A broadband lightning very high frequency radiation source positioning method based on ESPRIT algorithm

Abstract

The application discloses a wideband lightning VHF radiation source positioning method based on an ESPRIT algorithm, which comprises the following steps: step 1, constructing an orthogonal uniform linear VHF antenna array and collecting wideband lightning VHF signals; step 2, performing discrete Fourier transform on the wideband lightning VHF signals, dividing the wideband lightning VHF signals into J frequency points, and calculating the frequency domain values of the signals of each frequency point; step 3, dividing the orthogonal uniform linear VHF antenna array into two sub-arrays in the x-axis direction and the y-axis direction, using the ESPRIT algorithm to position each frequency point value of the signals in the two directions respectively, and obtaining the calculated incident angles of each frequency point in the two directions respectively; step 4, performing phase deblurring on the calculated incident angles of each frequency point in the two directions to obtain the real incident angles; and step 5, calculating the azimuth and elevation angles of the radiation source from the real incident angles. The application can realize rapid and fine positioning and imaging of lightning radiation sources.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing, and in particular relates to a broadband lightning very high frequency radiation source positioning method based on the ESPRIT algorithm. Background Art

[0002] The precise positioning of lightning very high frequency (VHF) radiation sources can effectively help analyze the development process of lightning channels, especially the capture and positioning of some weak radiation processes. This is very beneficial for analyzing and exploring the mechanism of lightning occurrence and development, and also promotes lightning protection and early warning.

[0003] Direction of arrival (DOA) estimation algorithms, such as electromagnetic time reversal (EMTR), multiple signal classification (MUSIC), and orthonormal propagator method (OPM), have been experimentally validated to maintain high positioning accuracy even under low signal-to-noise ratios (SNRs), and have garnered extensive attention and research. Under the same conditions, they offer superior positioning performance compared to traditional methods such as time of arrival (TOA) and interferometers, effectively capturing more weak emitters.

[0004] A limitation of the aforementioned high-precision positioning algorithms is that obtaining a refined lightning development path requires continuous data extraction using a sliding window. The global maximum search is then required for each sliding window data location, resulting in a slow and time-consuming computational process. Experiments have shown that for a 500ms segment of lightning VHF data, these algorithms require hundreds of hours to obtain a relatively refined lightning development path map. This is time-consuming and has limited practical research value. Currently, in the field of lightning VHF radiation source location, DOA estimation methods based on array signal processing are rarely used. In particular, methods that rapidly and finely estimate DOA based on direct solutions, such as the Estimating Signal Parameters via Rotational Invariance Techniques (ESPRTI), are rarely reported. Summary of the Invention

[0005] The purpose of the present invention is to provide a broadband lightning very high frequency radiation source positioning method based on the ESPRIT algorithm, and to apply the ESPRIT method based on array signal processing technology that can directly solve the DOA parameters to the field of broadband lightning very high frequency radiation source positioning to achieve rapid and refined positioning.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] A broadband lightning very high frequency radiation source location method based on the ESPRIT algorithm includes the following steps:

[0008] Step 1: Construct an orthogonal uniform linear VHF antenna array to collect broadband lightning VHF signals;

[0009] Step 2: Perform discrete Fourier transform on the broadband lightning VHF signal and divide it into J frequency points. The frequency domain expression of each frequency point signal is as follows:

[0010] X(f j )=A(f j )S(f j )+N(f j ),j∈[1,J]

[0011] Among them, f j Indicates the jth frequency point, X(f j ),S(f j ),N(f j ) represent the frequency domain expressions of the Fourier transformed received signal, radiation source, and noise, respectively, and A represents the manifold vector of the array antenna;

[0012] Step 3: Divide the orthogonal uniform linear VHF antenna array into two sub-arrays in the x-axis direction and the y-axis direction, and use the ESPRIT algorithm to locate the frequency domain signals of each frequency point in the x-axis direction and the y-axis direction respectively, and obtain the calculated incident angle v of the j-th frequency point in the two directions respectively. j and u j ,

