Very high frequency broadband radiation source positioning method based on energy weighted subspace fitting

Abstract

The invention discloses a very high frequency broadband radiation source positioning method based on energy weighted subspace fitting, and relates to the technical field of signal processing and radiation source imaging, and the method comprises the steps: carrying out the DFT processing of a lightning very high frequency broadband signal collected by an array, and obtaining any narrowband component; then characteristic decomposition is carried out on covariance matrixes of X-axis and Y-axis sub-arrays according to array receiving signals, main characteristic vectors are taken as signal sub-spaces, in order to emphasize the signal sub-spaces with higher energy, characteristic values are used for weighting, weighted signal sub-spaces are constructed, then the signal sub-spaces are fitted by using a least square method, and the signal sub-spaces with higher energy are obtained; the method comprises the following steps: further constructing a sub-band energy weighted spatial spectrum adapted to a very high frequency broadband signal, then carrying out spectrum peak search on the weighted spatial spectrum to obtain a spatial angle of a spectrum peak, and finally calculating the direction of arrival of a radiation source according to a spatial angle relation to obtain an azimuth angle and an elevation angle. According to the invention, aiming at a lightning very-high-frequency weak radiation source positioning problem, a lightning channel can be inverted more clearly.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of signal processing and radiation source positioning, in particular to a very high frequency broadband radiation source positioning method based on energy weighted subspace fitting. BACKGROUND

[0002] The lightning imaging method is an important support for the research of lightning science and protection. Lightning imaging is a technology that remotely measures electromagnetic radiation signals generated by atmospheric discharge through multiple antennas, and inversely calculates the direction or position of the radiation source based on a specific algorithm, thereby generating a two-dimensional or three-dimensional image of lightning activity. Subspace fitting algorithms are also widely used in radar and mobile communication fields. Unlike existing multiple signal classification methods, this method constructs a fitting relationship between a multidimensional array flow matrix and the signal subspace of the array received data, and converts it into a minimization problem, and finally searches for the position of the signal source through spatial spectrum search. This method not only ensures the resolution of the algorithm, but also has the ability to resolve and locate signals coherently. SUMMARY

[0003] In order to overcome the defects in the prior art, the present application provides a very high frequency broadband radiation source positioning method based on energy weighted subspace fitting, which can more clearly invert the lightning channel for lightning very high frequency weak radiation source positioning problems.

[0004] To achieve the above purpose, the technical scheme adopted by the present application is as follows: The very high frequency broadband radiation source positioning method based on energy weighted subspace fitting comprises: S1, receiving lightning very high frequency broadband signals using an L-shaped array, and performing discrete Fourier transform to obtain narrowband components, and constructing observation signals of an X-axis subarray and observation signals of a Y-axis subarray according to the narrowband components; S2, performing eigenvalue decomposition on the observation signals of the X-axis subarray to obtain an X-axis signal subspace, calculating the eigenvalue weight of the X-axis signal subspace, weighting and reconstructing the X-axis signal subspace, solving the residual power of the weighted and reconstructed X-axis signal subspace, and constructing a weighted one-dimensional spatial spectrum function based on the residual power to obtain the estimation value of the spatial angle formed by the radiation source and the X-axis; S3, performing eigenvalue decomposition on the observation signals of the Y-axis subarray to obtain a Y-axis signal subspace, calculating the eigenvalue weight of the Y-axis signal subspace, weighting and reconstructing the Y-axis signal subspace, solving the residual power of the weighted and reconstructed Y-axis signal subspace, and constructing a weighted one-dimensional spatial spectrum function based on the residual power to obtain the estimation value of the spatial angle formed by the radiation source and the Y-axis; S4, according to the spatial angles and the estimated value of the azimuth angle of the radiation source and the elevation angle .

[0005] Preferably, in step S2, the observation signals of the X-axis subarray a covariance matrix is constructed and eigenvalue decomposition is performed to separate the eigenvectors into a signal subspace and a noise subspace, and the specific formula is as follows: ; wherein, is the autocorrelation matrix of the signal, and there are eigenvalues, represents the signal subspace corresponding to the large eigenvalues, represents the noise subspace corresponding to the small eigenvalues, is the noise intensity, is the unit matrix, is the noise power, H represents the conjugate transpose, represents the expectation, is the steering vector of the X-axis subarray, is the observation signal of the X-axis subarray, is the narrowband component, represents time; the eigenvalue weight of the X-axis signal subspace is calculated, and the specific formula is as follows: ; wherein, is the weight corresponding to the eigenvalue; is the eigenvalue; is the dimension of the signal subspace, ; the weighted reconstruction of the X-axis signal subspace is performed by using the eigenvalue weight of the signal subspace, and the specific formula is as follows: ; wherein, is the weighted reconstruction of the X-axis signal subspace.

