High-precision DOA estimation method based on mobile synthetic virtual array

Abstract

The invention belongs to the technical field of new-generation information, and discloses a high-precision DOA estimation method based on a mobile synthetic virtual array. The method comprises the following steps: firstly, constructing a synthetic steering vector by using platform motion, breaking through physical aperture limitation, and establishing an equivalent large-aperture virtual observation model; secondly, aiming at the problem of grid mismatch, modeling out-of-grid errors by utilizing first-order Taylor expansion, and constructing a correction perception model; and then, under a hierarchical sparse Bayesian framework, iterative optimization is carried out through an EM algorithm, and signal power, noise precision and off-lattice parameters are jointly updated, so that a DOA closed-form solution is obtained. Through the synergistic effect of virtual aperture expansion and off-grid correction of the mobile platform, a grid quantization error platform is eliminated under a high signal-to-noise ratio, super-resolution estimation not limited by grid spacing is realized, the requirements of a new generation of electronic information technology for real-time monitoring and high spatial resolution of a moving target are met, and the method is suitable for large-scale popularization and application. And a key technical support is provided for sensing integration and high-precision movement detection.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of new generation information technology, and particularly relates to a high-precision DOA estimation method based on a moving synthetic virtual array. BACKGROUND

[0002] Direction of Arrival (DOA) estimation is a core technology for radar detection, radio monitoring and automatic driving perception, and its accuracy directly determines the positioning, tracking and identification performance of the system. Classical subspace-based algorithms, such as the MUSIC method and the ESPRIT method, have angle resolution limited by the Rayleigh limit and physical aperture, and it is difficult to break through the limit by increasing the number of array elements in a limited space such as a vehicle-mounted millimeter wave radar.

[0003] To break through this limit, researchers have proposed synthetic aperture technology based on a moving platform. Moving Synthetic Virtual Array (MSVA) uses the motion of the radar platform to synthesize a huge virtual spatial aperture in the time domain, which can theoretically obtain extremely narrow beam width and ultra-high spatial resolution. However, the extremely narrow beam generated by MSVA causes a more serious grid mismatch problem. Existing high-resolution sparse reconstruction algorithms, such as Sparse Bayesian Learning (SBL), usually discretize the angle space into a fixed grid. For the extremely narrow beam synthesized by MSVA, once the true DOA of the signal deviates from the preset grid, even a small deviation will introduce a huge modeling error, resulting in a significant error platform in the estimation accuracy at high signal-to-noise ratio. If the grid is simply encrypted to alleviate this problem, the computational complexity of the algorithm will be too high; if the grid is not dense enough, the high resolution advantage brought by MSVA will be swallowed up by the huge grid mismatch error.

[0004] To solve the grid mismatch problem, the Off-grid Sparse Bayesian Inference (OGSBI) framework proposed by Yang et al. can effectively eliminate the grid quantization error by modeling the off-grid error through first-order Taylor expansion, but this method fails to utilize the platform motion to expand the virtual aperture, and its performance is still limited when the physical aperture is limited.

[0005] Aiming at the problems of physical aperture limitation and grid mismatch existing in the existing DOA estimation method, the patent proposes a high-precision DOA estimation method based on mobile synthetic virtual array. The method synthesizes a large-aperture virtual array through array platform motion, breaking through the limitation of physical array aperture. At the same time, the off-grid sparse Bayesian learning (OGSBL) framework is adopted to accurately model the grid mismatch error by using the first-order Taylor expansion, which eliminates the grid quantization error platform while improving the spatial resolution, realizing the synergistic gain of "virtual aperture expansion" and "off-grid correction". SUMMARY

[0006] The patent proposes a DOA estimation method based on mobile synthetic virtual array and off-grid sparse Bayesian learning to solve the problems existing in the existing DOA estimation method. The method first establishes a MSVA signal model based on platform motion, constructs an equivalent large-aperture observation equation through Kronecker product, builds an off-grid sparse dictionary, and derives the dictionary matrix and its derivative matrix with respect to the angle. Finally, a hierarchical Bayesian model is adopted to iteratively optimize the signal power, off-grid parameter and noise variance by EM algorithm, realizing high-precision joint estimation of DOA. The method uses platform motion to expand the virtual aperture, significantly improving the spatial resolution. Through off-grid error correction, the grid quantization error is eliminated, avoiding the error platform under high signal-to-noise ratio conditions. Combined with the sparse Bayesian learning framework, the method maintains excellent performance under limited snapshots. Simulation experiments show that compared with the SBL and OGSBL methods under the uniform linear array and the SBL method under the moving platform, the method has significant improvement in spatial spectrum resolution and estimation accuracy, and has great application value in practical engineering.

