Target detection method based on magnetic multi-feature fusion

Abstract

The invention relates to the technical field of magnetic anomaly detection, in particular to a target detection method based on magnetic multi-feature fusion. Comprising the following steps: S1, removing environmental magnetic noise; s2, decomposing a measurement magnetic field into two parts by adopting a combination of a polynomial model and an autoregression model; s3, constructing OBF features, ME features and HMS features of the target based on the de-noised magnetic measurement data in S2, so as to comprehensively characterize the target from multiple dimensions; s4, adopting a p-norm as a detection index after feature fusion; and S5, calculating a cumulative distribution function of noise features by using kernel density estimation (KDE), determining a corresponding threshold according to a set false alarm rate (FAR), and outputting a detection result according to the threshold. The problems that an existing detection method is low in detection probability and large in detection false alarm rate under the conditions of low signal-to-noise ratio and large environment interference are solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of magnetic anomaly detection, and particularly relates to a target detection method based on multi-feature fusion of magnetism. BACKGROUND

[0002] The geomagnetic field is an inherent vector field of the earth, which is composed of field source components such as internal source field and external source field. The internal source field is a stable magnetic field, which is composed of 95% of the core field, 4% of the crust anomaly field and less than 1% of the external magnetic field, and changes extremely slowly with time, and has the characteristics of all-weather and all-region. When there is a magnetic target (containing iron, nickel, etc.) in the measurement area, the magnetic target will produce an induced magnetic field under the magnetization of the geomagnetic field, which in turn will change the original geomagnetic field distribution, that is, a magnetic anomaly is formed. The magnetic detection technology is to analyze the target magnetic measurement data, extract the magnetic anomaly characteristics generated by the target, and obtain the information of the target.

[0003] Compared with the geomagnetic field, the target magnetic anomaly signal is very small, and as the distance between the magnetic target and the sensor increases, the detected magnetic anomaly becomes smaller and smaller, which leads to the fact that the magnetic anomaly signal generated by the target at a long distance is usually buried in the background magnetic noise. The traditional magnetic anomaly detection technology is mostly based on single feature of the target for detection, and is affected by the problems of low signal-to-noise ratio, large background magnetic interference, etc., so the applicable scene is less, especially in complex environment, the detection effect is very limited. SUMMARY

[0004] The present application provides a target detection method based on multi-feature fusion of magnetism, which aims to detect and search for magnetic anomaly targets, and solves the problems of low detection probability and large false alarm rate of the existing detection method in the case of low signal-to-noise ratio and large environmental interference.

[0005] To achieve the above-mentioned purpose, the technical scheme of the present application is as follows:

[0006] The present application provides a target detection method based on multi-feature fusion of magnetism, which includes the following steps:

[0007] S1. Based on the sampling rate of the magnetic measurement data, the cutoff frequency and the order of the Butterworth filter are determined, and then the measured magnetic field data is filtered to remove the environmental magnetic noise;

[0008] S2. The influence of the background magnetic noise on the magnetic anomaly target signal is further reduced by geomagnetic field reconstruction, and the measured magnetic field is decomposed into two parts: deterministic trend item and fluctuation item by using the combination of polynomial model and autoregressive model;

[0009] S3. Based on the magnetic measurement data after S2 denoising processing, the OBF feature, ME feature and HMS feature of the target are constructed to comprehensively characterize the target from multiple dimensions;

[0010] S4. The p-norm is used as the detection index after feature fusion:

[0011]

[0012] wherein x i is a feature of the magnetic anomaly (OBF feature, ME feature and HHS feature), and p is a real number and p≥1;

[0013] S5. The cumulative distribution function of the noise feature is calculated using the kernel density estimation (KDE), the corresponding threshold is determined according to the set false alarm rate (FAR), and the detection result is output according to the threshold.

[0014] Further, the specific method of decomposing the measured magnetic field into two parts in S2 is: using a polynomial model to fit the geomagnetic signal to extract the long-term trend part; there is a set of geomagnetic measurement data y(x i ), wherein x i is position data; the least square method is used to fit the polynomial model to obtain the trend part The trend part is removed from the original signal to obtain the residual:

[0015]

[0016] The residual part is fitted using an autoregressive model to capture the local dependence between spatial positions; for each position x i , the neighborhood relationship is described by an adjacency matrix W; the autoregressive coefficient ρ and the spatial adjacency weight matrix W are estimated by maximum likelihood estimation fitting; the autoregressive model is used to realize the extraction of the fluctuating magnetic anomaly signal.

