AOA-TDOA combined based positioning method of very high frequency wideband radiation source

Abstract

The application discloses a VHF broadband radiation source positioning method based on AOA-TDOA combination, and relates to the fields of signal processing and lightning radiation source imaging technology.The method comprises the following steps: a non-uniform L-shaped lightning observation array is constructed, and the initial values of the angles between a radiation source and an X axis and a Y axis are respectively obtained by using a MUSIC algorithm; the initial values are fixed, and the initial values of inverse distances are obtained by one-dimensional grid search; a cost function which is jointly constrained by AOA and TDOA is constructed in two steps under the modified polar coordinates, an alternating cyclic optimization strategy is adopted to update the to-be-estimated parameters until the convergence threshold is satisfied; and finally, the elevation angle and the azimuth angle of the radiation source are calculated according to the effective narrowband components in the lightning VHF broadband signal, combined with the optimized parameters, and the positioning result is output.The application integrates the advantages of AOA and TDOA, improves the positioning precision and the convergence speed, adapts to the characteristics of the lightning VHF broadband signal, and has small positioning error and strong anti-interference.

Description

Technical Field

[0001] This invention relates to the fields of signal processing and lightning radiation source imaging technology, and specifically to a VHF broadband radiation source localization method based on AOA-TDOA joint. Background Technology

[0002] Lightning imaging is a crucial tool supporting research in lightning physics and the development of lightning protection technologies. This technology involves deploying multiple antennas to receive electromagnetic wave signals radiated by lightning discharges and using specific positioning algorithms to invert the spatial distribution of the radiation sources, thereby constructing two-dimensional or three-dimensional images of the lightning channel. Based on the lightning imaging results, the propagation characteristics of the lightning leader and the timing features of the discharge can be analyzed. This not only helps to reveal the mechanisms of lightning but also provides key parameters such as channel morphology and development speed for lightning strike risk assessment, thereby improving the scientific rigor and reliability of lightning protection designs for buildings and power facilities.

[0003] Existing lightning imaging methods are mainly divided into two categories: The first category is Time Difference of Arrival (TDOA) localization technology based on long baselines (approximately 20 kilometers). This type of method is typically used to determine the location of ground flash return strokes and detect the three-dimensional process of the entire lightning event. Its advantage lies in its high spatial resolution, but it requires high-precision time synchronization among multiple distributed stations, making system construction and site selection difficult, and resulting in high operation and maintenance costs. The second category is interferometric imaging technology based on short baselines (approximately 10 meters). This method can realize the inversion of the two-dimensional development process of lightning under single-station conditions, and has the advantages of flexible deployment and simple network construction. Meanwhile, some existing technologies have addressed the issues of poor adaptability, high noise interference, and low imaging efficiency of uniform arrays by constructing non-uniform antenna arrays and designing dimensionality-reducing propagation operators. However, they have not yet overcome the core bottleneck of joint estimation of high-dimensional parameters. Traditional lightning location methods require simultaneous estimation of high-dimensional parameters such as azimuth, elevation, and distance. The parameters are tightly coupled, and direct joint optimization easily leads to poor algorithm convergence and iterative divergence, with computational complexity increasing exponentially. This not only prolongs the location time but may also reduce the location accuracy due to insufficient parameter optimization, making it difficult to meet the needs of refined and rapid lightning location in complex scenarios. In addition, both traditional technologies and existing optimization schemes suffer from insufficient anti-interference capabilities and poor parameter estimation stability, further restricting the engineering application of lightning imaging technology. Summary of the Invention

[0004] The technical problem to be solved by this invention is how to address the issues of poor accuracy, high computational complexity, and poor anti-interference in traditional lightning location methods, which rely on single observation methods.

[0005] This invention solves the above-mentioned technical problems through the following technical means: a VHF broadband radiation source localization method based on AOA-TDOA joint, comprising: S1. Construct a non-uniform L-shaped lightning observation array. Receive broadband Very High Frequency (VHF) lightning signals using X-axis and Y-axis subarrays respectively. Obtain the angle between the radiation source and the X-axis using the MUSIC algorithm. initial value Angle with the Y-axis initial value ; S2, Fix the initial value and The initial value of the inverse distance is obtained through a one-dimensional grid search. , ; S3. Under the corrected polar coordinates, construct and optimize the cost function in two steps: using [ , [The parameter to be estimated] is used to construct a cost function constrained by both the Angle of Arrival (AOA) and the Time Difference of Arrival (TDOA). - Alternating Loop Optimization Update , until the preset convergence threshold is met; with [ , [ ] represents the parameter to be estimated. A cost function constrained by both AOA and TDOA is constructed, and [ ] is used. - Alternating Loop Optimization Update , Continue until the preset convergence threshold is met, and then output the optimized parameters. S4. Based on the narrowband component in the lightning VHF broadband signal and the optimized parameters, calculate the elevation angle and azimuth angle of the lightning radiation source and output the positioning result.

