Method for locating very high frequency broadband radiation sources based on energy-weighted subspace fitting

Abstract

The application discloses a very high frequency broadband radiation source positioning method based on energy weighted subspace fitting, and relates to the fields of signal processing and radiation source imaging technology. First, DFT processing is performed on the thunder and lightning very high frequency broadband signals collected by an array to obtain any narrowband component. Then, the covariance matrices of X-axis and Y-axis subarrays are respectively subjected to eigenvalue decomposition according to the array received signals, and the main eigenvectors are taken as the signal subspace. In order to emphasize the signal subspace with stronger energy, the eigenvalues are used for weighting to construct a weighted signal subspace. The signal subspace is further fitted by using the least square method, and a frequency band energy weighted space spectrum suitable for the very high frequency broadband signals is further constructed. Next, the weighted space spectrum is subjected to spectrum peak searching to obtain the spatial angle of the spectrum peak. Finally, the radiation source direction of arrival is calculated from the spatial angle relationship to obtain the azimuth angle and the elevation angle. The application can more clearly invert the thunder and lightning channel for the problem of positioning the thunder and lightning very high frequency weak radiation source.

Description

Technical Field

[0001] This invention relates to the fields of signal processing and radiation source localization technology, and in particular to a method for VHF broadband radiation source localization based on energy-weighted subspace fitting. Background Technology

[0002] Lightning imaging is a crucial support for research in lightning science and protection. It's a technique that uses multiple antennas to remotely sense electromagnetic radiation signals generated by atmospheric discharges and, based on specific algorithms, inverts the direction or location of the radiation source to generate two-dimensional or three-dimensional images of lightning activity. Subspace fitting algorithms are also widely used in radar and mobile communications. Unlike existing multiple signal classification methods, this type of method constructs a fitting relationship between a multi-dimensional array manifold matrix and the signal subspace of the array's received data, transforming it into a cost function minimization problem. Finally, it uses spatial spectrum search to determine the location of the signal source. This method ensures both algorithm resolution and the ability to decoherentize and locate signals. Summary of the Invention

[0003] To overcome the shortcomings of the prior art, this invention provides a VHF broadband radiation source localization method based on energy-weighted subspace fitting, which can more clearly invert the lightning channel for the problem of locating weak VHF lightning radiation sources.

[0004] To achieve the above objectives, the present invention adopts the following technical solution, including:

[0005] A method for locating VHF broadband radiation sources based on energy-weighted subspace fitting includes:

[0006] 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;

[0007] 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;

[0008] 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;

[0009] S4, based on the spatial angle and The estimated value is used to obtain the azimuth angle of the radiation source. and elevation angle .

[0010] Preferably, in step S2,

[0011] Based on the observation signals of the X-axis sub-array Construct the covariance matrix Then, feature decomposition is performed to divide the feature vector into a signal subspace and a noise subspace, as shown in the following formula:

[0012] ;

[0013] 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;

[0014] The eigenvalue weights for the X-axis signal subspace are calculated using the following formula:

[0015] ;

[0016] in, For the first The weights corresponding to each feature value; For the first One eigenvalue; It is the dimension of the signal subspace. ;

[0017] Using the eigenvalue weights of the signal subspace, the X-axis signal subspace is... The weighted reconstruction is performed using the following formula:

[0018] ;

[0019] in, This is the weighted reconstructed X-axis signal subspace.

[0020] Preferably, in step S2, the residual power is solved for the weighted reconstructed X-axis signal subspace using the least squares method, as follows:

[0021] 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;

[0022] 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;

[0023] because , to obtain the matrix The optimal solution: ;in, Indicates the number of elements in the X-axis subarray;

[0024] The obtained optimal solution Substitution In the middle, calculate the residual of the X-axis subarray. The specific formula is as follows:

[0025] ;

[0026] Solving for residual power P That is, residual The square of the Frobenius norm is given by the following formula:

[0027] ;

[0028] in, Represents the trace of a matrix;

[0029] For residual power P The expansion calculation is performed using the following formula:

[0030] ;

[0031] 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 .