[0017] Further, the specific method of constructing the OBF feature, ME feature and HMS feature of the target in S3 is:

[0018] S31. OBF feature construction: first, construct a suitable OBF group by orthogonalization method; second, project the original scalar measurement magnetic signal x(t) into the OBF space to obtain the corresponding coefficient; finally, take the energy function as the detection feature; finally, the OBF space is composed of three typical functions, which are expressed as:

[0019]

[0020] wherein: ω=D / R0, assuming that the target is stationary, taking the target as the origin, the sensor movement direction as the X axis, and the vertical upward as the Z axis, D is the horizontal coordinate of the sensor in the coordinate system, R0 is the minimum distance between the sensor and the target during the movement; based on the relationship between the parameters, the magnetic anomaly is expressed in the form of orthogonal basis function:

[0021]

[0022] where μ0is the vacuum permeability, M is the target magnetic moment, λ i is the coefficient related to the geomagnetic vector and the target magnetic moment vector; the OBF feature of the magnetic anomaly detection is:

[0023]

[0024] S32. ME feature construction, the positioning expression of the magnetic entropy feature is:

[0025]

[0026] where p(x(t)) represents the probability density function of the magnetic field x(t); the steps include: obtaining the residual magnetic field and estimating its probability density function PDF according to the background magnetic field constructed by the autoregressive model; calculating the corresponding magnetic entropy feature based on the estimated probability density function;

[0027] S33. HMS feature construction: using ensemble empirical mode decomposition (EEMD: Ensemble Empirical Mode Decomposition) to adaptively decompose x(t) to obtain a plurality of intrinsic mode function terms c(t) and a residual term r(t):

[0028]

[0029] where N represents the number of layers of empirical mode decomposition.

[0030] After obtaining the intrinsic mode function of the magnetic signal, the Hilbert transform is performed on each c i (t).

[0031]

[0032] The analytic signal z i (t) of c i (t) is obtained as follows:

[0033]

[0034] where: represents the instantaneous amplitude corresponding to the intrinsic mode function c i (t), θ i (t) = arctan(H i (c i (t)) / c i (t)) represents the instantaneous phase corresponding to the intrinsic mode function c i (t).

[0035] According to the instantaneous phase θ i (t), the corresponding instantaneous frequency ω i (t) is calculated as follows:

[0036]

[0037] The amplitude of the magnetic signal can be expressed as a function of time, instantaneous frequency, and the Hilbert spectrum H(ω, t) of the magnetic signal amplitude is obtained:

[0038]

[0039] According to the Hilbert spectrum H(ω, t), the marginal spectrum h(ω) of the magnetic signal is calculated as follows:

[0040]

[0041] Further, the specific method of outputting the detection result in S5 is:

[0042] Let the feature information of the background noise be X = {x1, x2, …, x N}, and the estimated probability density function f X (x) can be expressed as:

[0043]

[0044] Where N is the amount of data of the feature; h is the bandwidth parameter, which controls the width of the kernel function; K is the kernel function, usually a Gaussian kernel;

[0045] The probability density function obtained by the kernel density estimation can be further used to calculate the cumulative distribution function; the cumulative distribution function F X (x) is the integral of the probability density function, i.e.:

[0046]

[0047] Under the framework of KDE, the CDF is obtained by numerical integration of the estimated PDF; therefore, the KDE-estimated CDF is expressed as:

[0048]

[0049] Where H is the cumulative distribution function of the kernel function;

[0050] When performing magnetic anomaly target detection, the false alarm rate P FAR is set according to the needs, and the cumulative distribution function CDF and the false alarm rate P FAR can be used to determine the appropriate threshold size T, so that the CDF value satisfies:

[0051]

[0052] When the characteristic value of the magnetic field signal is greater than T, it indicates that a magnetic anomaly target is detected, otherwise it indicates that no magnetic anomaly target is detected.

[0053] The present application has the following advantages:

[0054] Enhanced noise immunity: The geomagnetic field reconstruction by Butterworth filter denoising and combination of polynomial model and autoregressive model can effectively remove background magnetic noise and environmental interference, preserve signal amplitude integrity, and improve the signal-to-noise ratio of magnetic anomaly signals, laying a high-quality data foundation for subsequent feature extraction.

