A 3D underwater electric field source localization method based on cross-array arrival angle estimation

Abstract

The present invention discloses a 3D underwater electric field source positioning method based on cross array arrival angle estimation, which belongs to the field of electromagnetic positioning detection. The steps of this method include: setting two groups of receiving electrode arrays to obtain the noise subspaces of the X-axis array signal and the Y-axis array signal, constructing a first spatial spectrum function of the signal source rotating around the X-axis and a second spatial spectrum function of the signal source rotating around the Y-axis, performing a two-dimensional search based on the first spatial spectrum function and the second spatial spectrum function, and then solving the search results based on the rotation mapping relationship in the spatial coordinate system to obtain the 3D coordinate result of the signal source. According to the array symmetry and matrix operation invariance, the present invention proposes a processing method for estimating the hypothetical arrival angle around the axis based on the cross array, converts the three-dimensional space search into two two-dimensional plane searches, and simplifies the direction of the dipole moment, thereby realizing the rapid and accurate positioning of the near-field space signal source.

Description

Technical Field

[0001] The invention belongs to the field of electromagnetic positioning detection, and in particular relates to an electric field source positioning method. Background Art

[0002] With the continuous development of the marine engineering field, underwater target detection and positioning technology has been widely concerned due to its indispensable leading role in resource development and positioning guidance. Compared with other positioning technologies (such as acoustic and optical positioning technologies), underwater electric field positioning technology has strong anti-interference ability, high accuracy, and fast signal propagation. It has incomparable advantages in actual high-precision short-range positioning scenarios and is widely used in navigation positioning, resource exploration, and unmanned cluster obstacle avoidance and communication.

[0003] However, due to the attenuation of high-frequency signals by the ocean medium, the signal reaching each sensor in the electrode array is no longer a plane wave, which means that the underwater target positioning problem is actually a near-field signal source positioning problem. At the same time, the signal received by each electrode sensor is a nonlinear function of the position, and many traditional positioning algorithms cannot be directly applied to underwater target parameter estimation. Furthermore, underwater electric field signals have polarization characteristics, and the signal form changes with the direction of the source. The above factors transform the original three-dimensional (3D) spatial parameter estimation of the target into a six-dimensional (6D) parameter estimation, which greatly increases the difficulty of solving and the amount of calculation, resulting in slow positioning speed and low accuracy. Summary of the invention

[0004] The present invention proposes a 3D underwater electric field source positioning method based on cross array arrival angle estimation, the purpose of which is to solve the problems of slow positioning speed and low accuracy in traditional methods.

[0005] The technical solution of the present invention is as follows:

[0006] A 3D underwater electric field source positioning method based on cross array arrival angle estimation, comprising the steps of:

[0007] Step 1, respectively setting a set of receiving electrode arrays on the X-axis and Y-axis of the spatial rectangular coordinate system, and the two sets of receiving electrode arrays are vertically crossed at the midpoint; respectively collecting the X-axis array signal and the Y-axis array signal of the signal source through the two sets of receiving electrode arrays;

[0008] Step 2, respectively calculating the covariance matrices of the X-axis array signal and the Y-axis array signal, and performing eigenvalue decomposition on the two covariance matrices to obtain the noise subspaces of the X-axis array signal and the Y-axis array signal;

[0009] Step 3, constructing a first spatial spectrum function of the signal source rotating around the X-axis and a second spatial spectrum function of the signal source rotating around the Y-axis;

[0010] Step 4: Perform a two-dimensional search based on the first spatial spectrum function to find a first imaginary angle estimation value and a first target distance corresponding to the spatial spectrum peak value, wherein the first imaginary angle estimation value refers to an imaginary angle of rotation of the signal source around the X-axis when the peak value of the first spatial spectrum function appears; perform a two-dimensional search based on the second spatial spectrum function to find a second imaginary angle estimation value and a second target distance corresponding to the spatial spectrum peak value; and determine the quadrant in which the signal source is located based on the first imaginary angle estimation value and the second imaginary angle estimation value;

[0011] Step 5: According to the rotation mapping relationship in the spatial coordinate system, the 3D coordinate result of the signal source is obtained based on the first imaginary angle estimation value, the first target distance, the second imaginary angle estimation value and the second target distance.