[0006] This invention constructs a non-uniform L-shaped lightning observation array and combines it with the MUSIC algorithm to obtain the initial value of the angle between the radiation source and the X / Y axis. The initial value of the inverse distance is then locked through a one-dimensional grid search, and finally, the angle is corrected using polar coordinates. , Inverse distance To optimize the variables, the maximum eigenvalue of the signal covariance matrix is ​​used as the cost function. Then, a two-step alternating cyclic optimization strategy is employed in corrected polar coordinates to accurately update the parameters to be estimated. Finally, the elevation and azimuth angles of the radiation source are calculated by combining the narrowband components of the broadband signal. This not only achieves unified adaptation of near-field and far-field positioning models, avoiding the accuracy gaps inherent in traditional scene-specific modeling, but also compensates for the deficiencies of a single observation dimension through deep fusion of AOA and TDOA information. Furthermore, by leveraging hierarchical optimization and parameter decoupling design, the computational complexity of joint estimation of high-dimensional parameters is significantly reduced, achieving rapid and stable convergence of the algorithm. This significantly improves the accuracy, efficiency, and anti-interference capability of VHF lightning radiation source positioning, fully meeting the practical needs of lightning physics research and lightning protection engineering design.

[0007] Furthermore, the angle between the radiation source and the X-axis is obtained using the MUSIC algorithm. initial value Angle with the Y-axis initial value ,include: S1.1, Define the X-axis subarray signal receiving model: Let the lightning VHF broadband signal received by the X-axis subarray be:

[0008] in, For the array element response, The signal waveform of a lightning radiation source. For arrival time, The time when the signal source begins to radiate. For the radiation source and the first The time delay caused by the distance between array elements For the first White noise at each array element; The noise-free version of the X-axis subarray observation signal is: ; The X-axis subarray received signal is represented in TDOA-associated form:

[0009] in, For the first TDOA between the first array element and the first array element; S1.2, signal discretization processing, sample covariance matrix calculation, dual-coordinate system TDOA adaptation, and MUSIC algorithm search are performed to obtain the initial value of the angle between the radiation source and the X-axis; for the Y-axis subarray, the signal data is received using the Y-axis subarray. Repeat the above steps to obtain the initial value of the angle between the radiation source and the Y-axis. .

[0010] Furthermore, the signal discretization processing and sample covariance matrix calculation in S1.2 are specifically as follows: right Discretization is performed to obtain discrete signals:

[0011] Based on discrete signals Calculate the sample covariance matrix:

[0012] in, For array element manifold, For signal, It is white noise. The discrete Fourier transform matrix is... The imaginary unit, This is the conjugate transpose of the matrix. , Sampling frequency, N is the number of snapshots.

[0013] Furthermore, the adaptation of the TDOA expression in the dual coordinate system in S1.2 includes: In the traditional Cartesian coordinate system, the expression for TDOA is:

[0014] in, Let be the speed of signal propagation. and Represent the position of the radiation source in the Cartesian coordinate system and the first The location of the sensor array This indicates the position of the first sensor array. In corrected polar coordinates, the expression for TDOA is:

[0015] in, For the speed of signal propagation, Indicates inverse distance. Indicates the angle of arrival. , indicating the first Each element returns to its origin. The square of the distance, , indicating the first The projection of the position vector of each array element onto the direction of the radiation source.

[0016] Furthermore, the initial value of the angle between the radiation source and the X-axis is obtained through the MUSIC algorithm, including: For the sample covariance matrix Eigenvalue decomposition yields the noise subspace. The MUSIC algorithm is then used to search for orthogonal steering vectors within the noise subspace; their spatial spectral function is:

[0017] in, For the X-axis subarray at the angle The array manifold vector below, The noise subspace matrix; Within the angle range Performing a one-dimensional search within will enable Angle that achieves the maximum value As an initial estimate of the direction of the radiation source, i.e. .

[0018] Furthermore, S2 includes: Will Substitute the largest eigenvalue of the signal covariance matrix Let be the cost function, such that the function is only related to the inverse distance. Univariate function:

[0019] In reverse distance The range of values Perform a one-dimensional grid search, divide the grid into discrete points, and calculate the values ​​of each grid point. Corresponding cost function value Select to make Grid points that achieve the maximum value , as the initial value of the inverse distance, i.e. .