[0007] A high-precision DOA estimation method based on mobile synthetic virtual array, which is applicable to a uniform linear array mounted on a moving platform, the array comprising array elements, the array element spacing is , wherein , is the signal wavelength; the platform moves along the array axis at a constant speed , and the radar system collects pulse period characterized in that the high-precision DOA estimation method based on mobile synthetic virtual array comprises the following steps:

[0008] Step 1: The data received by the uniform linear array within pulse period is vectorized, stacked and rearranged to construct an observation matrix with a dimension of , wherein is the equivalent number of array elements, is the number of snapshots.

[0009] Step two: calculate the spatial displacement of the platform relative to the initial position at the th pulse moment , and for each possible signal direction , calculate the additional phase increment caused by the platform displacement , , is the number of signal sources;

[0010] Step three: divide the spatial angular range into uniformly spaced grid points with grid spacing ; for each grid point , construct the dictionary matrix , the th column of which is: where denotes the Kronecker product, is the physical steering vector of the stationary array;

[0011] Step four: construct the derivative matrix , the th column of which is: where denotes the first-order partial derivative of with respect to ;

[0012] Step five: introduce the grid error vector and initialize it as an all-zero vector, set the maximum number of iterations and the convergence threshold , initialize the noise precision and its hyperparameters ;

[0013] Step six: obtain the initial value of the signal power vector using the correlation mapping of the synthesized dictionary matrix and the observation matrix ;

[0014] Step seven: start the iteration process, in the th iteration, calculate the modified perception matrix ; calculate the posterior covariance matrix and the posterior mean vector of the th snapshot, where denotes the diagonal matrix composed of the corresponding elements, and the superscript denotes the In the next iteration, the superscript -1 and These represent matrix inversion and conjugate transpose, respectively.

[0015] Step 8: Based on the posterior mean obtained in Step 7 and posterior covariance From the formula Update signal power vector ,in express The first in One element, Represents the posterior covariance matrix The first on the diagonal One element, To take the square of the modulus;

[0016] Step Nine: According to the formula Update noise accuracy ,in The total observation dimension of the data. It is the data fitting error. Represents the L2 norm. It is the error expectation correction term introduced by the uncertainty in signal estimation. Represents the trace of a matrix;

[0017] Step 10: Select signal power The largest Each index constitutes a support set. Constructing information about off-grid error linear equation system The updated value of the off-scale error is obtained by solving this system of linear equations, and the value greater than 1 is set to 1. The terms are restricted to boundary values, where, The coefficient matrix, It is a constant vector;

[0018] Step 11: According to the formula Calculate the signal power vector relative rate of change ;like Less than the convergence threshold Or the number of iterations reaches If the iteration fails, proceed to step eleven; otherwise, return to step seven to continue the next iteration.

[0019] Step 12: Calculate the spatial spectrum based on the posterior mean matrix, search for the grid angle corresponding to the spectral peak, and then... Calculate the final DOA estimate, where, for The index corresponding to the maximum value The preset grid angle corresponding to the index, The optimal de-grid error correction value corresponding to the index, that is, the iteration termination value.

[0020] Further, a high-precision DOA estimation method based on a mobile synthetic virtual array, the specific process of a vectorization stacking rearrangement of received data is as follows:

[0021] A1: record The complex signal received by the m-th physical array element in the n-th pulse period under the k-th snapshot, where , , ;

[0022] A2: for each snapshot , concatenate the data of the m-th physical array element obtained in the n-th pulse period in the order of pulse time to construct an equivalent observation column vector with a dimension of ;

[0023] A3: arrange the equivalent observation column vectors corresponding to all snapshots in the order of time number in turn, and finally form an equivalent observation matrix with a dimension of .

[0024] Further, in step six of the high-precision DOA estimation method based on the mobile synthetic virtual array, the calculation process of the signal power vector is as follows:

[0025] B1: calculate an intermediate correlation matrix with a dimension of ;

[0026] B2: extract the modulus value of each complex number element in the intermediate correlation matrix in step one to construct a real energy distribution reflecting the energy intensity of each grid point under each snapshot;

[0027] B3: perform arithmetic average processing on the real energy distribution along the time snapshot dimension according to the formula , and the obtained mean value vector is the initial value of the signal power vector .

[0028] Further, in step ten of the high-precision DOA estimation method based on the mobile synthetic virtual array, the coefficient matrix and the constant vector ​​​​​The construction mode of is as follows:

[0029] Coefficient matrix The first Element of Constant vector The first Element of Wherein, Support set index, representing the signal power screened Potential signal source position, The first Column vector of matrix , Conjugate operation of complex number, Re represents the real part operation.