[0006] Preferably, in step S2, the residual power of the weighted reconstruction of the X-axis signal subspace is solved by using the least square method, and the specific formula is as follows: there is a full-rank matrix such that holds; wherein, is the weighted reconstruction of the X-axis signal subspace, The guide vector for the X-axis subarray; Construct using the least squares method Find the matrix Least squares solution: ;in, Denotes the square of the Frobenius norm. Representation matrix The estimated value; H Indicates conjugate transpose; because , to obtain the matrix The optimal solution: ;in, Indicates the number of elements in the X-axis subarray; The obtained optimal solution Substitution In the middle, calculate the residual of the X-axis subarray. The specific formula is as follows: ; Solving for residual power P That is, residual The square of the Frobenius norm is given by the following formula: ; in, Represents the trace of a matrix; For residual power P The expansion calculation is performed using the following formula: ; in, The energy value of the signal subspace is a constant; The value of varies with the angle, when the steering vector With signal subspace The better the alignment, The larger the value, the more it minimizes the residual power. P Equivalent to maximizing .

[0007] Preferably, in step S2, a weighted one-dimensional spatial spectrum function is constructed for the observation signal of the X-axis subarray, and the specific formula is as follows: ; in, f j The first step after performing a discrete Fourier transform on a VHF broadband lightning signal. j One frequency point; E j For the first j Energy at each frequency point; Etot is the sum of energy of all frequency points; NO.s is the number of frequency points; represents a weighted one-dimensional spatial spectrum function; represents the conjugate transpose of the steering vector of the j th frequency point; represents the signal subspace of the j th frequency point; the least square method is applied to the observation signal of the X-axis subarray to obtain the estimation value of the spatial included angle .

[0008] Preferably, the specific processing manner of step S3 is the same as that of step S2.

[0009] Preferably, the L-shaped array is a non-uniform L-shaped array, and there are 7 antennas, denoted as , wherein the horizontal coordinates of the antennas are , respectively, and the vertical coordinates are all 0, and the antennas constitute an X-axis subarray; the vertical coordinates of the antennas are , respectively, and the horizontal coordinates are all 0, and the antennas constitute a Y-axis subarray. , are proportional coefficients.

[0010] Preferably, step S1 is specifically as follows: discrete Fourier transform is performed on the lightning VHF broadband signal to obtain narrowband components , represents time; the array received signal is written as: ; , wherein , are observation signals of the X-axis and Y-axis subarrays, respectively; is a steering vector of the array; is a Gaussian white noise signal; , are noise signals of the X-axis and Y-axis subarrays, respectively; the steering vector of the array is calculated , , and are steering vectors of the X-axis and Y-axis subarrays, respectively, and the specific formulae are as follows: ; ; , wherein is an imaginary unit; is an angular frequency; is an antenna is a distance between the antenna is a light speed; is a natural constant; is a steering vector of the X-axis subarray; is a steering vector of the Y-axis subarray; and are a first factor and a second factor, respectively; the first factor and the second factor are expressed as follows: ; ; wherein, “ ” represents an identity.

[0011] Preferably, in step S4, according to the estimated values of the spatial included angle and , the estimated value of the first factor is obtained and the estimated value of the second factor is obtained , so as to obtain the azimuth and the elevation of the radiation source: ; .

[0012] The application further provides an electronic device, which comprises a processor, a memory, and a computer program stored on the memory and executable on the processor, wherein the processor implements the energy-weighted subspace fitting-based very high frequency broadband radiation source positioning method when executing the computer program.

[0013] The application further provides a computer program product, which comprises computer programs / instructions, wherein the computer programs / instructions implement the energy-weighted subspace fitting-based very high frequency broadband radiation source positioning method when executed by a processor.

[0014] The application has the following advantages: (1) The application provides the energy-weighted subspace fitting-based very high frequency broadband radiation source positioning method, which can more clearly invert a lightning channel for lightning very high frequency weak radiation source positioning.