[0012] As a further improvement of the 3D underwater electric field source localization method based on cross array arrival angle estimation: there are two coordinates on both sides of the origin of the X-axis: There are electrodes on both sides of the coordinate origin on the Y axis. The X-axis and Y-axis share the electrode at the origin O of the coordinate system.

[0013] As a further improvement of the 3D underwater electric field source localization method based on cross array arrival angle estimation, the specific method of obtaining the noise subspace in step 2 is: assuming that the X-axis array signal is , the Y-axis array signal is , then the corresponding covariance matrices are: , , is the number of data sampling points, is the conjugate transpose operation;

[0014] Covariance matrix and Perform eigenvalue decomposition respectively. For any covariance matrix, let the number of electrodes of the corresponding receiving electrode array be , the number of signal sources is , then the eigenvalues ​​obtained are arranged in descending order as follows: , Sort by descending order eigenvalues, and the following The matrix composed of the eigenvectors corresponding to the eigenvalues ​​is taken as the noise subspace corresponding to the covariance matrix.

[0015] As a further improvement of the 3D underwater electric field source localization method based on cross array arrival angle estimation, the first spatial spectrum function in step 3 and the second spatial spectrum function They are:

[0016] ;

[0017] ;

[0018] in, is the distance between the signal source and the origin of the coordinate system when the imaginary signal source rotates around the X-axis, is the rotation angle of the imaginary signal source when it rotates around the X axis to the XOY plane, is the distance between the signal source and the origin of the coordinate system when the imaginary signal source rotates around the Y axis, is the rotation angle of the imaginary signal source when it rotates around the Y axis to the XOY plane; is the zenith angle of the signal source, is the direction vector of the signal source dipole moment vector, For the XOY plane A vector space of uniformly sampled orientations, and are the array manifolds of the receiving electrode arrays on the X-axis and Y-axis respectively, and They are the noise subspaces corresponding to the X-axis array signal and the Y-axis array signal respectively.

[0019] As a further improvement of the 3D underwater electric field source localization method based on cross array arrival angle estimation:

[0020] Array manifold of the X-axis receiving electrode array for:

[0021] ;

[0022] Assume that there are If there are electrodes, then the number ;in, The electrode positions in the receiving electrode array on the X-axis are numbered The amplitude factor of the electrode relative to the electrode at the origin of the coordinate system, ,in is the phase constant, is the signal source frequency, and are the magnetic permeability and electrical conductivity of seawater, Number the signal source on the X-axis The distance between electrodes, is the distance from the signal source to the electrode at the origin of the coordinate system; The electrode positions in the receiving electrode array on the X-axis are numbered The direction factor vector of the electrode, ,in , , is the X-axis unit direction vector, is the unit direction vector of the signal source dipole moment, The electrode positions in the receiving electrode array on the X-axis from the signal source are numbered as The unit direction vector of the electrode, is the transpose operation; The electrode positions in the receiving electrode array on the X-axis are numbered The phase factor vector of the electrode, ,in , is an imaginary unit; The electrode positions in the receiving electrode array on the X-axis from the signal source are numbered as The distance between the electrode and the distance between the signal source and the electrode at the origin of the coordinate system The difference between the two;

[0023] Array manifold of the Y-axis receiving electrode array for:

[0024] ;

[0025] Assume that there are electrodes, then ;in, The electrode positions in the receiving electrode array on the Y axis are numbered The amplitude factor of the electrode relative to the electrode at the origin of the coordinate system, , Number the signal source on the Y axis The distance between the electrodes; The electrode positions in the receiving electrode array on the Y axis are numbered The direction factor vector of the electrode, ,in , , is the unit direction vector of the Y axis, The electrode positions in the receiving electrode array on the Y axis are numbered as The unit direction vector of the electrode; The electrode positions in the receiving electrode array on the Y axis are numbered The phase factor vector of the electrodes, ,in , is an imaginary unit; The electrode positions in the receiving electrode array on the Y axis are numbered as The distance between the electrode and the distance between the signal source and the electrode at the origin of the coordinate system The difference between the two.