[0020] Furthermore, S3 includes: For the parameters to be optimized Its update is based on the Newton's method iterative formula:

[0021] The first derivative is:

[0022] The second derivative is:

[0023] in, For matrix The eigenvector corresponding to the largest eigenvalue. For the first 1 eigenvalue, For the corresponding eigenvalues The normalized eigenvectors, where M is the number of array elements; When the reverse distance is fixed Update azimuth When, solve:

[0024] in, Indicates the number of iterations; When the azimuth angle is fixed Update inverse distance When, solve:

[0025] After each iteration, check the convergence condition:

[0026] in, If the preset convergence threshold is not met, the iteration continues; if it is met, the final estimate is output. .

[0027] Furthermore, S4 includes: Based on all the narrowband components contained in the broadband lightning VHF signal, the angle formed between the VHF signal incident direction and the positive X-axis direction is denoted as . , ,according to Combine the angle update value obtained through iteration and , obtain parameters The estimated value ; The same processing is applied to the signal received by the Y-axis subarray to obtain the angle between the incident signal and the positive Y-axis direction. The estimate was obtained. .

[0028] Furthermore, the elevation angle of the lightning radiation source The calculation formula is:

[0029] The formula for calculating the azimuth angle is: .

[0030] This invention also provides a VHF broadband radiation source localization system based on AOA-TDOA joint, comprising: The array signal acquisition and initial angle acquisition module is used to construct a non-uniform L-shaped lightning observation array. It receives wideband VHF lightning signals based on X-axis and Y-axis subarrays, and obtains the angle between the radiation source and the X-axis using the MUSIC algorithm. initial value Angle with the Y-axis initial value ; Inverse distance initial value search module, used to fix the initial value and The initial value of the inverse distance is obtained through a one-dimensional grid search. , ; The parameter iterative optimization module is used to construct and optimize the cost function in two steps under corrected polar coordinates: with [ , [ ] is the parameter to be estimated. A cost function constrained by both the angle of arrival (AOA) and the time difference of arrival (TDOA) is constructed. - Alternating Loop Optimization Update , until the preset convergence threshold is met; with [ , [ ] represents the parameter to be estimated. A cost function constrained by both AOA and TDOA is constructed, and [ ] is used. - Alternating Loop Optimization Update , Continue until the preset convergence threshold is met, and then output the optimized parameters. The positioning result output module is used to calculate the elevation angle and azimuth angle of the lightning radiation source based on the narrowband component in the lightning VHF broadband signal and the optimized parameters, and output the positioning result.

[0031] The advantages of this invention are: (1) The present invention uses modified polar coordinates (MPR) to characterize the target position parameters (angles). ,angle Inverse distance This breaks down the model boundaries between near-field positioning and far-field direction finding, achieving unified adaptation for near-field and far-field scenarios and avoiding the accuracy gap problem caused by traditional scenario-specific modeling.

[0032] (2) This invention integrates the dual observation information of angle of arrival (AOA) and time difference of arrival (TDOA), fully explores the intrinsic correlation between the two types of signals, effectively complements the information defects of a single observation dimension, and greatly improves the accuracy and reliability of the positioning results.

[0033] (3) The present invention proposes - , Compared to the traditional Newton's method, the alternating optimization strategy accelerates the iterative convergence speed through parameter decoupling design, while optimizing the numerical calculation logic, enhancing the stability of the algorithm in complex scenarios, and reducing the risk of iterative divergence. Attached Figure Description

[0034] Figure 1 This is a flowchart of the VHF broadband radiation source localization method based on AOA-TDOA joint embodiment 1 of the present invention; Figure 2 This is a diagram of a non-uniform L-shaped array from Embodiment 1 of the present invention; Figure 3 This is a lightning imaging image of Embodiment 1 of the present invention. Detailed Implementation

[0035] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, 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.

[0036] Example 1 like Figure 1 As shown, the VHF broadband radiation source localization method based on AOA-TDOA joint includes: S1. Construct a non-uniform L-shaped lightning observation array. Receive wideband VHF lightning signals using X-axis and Y-axis subarrays respectively. Obtain the angle between the radiation source and the X-axis using the MUSIC algorithm. initial value Angle with the Y-axis initial value .

[0037] Specifically, the non-uniform L-shaped lightning observation array structure is as follows: Figure 2 As shown, Figure 2 The diagram illustrates the azimuth of the lightning radiation source. Angle of elevation and angle , Definition: The array is L-shaped on the XOY plane, where the X-axis is due south and the Y-axis is due east. In this embodiment, there are 4 antennas on both the X and Y axes (including the antenna at the origin), where V1, V2, V3, V4, V5, V6, and V7 represent numbered antennas. The horizontal coordinate of the antennas arranged on the X-axis is... ,in, This indicates the distance between antenna V1 and antenna V2. The antennas on the Y-axis are arranged in the same way as the antennas on the X-axis.