[0030] Further, a high-precision DOA estimation method based on a mobile synthetic virtual array, in step twelve, the estimation process of is as follows: according to the formula Calculate the average power of each grid point On all fast shots, arrange the spatial power spectrum vector In index order, search for the Maximum value in The first Peak value, and the grid index corresponding to the first Peak value is recorded as .

[0031] Compared with the prior art, the technical scheme of the present application has the following technical effects:

[0032] 1. The present application uses the mobile synthetic virtual array technology to expand the virtual aperture by platform motion, breaks through the Rayleigh limit constraint of the physical array aperture, significantly improves the spatial resolution, and has a narrower main lobe width and stronger resolution ability compared with the static array method;

[0033] 2. The present application adopts the off-grid sparse Bayesian framework, accurately models the grid mismatch error through first-order Taylor expansion, adaptively optimizes the off-grid parameters in EM iteration, effectively eliminates the grid quantization error, avoids the error platform phenomenon under high signal-to-noise ratio conditions, and realizes continuous improvement of estimation accuracy;

[0034] 3. The present application can maintain excellent performance under limited fast shot conditions through hierarchical Bayesian model and EM algorithm, and automatically realize joint optimization estimation of signal power, off-grid parameters and noise variance, and has strong algorithm robustness;

[0035] 4, The application realizes the synergistic gain of "virtual aperture expansion" and "off-grid correction", and with the increase of the number of synthetic pulses, the performance potential brought by aperture expansion can be fully released, the estimation error is continuously reduced, and a truly super-resolution DOA estimation is realized. BRIEF DESCRIPTION OF DRAWINGS

[0036] Figure 1 The figure is a schematic diagram of the mobile synthetic virtual array of the patent;

[0037] Figure 2 The figure is a power spectrum diagram of the simulation experiment of the signal processing method and other methods of the patent;

[0038] Figure 3 The figure is a partial enlarged result diagram of the power spectrum diagram of the simulation experiment of the signal processing method and other methods of the patent;

[0039] Figure 4 The figure is a relationship curve between the root mean square error and the signal-to-noise ratio of the signal processing method of the patent;

[0040] Figure 5 The figure is a relationship curve between the root mean square error and the number of snapshots of the signal processing method of the patent;

[0041] Figure 6 The figure is a relationship curve between the root mean square error and the number of synthetic pulses of the signal processing method of the patent. DETAILED DESCRIPTION

[0042] The application will be further described in combination with embodiments and drawings:

[0043] First embodiment: Figure 1 The model structure of the mobile synthetic virtual array used by the application is given. The number of physical array elements in the ULA is , the spacing between the array elements is , the mobile platform moves along the array axis at a speed of , the radar system transmits pulses with a pulse repetition interval of . There are unrelated far-field narrowband signal sources incident to the ULA, the incident angles are , the carrier frequency is 77 GHz, the wavelength , the number of snapshots , the signal-to-noise ratio , the angle search range is , the grid interval , the convergence threshold , and the maximum number of iterations .

[0044] The DOA estimation is performed by using the above conditions, and the specific implementation process is as follows:

[0045] Step one: the data received by the uniform linear array in one pulse period is vectorized, stacked and rearranged to construct an observation matrix with dimensions of , wherein is the equivalent number of array elements, is the number of snapshots;

[0046] Step two: the spatial displacement of the platform relative to the initial position at the th pulse moment is calculated, and for each possible signal direction , the additional phase increment generated by the platform displacement is calculated , wherein , , , is the number of signal sources;

[0047] Step three: the spatial angle range is divided into uniformly spaced grid points , and the grid interval is ; for each grid point , a dictionary matrix is constructed, and the th column of the matrix is: , wherein denotes the Kronecker product, is the physical steering vector of the stationary array;

[0048] Step four: a derivative matrix is constructed, and the th column of the matrix is: , wherein denotes the first-order partial derivative of with respect to ;

[0049] Step five: the off-grid error vector is introduced and initialized as a zero vector, the maximum number of iterations and the convergence threshold are set, the noise precision and its hyperparameters are initialized;

[0050] Step six: the initial value of the signal power vector is obtained by using the correlation mapping of the synthesized dictionary matrix and the observation matrix ;

[0051] ​​Step 7: Begin the iteration process, at the... In this iteration, the corrected perception matrix is ​​calculated. Calculate the posterior covariance matrix. With the The posterior mean vector of each snapshot ,in, Represents a diagonal matrix consisting of corresponding elements, with superscripts. Indicates the first In the next iteration, the superscript -1 and These represent matrix inversion and conjugate transpose, respectively.

