A magnetic anomaly signal detection method based on whitening filtering and information entropy

Abstract

The invention discloses a magnetic anomaly signal detection method based on the combination of whitening filtering and information entropy, which relates to the field of magnetic target detection and comprises the following steps: collecting magnetic field data, the magnetic field data is used to obtain magnetic anomaly signals, wherein the background noise of the magnetic field data is colored noise with non-Gaussian distribution; constructing an AR autoregressive model, the AR autoregressive model is used to perform whitening processing on the colored noise of the magnetic field data; based on the AR autoregressive model, the magnetic field data is whitened; according to the whitened magnetic field data, information entropy is obtained, and according to the information entropy, the magnetic anomaly signal is obtained; the invention improves the problem that the detection efficiency of the original information entropy detection algorithm is weakened under the condition of non-Gaussian colored noise, and improves the signal-to-noise ratio of target magnetic anomaly detection.

Description

Technical Field

[0001] The present invention relates to the field of magnetic target detection, and in particular to a magnetic anomaly signal detection method based on the combination of whitening filtering and information entropy. Background Art

[0002] Magnetic targets in the geomagnetic field will generate static magnetic fields due to magnetization, thus changing the distribution of the original magnetic field. The detection of targets can be achieved by measuring geomagnetic anomalies. Common magnetic field sensors used for target detection mainly include fluxgate magnetometers that measure three components and optically pumped magnetometers that measure the total magnetic field. Optically pumped magnetometers have the advantage of not being affected by the carrier's posture, so they can be carried on mobile carrier platforms to achieve magnetic detection of targets. Optically pumped magnetometers are a scalar magnetic field measuring instrument. The total field information they measure is the projection of the magnetic anomaly on the geomagnetic field. Usually, the target magnetic field intensity is much smaller than the geomagnetic field, and the geomagnetic field has the characteristic of slow changes and can be approximately regarded as a DC component. Therefore, the common processing method is to obtain the target magnetic anomaly signal through bandpass filtering. The filtering frequency band is determined according to the relative movement speed between the target and the mobile carrier platform.

[0003] Currently, common magnetic anomaly detection methods are mainly divided into two categories. One is the detection method based on the target signal characteristics, such as the orthogonal basis (OBF) detection method, and the other is the detection method based on the different statistical characteristics of noise and signals, such as the information entropy detection method and the high-order zero-crossing detection method.

[0004] The detection effect of magnetic anomaly detection method based on orthogonal basis is good, but this method adopts several assumptions: 1. The magnetic target can be regarded as a single magnetic dipole model; 2. During detection, the target moves in a straight line; 3. The characteristic time of target detection is known. If the above conditions cannot be met at the same time, for example, when the distance to the magnetic target is close or the target does not move in a straight line, the detection performance of the orthogonal basis detection method will decrease. The information entropy detection method has the advantage of not being constrained by the above conditions, and can detect target magnetic anomalies under the condition of non-linear motion of the target. However, the traditional information entropy detection method is obtained under the assumption that the background noise follows the Gaussian distribution. However, in actual situations, the magnetic field noise is usually non-Gaussian distributed colored noise, so the efficiency of the information entropy detection method will be reduced. Summary of the invention

[0005] In order to address the problem that the current detection algorithm for target magnetic anomalies using information entropy has reduced detection efficiency under non-Gaussian colored noise, the purpose of the present invention is to propose a magnetic anomaly detection method that combines whitening filtering with information entropy. The detection method first uses an AR autoregressive model to pre-whiten the colored noise, and then obtains information entropy from the whitened magnetic field data, thereby realizing the detection of target magnetic anomalies.

[0006] In order to achieve the above technical objectives, the present invention provides a method for detecting magnetic anomaly signals based on the combination of whitening filtering and information entropy, comprising the following steps:

[0007] Collecting magnetic field data, where the magnetic field data is used to obtain magnetic anomaly signals, wherein the background noise of the magnetic field data is colored noise with non-Gaussian distribution;

[0008] Construct an AR autoregressive model, which is used to whiten the colored noise of magnetic field data;

[0009] Based on the AR autoregressive model, the magnetic field data is whitened;

[0010] According to the whitened magnetic field data, information entropy is obtained, and according to the information entropy, a magnetic anomaly signal is obtained.

[0011] Preferably, in the process of constructing the AR autoregressive model, the first expression of the magnetic field measurement sequence of the magnetic field data is:

[0012]

[0013] Where x(n) is the magnetic field measurement sequence, w(n) is Gaussian white noise, P represents the first P sampling points, a k is the model coefficient.