[0026] As a further improvement of the 3D underwater electric field source localization method based on cross array arrival angle estimation, the specific search method in step 4 is: respectively set the first target distance Distance to second target The distance sampling interval, the first hypothetical angle estimate and the second hypothetical angle estimate The angular sampling interval and the direction vector of the signal source dipole moment vector The sampling interval of

[0027] According to the following formula, a two-dimensional search is performed based on the first spatial spectrum function to find the spectrum peak in the first spatial spectrum function. The distance and imaginary angle corresponding to the spectrum peak are the first target distance and the first imaginary angle estimate :

[0028] ;

[0029] According to the following formula, a two-dimensional search is performed based on the second spatial spectrum function to find the spectrum peak in the second spatial spectrum function. The distance and imaginary angle corresponding to the spectrum peak are the second target distance and the second hypothetical angle estimate :

[0030] .

[0031] As a further improvement of the 3D underwater electric field source positioning method based on cross-array arrival angle estimation, in step 4, when two spectral peaks appear in the two-dimensional search of a certain spatial spectrum function, the quadrant where the spectral peaks in the two search results appear simultaneously is taken as the actual quadrant where the signal source is located.

[0032] As a further improvement of the 3D underwater electric field source localization method based on cross array arrival angle estimation, in step 5, the 3D coordinate result is calculated as follows:

[0033] Radial distance ;

[0034] Zenith angle ;

[0035] Azimuth ;

[0036] in, , , and are the first target distance and the second target distance respectively, and are the first imaginary angle estimation value and the second imaginary angle estimation value respectively.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] According to the array symmetry and matrix operation invariance, the present invention proposes a processing method for estimating the hypothetical around-axis arrival angle based on a cross array, converts the three-dimensional space search into two two-dimensional plane searches, and simplifies the dipole moment direction, thereby realizing fast and accurate positioning of near-field spatial signal sources. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 This is the corresponding relationship diagram of the cross array rotation around the axis. is the direction vector of the signal source dipole moment, is the direction vector of the signal source position, and They are and Rotation angle around the X axis The direction vector obtained when the signal source reaches the XOY plane, and They are and Rotation angle around the Y axis The direction vector obtained when the signal source reaches the XOY plane;

[0040] Figure 2 It is a two-dimensional spectrum peak diagram obtained by assuming that DOA estimation is performed around the X-axis when the signal-to-noise ratio is 30dB in a specific implementation manner;

[0041] Figure 3 It is a two-dimensional spectrum peak diagram obtained by assuming that DOA estimation is performed around the X-axis when the signal-to-noise ratio is 20dB in a specific implementation manner;

[0042] Figure 4 It is a two-dimensional spectrum peak diagram obtained by assuming that DOA estimation is performed around the X-axis when the signal-to-noise ratio is 10dB in a specific implementation manner;

[0043] Figure 5 It is a two-dimensional spectrum peak diagram obtained by assuming that DOA estimation is performed around the Y axis when the signal-to-noise ratio is 30 dB in a specific implementation manner;

[0044] Figure 6 It is a two-dimensional spectrum peak diagram obtained by assuming that DOA estimation is performed around the Y axis when the signal-to-noise ratio is 20 dB in a specific implementation manner;

[0045] Figure 7 It is a two-dimensional spectrum peak diagram obtained by assuming that DOA estimation is performed around the Y axis when the signal-to-noise ratio is 10 dB in a specific implementation manner;

[0046] Figure 8It is a azimuth spatial spectrum slice diagram of the hypothetical DOA estimation around the X-axis at different signal-to-noise ratios when the distance is 70m in a specific implementation method;