[0015] (2) The application adopts a non-uniform L-shaped lightning observation array, thereby improving the imaging accuracy and the anti-fuzzing performance of the system.​

[0016] (3) The present invention uses the energy of each frequency component as a weight for fusion, so that the frequency components with high signal-to-noise ratio and strong energy have a greater weight in DOA (direction of arrival) estimation, while the influence of frequency components with low signal-to-noise ratio and noise pollution is automatically suppressed.

[0017] (4) The present invention adopts a subspace fitting framework instead of the classic subspace orthogonal framework. The subspace fitting finds the steering vector that best matches the entire signal subspace through the least squares criterion. Its statistical performance is better, especially in the case of low signal-to-noise ratio, few snapshots or coherent sources. The estimated variance is usually smaller than that of the MUSIC algorithm. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the non-uniform L-shaped lightning observation array of the present invention.

[0019] Figure 2 This is a schematic diagram of the VHF waveform acquired by the present invention.

[0020] Figure 3 This is a positioning diagram for the present invention.

[0021] Figure 4 Comparison chart of 1D-MUSIC positioning results.

[0022] Figure 5 This is a flowchart of the VHF broadband radiation source localization method based on energy-weighted subspace fitting according to the present invention. Detailed Implementation

[0023] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] This invention employs a non-uniform L-shaped lightning observation array structure, as shown in the specific array diagram below. Figure 1 As shown, and in Figure 1 The diagram illustrates the azimuth of the lightning radiation source. Angle of elevation and spatial angle and Definition; Spatial Angle and This refers to the spatial angles between the radiation source and the X-axis and Y-axis, respectively. The array is L-shaped in the XOY plane, where the X-axis is due south and the Y-axis is due east. There are 4 antennas on each of the X and Y axes (including the antenna at the origin), for a total of 7 antennas, denoted as . The antennas arranged on the X axis have the horizontal coordinates in turn , and the vertical coordinates are all 0, and the antennas form an X axis subarray. The antennas on the Y axis are arranged in the same way as the antennas on the X axis, the vertical coordinates of the antennas arranged on the Y axis have the horizontal coordinates in turn , and the vertical coordinates are all 0, and the antennas form a Y axis subarray.

[0025] As shown in Figure 2 , it is a schematic diagram of a very high frequency waveform collected by the non-uniform L-shaped lightning observation array of the application.

[0026] The very high frequency broadband radiation source positioning method based on energy weighted subspace fitting of the application firstly performs DFT (Discrete Fourier Transform) processing on the lightning very high frequency broadband signals collected by the array to obtain any narrowband component, then performs eigenvalue decomposition on the covariance matrices of the X axis and Y axis subarrays according to the array received signals, respectively, takes the main eigenvectors as the signal subspace, in order to emphasize the signal subspace with stronger energy, uses the eigenvalues for weighting, constructs a weighted signal subspace, and then uses the least square method to fit the signal subspace, and finally calculates the subspace fitting spectrum by using the reciprocal of the residual power. Since the lightning radiation electromagnetic signal and the actual received signal of the collection system are both very high frequency broadband signals, a frequency band energy weighted space spectrum suitable for very high frequency broadband signals is further constructed, then the weighted space spectrum is searched for a spectrum peak, the spatial angle of the spectrum peak is obtained, and finally the azimuth and elevation angles are obtained by calculating the spatial angle relationship of the radiation source wave direction.

[0027] As shown in Figure 5 , the method of the application specifically includes the following steps: S1, receiving lightning very high frequency broadband signals by using a non-uniform L-shaped lightning observation array.

[0028] A VHF signal (Very High Frequency signal) is a typical broadband signal, and the difference in frequency leads to the difference in signal subspace, so the VHF signal is subjected to Discrete Fourier Transform (DFT), and any narrowband component , represents time.

[0029] Suppose that far-field signal sources are incident on a certain spatial plane array, the array is composed of array elements, the array element positions are , , and the VHF signals are incident on the far field at different azimuth angles and elevation angles . non-uniform linear array of elements, narrowband component from far field with direction incident to L-shaped lightning observation array located in XOY plane. Array receives signal can be written as follows, specific formula as follows: ; wherein, , are narrowband received signals of X-axis and Y-axis subarrays, i.e. observation signals of X-axis and Y-axis subarrays respectively; is steering vector of array; is Gaussian white noise signal, , are noise signals of X-axis and Y-axis subarrays respectively; steering vector of array is calculated , , and are steering vectors of X-axis and Y-axis subarrays respectively, specific formula as follows: ; ; wherein, is imaginary unit; is angular frequency; is distance between antenna and antenna ; is light speed; is natural constant; is steering vector of X-axis subarray; is steering vector of Y-axis subarray; and are first factor and second factor respectively.