[0014] Preferably, in the process of constructing the AR autoregressive model, x(nm) is multiplied at both ends of the first expression to obtain a second expression, which is:

[0015]

[0016] Simplify the second expression into the third expression, which is:

[0017]

[0018] in,

[0019] Preferably, during the whitening process,

[0020] When m>0, the third expression is:

[0021] When m = 0, the variance of white noise is

[0022] According to the third expression and the variance of the white noise, a fourth expression is obtained. The fourth expression is used to calculate the model coefficients of the P-order AR autoregressive model. The fourth expression is:

[0023]

[0024] Preferably, according to the fourth expression and the first expression, an AR autoregressive model is constructed, and the AR autoregressive model is:

[0025]

[0026] Among them, a0=1.

[0027] Preferably, in the process of obtaining the information entropy of the background noise, the number of measurement points of the sliding window of the magnetic field detection is L, and the information entropy of the sliding window is:

[0028]

[0029] Among them, I(y i ) is information entropy, y i is the magnetic field value after whitening filtering, p(y n ) represents the probability density function of the magnetic field value after filtering.

[0030] Preferably, in the process of obtaining the information entropy of the background noise, the mean μ and variance σ of the whitened magnetic field data are extracted. 2 , obtain the probability density function of the Gaussian distribution;

[0031] The mean μ is:

[0032] Variance σ 2 for

[0033] Where M is the number of sampling points;

[0034] The probability density function is:

[0035]

[0036] According to the probability density function, y i The probability is:

[0037]

[0038] Preferably, a magnetic anomaly signal detection system using the magnetic anomaly signal detection method comprises:

[0039] A data acquisition module, used for collecting magnetic field data;

[0040] The preprocessing module is used to build an AR autoregressive model and perform whitening on the magnetic field data;

[0041] The magnetic anomaly signal detection module is used to obtain information entropy according to the whitened magnetic field data, and obtain the magnetic anomaly signal according to the information entropy.

[0042] The present invention discloses the following technical effects:

[0043] In the method provided by the present invention, since the information entropy of the background noise is usually large, when a target magnetic anomaly appears, the information entropy value will decrease, so the detection of the target magnetic anomaly can be achieved. In addition, the present invention can improve the problem of weakened detection efficiency of the original information entropy detection algorithm under non-Gaussian colored noise conditions, and improve the signal-to-noise ratio of target magnetic anomaly detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0045] Figure 1 It is a schematic diagram of the process of the present invention.

[0046] Figure 2 A time domain diagram of the measurement noise according to the present invention;

[0047] Figure 3 is the measurement noise distribution histogram of the present invention;

[0048] Figure 4 It is a time domain diagram of a measured magnetic field sequence with superimposed measurement noise of the target magnetic anomaly described in the present invention;

[0049] Figure 5 It is a time domain diagram of the measured magnetic field sequence after passing through a whitening filter according to the present invention;

[0050] Figure 6 It is the magnetic field distribution histogram after whitening filtering as described in the present invention;

[0051] Figure 7 is the information entropy of the original measured magnetic field sequence described in the present invention;

[0052] Figure 8 It is the information entropy of the magnetic field after whitening filtering described in the present invention. DETAILED DESCRIPTION

[0053] In order to make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all of the embodiments. The components of the embodiments of the present application generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the application claimed for protection, but merely represents the selected embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without making creative work belong to the scope of protection of the present application.

[0054] like Figure 1-8 As shown, the present invention provides a method for detecting magnetic anomaly signals based on the combination of whitening filtering and information entropy, comprising the following steps:

[0055] Collecting magnetic field data, where the magnetic field data is used to obtain magnetic anomaly signals, wherein the background noise of the magnetic field data is colored noise with non-Gaussian distribution;

[0056] Construct an AR autoregressive model, which is used to whiten the colored noise of magnetic field data;

[0057] Based on the AR autoregressive model, the magnetic field data is whitened;

[0058] According to the whitened magnetic field data, information entropy is obtained, and according to the information entropy, a magnetic anomaly signal is obtained.

[0059] Further preferably, in the process of constructing the AR autoregressive model, the first expression of the magnetic field measurement sequence of the magnetic field data is:

[0060]

[0061] Where x(n) is the magnetic field measurement sequence, w(n) is Gaussian white noise, P represents the first P sampling points, and ak is the model coefficient.