[0013] Assume that the azimuth and elevation angles of the far-field broadband incident signal are θ, then the calculated incident angle v for each frequency point in the x-axis direction is j and The relationship of θ is expressed as:

[0014]

[0015] Similarly, the calculated incident angle u for each frequency point in the y-axis direction is j and The relationship of θ is expressed as:

[0016]

[0017] Wherein, J represents the number of frequency points;

[0018] Step 4: Perform phase deambiguation on the calculated incident angles for each frequency point in both the x-axis and y-axis directions to obtain the true incident angles. Specifically:

[0019] In the ESPRIT algorithm, phase ambiguity occurs during phase difference calculation because the phase difference is calculated using the phase angle. It can be seen that:

[0020]

[0021] Among them, arg() represents the phase calculation of the complex number, and z represents the complex number result calculated by the ESPRIT algorithm. represents the calculated phase difference, while φ represents the actual phase difference, and there is a phase difference of several 2π between the two;

[0022] For each different frequency point f j , the calculated phase difference arg(z j ) satisfies the following relationship:

[0023]

[0024] c represents the speed of light, d represents the spacing of the array antenna, α j Represents the unresolved ambiguity incident angle of the jth frequency point. Due to the phase ambiguity problem, the α calculated by the above formula is j Not the same, only when the phase difference of each frequency point compensates the correct phase ambiguity term, all α j It should be consistent, that is, as follows:

[0025]

[0026] Define a slope value sl as follows:

[0027]

[0028] Define a slope difference, the expression is as follows:

[0029]

[0030] When the phase difference of each frequency point correctly compensates for the ambiguity phase, the overall slope difference will reach the minimum value, that is:

[0031]

[0032] At this time, the deblurred incident angle α' after compensationj Expressed as:

[0033]

[0034] For broadband signals, the incident angle is determined by the following multi-frequency deambiguation incident angle weighted average method:

[0035]

[0036] Among them, ρ j Indicates the maximum eigenvalue of the signal subspace of the jth frequency point, representing the strength of the signal; in the two-dimensional positioning of the present invention, v j and u j Represents the calculated incident angle of the jth frequency point in the x-axis and y-axis directions, but this angle has not been defuzzified, so for v j and u j , respectively use the method of step 4 to perform defuzzification operation, that is, let α j Equal to v j and u j , and then perform phase deambiguation to finally obtain the calculated incident angles v and u of the broadband signal in the x-axis and y-axis directions;

[0037] Step 5: Calculate the azimuth and elevation angles of the radiation source from the true incident angles in the two directions, specifically:

[0038]

[0039] Furthermore, the frequency domain signals of each frequency point on the x-axis and y-axis in step 3 are located using the ESPRIT algorithm to obtain the calculated incident angle v of the j-th frequency point in the two directions of the two axes. j and u j , specifically:

[0040] For a given uniform linear array of M antennas, assuming that there are N narrowband radiation sources in the far field transmitting to the array antenna, the signal received by the array antenna is expressed as follows:

[0041] X(t)=AS(t)+N(t)

[0042] Where X(t), S(t), and N(t) represent the arrival signal, radiation source signal, and noise received by the array antenna, respectively; A represents the array manifold vector;

[0043] A=[a(β1),a(β2),...,a(β N )]

[0044]

[0045] βn represents the incident angle of the nth radiation source, λ n represents the wavelength of the signal, and d represents the spacing of the array antenna;

[0046] make Then A in the above formula can be rewritten as:

[0047]

[0048] Divide this linear array into two sub-arrays X1 and X2, which are the 1st to M-1st and 2nd to Mth items of array X respectively. The signals received by the two sub-arrays are expressed as follows:

[0049] X1(t)=A1S(t)+N1(t)

[0050] X2(t)=A2S(t)+N2(t)

[0051] Therefore, the following relationship exists:

[0052] A2=A1Φ

[0053]

[0054] The above formula shows that the manifold vectors of the two linear subarrays differ by only a fixed phase difference, and this phase difference represents the direction of the incoming wave from the radiation source. Therefore, the DOA parameter of the radiation source can be obtained by solving Φ.