[0030] first factor and second factor are expressed as follows: ; ; wherein, " " " represents identity.

[0031] S2, perform eigenvalue decomposition on the observed signal of the X-axis subarray to obtain the X-axis signal subspace; calculate the eigenvalue weights of the X-axis signal subspace and reconstruct the X-axis signal subspace using weighted averages; solve for the residual power in the weighted reconstructed X-axis signal subspace, and the reciprocal of the residual power is the spatial spectrum value; based on the residual power, construct a weighted one-dimensional spatial spectrum function for the observed signal of the X-axis subarray to obtain the spatial angle formed by the radiation source and the X-axis. The estimated value.

[0032] Step S2 is detailed below: S21, based on the observation signal of the X-axis subarray Construct the covariance matrix Then, feature decomposition is performed, dividing the feature vector into a signal subspace and a noise subspace. The specific formula is as follows: ; in, Let be the autocorrelation matrix of the signal; express The signal subspace corresponding to each large eigenvalue; express The noise subspace corresponding to each small eigenvalue; Noise intensity; It is the identity matrix; Noise power; H Indicates conjugate transpose; It expresses expectation.

[0033] S22, calculate the eigenvalue weights of the X-axis signal subspace, and reconstruct the X-axis signal subspace using weighted averages.

[0034] To improve the accuracy and robustness of DOA estimation (direction of arrival estimation), eigenvalue weights are constructed in the signal subspace, with the specific formula as follows: ; in, For the first The weights corresponding to each feature value; For the first One eigenvalue; It refers to the dimension of the signal subspace, that is, the number of eigenvalues ​​corresponding to the signal subspace. .

[0035] The signal subspace is reconstructed using eigenvalue weights, as shown in the following formula: ; in, This is the signal subspace for weighted reconstruction.

[0036] S23, Solve for residual power using the least squares method.

[0037] signal subspace The subspace spanned by the array steering vectors is essentially the same space, and the specific formula is as follows: ; Wherein, Indicates the spanned space.

[0038] There is a full rank matrix , such that the following formula is established, and the specific formula is as follows: ; Using the least square method to construct the following formula, find the estimate of the matrix When the following formula is established, the signal subspace can be best fitted, and the least square error is minimum, and the specific formula is as follows: ; Wherein, Indicates the square of Frobenius norm; Indicates the estimated value of the matrix .

[0039] For the above formula, fix , the least square solution of the matrix T can be obtained, and the specific formula is as follows: ; Because , the above formula can be transformed to obtain the optimal solution of the matrix , and the specific formula is as follows: ; Wherein, Indicates the number of elements of the X-axis subarray.

[0040] Further, the optimal solution obtained Is substituted into the original objective function to calculate the residual error Of the X-axis subarray, and the specific formula is as follows: ; According to the following formula, the residual power P , that is, the square of Frobenius norm of the residual , is solved, and the specific formula is as follows: ; Wherein, Indicates the trace of the matrix.

[0041] The residual power P Is expanded and calculated, and the specific formula is as follows: ; in, The energy value of the signal subspace is a constant and is independent of the search angle; The value of varies with the angle, when the steering vector With signal subspace The better the alignment, the larger its value. This is to minimize the residual power. P According to the above formula, minimizing the residual power P Equivalent to maximizing .

[0042] S24. Construct a weighted one-dimensional spatial spectrum function for the observation signal of the X-axis subarray to obtain the spatial angle formed by the radiation source and the X-axis. The estimated value.

[0043] The spatial angle formed between the incident direction of the lightning VHF broadband signal and the positive X-axis is denoted as . , According to the first factor Least squares optimization was applied to the X-axis subarray received signal to obtain the spatial angle. The estimated value is then used to obtain the parameter. The estimated value .

[0044] Considering all narrowband components contained in the VHF broadband lightning signal, the observed signal of the X-axis subarray... The weighted one-dimensional spectral function is constructed as follows: ; in, f j The first step after performing a discrete Fourier transform on a VHF broadband lightning signal. j One frequency point; E j For the first j Energy at each frequency point; E tot The sum of the energy at all frequency points equals ; NO.s The number of frequency points; Represents the weighted one-dimensional spectral function; Indicates the first j The guiding vector at each frequency point; Indicates the first j The signal subspace at each frequency point.