[0055] Multi-dimensional accurate characterization of target: OBF feature, ME feature and HMS feature are constructed to comprehensively characterize the target from different dimensions such as magnetic field energy distribution, noise mode change and time-frequency information, breaking through the limitations of traditional single feature detection and improving the capture ability of weak magnetic anomaly targets.

[0056] Enhanced feature fusion balance: p-norm is used as the feature fusion detection index to balance the contribution weight of different dimensional features, avoid false detection caused by excessive single feature value, enhance the robustness of features to noise, and make the detection result more stable and reliable.

[0057] Adaptive threshold optimization detection: Kernel Density Estimation (KDE) is used to calculate the cumulative distribution function of noise features, and the threshold is adaptively determined according to the set false alarm rate (FAR) to realize dynamic optimization of detection threshold, effectively reduce the false alarm rate, and improve the accuracy and reliability of target detection in complex environments.

[0058] Expand the application scenario: This method significantly improves the detection performance in low signal-to-noise ratio, strong background interference and other complex environments through multi-feature fusion and noise suppression technology, expands the application scenario of magnetic anomaly detection technology, and is especially suitable for long-distance weak magnetic target detection and search tasks. BRIEF DESCRIPTION OF DRAWINGS

[0059] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiment or prior art description. Obviously, the drawings in the following description only some embodiments of the present application, and for those skilled in the art, other drawings can be obtained without creative labor on the basis of the structure shown in these drawings.

[0060] Figure 1 It is a flow chart of the target detection method based on the magnetic multi-feature fusion of the present application. DETAILED DESCRIPTION

[0061] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative efforts belong to the scope of the present application.

[0062] It should be noted that if the embodiments of the present application involve directional indications (such as up, down, left, right, front, back, etc.), the directional indications are only used to explain the relative position relationship, motion condition, etc. between components in a certain posture (as shown in the drawings), and if the certain posture changes, the directional indications also change accordingly.

[0063] In addition, if the embodiments of the present application involve descriptions such as "first", "second", etc., the descriptions of "first", "second", etc. are only for description purposes, and cannot be understood as indicating or implying the relative importance of the indicated technical features or implicitly indicating the number of the indicated technical features. Therefore, the features limited by "first" and "second" can explicitly or implicitly include at least one of the features. In addition, the meaning of "and / or" appearing throughout the text is that it includes three parallel schemes, for example, "A and / or B" includes A scheme, or B scheme, or A and B schemes. In addition, the technical solutions of each embodiment can be combined with each other, but it must be based on the fact that a person skilled in the art can realize it, and when the combination of technical solutions appears contradictory or unachievable, it should be considered that the combination of technical solutions does not exist and is not within the scope of protection claimed by the present application.

[0064] The present application proposes a target detection method based on magnetic multi-feature fusion, mainly including environmental magnetic noise denoising, background geomagnetic field denoising, target multi-magnetic feature construction, multi-feature fusion, adaptive threshold determination and output of detection results according to the threshold. The method reduces the influence of the background magnetic field on the target magnetic anomaly signal through magnetic measurement data preprocessing, represents the target from multiple dimensions by constructing orthogonal basis function (OBF: Orthonormalized Basis Function) features, entropy magnetic (ME: Minimum Entropy) features and marginal spectrum (HMS: Hilbert Marginal Spectrum) features, etc., realizes the balance of target multi-dimensional feature fusion by using a multi-feature fusion processing algorithm, improves the relative weight of weak signals, and enhances the robustness of features to noise.

[0065] As shown in Figure 1 The target detection method specifically includes the following steps:

[0066] S1. Determine the cutoff frequency and order of the Butterworth filter based on the sampling rate of the magnetic measurement data, then filter the measured magnetic field data to remove environmental magnetic noise; Specifically, to better remove the interference of background magnetic noise on the magnetic anomaly target signal, a Butterworth filter is used for filtering, which can effectively preserve the amplitude integrity of the signal and is suitable for applications sensitive to signal distortion. At the same time, it realizes good transition performance between passband and stopband and is easy to implement. Among them, the Butterworth filter is a classic linear filter widely used in the field of signal processing, mainly used for frequency selective processing of signals, such as filtering noise or extracting signals in a specific frequency range.