[0055] The covariance matrix of the signal received by the array antenna is expressed as follows:

[0056] R X =E[XX H ]=AR S A H +R N

[0057] Among them, R X and R S Represent the covariance matrix of the received signal and the radiation source respectively, H represents the conjugate transpose, and R X Perform eigenvalue decomposition to obtain the following formula:

[0058]

[0059] Among them U S and U N Represent the signal subspaces of the radiation source and noise respectively. Since the signal subspace and the space spanned by the array manifold vector are the same, there exists a non-singular matrix T that satisfies the following formula:

[0060] U S =AT

[0061] The corresponding expressions of the two sub-arrays are written as follows:

[0062] U1=A1T

[0063] U2=A2T=A1ΦT

[0064] Therefore, we can get:

[0065] U1T -1 ΦT=A1ΦT=U2

[0066] Let Ψ = T -1 ΦT, we get:

[0067] U1Ψ=U2

[0068] By calculating Ψ and then performing eigenvalue decomposition on it, we can obtain its diagonal matrix value Φ, thereby solving the DOA parameter of the radiation source. The incident angle of the radiation source is obtained by the following formula:

[0069]

[0070] For a single radiation source, let N = 1, that is, only β1 is taken as the incident angle of the radiation source;

[0071] Calculate the incident angle v in the x-axis direction j When the M antennas of the uniform linear array are replaced by the antennas on the x-axis, X(t) is replaced by X(f j ), and the remaining calculation steps are the same as described above.

[0072]

[0073] Among them, d x Indicates the spacing between antennas on the x-axis.

[0074] Similarly, when calculating the incident angle u in the y-axis direction j When the M antennas of the uniform linear array are replaced by antennas on the y-axis, X(t) is replaced by X(f j ), and the remaining calculation steps are the same as described above.

[0075]

[0076] Among them, d y Indicates the spacing between antennas on the y-axis.

[0077] Furthermore, the orthogonal uniform linear VHF antenna array in step 1 is an L-shaped uniform linear VHF antenna array, which has a total of 7 antennas, one located at the coordinate origin, and the other 3 evenly distributed on the orthogonal x-axis and y-axis.

[0078] Furthermore, the interval between adjacent antennas on the x-axis and the y-axis is 9 m.

[0079] Compared with the prior art, the present invention has the following effects:

[0080] (1) The present invention applies the ESPRIT algorithm to the field of broadband lightning very high frequency radiation source positioning, which can realize rapid and refined positioning and imaging of lightning radiation sources.

[0081] (2) The present invention provides a fast and efficient multi-frequency point phase difference ambiguity resolution method, which can achieve accurate estimation of the actual phase difference. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 is a schematic diagram of a uniform linear array antenna;

[0083] Figure 2 Schematic diagram of the L-shaped uniform linear lightning VHF antenna array used in the present invention;

[0084] Figure 3 This is the positioning imaging result of the method of the present invention on the very high frequency data of an artificial lightning strike;

[0085] Figure 4 This is the positioning imaging result of the broadband interferometer positioning algorithm on the very high frequency data of the same artificial lightning. DETAILED DESCRIPTION

[0086] The implementation of the present invention is described in detail below with reference to specific embodiments and drawings.

[0087] A broadband lightning very high frequency radiation source location method based on the ESPRIT algorithm includes the following steps:

[0088] Step 1: Construct an orthogonal uniform linear VHF antenna array to collect broadband lightning VHF signals;

[0089] Step 2: Perform discrete Fourier transform on the broadband lightning VHF signal and divide it into J frequency points. The frequency domain expression of each frequency point signal is as follows:

[0090] X(f j )=A(f j )S(f j )+N(f j ),j∈[1,J]

[0091] Among them, X(f j ),S(f j ),N(f j ) represents the frequency domain expression of the Fourier transformed received signal, radiation source, and noise. A represents the manifold vector of the array antenna.