[0045] S3. Perform eigenvalue decomposition on the observed signal of the Y-axis subarray to obtain the Y-axis signal subspace; calculate the eigenvalue weights of the Y-axis signal subspace and reconstruct the Y-axis signal subspace using weighted methods; solve for the residual power in the weighted reconstructed Y-axis signal subspace, and the reciprocal of the residual power is the spatial spectrum value; based on the residual power, construct a weighted one-dimensional spatial spectrum function for the observed signal of the Y-axis subarray to obtain the spatial angle formed by the radiation source and the Y-axis. The estimated value.

[0046] The specific processing method for step S3 is the same as that for step S2: Based on the observation signals of the Y-axis subarray Construct the covariance matrix Then, feature decomposition is performed to divide the feature vector into signal subspaces. and noise subspace ; Constructing the signal subspace Eigenvalue weights, utilizing signal subspace Eigenvalue weights for the signal subspace Perform weighted reconstruction to obtain the weighted reconstructed signal subspace. ; Solving for residual power using the least squares method; By constructing a weighted one-dimensional spatial spectrum function from the observed signals of the Y-axis subarray, the spatial angle formed by the incident direction of the lightning VHF broadband signal and the positive Y-axis direction can be obtained. The estimated value is then used to obtain the second factor. The estimated value .

[0047] S4, based on the spatial angle and The estimated value is used to obtain the azimuth angle of the radiation source. and elevation angle .

[0048] According to the spatial angle and The estimated value is used to obtain the first factor. The estimated value Second Factor The estimated value Then, the azimuth angle is obtained from the following formula. With elevation angle The specific formula is as follows: ; ; Figure 3 The positioning results generated by the method of this invention in MATLAB software show both time and elevation angle. The change relationship between time and elevation angle. Figure 4 The positioning result generated by the existing 1D-MUSIC method under MATLAB software shows the change relationship between time and elevation angle .

[0049] The above is only a preferred embodiment of the present application, and is not intended to limit the present application. Any modification, equivalent replacement and improvement within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for locating VHF broadband radiation sources based on energy-weighted subspace fitting, characterized in that, include: S1, using an L-shaped array to receive the VHF broadband signal of lightning, and performing a discrete Fourier transform to obtain the narrowband component, and constructing the observation signal of the X-axis subarray and the observation signal of the Y-axis subarray based on the narrowband component; S2, perform eigenvalue decomposition on the observed signal of the X-axis subarray to obtain the X-axis signal subspace; calculate the eigenvalue weights of the X-axis signal subspace and reconstruct the X-axis signal subspace using weighted methods; solve for the residual power in the weighted reconstructed X-axis signal subspace; based on the residual power, construct a weighted one-dimensional spatial spectrum function for the observed signal of the X-axis subarray to obtain the spatial angle formed by the radiation source and the X-axis. The estimated value; S3. Perform eigenvalue decomposition on the observed signal of the Y-axis subarray to obtain the Y-axis signal subspace; calculate the eigenvalue weights of the Y-axis signal subspace and reconstruct the Y-axis signal subspace using weighted methods; solve for the residual power in the weighted reconstructed Y-axis signal subspace; based on the residual power, construct a weighted one-dimensional spatial spectrum function for the observed signal of the Y-axis subarray to obtain the spatial angle formed by the radiation source and the Y-axis. The estimated value; S4, based on the spatial angle and The estimated value is used to obtain the azimuth angle of the radiation source. and elevation angle .

2. The VHF broadband radiation source localization method based on energy-weighted subspace fitting according to claim 1, characterized in that, In step S2, based on the observation signal of the X-axis subarray... Constructing the covariance matrix Then, feature decomposition is performed, dividing the feature vector into a signal subspace and a noise subspace, as shown in the following formula: in, The autocorrelation matrix of the signal is... 1 eigenvalue, express The signal subspace corresponding to each large eigenvalue express The noise subspace corresponding to each small eigenvalue For noise intensity, It is the identity matrix. For noise power, H This indicates the conjugate transpose. Expressing expectations, The guide vector for the X-axis subarray. The observation signal for the X-axis subarray. For narrowband components, Indicates time; The specific formula for calculating the eigenvalue weights of the X-axis signal subspace is as follows: in, For the first The weights corresponding to each feature value; For the first One eigenvalue; It is the dimension of the signal subspace. ; Using the eigenvalue weights of the signal subspace, the X-axis signal subspace is... The weighted reconstruction is performed using the following formula: in, This is the weighted reconstructed X-axis signal subspace.