[0047] Fig. 9 It is a range space spectrum section diagram of the hypothetical DOA estimation around the X-axis under different signal-to-noise ratios when the azimuth angle is 115.5° in a specific implementation manner;

[0048] Fig.10 It is a azimuth spatial spectrum slice diagram of the hypothetical DOA estimation around the Y axis at different signal-to-noise ratios when the distance is 70m in a specific implementation manner;

[0049] Fig.11 It is a range space spectrum slice diagram of the imaginary DOA estimation around the Y axis under different signal-to-noise ratios when the azimuth angle is 131.5° in a specific implementation manner;

[0050] Fig.12 It is a scatter plot of the distribution of zenith angle and azimuth angle under different signal-to-noise ratios in a specific implementation manner. DETAILED DESCRIPTION

[0051] The technical solution of the present invention is described in detail below in conjunction with the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments.

[0052] A 3D underwater electric field source positioning method based on cross array arrival angle estimation, comprising the steps of:

[0053] Step 1: Set a set of receiving electrode arrays on the X-axis and Y-axis of the spatial rectangular coordinate system, respectively, and the two sets of receiving electrode arrays are vertically crossed at the midpoint. The X-axis array signal and the Y-axis array signal of the signal source are respectively collected by the two sets of receiving electrode arrays.

[0054] In this embodiment, Figure 1 The number of electrodes in the two groups of receiving electrode arrays placed vertically and symmetrically is 41, of which 21 are arranged in the X-axis direction and 21 are arranged in the Y-axis direction, and the two share the center point O electrode.

[0055] Step 2: Calculate the covariance matrices of the X-axis array signal and the Y-axis array signal respectively, and perform eigenvalue decomposition on the two covariance matrices respectively to obtain the noise subspaces of the X-axis array signal and the Y-axis array signal respectively.

[0056] Specifically, let the X-axis array signal be , the Y-axis array signal is , then the corresponding covariance matrices are: , , is the number of data sampling points, is the conjugate transpose operation.

[0057] Covariance matrix and Perform eigenvalue decomposition respectively. For any covariance matrix, let the number of electrodes of the corresponding receiving electrode array be , the number of signal sources is , then the eigenvalues ​​obtained are arranged in descending order as follows: , Sort by descending order eigenvalues, and the following The matrix composed of the eigenvectors corresponding to the eigenvalues ​​is used as the noise subspace corresponding to the covariance matrix. In this embodiment, the noise subspaces corresponding to the X-axis array signal and the Y-axis array signal are respectively recorded as and .

[0058] Step 3: construct a first spatial spectrum function of the signal source rotating around the X-axis and a second spatial spectrum function of the signal source rotating around the Y-axis.

[0059] Specifically, the first spatial spectrum function and the second spatial spectrum function They are:

[0060] ;

[0061] ;

[0062] in, is the distance between the signal source and the origin of the coordinate system when the imaginary signal source rotates around the X-axis, is the rotation angle of the imaginary signal source when it rotates around the X axis to the XOY plane, is the distance between the signal source and the origin of the coordinate system when the imaginary signal source rotates around the Y axis, It is the rotation angle of the imaginary signal source when it rotates around the Y axis to the XOY plane. is the zenith angle of the signal source, is the direction vector of the signal source dipole moment vector, For the XOY plane A vector space of uniformly sampled orientations, and are the array manifolds of the receiving electrode arrays on the X-axis and Y-axis respectively, and They are the noise subspaces corresponding to the X-axis array signal and the Y-axis array signal respectively.