[0067] S2. Based on the filtered magnetic field data, further reduce the influence of background magnetic noise on the magnetic anomaly target signal through geomagnetic field reconstruction, use the combination of polynomial model and autoregressive model to decompose the measured magnetic field into two parts: deterministic trend item (polynomial trend) and fluctuation item. Among them, the deterministic trend item is used as the background geomagnetic field elimination, and the fluctuation item is used as the magnetic anomaly data further extraction.

[0068] S3. Based on the magnetic measurement data after S2 denoising processing, construct the OBF feature, ME feature and HMS feature of the target to comprehensively characterize the target from multiple dimensions.

[0069] S4. Use p-norm as the detection index after feature fusion:

[0070]

[0071] Where: x i is the feature of the magnetic anomaly (OBF feature, ME feature and HMS feature), p is a real number, and p≥1;

[0072] This enhances the robustness of the feature to noise and balances smaller features with larger features, achieving balance in multi-dimensional feature fusion. Specifically, the OBF feature characterizes the magnetic anomaly through the target magnetic field signal, the ME feature characterizes the magnetic anomaly through the change of magnetic noise mode, and the HMS feature characterizes the magnetic anomaly through the time-frequency information of the magnetic signal, that is, the magnetic anomaly target can be characterized through different dimensions to improve the detection performance. Due to the difference in dimensions, there may be differences in feature information values, such as smaller features that may carry important magnetic anomaly information.

[0073] This fusion strategy characterizes the magnetic anomaly signal from different dimensions, enhances the contribution of smaller feature information to the detection index, and reduces the contribution of larger feature values to the detection index, thereby achieving balance in multi-dimensional feature fusion. It can effectively reduce false positives caused by excessive single feature information, making the detection result more robust.

[0074] S5. Addressing the threshold determination problem in S4, kernel density estimation (KDE) is used to calculate the cumulative distribution function of the noise characteristics. The corresponding threshold is determined based on the set false alarm rate (FAR), and the detection result is output according to the threshold. KDE is a non-parametric estimation method used to estimate an unknown probability density function (PDF).

[0075] Furthermore, the specific method for decomposing the measured magnetic field into two parts as described in S2 is as follows: A polynomial model is used to fit the geomagnetic signal, and the long-term trend component is extracted. Assume there is a set of geomagnetic measurement data y(x... i ), where x i This is location data. The least squares method can be used to fit a polynomial model to obtain the trend component of the signal. The deterministic trend component is removed from the original signal to obtain the residual (i.e., the volatility term after trend removal):

[0076]

[0077] An autoregressive model is used to fit the residuals, capturing local dependencies between spatial locations. For each location x i The neighborhood relationships are described by the adjacency matrix W. The autoregressive coefficients ρ and the spatial adjacency weight matrix W are estimated through maximum likelihood estimation. The autoregressive model is then used to extract the magnetic anomaly signal from the fluctuation term.

[0078] Furthermore, the specific methods for constructing the OBF features, ME features, and HMS features of the target in S3 are as follows:

[0079] S31. OBF Feature Construction: First, a suitable set of OBFs is constructed using orthogonalization. Second, the original scalar-measured magnetic signal x(t) is projected into the OBF space to obtain the corresponding coefficients. Finally, the energy function is considered as a detection feature. Ultimately, the OBF space consists of three typical functions, which can be expressed as:

[0080]

[0081] in: ω = D / R0, assuming the target is stationary, with the target as the origin, the sensor's motion direction as the X-axis, and the vertical upward direction as the Z-axis. D is the abscissa of the sensor in this coordinate system, and R0 is the minimum distance between the sensor and the target during motion. Based on the relationship between the parameters, the magnetic anomaly is represented in the form of orthogonal basis functions:

[0082]

[0083] In the formula, μ0 is the free permeability, M is the target magnetic moment, and λ is the target magnetic moment. iis the coefficient related to the geomagnetic vector and the target magnetic moment vector. The OBF feature of the magnetic anomaly detection is:

[0084]

[0085] S32. ME feature construction: the presence of the magnetic target changes the background magnetic field noise distribution, and the magnetic entropy can be used to detect the distribution change of the magnetic noise, which can be used as a feature for weak magnetic anomaly detection. The positioning of the magnetic entropy feature can be expressed as:

[0086]

[0087] where p(x(t)) represents the probability density function of the magnetic field x(t). The construction steps are as follows: according to the background magnetic field constructed by the autoregressive model, the residual magnetic field is obtained and its probability density function PDF is estimated; based on the estimated probability density function, the corresponding ME feature is calculated.