[0052] Step 8: Based on the posterior mean obtained in Step 7 and posterior covariance From the formula Update signal power vector ,in express The first in One element, Represents the posterior covariance matrix The first on the diagonal One element, To take the square of the modulus;

[0053] Step Nine: According to the formula Update noise accuracy ,in The total observation dimension of the data. It is the data fitting error. Describing the L2 norm, It is the error expectation correction term introduced by the uncertainty in signal estimation. Represents the trace of a matrix;

[0054] Step 10: Select signal power The largest Each index constitutes a support set. Constructing information about off-grid error linear equations The updated value of the off-scale error is obtained by solving this system of linear equations, and the value greater than 1 is set to 1. The terms are restricted to boundary values, where, The coefficient matrix, It is a constant vector;

[0055] Step 11: According to the formula Calculate the signal power vector relative rate of change ;like Less than the convergence threshold Or the number of iterations reaches If yes, terminate the iteration and go to step 11; otherwise, return to step 7 to continue the next iteration.

[0056] Step 12: Calculate the spatial spectrum according to the posterior mean matrix, search the grid angle corresponding to the spectral peak, and obtain the final DOA estimation value according to . . . . . .

[0057] Further, a high-precision DOA estimation method based on a mobile synthetic virtual array includes the following steps:

[0058] A1: Let . . . . . . .

[0059] A2: For each snapshot , concatenate the data of the physical array elements in the pulse time sequence to construct an equivalent observation column vector . . . .

[0060] A3: Arrange the equivalent observation column vectors corresponding to all snapshots in the time sequence . . .

[0061] Further, the calculation process of the signal power vector in step 6 is as follows:

[0062] B1: Calculate an intermediate correlation matrix .

[0063] B2: Extract the modulus of each complex number element in the intermediate correlation matrix in step 1 to construct a real energy distribution reflecting the energy intensity of each grid point at each snapshot.

[0064] B3: According to the formula The real energy distribution is subjected to an arithmetic mean along the time snapshot dimension, and the resulting mean vector is the signal power vector. The initial value.

[0065] Furthermore, in a high-precision DOA estimation method based on a moving synthetic virtual array, in step ten, the coefficient matrix... and constant vector The construction method is as follows:

[0066] coefficient matrix The element constant vector The element ,in, The support set index represents the signal power filtered. Location of potential signal sources For matrix The column vectors, Re denotes the conjugate operation for complex numbers, and Re denotes the operation of taking the real part.

[0067] Furthermore, in a high-precision DOA estimation method based on a moving synthetic virtual array, in step twelve, the... The estimation process is as follows: According to the formula Calculate each grid point The spatial power spectrum vector is obtained by arranging the average power across all snapshots in index order. ,exist The search value with the largest value A peak, and the The grid indices corresponding to the peak values ​​are denoted as follows: .

[0068] The patented method based on the above conditions was simulated using MATLAB simulation software, and the DOA estimation results of the patented method are as follows: Figure 2 , 3 As shown. By Figure 2 , 3 Experimental results show that, under the conditions of this example, the MSVA-OGSBL method can accurately estimate the incident angles of the four signal sources. Its normalized spatial spectrum has a significantly narrower main lobe width than the ULA-SBL and ULA-OGSBL methods. The spectral peaks are precisely aligned with the true DOA positions (pink dashed lines). There is no peak shift phenomenon as seen in the gridding method, and the sidelobe level is below -20dB, demonstrating excellent spatial resolution and estimation accuracy.

[0069] The second embodiment: study the relationship between the RMSE of the signal processing method of the patent and the signal-to-noise ratio, and the effect diagram obtained is as shown in Figure 4 The comparison curves of the ULA-SBL method, the ULA-OGSBL method and the MSVA-SBL method are also given. The application conditions of the method are as follows:

[0070] The method is based on mobile ULA, and the array structure of the ULA is as shown in Figure 1 There are unrelated far-field narrow-band signal sources incident into the ULA, and the reference incident angles are In each Monte Carlo simulation experiment, the real signal incident angle is dynamically generated: on the basis of the above reference angle, a randomly generated grid offset is superimposed, the carrier frequency is 77 GHz, , , , , SNR starts from-5 dB and increases by 5 dB to 20 dB, 200 times of Monte Carlo simulation experiment is performed at different SNRs each time, the angle search range is , the grid interval is , the convergence threshold is , and the maximum iteration number is , and simulation is performed through MATLAB software.