[0063] Array manifold of the X-axis receiving electrode array for:

[0064] ;

[0065] Assume that there are If there are electrodes, then the number ;in, The electrode positions in the receiving electrode array on the X-axis are numbered The amplitude factor of the electrode relative to the electrode at the origin of the coordinate system, ,in is the phase constant, is the signal source frequency, and are the magnetic permeability and electrical conductivity of seawater, Number the signal source on the X-axis The distance between electrodes, is the distance from the signal source to the electrode at the origin of the coordinate system; The electrode positions in the receiving electrode array on the X-axis are numbered The direction factor vector of the electrode, ,in , , is the X-axis unit direction vector, is the unit direction vector of the signal source dipole moment, The electrode positions in the receiving electrode array on the X-axis from the signal source are numbered as The unit direction vector of the electrode, is the transpose operation; The electrode positions in the receiving electrode array on the X-axis are numbered The phase factor vector of the electrodes, ,in , is an imaginary unit; The electrode positions in the receiving electrode array on the X-axis from the signal source are numbered as The distance between the electrode and the distance between the signal source and the electrode at the origin of the coordinate system The difference between the two.

[0066] Similarly, the array manifold of the Y-axis receiving electrode array for:

[0067] ;

[0068] Assume that there are If there are electrodes, then the number ;in, The electrode positions in the receiving electrode array on the Y axis are numbered The amplitude factor of the electrode relative to the electrode at the origin of the coordinate system, , Number the signal source on the Y axis The distance between the electrodes; The electrode positions in the receiving electrode array on the Y axis are numbered The direction factor vector of the electrode, ,in , is the unit direction vector of the Y axis, The electrode positions in the receiving electrode array on the Y axis are numbered as The unit direction vector of the electrode; The electrode positions in the receiving electrode array on the Y axis are numbered The phase factor vector of the electrodes, ,in , is an imaginary unit; The electrode positions in the receiving electrode array on the Y axis are numbered as The distance between the electrode and the distance between the signal source and the electrode at the origin of the coordinate system The meanings of other symbolic variables are consistent with the corresponding symbolic variables in the X-axis receiving electrode array manifold.

[0069] The first spatial spectrum function and the second spatial spectrum function Built on the following principles:

[0070] First, the calculation formula of the voltage signal of each electrode can be derived based on the electric field propagation formula of the electric dipole infinite conductive medium. By removing the same term in the voltage signal formula of each electrode, which is the function of the attenuation of the signal propagation path, the voltage signal along the electrode can be obtained. Array manifold of axially aligned electrodes And along Array manifold of axially aligned electrodes , and the array manifold is only related to the structural arrangement of the receiving array, the signal frequency, etc., and has nothing to do with the dipole source related parameters. The array manifold calculation formula here is common knowledge in the field and will not be elaborated.

[0071] Then, based on the array symmetry and matrix operation invariance, the above array manifold is reduced in dimension and simplified:

[0072] In the above array manifold, there exists and Here it is assumed that and The vectors obtained by rotating around the X-axis by a certain angle are and According to the properties of matrix rotation operations, the sensor signal operations arranged along the X-axis have the following equivalent relationship:

[0073] ;

[0074] ;

[0075] in, is the unit vector in the positive direction of the X-axis. That is, after the signal source rotates around the X-axis by an angle, the array manifold remains unchanged from the original position array manifold operation, and is not transferred by the spatial position. In this way, the signal source can be rotated around the X-axis by an appropriate angle to the corresponding position on the XOY plane, and the array manifolds of the signals received at the two positions are the same and equivalent.

[0076] Similarly, assuming and The vectors obtained by rotating around the Y axis by a certain angle are and , the superscript y represents the rotation around the X-axis. The array manifold of the sensor signal arranged along the Y-axis also satisfies a similar equivalence relationship:

[0077] ;

[0078] ;

[0079] in, is the unit vector in the positive direction of the Y axis. Obviously, the signal source can be equivalent to the corresponding position of the XOY plane after rotating around the Y axis at an appropriate angle, and the array manifolds of the signals received at the two positions are the same and equivalent.