[0032] 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:

[0033] ;

[0034] 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;

[0035] The observation signal of the X-axis subarray is optimized using the least squares method to obtain the spatial angle. The estimated value.

[0036] Preferably, the specific processing method of step S3 is the same as that of step S2.

[0037] Preferably, 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.

[0038] Preferably, step S1 is as follows:

[0039] The narrowband component is obtained by performing a discrete Fourier transform on the VHF broadband lightning signal. , Indicates time;

[0040] Array receives signals Written as:

[0041] ;

[0042] 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.

[0043] 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:

[0044] ;

[0045] ;

[0046] 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.

[0047] First Factor Second Factor The expression is as follows:

[0048] ;

[0049] ;

[0050] in," " indicates that it is always equal to.

[0051] Preferably, 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 :

[0052] ;

[0053] .

[0054] The present invention also provides an electronic device, which 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.

[0055] The present invention also provides a computer program product comprising a computer program / instruction that, when executed by a processor, implements the aforementioned method for locating VHF broadband radiation sources based on energy-weighted subspace fitting.

[0056] The advantages of this invention are:

[0057] (1) This invention provides a method for locating VHF broadband radiation sources based on energy-weighted subspace fitting, which can more clearly invert the lightning channel for the problem of locating weak VHF radiation sources of lightning.

[0058] (2) The present invention uses a non-uniform L-shaped lightning observation array, which improves the imaging accuracy and anti-blurring performance of the system.

[0059] (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.

[0060] (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

[0061] Figure 1 This is a schematic diagram of the non-uniform L-shaped lightning observation array of the present invention.

[0062] Figure 2 This is a schematic diagram of the VHF waveform acquired by the present invention.

[0063] Figure 3 This is a positioning diagram for the present invention.

[0064] Figure 4 Comparison chart of 1D-MUSIC positioning results.

[0065] 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

[0066] 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.

[0067] 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 . Antenna positioned on the X-axis The x-coordinates are as follows: The vertical axis is 0, and the antenna is 0. This forms the X-axis subarray. The antennas on the Y-axis are arranged in the same manner as those on the X-axis. The ordinates are as follows: The horizontal axis is 0, and the antenna is... This forms a Y-axis subarray.

[0068] like Figure 2 The image shown is a schematic diagram of the very high frequency waveform acquired by the non-uniform L-shaped lightning observation array of the present invention.

[0069] The present invention provides a VHF broadband radiation source localization method based on energy-weighted subspace fitting. First, the VHF broadband lightning signal acquired by the array is processed using Discrete Fourier Transform (DFT) to obtain any narrowband component. Then, based on the received signal, the covariance matrices of the X-axis and Y-axis subarrays are eigenvalued, and the principal eigenvectors are taken as the signal subspace. To emphasize the signal subspace with stronger energy, eigenvalues ​​are used for weighting to construct a weighted signal subspace. The signal subspace is then fitted using the least squares method, and finally, the subspace fitting spectrum is calculated using the reciprocal of the residual power. Since both the lightning radiated electromagnetic signal and the actual received signal from the acquisition system are VHF broadband signals, a frequency-band energy-weighted spatial spectrum adapted to the VHF broadband signal is further constructed. Next, a peak search is performed on the weighted spatial spectrum to obtain the spatial angles of the peaks. Finally, the azimuth and elevation angles of the radiation source are calculated from the spatial angle relationships.

[0070] like Figure 5 As shown, the method of the present invention specifically includes the following steps:

[0071] S1 uses a non-uniform L-shaped lightning observation array to receive VHF broadband lightning signals.

[0072] VHF (Very High Frequency) signals are typical broadband signals. The differences in frequency lead to variations in the signal subspace. Therefore, performing a Discrete Fourier Transform (DFT) on a VHF signal yields any narrowband component. , Indicates time.