3. The method for locating VHF broadband radiation sources based on energy-weighted subspace fitting according to claim 1, characterized in that, In step S2, the residual power is solved for the weighted reconstructed X-axis signal subspace using the least squares method, as follows: There exists a matrix of full rank. , making Established; among them, For the weighted reconstructed X-axis signal subspace, The guide vector for the X-axis subarray; Construct using the least squares method Find the matrix Least squares solution: ;in, Denotes the square of the Frobenius norm. Representation matrix The estimated value; H Indicates conjugate transpose; because , to obtain the matrix The optimal solution: ;in, Indicates the number of elements in the X-axis subarray; The obtained optimal solution Substitution In the middle, calculate the residual of the X-axis subarray. The specific formula is as follows: Solving for residual power P That is, residual The square of the Frobenius norm is given by the following formula: in, Represents the trace of a matrix; For residual power P The expansion calculation is performed using the following formula: in, The energy value of the signal subspace is a constant; The value of varies with the angle, when the steering vector With signal subspace The better the alignment, The larger the value, the more it minimizes the residual power. P Equivalent to maximizing .

4. The VHF broadband radiation source localization method based on energy-weighted subspace fitting according to claim 3, characterized in that, In step S2, a weighted one-dimensional spatial spectrum function is constructed for the observation signal of the X-axis subarray, and the specific formula is as follows: in, f j The first step after performing a discrete Fourier transform on a VHF broadband lightning signal. j One frequency point; E j For the first j Energy at each frequency point; E tot It is the sum of the energy at all frequency points; NO.s The number of frequency points; Represents the weighted one-dimensional spectral function; Indicates the first j The conjugate transpose of the steering vector at each frequency point; Indicates the first j The signal subspace of each frequency point; The observation signal of the X-axis subarray is optimized using the least squares method to obtain the spatial angle. The estimated value.

5. The VHF broadband radiation source localization method based on energy-weighted subspace fitting according to any one of claims 1-4, characterized in that, The specific processing method of step S3 is the same as that of step S2.

6. The VHF broadband radiation source localization method based on energy-weighted subspace fitting according to claim 1, characterized in that, The L-shaped array is a non-uniform L-shaped array with a total of 7 antennas, denoted as . Among them, antenna The x-coordinates are as follows: The vertical axis is 0, and the antenna is 0. Constructing an X-axis subarray; antenna The ordinates are as follows: The horizontal axis is 0, and the antenna is... Construct a Y-axis subarray; , This is the proportionality coefficient.

7. The VHF broadband radiation source localization method based on energy-weighted subspace fitting according to claim 6, characterized in that, Step S1 is as follows: The narrowband component is obtained by performing a discrete Fourier transform on the VHF broadband lightning signal. , Indicates time; Array receives signals Written as: in, , These are the observation signals of the X-axis and Y-axis subarrays, respectively; This is the guiding vector of the array; It is a Gaussian white noise signal; , These are the noise signals for the X-axis and Y-axis subarrays, respectively. Compute the steering vector of the array , , and These are the guide vectors for the X-axis and Y-axis subarrays, respectively, and the specific formulas are as follows: in, The imaginary unit; Angular frequency; For antenna With antenna The distance between them; The speed of light; It is a natural constant; The guide vector for the X-axis subarray; The guiding vector for the Y-axis subarray; and These are the first factor and the second factor, respectively. First Factor Second Factor The expression is as follows: in," " indicates that it is always equal to.

8. The VHF broadband radiation source localization method based on energy-weighted subspace fitting according to claim 7, characterized in that, In step S4, based on the spatial angle and The estimated value is used to obtain the first factor. The estimated value Second Factor The estimated value Thus, the azimuth angle of the radiation source is obtained. With elevation angle : 。 9. An electronic device, characterized in that, It includes a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the VHF broadband radiation source localization method based on energy-weighted subspace fitting as described in any one of claims 1-8.

10. A computer program product, characterized in that, It includes a computer program / instruction that, when executed by a processor, implements the VHF broadband radiation source localization method based on energy-weighted subspace fitting as described in any one of claims 1-8.

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