[0062] Further preferably, in the process of constructing the AR autoregressive model, both ends of the first expression are multiplied by x(nm) to obtain a second expression, and the second expression is:

[0063]

[0064] Simplify the second expression into the third expression, which is:

[0065]

[0066] in,

[0067] Further preferably, during the whitening process,

[0068] When m>0, the third expression is:

[0069] When m = 0, the variance of white noise is

[0070] According to the third expression and the variance of the white noise, a fourth expression is obtained. The fourth expression is used to calculate the model coefficients of the P-order AR autoregressive model. The fourth expression is:

[0071]

[0072] Further preferably, according to the fourth expression and the first expression, an AR autoregressive model is constructed, and the AR autoregressive model is:

[0073]

[0074] Among them, a0=1.

[0075] Further preferably, in the process of obtaining the information entropy of the background noise, the number of measurement points of the sliding window of the magnetic field detection is L, and the information entropy of the sliding window is:

[0076]

[0077] Among them, I(y i ) is information entropy, y i is the magnetic field value after whitening filtering, p(y n ) represents the probability density function of the magnetic field value after filtering.

[0078] Further preferably, in the process of obtaining the information entropy of the background noise, the mean μ and variance σ of the whitened magnetic field data are extracted: 2 , obtain the probability density function of the Gaussian distribution;

[0079] The mean μ is:

[0080] Variance σ 2 for

[0081] Where M is the number of sampling points;

[0082] The probability density function is:

[0083]

[0084] According to the probability density function, y i The probability is:

[0085]

[0086] Further preferably, a magnetic anomaly signal detection system using the magnetic anomaly signal detection method comprises:

[0087] A data acquisition module, used for collecting magnetic field data;

[0088] The preprocessing module is used to build an AR autoregressive model and perform whitening on the magnetic field data;

[0089] The magnetic anomaly signal detection module is used to obtain information entropy according to the whitened magnetic field data, and obtain the magnetic anomaly signal according to the information entropy.

[0090] Example 1: Assume that the measured value of the magnetic field is non-Gaussian colored noise with a power spectral density of 1 / f α According to the AR autoregressive model, assuming it is a P-order AR model, the sampling point x(n) can be represented by a linear combination of the values ​​of the first P sampling points and a Gaussian white noise superimposed on it. The expression is as follows:

[0091]

[0092] Where x(n) is the magnetic field measurement sequence and w(n) is Gaussian white noise.

[0093] Multiplying both ends of equation (1) by x(nm) yields:

[0094]

[0095] Simplifying, we get:

[0096]

[0097] Among them, the cross-correlation function R xw (m) can be expressed as follows

[0098]

[0099] From the above formula we can get

[0100]

[0101] Substituting equation (5) into equation (3) yields

[0102] When m>0,

[0103] When m = 0, the variance of white noise can be obtained as:

[0104]

[0105] Combining equation (6) and equation (7), we can get

[0106]

[0107] Then the coefficients a1, a2…a of the P-order AR autoregressive model can be calculated by formula (8): P Transforming formula (1) yields

[0108]

[0109] Where a0=1, the input of formula (9) is a colored noise sequence, and the output is Gaussian white noise. Formula (9) can realize the process of whitening colored noise.

[0110] Next, we can use information entropy to detect magnetic anomalies. The background magnetic field measurement signal after whitening obeys the Gaussian distribution. Select a section of magnetic background noise after whitening filtering to calculate the Gaussian distribution. The mean and variance can be obtained by the following formula:

[0111]

[0112]

[0113] Among them, y i is the magnetic field value after whitening filtering, and M is the number of sampling points. Then the probability density function of Gaussian distribution is

[0114]

[0115] According to the probability density function, y i The probability of

[0116]

[0117] The above formula can be used to calculate the probability corresponding to each measurement point. According to the definition of information entropy, assuming that the number of measurement points in the sliding window of magnetic field detection is L, the information entropy of the sliding window is:

[0118]

[0119] Example 2: The formula of the magnetic dipole model is as follows:

[0120]

[0121] Where m is the magnetic moment of the target, r is the distance vector from the target to the measurement point, and μ is the magnetic permeability. In air, μ≈4π×10 -7 Tm / A.

[0122] Assume that the magnetic moment of the target is m = (100000, -50000, -50000) Am 2 The aircraft flies in a straight line at a speed of 60m / s. The horizontal distance of the target from the nearest point of the aircraft route is 100m, and the vertical distance is 400m. It is assumed that the sampling rate of the optically pumped magnetometer carried by the aircraft is 10Hz.