[0092] Step 3: Divide the orthogonal uniform linear VHF antenna array into two sub-arrays in the x-axis direction and the y-axis direction, and use the ESPRIT algorithm to locate the frequency domain signals of each frequency point in the x-axis direction and the y-axis direction respectively, and obtain the calculated incident angle v of the j-th frequency point in the two directions respectively. j and u j , specifically:

[0093] Assume that the azimuth and elevation angles of the far-field broadband incident signal are θ, then the calculated incident angle v for each frequency point in the x-axis direction is j and The relationship of θ is expressed as:

[0094]

[0095] Similarly, the calculated incident angle u for each frequency point in the y-axis direction is j and The relationship of θ is expressed as:

[0096]

[0097] Wherein, J represents the number of frequency points.

[0098] Step 4: Perform phase deambiguation on the calculated incident angles at each frequency point in both directions to obtain the true incident angles, specifically:

[0099] In the phase difference calculation process of the ESPRIT algorithm, phase ambiguity may occur because the phase difference is calculated by the phase angle. It can be seen that:

[0100]

[0101] Among them, arg() represents the phase calculation of the complex number, and z represents the complex number result calculated by the ESPRIT algorithm. represents the calculated phase difference, while φ represents the actual phase difference, and there is a phase difference of several 2π between the two;

[0102] In order to solve the phase ambiguity problem, the present invention proposes a minimum slope difference criterion. The specific principle is as follows: for each different frequency point f j , the calculated phase difference arg(z j ) satisfies the following relationship:

[0103]

[0104] c represents the speed of light, d represents the spacing of the array antenna, α jRepresents the unresolved ambiguity incident angle of the jth frequency point. Due to the phase ambiguity problem, the α calculated by the above formula is j Not the same, only when the phase difference of each frequency point compensates the correct phase ambiguity term, all α j It should be consistent, that is, as follows:

[0105]

[0106] Define a slope value sl as follows:

[0107]

[0108] Define a slope difference, the expression is as follows:

[0109]

[0110] When the phase difference of each frequency point correctly compensates for the ambiguity phase, the overall slope difference will reach the minimum value, that is:

[0111]

[0112] At this time, the deblurred incident angle α' after compensation j Expressed as:

[0113]

[0114] For broadband signals, the incident angle is determined by the following multi-frequency deambiguation incident angle weighted average method:

[0115]

[0116] Among them, ρ j Indicates the maximum eigenvalue of the signal subspace of the jth frequency point, representing the strength of the signal; in the two-dimensional positioning of the present invention, v j and u j Represents the calculated incident angle of the jth frequency point in the x-axis and y-axis directions, but this angle has not been defuzzified, so for v j and u j , respectively use the method of step 4 to perform defuzzification operation, that is, let α j Equal to v j and u j , and then perform phase deambiguation to finally obtain the calculated incident angles v and u of the broadband signal in the x-axis and y-axis directions;

[0117] Step 5: Calculate the azimuth and elevation angles of the radiation source from the true incident angles in the two directions, specifically:

[0118]

[0119] Preferably, the frequency domain signals of each frequency point on the x-axis and y-axis in step 3 are positioned using the ESPRIT algorithm to obtain the calculated incident angle v of the j-th frequency point in the two directions of the two axes respectively. j and u j , specifically:

[0120] like Figure 1 As shown in , for a given uniform linear array of M antennas, assuming that there are N narrowband radiation sources in the far field transmitting to the array antenna, the signal received by the array antenna is expressed as follows:

[0121] X(t)=AS(t)+N(t)

[0122] Where X(t), S(t), and N(t) represent the arrival signal, radiation source signal, and noise received by the array antenna, respectively; A represents the array manifold vector;

[0123] A=[a(β1),a(β2),...,a(β N )]

[0124]

[0125] β n represents the incident angle of the nth radiation source, λ n represents the wavelength of the signal, and d represents the spacing of the array antenna;

[0126] make Then A in the above formula can be rewritten as:

[0127]

[0128] Divide this linear array into two sub-arrays X1 and X2, which are the 1st to M-1st and 2nd to Mth items of array X respectively. The signals received by the two sub-arrays are expressed as follows:

[0129] X1(t)=A1S(t)+N1(t)

[0130] X2(t)=A2S(t)+N2(t)

[0131] Therefore, the following relationship exists:

[0132] A2=A1Φ

[0133]

[0134] The above formula shows that the manifold vectors of the two linear subarrays differ by only a fixed phase difference, and this phase difference represents the direction of the incoming wave from the radiation source. Therefore, the DOA parameter of the radiation source can be obtained by solving Φ.