[0080] Furthermore, during the rotation of the signal source around the X-axis and the Y-axis, the Z-axis dipole moment component always contributes to the coordinate axis arrangement signal to be 0. Assuming that the Z-axis dipole moment component The vectors obtained by rotating around the X-axis and the Y-axis by a certain angle are and :

[0081] ;

[0082] ;

[0083] ;

[0084] ;

[0085] It can be seen that when the signal source is rotated around the X-axis and Y-axis to the XOY plane, the array manifold operation relationship of the X-axis and Y-axis remains unchanged. At the same time, the Z-direction component of the dipole moment with a contribution of 0 can be ignored. The signal source can be rotated around the axis and then equivalently searched on the XOY plane to simplify the search dimension. At this time, there is a zenith angle π / 2. Finally, the orthogonal relationship between the noise eigenvector and the signal direction vector is used, combined with the equivalent relationship between the simplified array manifold and the signal source after rotation around the axis, to obtain the first spatial spectrum function and the second spatial spectrum function.

[0086] Step 4: Perform a two-dimensional search based on the first spatial spectrum function to find the first imaginary angle estimation value and the first target distance corresponding to the peak value of the spatial spectrum, wherein the first imaginary angle estimation value refers to the imaginary angle of rotation of the signal source around the X-axis when the peak value of the first spatial spectrum function appears; perform a two-dimensional search based on the second spatial spectrum function to find the second imaginary angle estimation value and the second target distance corresponding to the peak value of the spatial spectrum. Determine the quadrant in which the signal source is located based on the first imaginary angle estimation value and the second imaginary angle estimation value.

[0087] Specifically, the first target distance is set respectively Distance to second target The distance sampling interval, the first hypothetical angle estimate and the second hypothetical angle estimate The angular sampling interval and the direction vector of the signal source dipole moment vector The sampling interval.

[0088] According to the following formula, a two-dimensional search is performed based on the first spatial spectrum function to find the spectrum peak in the first spatial spectrum function. The distance and imaginary angle corresponding to the spectrum peak are the first target distance and the first imaginary angle estimate :

[0089] .

[0090] According to the following formula, a two-dimensional search is performed based on the second spatial spectrum function to find the spectrum peak in the second spatial spectrum function. The distance and imaginary angle corresponding to the spectrum peak are the second target distance and the second hypothetical angle estimate :

[0091] .

[0092] Since the sine function is Range and cosine function in Due to the symmetry and same-sign characteristics, there may be two spectrum peaks in the two-dimensional search of a certain spatial spectrum function (complementary azimuths and equal distances). In this case, the quadrant where the spectrum peak searched by the other spatial spectrum function is located should be determined, and the quadrant where the spectrum peaks in the two search results appear at the same time should be regarded as the actual quadrant where the signal source is located.

[0093] Step 5: According to the rotation mapping relationship in the spatial coordinate system, the 3D coordinate result of the signal source is obtained based on the first imaginary angle estimation value, the first target distance, the second imaginary angle estimation value and the second target distance.

[0094] The 3D coordinate results include:

[0095] Radial distance ;

[0096] Zenith angle ;

[0097] Azimuth ;

[0098] in, , , and are the first target distance and the second target distance respectively, and are the first imaginary angle estimation value and the second imaginary angle estimation value respectively.

[0099] The following comparative experiments verify the effectiveness and superiority of this method:

[0100] use Figure 1 The cross-array electrode sensor shown detects an electric dipole source. Spatial location of the electric dipole source Set to , the dipole moment vector Set to , dipole moment strength Set to , the signal frequency is set to 100 Hz, the number of snapshots is set to 600, and the conductivity of the seawater medium is Set to S / m Seawater medium magnetic permeability Set to 1. In actual estimation, the relevant parameters of the electric dipole source are unknown, but other parameters are known.

[0101] Table 1 - Experimental results at different signal-to-noise ratios.

[0102]

[0103] As shown in Table 1, this method can obtain relatively accurate distance and angle values ​​under different signal-to-noise ratios, and the positioning error meets the requirements.

[0104] It should be noted that Figures 2 to 4 There is only one peak position (dark red) in the spectrum, while Figures 5 to 7There are two peak positions under different signal-to-noise ratios. This is because the Y-axis coordinate is a sin function relationship. In the range of 0~2π, the sin function has a symmetrical and equal-sign characteristic, so there are two peaks with equal amplitudes and complementary azimuth angles in the DOA diagram around the Y axis. At this time, combined with the judgment that the DOA estimation around the X axis only appears in the second quadrant, the DOA estimation around the Y axis takes the second quadrant angle.