[0038] The AOA direct positioning model ignores the correlation between signals, which leads to a failure to fully exploit the potential correlation information between signal sources, thus limiting its positioning accuracy. In contrast, AOA-TDOA jointly considers the signal correlation between arrays, and by combining AOA and TDOA information, it can provide higher positioning accuracy in complex propagation environments.

[0039] A non-uniform L-shaped lightning observation array is used to locate radiation source targets. However, unlike localization methods that rely solely on AOA information, the AOA-TDOA joint method fully utilizes the TDOA of each array and combines it with AOA information, thereby improving the overall accuracy and reliability of the localization.

[0040] Define the X-axis subarray signal receiving model: Let the wideband VHF lightning signal received by the X-axis subarray be:

[0041] in, The signal waveform of a lightning radiation source. The time when the signal source begins to radiate. For the radiation source and the first The time delay caused by the distance between array elements For the first White noise at each array element For the array element response, This refers to the arrival time.

[0042] The noise-free version of the X-axis subarray observation signal is: .

[0043] The X-axis subarray received signal is represented in TDOA-associated form:

[0044] in, For the first TDOA between the first array element and the first array element.

[0045] right Discretization is performed to obtain discrete signals:

[0046] Based on discrete signals Calculate the sample covariance matrix:

[0047] in, For array element manifold, For signal, It is white noise. The discrete Fourier transform matrix is... The imaginary unit, This is the conjugate transpose of the matrix. , Sampling frequency, N is the number of snapshots.

[0048] In the traditional Cartesian coordinate system, the expression for TDOA is:

[0049] in, Let be the speed of signal propagation. and Represent the position of the radiation source in the Cartesian coordinate system and the first The location of the sensor array This is the position of the first sensor array.

[0050] In corrected polar coordinates, the expression for TDOA is:

[0051] in, For the speed of signal propagation, Indicates inverse distance. Indicates the angle of arrival. , indicating the first Each element returns to its origin. The square of the distance. , indicating the first The projection of the position vector of each array element onto the direction of the radiation source.

[0052] For the sample covariance matrix Eigenvalue decomposition is performed to separate the signal subspace from the noise subspace. The core of the MUSIC algorithm is to search for a steering vector that makes the noise subspace orthogonal; its spatial spectral function is defined as:

[0053] in, For the X-axis subarray at the angle The array manifold vector (guiding vector) is given below. For non-uniform arrays, Precise calculations are required based on the actual physical location of the array elements. For the reason The noise subspace matrix is ​​composed of the eigenvectors corresponding to the small eigenvalues.

[0054] Within the angle range Perform a one-dimensional search within (e.g., from 0° to 180°) to find the... Angle that achieves the maximum value The angle corresponding to this peak value is the initial estimate of the radiation source direction, i.e. .

[0055] Through the above steps, a high-quality initial estimate of the angle between the radiation source and the X-axis was obtained. For the other dimension of the L-shaped array (the angle with the Y-axis) Its initialization process is exactly the same, requiring only the use of the Y-axis subarray data. Repeat the above steps to obtain .

[0056] S2, Fix the initial value and The initial value of the inverse distance is obtained through a one-dimensional grid search. , .

[0057] Specifically, in obtaining the initial angle value and After that, the next step is to initialize the inverse distance. The specific steps are as follows: S2.1 Constructing information about inverse distance The cost function.

[0058] The initial angle value obtained in the previous step and It is fixed as a known quantity.

[0059] Will Substituting into the cost function of direct localization, i.e., the largest eigenvalue of the signal covariance matrix... At this point, the function is only about the inverse distance. Univariate function:

[0060] Matrix Q is a Hermitian matrix (i.e., a conjugate symmetric matrix) whose elements reflect the correlation between signals received by different arrays. Its specific form is closely related to the observations in the array network. The Okay, number Column elements can be represented as:

[0061] in, It is a Discrete Fourier Transform (DFT) matrix used to convert signals to the frequency domain, which facilitates the handling of time delays; This indicates the conjugate transpose.

[0062] S2.2, One-dimensional grid search.

[0063] In reverse distance Perform a one-dimensional grid search across all possible values.

[0064] Value range: The theoretical minimum value is 0 (corresponding to the far field), and the maximum value is... The closest distance that the system can locate Decision (e.g.) (corresponding to the nearest 10 meters).

[0065] Search process: within the range [0, ... The interior is uniformly divided into a series of discrete grid points. For each grid point Calculate the corresponding cost function value. .