[0123] Assume that the magnetic field signal collected by the optical pump magnetometer is a signal with a power spectrum density of 1 / f after bandpass filtering. α The colored noise of (α=1.2) has a sampling duration of 120s. The time domain distribution of the colored noise is shown in Figure 2 As shown, draw the distribution histogram of the measurement noise, such as Figure 3 As shown in Figure 2, the distribution histogram shows that the colored noise is a non-Gaussian distribution. If the distribution is directly calculated using equations (10) and (11), deviations will occur. Therefore, the efficiency is weakened when information entropy is directly used for detection.

[0124] The magnetic anomaly signal of the target is calculated by the magnetic dipole formula (15), and then the generated colored noise signal is superimposed. Figure 4 It is a time domain diagram of the measured magnetic field sequence with the target magnetic anomaly superimposed on the measurement noise. The whitening filtering method proposed in the present invention is used to perform whitening filtering on the original measurement sequence. The order of the AR model is selected as 5, and a period of background noise data with a time length of 12s is selected to calculate the whitening filtering coefficient using formula (8). After the calculation is completed, the measured magnetic field sequence is whitened and filtered using formula (9). The filtering result is as follows: Figure 5 As shown in the figure, the distribution of the magnetic field after whitening filtering is statistically analyzed by histogram. The results are as follows Figure 6 As shown, it can be seen that the magnetic field distribution after whitening filtering approximately obeys the Gaussian distribution. Therefore, the mean calculation formula (10) and variance calculation formula (11) in the Gaussian distribution can be used to calculate the relevant parameters, and then the Gaussian distribution function of the magnetic field after whitening is obtained. Then, according to the calculation formula of information entropy, the number of measurement points of the sliding window of magnetic anomaly detection is 50, and the information entropy value of the magnetic field after whitening is calculated. After calculation, the signal-to-noise ratio of the original signal is 9.23dB, and the signal-to-noise ratio can be obtained by directly performing information entropy detection on the original signal. The information entropy signal-to-noise ratio after whitening filtering of the original magnetic field is 16.02dB, which can improve the signal-to-noise ratio by 5.8dB. Therefore, the magnetic anomaly signal detection method combining whitening filtering and information entropy proposed in the present invention can be applied to the detection of magnetic anomaly signals under non-Gaussian distribution colored noise conditions, which can significantly improve the signal-to-noise ratio of magnetic anomaly signals and improve detection efficiency.

Claims

1. A magnetic anomaly signal detection method based on whitening filtering combined with information entropy, characterized in that: The following steps are involved: Collecting magnetic field data, where the magnetic field data is used to obtain magnetic anomaly signals, wherein the magnetic field data has non-Gaussian distribution and colored noise; Constructing an AR autoregressive model, wherein the AR autoregressive model is used to whiten the colored noise of the magnetic field data; Based on the AR autoregressive model, performing the whitening process on the magnetic field data; Acquire information entropy according to the whitened magnetic field data, and acquire the magnetic anomaly signal according to the information entropy; In the process of constructing the AR autoregressive model, the first expression of the magnetic field measurement sequence of the magnetic field data is: Where x(n) is the magnetic field measurement sequence, w(n) is Gaussian white noise, P represents the first P sampling points, a k is the model coefficient; In the process of constructing the AR autoregressive model, both ends of the first expression are multiplied by x(nm) to obtain a second expression, which is: The second expression is simplified into a third expression, which is: in, During the whitening process, When m>0, the third expression is: When m = 0, the variance of white noise is According to the third expression and the variance of the white noise, a fourth expression is obtained, and the fourth expression is used to calculate the model coefficient of the P-order AR autoregressive model. The fourth expression is:

2. According to claim 1, a method for detecting magnetic abnormality signals based on the combination of whitening filtering and information entropy, characterized in that: According to the fourth expression and the first expression, the AR autoregressive model is constructed, and the AR autoregressive model is: Among them, a0=1.

3. According to claim 2, a magnetic abnormal signal detection method based on whitening filtering combined with information entropy is characterized in that: In the process of obtaining the information entropy of the background noise, the number of measurement points of the sliding window of the magnetic field detection is L, and the information entropy of the sliding window is: Among them, I(y i ) is information entropy, y i is the magnetic field value after whitening filtering, p(y n ) represents the probability density function of the magnetic field value after filtering.

4. According to claim 3, a method for detecting magnetic abnormality signals based on the combination of whitening filtering and information entropy, characterized in that: In the process of obtaining the information entropy of the background noise, the mean μ and variance σ of the whitened magnetic field data are extracted. 2 , get the probability density function of Gaussian distribution; The mean μ is: The variance σ 2 for Where M is the number of sampling points; The probability density function is: According to the probability density function, y i The probability is:

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