[0088] S33. HMS feature construction: use ensemble empirical mode decomposition (EEMD) to adaptively decompose x(t) to obtain multiple intrinsic mode function terms c(t) and a residual term r(t):

[0089]

[0090] where N represents the number of empirical mode decomposition layers.

[0091] After obtaining the intrinsic mode function of the magnetic signal, the Hilbert transform is performed on each c i (t) to obtain the analytic signal z i (t) of c i (t), as follows:

[0092]

[0093] i i

[0094]

[0095] where: represents the instantaneous amplitude of the intrinsic mode function c i (t), and θ i (t) = arctan(H i (c i (t)) / c i (t)) represents the instantaneous phase of the intrinsic mode function c i (t).

[0096] According to the instantaneous phase θ i (t), the corresponding instantaneous frequency ωi (t), as follows:

[0097]

[0098] The amplitude of a magnetic signal can be expressed as a function of time and instantaneous frequency. The Hilbert spectrum H(ω,t) of the magnetic signal amplitude can be obtained as follows:

[0099]

[0100] Based on the Hilbert spectrum H(ω,t), the marginal spectrum h(ω) of the magnetic signal is calculated as follows:

[0101]

[0102] Furthermore, the specific method for outputting the detection results in S5 is as follows:

[0103] Assume the background noise features are X = {x1, x2, ..., x...} N The probability density function f is estimated through kernel density estimation (KDE). X (x) can be represented as:

[0104]

[0105] Where: N is the amount of feature data; h is the bandwidth parameter, which controls the width of the kernel function; K is the kernel function, usually a Gaussian kernel is chosen.

[0106] The probability density function obtained from the kernel density estimate can be further used to calculate the cumulative distribution function (CDF). The cumulative distribution function F... X (x) is the integral of the probability density function, i.e.:

[0107]

[0108] Within the framework of KDE, the cumulative distribution function (CDF) is obtained by numerically integrating the estimated probability density function (PDF). Therefore, the CDF estimated by KDE can be expressed as:

[0109]

[0110] Where H is the cumulative distribution function of the kernel function.

[0111] When detecting magnetic anomalies, the false alarm rate P should be set as needed. FAR Using the cumulative distribution function (CDF) and the false alarm rate (P)FAR , the CDF value satisfies:

[0112]

[0113] When the eigenvalue of the magnetic field signal is greater than T, it indicates that the magnetic anomaly target is detected, otherwise it indicates that the magnetic anomaly target is not detected.

[0114] The above only describes optional embodiments of the present application, and does not limit the patent scope of the present application. Any equivalent structure transformation made by using the content of the present application specification and drawings, or direct / indirect application in other related technical fields under the inventive concept of the present application is included in the patent protection scope of the present application.

Claims

1. A target detection method based on magnetic multi-feature fusion, characterized in that, Includes the following steps: S1. Based on the sampling rate of the magnetic measurement data, determine the cutoff frequency and order of the Butterworth filter, and then filter the measured magnetic field data to remove environmental magnetic noise; S2. Further reduce the influence of background magnetic noise on the magnetic anomaly target signal by geomagnetic field reconstruction. The measured magnetic field is decomposed into two parts by a combination of a multinomial model and an autoregressive model: a deterministic trend term and a fluctuation term. S3. Based on the denoised magnetic measurement data from S2, construct the OBF, ME, and HMS features of the target to comprehensively characterize the target from multiple dimensions. S4. The p-norm is used as the detection metric after feature fusion: Where: x i The characteristics of a magnetic anomaly are given by P, where P is a real number and p≥1; S5. Calculate the cumulative distribution function of the noise characteristics using kernel density estimation, determine the corresponding threshold based on the set false alarm rate, and output the detection results based on the threshold.