[0066] S2.3 Determine the initial values.

[0067] Compare the cost function values ​​at all grid points and select the one that makes... The grid point that gets the maximum value This is used as the initial value for the inverse distance, i.e. .

[0068] Similarly, Substituting the cost function of direct localization, the corresponding inverse distance is obtained through a one-dimensional grid search. initial value .

[0069] S3. Under the corrected polar coordinates, construct and optimize the cost function in two steps: using [ , [ ] is the parameter to be estimated. A cost function constrained by both the angle of arrival (AOA) and the time difference of arrival (TDOA) is constructed. - Alternating Loop Optimization Update , until the preset convergence threshold is met; with [ , [ ] represents the parameter to be estimated. A cost function constrained by both AOA and TDOA is constructed, and [ ] is used. - Alternating Loop Optimization Update , The process continues until the preset convergence threshold is met, at which point the optimized parameters are output.

[0070] Specifically, the alternating optimization loop of the synchronous AOA-TDOA direct positioning algorithm based on modified polar coordinates is fundamentally about decomposing the complex multidimensional joint optimization problem into sequentially executed single-parameter optimization subproblems. This process, by fixing some parameters and optimizing the remaining ones, gradually approaches the optimal solution, ultimately achieving high-precision estimation of the radiation source's location parameters.

[0071] The core of the loop is to maximize the largest eigenvalue of the signal covariance matrix. The cost function is as follows:

[0072] in, To correct the position parameter vector in polar coordinates, It is the largest eigenvalue.

[0073] For the parameters to be optimized Its update is based on the Newton's method iterative formula:

[0074] The formula for calculating the first derivative is:

[0075] in, For matrix The eigenvector corresponding to the largest eigenvalue.

[0076] The formula for calculating the second derivative is:

[0077] in, For the first 1 eigenvalue, For the corresponding eigenvalues The normalized eigenvectors, where M is the number of array elements.

[0078] Specifically, regarding the update of each parameter, when the inverse distance is fixed... Update azimuth When, solve:

[0079] in, Indicates the number of iterations.

[0080] This is equivalent to using subarray data along the X-axis to optimize azimuth estimation while keeping the distance constant.

[0081] When the azimuth angle is fixed Update inverse distance When, solve:

[0082] This is equivalent to optimizing the distance estimate along a ray with a fixed direction. Using inverse distance instead of direct distance for optimization ensures that, under far-field conditions (…),… →0) Numerical stability of the optimization process.

[0083] After each iteration, determine whether the convergence condition is met:

[0084] in, If the convergence threshold is not met, the iteration continues; if the convergence condition is met, the final estimated value is output. Similarly, the parameters to be optimized... Construct a cost function jointly constrained by AOA and TDOA, and adopt... - Alternating Loop Optimization Update , The process continues until the preset convergence threshold is met, at which point the optimized parameters are output.

[0085] This - , - The alternating optimization strategy significantly reduces computational complexity by decomposing the high-dimensional problem. The embedded grid search enhances the algorithm's ability to escape local optima, while Newton's law guarantees fast convergence accuracy near the truth value. The entire framework exhibits excellent numerical stability in corrected polar coordinates and can effectively handle both near and far-field localization problems.

[0086] S4. Based on the narrowband component in the VHF broadband signal of lightning, and combined with the optimized parameters, calculate the elevation angle and azimuth angle of the lightning radiation source, and output the positioning result.

[0087] Specifically, based on all the narrowband components contained in the broadband lightning VHF signal, the angle formed between the VHF signal incident direction and the positive X-axis direction is denoted as... , .according to The previous results and Thus, the parameters are obtained. Estimate .

[0088] By performing the same processing on the signal received by the Y-axis subarray, the angle between the incident signal and the positive Y-axis direction can be obtained. The estimate. Based on Figure 2 ,get .

[0089] Based on the above steps, we obtain... , Then, the elevation angle is obtained from the following formula. The specific formula is as follows:

[0090] And azimuth There are four possible scenarios, and the calculation formula is as follows:

[0091] like Figure 3 This is a lightning image; the horizontal axis represents the azimuth, the vertical axis represents the elevation, and the colors change over time.

[0092] Example 2 Based on Embodiment 1, Embodiment 2 of the present invention also provides a VHF broadband radiation source localization system based on AOA-TDOA joint, comprising: The array signal acquisition and initial angle acquisition module is used to construct a non-uniform L-shaped lightning observation array. It receives wideband VHF lightning signals based on X-axis and Y-axis subarrays, and obtains the angle between the radiation source and the X-axis using the MUSIC algorithm. initial value Angle with the Y-axis initial value .