[0073] Assume there is A far-field signal source is incident on a spatial planar array, and the array consists of... It consists of several array elements, and the positions of the array elements are as follows: , VHF signals at different azimuth angles and elevation angle From far-field incidence to containing On a non-uniform linear matrix with elements, narrowband components From the far field in the direction The incident signal is projected onto an L-shaped lightning observation array located in the XOY plane. The array receives the signal. It can be written in the following form, with the specific formula as follows:

[0074] ;

[0075] in, , These are the narrowband receiver signals of the X-axis and Y-axis subarrays, respectively, i.e., the observation signals of the X-axis and Y-axis subarrays; 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.

[0076] 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:

[0077] ;

[0078] ;

[0079] 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.

[0080] First Factor Second Factor The expression is as follows:

[0081] ;

[0082] ;

[0083] in," " indicates that it is always equal to.

[0084] 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.

[0085] Step S2 is detailed below:

[0086] 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:

[0087] ;

[0088] 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.

[0089] S22, calculate the eigenvalue weights of the X-axis signal subspace, and reconstruct the X-axis signal subspace using weighted averages.

[0090] To improve the accuracy and robustness of DOA estimation (direction of arrival estimation), eigenvalue weights are constructed for the signal subspace, with the specific formula as follows:

[0091] ;

[0092] 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. .

[0093] The signal subspace is reconstructed using eigenvalue weights, as shown in the following formula:

[0094] ;

[0095] in, This is the signal subspace for weighted reconstruction.

[0096] S23, Solve for residual power using the least squares method.

[0097] signal subspace The subspace spanned by the array guide vector is essentially the same space, as shown in the following formula:

[0098] ;

[0099] in, This represents Zhang Cheng's space.

[0100] There exists a matrix of full rank. This makes the following formula true, as shown in the following formula:

[0101] ;

[0102] Construct the following equation using the least squares method, and find the matrix that makes the following equation true. The estimate best fits the signal subspace, and the least squares error between the two is minimized. The specific formula is as follows:

[0103] ;

[0104] in, Denotes the square of the Frobenius norm; Representation matrix The estimated value.

[0105] For the above formula, fixed The least-squares solution to matrix T can be found using the following formula:

[0106] ;

[0107] And because Therefore, the above equation can be transformed to obtain the matrix. The optimal solution is given by the following formula:

[0108] ;

[0109] in, This indicates the number of elements in the X-axis subarray.

[0110] The obtained optimal solution Substitute into the original objective function to calculate the residual of the X-axis subarray. The specific formula is as follows:

[0111] ;

[0112] The residual power can be calculated using the following formula. P That is, residual The square of the Frobenius norm is given by the following formula:

[0113] ;

[0114] in, Represents the trace of a matrix.

[0115] For residual power P The expansion calculation is performed using the following formula:

[0116] ;

[0117] 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 .

[0118] 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.

[0119] 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 .

[0120] 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:

[0121] ;

[0122] 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.

[0123] 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.

[0124] The specific processing method for step S3 is the same as that for step S2:

[0125] 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 ;

[0126] 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. ;

[0127] Solving for residual power using the least squares method;

[0128] 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 .

[0129] S4, based on the spatial angle and The estimated value is used to obtain the azimuth angle of the radiation source. and elevation angle .

[0130] 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:

[0131] ;

[0132] ;

[0133] Figure 3 The positioning results generated by the method of this invention in MATLAB software show both time and elevation angle. The changing relationship. Figure 4 The positioning results generated by existing 1D-MUSIC methods in MATLAB software show time and elevation angle. The changing relationship.

[0134] The above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

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 ; 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 ; 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.

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... Construct 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 eigenvalue weights for the X-axis signal subspace are calculated using the following formula: 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 VHF broadband radiation source localization method based on energy-weighted subspace fitting according to any one of claims 1, characterized in that, The specific processing method of step S3 is the same as that of step S2.

4. 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 x-coordinates are all 0, antenna Construct a Y-axis subarray; , This is the proportionality coefficient.

5. The VHF broadband radiation source localization method based on energy-weighted subspace fitting according to claim 4, 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.

6. The VHF broadband radiation source localization method based on energy-weighted subspace fitting according to claim 5, 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 : 。 7. 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 1-6.

8. 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 1-6.

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