2. The target detection method based on magnetic multi-feature fusion according to claim 1, characterized in that, The specific method for decomposing the measured magnetic field into two parts as described in S2 is as follows: A polynomial model is used to fit the geomagnetic signal, and the long-term trend component is extracted; Given a set of geomagnetic measurement data y(x... i ), where x i It's location data; The least squares method is used to fit a polynomial model to obtain the trend part of the signal. Remove the trend component from the original signal to obtain the residual: An autoregressive model is used to fit the residuals, capturing local dependencies between spatial locations; for each location x i The neighborhood relationships are described by the adjacency matrix W; the autoregressive coefficients ρ and the spatial adjacency weight matrix W are estimated by fitting the maximum likelihood estimation. An autoregressive model was used to extract magnetic anomaly signals from the fluctuation term.

3. The target detection method based on magnetic multi-feature fusion according to claim 1, characterized in that, The specific methods for constructing the OBF, ME, and HMS features of a target in S3 are as follows: S31. OBF Feature Construction: First, a suitable OBF set is constructed using orthogonalization. Second, the original scalar measured magnetic signal x(t) is projected into the OBF space to obtain the corresponding coefficients. Finally, the energy function is considered as a detection feature. Ultimately, the OBF space consists of three typical functions, which are expressed as follows: in: ω = D / R0, assuming the target is stationary, with the target as the origin, the sensor's motion direction as the X-axis, and the vertical upward direction as the Z-axis. D is the abscissa of the sensor in this coordinate system, and R0 is the minimum distance between the sensor and the target during motion. Based on the relationship between the parameters, the magnetic anomaly is represented in the form of orthogonal basis functions: In the formula, μ0 is the free permeability, M is the target magnetic moment, and λ is the target magnetic moment. i These are coefficients related to the geomagnetic vector and the target magnetic moment vector; the OBF characteristic of magnetic anomaly detection is: S32.ME feature construction, the localization of magnetic entropy features is represented as follows: Where p(x(t)) represents the probability density function of the magnetic field x(t); the steps include: obtaining the residual magnetic field and estimating its probability density function PDF based on the background magnetic field constructed by the autoregressive model; and calculating the corresponding magnetic entropy feature based on the estimated probability density function. S33. HMS Feature Construction: Adaptive decomposition of x(t) is performed using ensemble empirical mode decomposition to obtain multiple intrinsic mode function terms c(t) and a residual term r(t): In the formula, N represents the number of levels in the empirical pattern decomposition; After obtaining the intrinsic mode functions of the magnetic signal, for each c i (t) Perform Hilbert transform: Get c i The analytic signal z of (t) i (t), as follows: in: Represents the intrinsic mode function c i The instantaneous amplitude corresponding to (t), θ i (t)=arctan(H i (c i (t)) / c i (t) represents the intrinsic mode function c. i (t) corresponds to the instantaneous phase; Based on the instantaneous phase θ i (t), calculate the corresponding instantaneous frequency ω i (t), as follows: The amplitude of a magnetic signal can be expressed as a function of time and instantaneous frequency. The Hilbert spectrum H(ω,t) of the magnetic signal amplitude can be obtained as follows: Based on the Hilbert spectrum H(ω,t), the marginal spectrum h(ω) of the magnetic signal is calculated as follows:

4. The target detection method based on magnetic multi-feature fusion according to claim 1, characterized in that, The specific method for outputting detection results in S5 is as follows: Let the characteristic information of the background noise be X = {x1, x2, ..., x...} N }, through kernel density estimation, the estimated probability density function f X (x) is represented as: Where: N is the amount of feature data; h is the bandwidth parameter, which controls the width of the kernel function; K is the kernel function, usually a Gaussian kernel is chosen; The probability density function obtained from the kernel density estimate can be further used to calculate the cumulative distribution function; the cumulative distribution function F X (x) is the integral of the probability density function, i.e.: Within the framework of KDE, the cumulative distribution function is obtained by numerically integrating the estimated probability density function; therefore, the CDF estimated by KDE is expressed as: Where: H is the cumulative distribution function of the kernel function; When detecting magnetic anomalies, the false alarm rate P should be set as needed. FAR Using the cumulative distribution function (CDF) and the false alarm rate (P) FAR It is possible to determine a suitable threshold size T such that the CDF value satisfies: When the characteristic value of the magnetic field signal is greater than T, it indicates that a magnetic anomaly target has been detected; otherwise, it indicates that no magnetic anomaly target has been detected.

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