[0093] Specifically, it includes: an X-axis subarray modeling unit, used to set the lightning VHF broadband signal received by the X-axis subarray as:

[0094] in, The signal waveform of a lightning radiation source. The time when the signal source begins to radiate. For the radiation source and the first The time delay caused by the distance between array elements For the first White noise at each array element For the array element response, This refers to the arrival time.

[0095] The noise-free version of the X-axis subarray observation signal is: .

[0096] The X-axis subarray received signal is represented in TDOA-associated form:

[0097] in, For the first TDOA between the first array element and the first array element.

[0098] The initial value estimation unit is used for signal discretization, sample covariance matrix calculation, dual-coordinate system TDOA adaptation, and MUSIC algorithm search to obtain the initial value of the angle between the radiation source and the X-axis; for the Y-axis subarray, it uses the Y-axis subarray to receive signal data. Signal discretization, sample covariance matrix calculation, dual-coordinate system TDOA adaptation, and MUSIC algorithm search are performed to obtain the initial value of the angle between the radiation source and the Y-axis. .include: The signal discretization processing subunit is used for... Discretization is performed to obtain discrete signals:

[0099] Sample covariance matrix calculation subunit, used for discrete signals Calculate the sample covariance matrix:

[0100] in, For array element manifold, For signal, It is white noise. The discrete Fourier transform matrix is... The imaginary unit, This is the conjugate transpose of the matrix. , Sampling frequency, N is the number of snapshots.

[0101] The dual-coordinate TDOA adapter sub-element is used to construct TDOA expressions in Cartesian coordinates and modified polar coordinates.

[0102] In the traditional Cartesian coordinate system, the expression for TDOA is:

[0103] in, Let be the speed of signal propagation. and Represent the position of the radiation source in the Cartesian coordinate system and the first The location of the sensor array This is the position of the first sensor array.

[0104] In corrected polar coordinates, the expression for TDOA is:

[0105] in, For the speed of signal propagation, Indicates inverse distance. Indicates the angle of arrival. , indicating the first Each element returns to its origin. The square of the distance, , indicating the first The projection of the position vector of each array element onto the direction of the radiation source.

[0106] The MUSIC algorithm searches for subunits to perform a sample covariance matrix analysis. Eigenvalue decomposition yields the noise subspace. The MUSIC algorithm is then used to search for orthogonal steering vectors within the noise subspace; their spatial spectral function is:

[0107] in, For the X-axis subarray at the angle The array manifold vector below, For the reason The noise subspace matrix is ​​composed of the eigenvectors corresponding to the small eigenvalues.

[0108] Within the angle range Performing a one-dimensional search within will enable Angle that achieves the maximum value As an initial estimate of the direction of the radiation source, i.e. .

[0109] Inverse distance initial value search module, used to fix initial values and The initial value of the inverse distance is obtained through a one-dimensional grid search. , .

[0110] Specifically, this includes: cost function building units, used to... Substitute the largest eigenvalue of the signal covariance matrix For a direct localization model with a cost function, make the function only relevant to the inverse distance. Univariate function:

[0111] One-dimensional grid search unit, used for inverse distance The range of values Perform a one-dimensional grid search, divide the grid into discrete points, and calculate the values ​​of each grid point. Corresponding cost function value .

[0112] Initial value confirmation unit, used to select... Grid points that achieve the maximum value , as the initial value of the inverse distance, i.e. .

[0113] The parameter iterative optimization module is used to construct and optimize the cost function in two steps under corrected polar coordinates: with [ , [ ] is the parameter to be estimated. A cost function constrained by both the angle of arrival (AOA) and the time difference of arrival (TDOA) is constructed. - Alternating Loop Optimization Update , until the preset convergence threshold is met; with [ , [ ] represents the parameter to be estimated. A cost function constrained by both AOA and TDOA is constructed, and [ ] is used. - Alternating Loop Optimization Update , The process continues until the preset convergence threshold is met, at which point the optimized parameters are output.

[0114] Specifically, for the parameters to be optimized Its update is based on the Newton's method iterative formula:

[0115] The first derivative is:

[0116] The second derivative is:

[0117] in, Let M be the eigenvector corresponding to the largest eigenvalue of matrix Q, and M be the number of matrix elements.

[0118] Optimization unit, used when fixed inverse distance Update azimuth When, solve:

[0119] in, Indicates the number of iterations.

[0120] Optimization unit, used when the azimuth angle is fixed. Update inverse distance When, solve:

[0121] The convergence check unit is used to check the convergence condition after each iteration.

[0122] in, If the preset convergence threshold is not met, the iteration continues; otherwise, the final estimated value is output. .