[0135] The covariance matrix of the signal received by the array antenna can be expressed as follows:

[0136] R X =E[XX H ]=AR S A H +R N

[0137] Among them, R X and R S Represent the covariance matrix of the received signal and the radiation source respectively, H represents the conjugate transpose, and R X Perform eigenvalue decomposition to obtain the following formula:

[0138]

[0139] Among them U S and U N Represent the signal subspaces of the radiation source and noise respectively. Since the signal subspace and the space spanned by the array manifold vector are the same, there exists a non-singular matrix T that satisfies the following formula:

[0140] U S =AT

[0141] The corresponding expressions of the two sub-arrays can be written as follows:

[0142] U1=A1T

[0143] U2=A2T=A1ΦT

[0144] Therefore, we can get:

[0145] U1T -1 ΦT=A1ΦT=U2

[0146] Let Ψ = T -1 ΦT, we can get:

[0147] U1Ψ=U2

[0148] By calculating Ψ and then performing eigenvalue decomposition on it, we can obtain its diagonal matrix value Φ, thereby solving the DOA parameter of the radiation source. The incident angle of the radiation source is obtained by the following formula:

[0149]

[0150] Calculate the incident angle v in the x-axis direction j When the M antennas of the uniform linear array are replaced by the antennas on the x-axis, X(t) is replaced by X(f j ), and the remaining calculation steps are the same as described above.

[0151]

[0152] Among them, d x Indicates the spacing between antennas on the x-axis.

[0153] Similarly, when calculating the incident angle u in the y-axis direction j When the M antennas of the uniform linear array are replaced by antennas on the y-axis, X(t) is replaced by X(f j ), and the remaining calculation steps are the same as described above.

[0154]

[0155] Among them, d y Indicates the spacing between antennas on the y-axis.

[0156] Preferably, combined Figure 2 The orthogonal uniform linear VHF antenna array in step 1 is an L-shaped uniform linear VHF antenna array. The array has a total of 7 antennas, one located at the coordinate origin, and the other 3 evenly distributed on the orthogonal x-axis and y-axis, with an interval of 9m between adjacent antennas.

[0157] Example

[0158] The first step is to use a sliding window to extract lightning very high frequency data in sequence. The very high frequency data used in the present invention is Figure 2 The array antenna shown in the figure has a system sampling rate of 500 MHz and a sliding window length of 512 sampling points, or 1.024 μs. The sliding window data is subjected to a discrete Fourier transform to obtain the frequency values.

[0159] In the second step, the 20 frequency points with the highest energy values ​​are selected and the above-mentioned broadband ESPRIT algorithm is used to calculate and obtain the final positioning imaging result.

[0160] Figure 3 and Figure 4 The positioning imaging results of the method of the present invention and the existing broadband interferometer method on the very high frequency data of an artificial lightning strike are respectively shown. Figure 3For example, the figure is divided into two sub-figures: the lower sub-figure is an elevation-azimuth plot. The horizontal axis represents the azimuth angle, ranging from 0 to 360°, and the vertical axis represents the elevation angle, ranging from 0 to 90°. This sub-figure depicts the position and changes of the radiation source in a two-dimensional coordinate system. The color changes indicate the chronological order, corresponding to the color bar on the right. The upper sub-figure is an elevation-time plot. The horizontal axis represents the time, ranging from 0 to 500ms. The vertical axis has the same meaning as the vertical axis in the lower sub-figure. This sub-figure depicts the variation of the radiation source's elevation angle, or altitude, over time. The number in the box in the lower left indicates the number of radiation source locations depicted in the figure. Figure 4 The subgraph structure and meaning in Figure 3 Stay consistent.