[0105] like Figures 8 to 11 In the true distance section diagram, the spectrum peaks are obtained at the azimuth angles around the real position, a single peak is obtained around the X axis, and a double peak is obtained around the Y axis. In the true position azimuth angle section diagram around the axis, the spectrum peak appears at the true distance. In summary, the positioning effect of the present invention is good and accurate.

[0106] like Fig.12 The estimated angular position is relatively centralized and accurate, and the estimation error is kept within ±1°, which shows that in the near-field three-dimensional positioning scenario, the accuracy is high and relatively stable, and it can be well applied in practical engineering.

[0107] It should be noted that it is obvious to those skilled in the art that the present invention is not limited to the details of the above exemplary embodiments, and that the present invention can be implemented in other specific forms without departing from the spirit or essential features of the present invention. The scope of the present invention is defined by the claims rather than the above description.

Claims

1. A 3D underwater electric field source localization method based on cross array arrival angle estimation, characterized in that the steps include: Step 1, respectively setting a set of receiving electrode arrays on the X-axis and Y-axis of the spatial rectangular coordinate system, and the two sets of receiving electrode arrays cross vertically at the midpoint; The X-axis array signal and the Y-axis array signal of the signal source are respectively collected by two groups of receiving electrode arrays; Step 2, respectively calculating the covariance matrices of the X-axis array signal and the Y-axis array signal, and performing eigenvalue decomposition on the two covariance matrices to obtain the noise subspaces of the X-axis array signal and the Y-axis array signal; Step 3, constructing a first spatial spectrum function of the signal source rotating around the X-axis and a second spatial spectrum function of the signal source rotating around the Y-axis; The first spatial spectrum function in step 3 and the second spatial spectrum function They are: ； ； in, is the distance between the signal source and the origin of the coordinate system when the imaginary signal source rotates around the X-axis, is the rotation angle of the imaginary signal source when it rotates around the X axis to the XOY plane, is the distance between the signal source and the origin of the coordinate system when the imaginary signal source rotates around the Y axis, is the rotation angle of the imaginary signal source when it rotates around the Y axis to the XOY plane; is the zenith angle of the signal source, is the direction vector of the signal source dipole moment vector, For the XOY plane A vector space of uniformly sampled orientations, and are the array manifolds of the receiving electrode arrays on the X-axis and Y-axis respectively, and are the noise subspaces corresponding to the X-axis array signal and the Y-axis array signal respectively; Array manifold of the X-axis receiving electrode array for: ； Assume that there are If there are electrodes, then the number ;in, The electrode positions in the receiving electrode array on the X-axis are numbered The amplitude factor of the electrode relative to the electrode at the origin of the coordinate system, ,in is the phase constant, is the signal source frequency, and are the magnetic permeability and electrical conductivity of seawater, Number the signal source on the X-axis The distance between electrodes, is the distance from the signal source to the electrode at the origin of the coordinate system; The electrode positions in the receiving electrode array on the X-axis are numbered The direction factor vector of the electrode, ,in , , is the X-axis unit direction vector, is the unit direction vector of the signal source dipole moment, The electrode positions in the receiving electrode array on the X-axis from the signal source are numbered as The unit direction vector of the electrode, is the transpose operation; The electrode positions in the receiving electrode array on the X-axis are numbered The phase factor vector of the electrodes, ,in , is an imaginary unit; The electrode positions in the receiving electrode array on the X-axis from the signal source are numbered as The distance between the electrode and the distance between the signal source and the electrode at the origin of the coordinate system The difference between the two; Array manifold of the Y-axis receiving electrode array for: ； Assume that there are electrodes, then ;in, The electrode positions in the receiving electrode array on the Y axis are numbered The amplitude factor of the electrode relative to the electrode at the origin of the coordinate system, , Number the signal source on the Y axis The distance between the electrodes; The electrode positions in the receiving electrode array on the Y axis are numbered The direction factor vector of the electrode, ,in , , is the unit direction vector of the Y axis, The electrode positions in the receiving electrode array on the Y axis are numbered as The unit direction vector of the electrode; The electrode positions in the receiving electrode array on the Y axis are numbered The phase factor vector of the electrodes, ,in , is an imaginary unit; The electrode positions in the receiving electrode array on the Y axis are numbered as The distance between the electrode and the distance between the signal source and the electrode at the origin of the coordinate system The difference between the two; Step 4: Perform a two-dimensional search based on the first spatial spectrum function to find a first imaginary angle estimation value and a first target distance corresponding to the spatial spectrum peak value, wherein the first imaginary angle estimation value refers to an imaginary angle of rotation of the signal source around the X-axis when the peak value of the first spatial spectrum function appears; perform a two-dimensional search based on the second spatial spectrum function to find a second imaginary angle estimation value and a second target distance corresponding to the spatial spectrum peak value; and determine the quadrant in which the signal source is located based on the first imaginary angle estimation value and the second imaginary angle estimation value; Step 5: According to the rotation mapping relationship in the spatial coordinate system, the 3D coordinate result of the signal source is obtained based on the first imaginary angle estimation value, the first target distance, the second imaginary angle estimation value and the second target distance.