[0123] The positioning result output module is used to calculate the elevation angle and azimuth angle of the lightning radiation source based on the narrowband component in the lightning VHF broadband signal and the optimized parameters, and output the positioning result.

[0124] Specifically, the spatial spectrum verification unit is used to determine the angle between the VHF signal incident direction and the positive X-axis direction based on all narrowband components contained in the broadband lightning VHF signal. , ,according to Combine the angle update value obtained through iteration and , obtain parameters The estimated value .

[0125] The same processing is applied to the signal received by the Y-axis subarray to obtain the angle between the incident signal and the positive Y-axis direction. Estimate .

[0126] Angle calculation unit, used to combine and The elevation angle of the radiation source can be calculated using the following formula. and azimuth : Elevation angle of lightning radiation source The calculation formula is:

[0127] Azimuth The calculation formula is: .

[0128] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A VHF broadband radiation source localization method based on AOA-TDOA joint method, characterized in that, include: S1. Construct a non-uniform L-shaped lightning observation array. Receive wideband VHF lightning signals using X-axis and Y-axis subarrays respectively. Obtain the angle between the radiation source and the X-axis using the MUSIC algorithm. initial value Angle with the Y-axis initial value ;include: S1.1, Define the X-axis subarray signal receiving model: Let the lightning VHF broadband signal received by the X-axis subarray be: in, For the array element response, The signal waveform of a lightning radiation source. For arrival time, The time when the signal source begins to radiate. For the radiation source and the first The time delay caused by the distance between array elements For the first White noise at each array element; The noise-free version of the X-axis subarray observation signal is: ; The X-axis subarray received signal is represented in TDOA-associated form: in, For the first TDOA between the first array element and the first array element; S1.2, signal discretization processing, sample covariance matrix calculation, dual-coordinate system TDOA adaptation, and MUSIC algorithm search are performed to obtain the initial value of the angle between the radiation source and the X-axis; for the Y-axis subarray, the signal data is received using the Y-axis subarray. Repeat the above steps to obtain the initial value of the angle between the radiation source and the Y-axis. ; Dual coordinate system TDOA adaptation includes: In the traditional Cartesian coordinate system, the expression for TDOA is: in, Let be the speed of signal propagation. and Represent the position of the radiation source in the Cartesian coordinate system and the first The location of the sensor array This indicates the position of the first sensor array. In corrected polar coordinates, the expression for TDOA is: in, For the speed of signal propagation, Indicates inverse distance. Indicates the angle of arrival. , indicating the first Each element returns to its origin. The square of the distance, , indicating the first The projection of the position vectors of each array element onto the direction of the radiation source; S2, Fix the initial value and The initial value of the inverse distance is obtained through a one-dimensional grid search. , ; S3. Under the corrected polar coordinates, construct and optimize the cost function in two steps: using [ , [ ] is the parameter to be estimated. A cost function constrained by both the angle of arrival (AOA) and the time difference of arrival (TDOA) is constructed. - Alternating Loop Optimization Update , until the preset convergence threshold is met; with [ , [ ] represents the parameter to be estimated. A cost function constrained by both AOA and TDOA is constructed, and [ ] is used. - Alternating Loop Optimization Update , Continue until the preset convergence threshold is met, and then output the optimized parameters. S4. Based on the narrowband component in the lightning VHF broadband signal and the optimized parameters, calculate the elevation angle and azimuth angle of the lightning radiation source and output the positioning result.

2. The VHF broadband radiation source localization method based on AOA-TDOA joint as described in claim 1, characterized in that, The signal discretization and sample covariance matrix calculation in S1.2 are as follows: right Discretization is performed to obtain discrete signals: Based on discrete signals Calculate the sample covariance matrix: in, For array element manifold, For signal, It is white noise. It is the discrete Fourier transform matrix. The imaginary unit, This is the conjugate transpose of the matrix. , Sampling frequency, , This represents the number of snapshots.

3. The VHF broadband radiation source localization method based on AOA-TDOA joint as described in claim 1, characterized in that, The initial value of the angle between the radiation source and the X-axis is obtained by searching using the MUSIC algorithm, including: For the sample covariance matrix Eigenvalue decomposition yields the noise subspace. The MUSIC algorithm is then used to search for orthogonal steering vectors within the noise subspace; their spatial spectral function is: in, For the X-axis subarray at the angle The array manifold vector below, The noise subspace matrix; Within the angle range Performing a one-dimensional search within will enable Angle that achieves the maximum value As an initial estimate of the direction of the radiation source, i.e. .

