefficient; It is the regression value of the j-th regression coefficient.

[0096] The rejection field is:

[0097] |T j |≥t α / 2 (na-1)

[0098] Where α is the significance level.

[0099] The p-value of the t-test statistic is the probability of significance of the t-statistic. If p >= α, the null hypothesis is accepted, and the explanatory variables have no significant effect on the dependent variable; if p < α, the null hypothesis is rejected, and the alternative hypothesis is accepted, indicating that the j-th regression coefficient b j The corresponding variable X i It has a significant impact.

[0100] The compensation coefficients are solved for the constructed heading model. Then, in the compensation phase, the corresponding heading model and compensation coefficients are adaptively assigned to perform aeromagnetic compensation on the compensated flight data. The compensation system is evaluated and a compensation image is plotted by comparing the standard deviation (STD) and improvement ratio (IR) of the magnetic interference before and after compensation.

[0101]

[0102] Where μ is the arithmetic mean of the variables, STD u and STD c These are the standard deviations of uncompensated and compensated magnetic interference, respectively.

[0103] An experiment was conducted according to the method of the present invention to verify its feasibility. The experimental procedure is as follows: After the UAV performed calibration flight and compensation flight, flight data were obtained respectively, and then the above-mentioned aeromagnetic compensation method based on adaptive modeling was used. The calibration flight data ( Figure 2 Adaptive allocation of variables constructs an optimal heading model to compensate for flight data. Figure 3 Compensation is performed. Taking the northward heading of the calibration flight as an example, the adaptive modeling process is shown in Table 2:

[0104] Table 2

[0105]

[0106] The final heading model is [X1,X2,X3,X5,X7,X8,X9,X] 10 ,X 13 ,X 15 ,X 16 ,X 17 ,X 18 The variables in the model exhibit low multicollinearity and high significance, which can suppress the impact of multicollinearity on magnetic interference compensation. Subsequently, the compensation coefficients of the heading model are solved using the least squares method and ridge regression method, respectively, and compensation is applied to the compensated flight. The compensation results are as follows: Figure 4 As shown, taking the northbound heading as an example, when using the LS method for compensation, the heading model reduces the STD to 0.182 and the IR to 7.126. When using the RR method for compensation, the heading model reduces the STD to 0.126 and the IR to 10.294. This demonstrates that the heading model effectively reduces the effects of multicollinearity, achieving high-precision aeromagnetic compensation. Furthermore, the RR method has a stronger fitting ability than the LS method, possessing higher compensation accuracy and greater stability.

[0107] In summary, this invention provides an adaptive modeling-based aeromagnetic compensation method. Considering the influence of aircraft heading and attitude changes, it analyzes the relationship between aircraft attitude angles and TL model variables under different headings, proving that the variables leading to multicollinearity in the model are related to the flight heading. Based on this, by adaptively allocating variables with smaller and larger contributions to multicollinearity, different heading models are established to describe the magnetic interference of the aircraft under different headings, thereby reducing multicollinearity. Compensation using the method of this invention on measured data demonstrates the feasibility of this method.

[0108] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An aeromagnetic compensation method based on adaptive modeling, characterized in that, The method includes: Step S1: Automatically identify the heading of the calibration flight data and obtain a dataset of the four headings of the calibration flight; Step S2: Calculate the VIF value of each variable in the TL equation, and repeatedly eliminate the variable with the largest VIF until the multicollinearity among the remaining variables is less than the set threshold. Step S3: Perform t-tests on the remaining variables after step S2, repeatedly eliminating variables with low significance until the final assigned variables are highly significant and contribute little to multicollinearity. The inspection specifically includes: Null hypothesis Alternative hypothesis in ; It is the first One regression coefficient; TL model variables The number of; The statistic is: ， in It's about freedom; It is the number of samples; It is the first The standard deviation of each regression coefficient; It is the first The regression values ​​of each regression coefficient; The rejection field is: ， in It is the significance level; The p-value of the test statistic The significance probability of a statistic, if p>= If p < 0, then the null hypothesis is accepted, and the explanatory variables have no significant effect on the dependent variable; if p < 0. If the null hypothesis is rejected and the alternative hypothesis is accepted, then the first hypothesis is rejected. regression coefficients The corresponding variable It has a significant impact; Step S4: Perform steps S2 and S3 on the datasets of the four headings of the calibration flight respectively to obtain the four heading models constructed by the final assigned variables; Step S5: Calculate the four sets of compensation coefficients corresponding to the four heading models; Step S6: Automatically identify the heading of the compensated flight data and obtain the four heading datasets for the compensated flight; Step S7: Automatically assign the heading model and compensation coefficients corresponding to the four heading datasets of the compensated flight; Step S8: Perform magnetic interference compensation based on the corresponding heading model and compensation coefficient to obtain the compensated magnetic interference.

2. The aeromagnetic compensation method based on adaptive modeling according to claim 1, characterized in that, For the Given several variables, calculate the VIF as follows: ， in, It is the independent variable The coefficient of determination between the residual independent variables in the linear regression model value.

3. The aeromagnetic compensation method based on adaptive modeling according to claim 1, characterized in that, The TL equation is: ， in It consists of a set of column vectors composition; It is a column vector; ， in Depend on and The 18 variables formed They are The derivative; It is the direction cosine of the Earth's magnetic field in three directions in the aircraft coordinate system.

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