2. The 3D underwater electric field source localization method based on cross array arrival angle estimation according to claim 1, characterized in that: There are two coordinates on both sides of the origin of the X-axis. There are electrodes on both sides of the coordinate origin on the Y axis. The X-axis and Y-axis share the electrode at the origin O of the coordinate system.

3. The 3D underwater electric field source localization method based on cross array arrival angle estimation according to claim 1, characterized in that: The specific method of obtaining the noise subspace in step 2 is: assuming that the X-axis array signal is , the Y-axis array signal is , then the corresponding covariance matrices are: , , is the number of data sampling points, is the conjugate transpose operation; Covariance matrix and Perform eigenvalue decomposition respectively. For any covariance matrix, let the number of electrodes of the corresponding receiving electrode array be , the number of signal sources is , then the eigenvalues ​​obtained are arranged in descending order as follows: , In descending order eigenvalues, and the following The matrix composed of the eigenvectors corresponding to the eigenvalues ​​is taken as the noise subspace corresponding to the covariance matrix.

4. The 3D underwater electric field source localization method based on cross array arrival angle estimation according to claim 1, characterized in that: The specific search method in step 4 is: set the first target distance respectively Distance to second target The distance sampling interval, the first hypothetical angle estimate and the second hypothetical angle estimate The angular sampling interval and the direction vector of the signal source dipole moment vector The sampling interval of According to the following formula, a two-dimensional search is performed based on the first spatial spectrum function to find the spectrum peak in the first spatial spectrum function. The distance and imaginary angle corresponding to the spectrum peak are the first target distance and the first imaginary angle estimate : ； According to the following formula, a two-dimensional search is performed based on the second spatial spectrum function to find the spectrum peak in the second spatial spectrum function. The distance and imaginary angle corresponding to the spectrum peak are the second target distance and the second hypothetical angle estimate : 。 5. The 3D underwater electric field source localization method based on cross array arrival angle estimation according to claim 1, characterized in that: In step 4, when two spectrum peaks appear in the two-dimensional search of a certain spatial spectrum function, the quadrant where the spectrum peaks in the two search results appear simultaneously is taken as the actual quadrant where the signal source is located.

6. The 3D underwater electric field source localization method based on cross array arrival angle estimation according to claim 1, characterized in that: In step 5, the 3D coordinate results are calculated as follows: Radial distance ; Zenith angle ; Azimuth ; in, , , and are the first target distance and the second target distance respectively, and are the first imaginary angle estimation value and the second imaginary angle estimation value respectively.

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