4. The VHF broadband radiation source localization method based on AOA-TDOA joint as described in claim 1, characterized in that, S2 includes: Will Substitute the largest eigenvalue of the signal covariance matrix Let be the cost function, such that the cost function is about the inverse distance. Univariate function: In reverse distance The range of values Perform a one-dimensional grid search, divide the grid into discrete points, and calculate the values ​​of each grid point. The corresponding cost function value Select to make Grid points that achieve the maximum value , as the initial value of the inverse distance, i.e. .

5. The VHF broadband radiation source localization method based on AOA-TDOA joint as described in claim 1, characterized in that, S3 includes: For the parameters to be optimized Its update is based on the Newton's method iterative formula: The first derivative is: The second derivative is: in, For matrix The eigenvector corresponding to the largest eigenvalue. For the first 1 eigenvalue, For the corresponding eigenvalues The normalized eigenvectors, where M is the number of array elements; When the reverse distance is fixed Update azimuth When, solve: in, Indicates the number of iterations; When the azimuth angle is fixed Update inverse distance When, solve: After each iteration, check the convergence condition: in, If the preset convergence threshold is not met, the iteration continues; if it is met, the final estimate is output. .

6. The VHF broadband radiation source localization method based on AOA-TDOA joint as described in claim 1, characterized in that, S4 includes: Based on all the narrowband components contained in the broadband lightning VHF signal, the angle formed between the VHF signal incident direction and the positive X-axis direction is denoted as... , ,according to Combine the angle update value obtained through iteration and , obtain parameters The estimated value ; The same processing is applied to the signal received by the Y-axis subarray to obtain the angle between the incident signal and the positive Y-axis direction. The estimate was obtained. .

7. The VHF broadband radiation source localization method based on AOA-TDOA joint as described in claim 6, characterized in that, The elevation angle of the lightning radiation source The calculation formula is: The formula for calculating the azimuth angle is: 。 8. A VHF broadband radiation source localization system based on AOA-TDOA joint, characterized in that, include: The array signal acquisition and initial angle acquisition module is used to construct a non-uniform L-shaped lightning observation array. It receives wideband VHF lightning signals based on X-axis and Y-axis subarrays, and obtains the angle between the radiation source and the X-axis using the MUSIC algorithm. initial value Angle with the Y-axis initial value Includes: an X-axis subarray modeling unit, used to set the lightning VHF broadband signal received by the X-axis subarray as: in, The signal waveform of a lightning radiation source. The time when the signal source begins to radiate. For the radiation source and the first The time delay caused by the distance between array elements For the first White noise at each array element For the array element response, Arrival time; The noise-free version of the X-axis subarray observation signal is: ; The X-axis subarray received signal is represented in TDOA-associated form: in, For the first TDOA between the first array element and the first array element; The initial value estimation unit is used for signal discretization, sample covariance matrix calculation, dual-coordinate system TDOA adaptation, and MUSIC algorithm search to obtain the initial value of the angle between the radiation source and the X-axis; for the Y-axis subarray, it uses the Y-axis subarray to receive signal data. Signal discretization, sample covariance matrix calculation, dual-coordinate system TDOA adaptation, and MUSIC algorithm search are performed to obtain the initial value of the angle between the radiation source and the Y-axis. ;include: Dual coordinate system TDOA adapter subunit, used to construct TDOA expressions in Cartesian coordinates and modified polar coordinates; In the traditional Cartesian coordinate system, the expression for TDOA is: in, Let be the speed of signal propagation. and Represent the position of the radiation source in the Cartesian coordinate system and the first The location of the sensor array This indicates the position of the first sensor array. In corrected polar coordinates, the expression for TDOA is: in, For the speed of signal propagation, Indicates inverse distance. Indicates the angle of arrival. , indicating the first Each element returns to its origin. The square of the distance, , indicating the first The projection of the position vectors of each array element onto the direction of the radiation source; Inverse distance initial value search module, used to fix the initial value and The initial value of the inverse distance is obtained through a one-dimensional grid search. , ; The parameter iterative optimization module is used to construct and optimize the cost function in two steps under corrected polar coordinates: with [ , [ ] is the parameter to be estimated. A cost function constrained by both the angle of arrival (AOA) and the time difference of arrival (TDOA) is constructed. - Alternating Loop Optimization Update , until the preset convergence threshold is met; with [ , [ ] represents the parameter to be estimated. A cost function constrained by both AOA and TDOA is constructed, and [ ] is used. - Alternating Loop Optimization Update , Continue until the preset convergence threshold is met, and then output the optimized parameters. The positioning result output module is used to calculate the elevation angle and azimuth angle of the lightning radiation source based on the narrowband component in the lightning VHF broadband signal and the optimized parameters, and output the positioning result.

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