[0161] Figure 3 The method of the present invention located 49,181 radiation sources, and Figure 4 The medium- and wideband interferometer method located 30,256 radiation sources. In contrast, the lightning channel development map obtained by the present method is more detailed and includes more lightning development branches, demonstrating the superior positioning performance of this method. This segment of VHF data lasted 500ms, and the present method took a total of 30 minutes, which is comparable to the broadband interferometer method.

[0162] The present invention combines the array signal processing technology ESPRIT algorithm with the lightning very high frequency radiation source positioning, which can directly solve the two-dimensional DOA parameters without the need for full-space maximum value search. It has a fast calculation speed while finely positioning the radiation source.

[0163] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art should understand that the present invention is not limited to the foregoing embodiments. The foregoing embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed in the present invention is defined by the appended claims and their equivalents.

Claims

1. A broadband lightning VHF radiation source location method based on the ESPRIT algorithm, characterized in that: The following steps are involved: Step 1: Construct an orthogonal uniform linear VHF antenna array to collect broadband lightning VHF signals; Step 2: Perform discrete Fourier transform on the broadband lightning VHF signal and divide it into J frequency points. The frequency domain expression of each frequency point signal is as follows: X(f j )=A(f j )S(f j )+N(f j ),j∈[1,J] Among them, f j Indicates the jth frequency point, X(f j ),S(f j ),N(f j ) represent the frequency domain expressions of the Fourier transformed received signal, radiation source, and noise, respectively, and A represents the manifold vector of the array antenna; Step 3: Divide the orthogonal uniform linear VHF antenna array into two sub-arrays in the x-axis direction and the y-axis direction, and use the ESPRIT algorithm to locate the frequency domain signals of each frequency point in the x-axis direction and the y-axis direction respectively, and obtain the calculated incident angle v of the j-th frequency point in the two directions respectively. j and u j , Assume that the azimuth and elevation angles of the far-field broadband incident signal are θ, then the calculated incident angle v for each frequency point in the x-axis direction is j and The relationship of θ is expressed as: Similarly, the calculated incident angle u for each frequency point in the y-axis direction is j and The relationship of θ is expressed as: Wherein, J represents the number of frequency points; Step 4: Perform phase deambiguation on the calculated incident angles for each frequency point in both the x-axis and y-axis directions to obtain the true incident angles. Specifically: In the ESPRIT algorithm, phase ambiguity occurs during phase difference calculation because the phase difference is calculated using the phase angle. It can be seen that: Among them, arg() represents the phase calculation of the complex number, and z represents the complex number result calculated by the ESPRIT algorithm. represents the calculated phase difference, while φ represents the actual phase difference, and there is a phase difference of several 2π between the two; For each different frequency point f j , the calculated phase difference arg(z j ) satisfies the following relationship: c represents the speed of light, d represents the spacing of the array antenna, α j Represents the unresolved ambiguity incident angle of the jth frequency point. Due to the phase ambiguity problem, the α calculated by the above formula is j Not the same, only when the phase difference of each frequency point compensates the correct phase ambiguity term, all α j It should be consistent, that is, as follows: Define a slope value sl as follows: Define a slope difference, the expression is as follows: When the phase difference of each frequency point correctly compensates for the ambiguity phase, the overall slope difference will reach the minimum value, that is: At this time, the deblurred incident angle α' after compensation j Expressed as: For broadband signals, the incident angle is determined by the following multi-frequency deambiguation incident angle weighted average method: Among them, ρ j Indicates the maximum eigenvalue of the signal subspace at the jth frequency point, representing the strength of the signal; v j and u j Represents the calculated incident angle of the jth frequency point in the x-axis and y-axis directions, but this angle has not been defuzzified, so for v j and u j , respectively use the method of step 4 to perform defuzzification operation, that is, let α j Equal to v j and u j , and then perform phase deambiguation to finally obtain the calculated incident angles v and u of the broadband signal in the x-axis and y-axis directions; Step 5: Calculate the azimuth and elevation angles of the radiation source from the true incident angles in the two directions, specifically:

2. The broadband lightning VHF radiation source location method based on the ESPRIT algorithm according to claim 1 is characterized in that: In step 3, the frequency domain signals of each frequency point on the x-axis and y-axis are located using the ESPRIT algorithm, and the calculated incident angle v of the jth frequency point in the two directions of the two axes is obtained respectively. j and u j , specifically: For a given uniform linear array of M antennas, assuming that there are N narrowband radiation sources in the far field transmitting to the array antenna, the signal received by the array antenna is expressed as follows: X(t)=AS(t)+N(t) Where X(t), S(t), and N(t) represent the arrival signal, radiation source signal, and noise received by the array antenna, respectively; A represents the array manifold vector; A=[a(β1),a(β2),...,a(β N )] β n represents the incident angle of the nth radiation source, λ n represents the wavelength of the signal, and d represents the spacing of the array antenna; make Then A in the above formula can be rewritten as: Divide this linear array into two sub-arrays X1 and X2, which are the 1st to M-1st and 2nd to Mth items of array X respectively. The signals received by the two sub-arrays are expressed as follows: X1(t)=A1S(t)+N1(t) X2(t)=A2S(t)+N2(t) Therefore, the following relationship exists: A2=A1Φ The above formula shows that the manifold vectors of the two linear subarrays differ by only a fixed phase difference, and this phase difference represents the direction of the incoming wave from the radiation source. Therefore, the DOA parameter of the radiation source can be obtained by solving Φ. The covariance matrix of the signal received by the array antenna is expressed as follows: R X =E[XX H ]=AR S A H +R N Among them, R X and R S Represent the covariance matrix of the received signal and the radiation source respectively, H represents the conjugate transpose, and R X Perform eigenvalue decomposition to obtain the following formula: Among them U S and U N Represent the signal subspaces of the radiation source and noise respectively. Since the signal subspace and the space spanned by the array manifold vector are the same, there exists a non-singular matrix T that satisfies the following formula: U S =AT The corresponding expressions of the two sub-arrays are written as follows: U1=A1T U2=A2T=A1ΦT Therefore, we can get: U1T -1 ΦT=A1ΦT=U2 Let Ψ = T -1 ΦT, we get: U1Ψ=U2 By calculating Ψ and then performing eigenvalue decomposition on it, we can obtain its diagonal matrix value Φ, thereby solving the DOA parameter of the radiation source. The incident angle of the radiation source is obtained by the following formula: Calculate the incident angle v in the x-axis direction j When the M antennas of the uniform linear array are replaced by the antennas on the x-axis, X(t) is replaced by X(f j ) instead, we get: Among them, d x Indicates the spacing between antennas on the x-axis; Similarly, when calculating the incident angle u in the y-axis direction j When the M antennas of the uniform linear array are replaced by antennas on the y-axis, X(t) is replaced by X(f j ) instead, we get: Among them, d y Indicates the spacing between antennas on the y-axis.

3. The broadband lightning VHF radiation source location method based on the ESPRIT algorithm according to claim 2 is characterized in that: The orthogonal uniform linear VHF antenna array in step 1 is an L-shaped uniform linear VHF antenna array, which has a total of 7 antennas.

4. The broadband lightning VHF radiation source location method based on the ESPRIT algorithm according to claim 3 is characterized in that: Among the 7 antennas, one is located at the origin of the coordinate system, and the other 3 are evenly distributed on the orthogonal x-axis and y-axis.

5. The broadband lightning VHF radiation source location method based on the ESPRIT algorithm according to claim 3 is characterized in that: The distance between adjacent antennas on the x-axis and y-axis is 5-10m.

6. The broadband lightning VHF radiation source location method based on the ESPRIT algorithm according to claim 5, characterized in that: The distance between adjacent antennas on the x-axis and y-axis is 9m.

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