[0071] It can be known from the analysis Figure 4 that the RMSE of the four methods will gradually decrease with the increase of the signal-to-noise ratio. After SNR>5 dB, the grid method (ULA-SBL and MSVA-SBL) appears obvious error platform phenomenon, and the MSVA-SBL is stalled at about 0.3 RMSE when SNR approaches 5 dB, and no matter how SNR is improved, the accuracy is limited by the quantization error of the preset grid. In comparison, the off-grid method (ULA-OGSBL and MSVA-OGSBL) continues to decline in the high SNR area, effectively avoiding the error platform. The RMSE of the MSVA-OGSBL method of the patent is the lowest under all SNR conditions, and the RMSE is close to 0.01 when SNR=20 dB, which is about 30 times lower than that of the MSVA-SBL method, verifying that the off-grid sparse Bayesian learning can effectively eliminate the grid quantization error and realize high-precision DOA estimation.

[0072] The third embodiment: study the relationship between the RMSE of the signal processing method of the patent and the number of snapshots, and the effect diagram obtained is as shown in Figure 5As shown, comparison curves of the ULA-SBL method, ULA-OGSBL method, and MSVA-SBL method are also presented. The application conditions of the method of this invention are as follows:

[0073] The method of this invention is based on a mobile ULA, and the array structure of the ULA is as follows: Figure 1 As shown, there are An uncorrelated far-field narrowband signal source is incident on the ULA, with reference incident angles of respectively. In each Monte Carlo simulation experiment, the actual signal incident angle is dynamically generated: based on the aforementioned reference angle, a randomly generated off-grid offset is superimposed, and the carrier frequency... 77 GHz , , , , The number of snapshots starts at 50 and increases to 300 in increments of 50. 200 Monte Carlo simulations are performed at each different number of snapshots, with the angle search range being... Grid spacing Convergence threshold Maximum number of iterations Simulations were performed using MATLAB software.

[0074] analyze Figure 5 It can be seen that the RMSE of all four methods decreases with the increase of the number of snapshots. In comparison, the MSVA-OGSBL method proposed in this patent can fully utilize the statistical gain brought about by the increase in the number of snapshots. As the number of snapshots increases from 50 to 300, the RMSE curve of this method continues to decrease monotonically without showing a saturation trend. When the number of snapshots is 300, its RMSE drops to approximately 0.04. Compared to the MSVA-SBL method, which also uses synthetic aperture but does not perform off-grid correction, the accuracy is improved by approximately 4 times. This result strongly verifies that the present invention, by introducing off-grid error parameters and performing joint iterative updates, can effectively eliminate grid quantization errors, maintain extremely high estimation accuracy even with few snapshots, and exhibit excellent asymptotic performance as the amount of data increases.

[0075] Fourth embodiment: The relationship between RMSE and the number of synthesized pulses in the signal processing method of this patent is studied, and the resulting effect is shown in the figure below. Figure 6 As shown, a comparison curve of the MSVA-SBL method is also presented. The application conditions of the method of this invention are as follows:

[0076] The method of this invention is based on a mobile ULA, and the array structure of the ULA is as follows: Figure 1 As shown, there are A number of uncorrelated far-field narrowband signal sources are incident into the ULA with their reference incident angles being In each Monte Carlo simulation experiment, the true signal incident angles are dynamically generated: on the basis of the above reference angles, a randomly generated off-grid offset is superimposed respectively, the carrier frequency is 77 GHz, , , , , , the number of synthetic pulses starts from 4 and increases by 2 to 12, each time in a different 200 times of Monte Carlo simulation experiments are carried out, the angle search range is , the grid interval , the convergence threshold , the maximum number of iterations , and the simulation is carried out by MATLAB software.

[0077] Analysis Figure 6 It can be seen that with the increase of the number of synthetic pulses , the RMSE of the MSVA-SBL method decreases to about 0.2 and then no longer decreases significantly, showing a clear saturation trend. This is because although increasing the number of pulses expands the virtual aperture and improves the physical level Rayleigh resolution, the accuracy bottleneck of the gridding method is always limited by the preset grid interval. Even if the beam is narrowed, the estimation result is still forced to be quantized to the nearest grid point. In contrast, the MSVA-OGSBL method proposed in this patent can fully utilize the performance improvement brought by aperture expansion. With the increase of N, the RMSE curve shows a continuous and monotonous downward trend, and when , the RMSE is close to 0 . This shows that on the basis of the large aperture virtual array providing higher angle resolution potential, the off-grid sparse Bayesian learning accurately corrects the grid error through the first-order Taylor expansion, so that the final estimation accuracy is no longer subject to the grid density, realizing the true sense of super-resolution estimation.

[0078] This result strongly proves the necessity of introducing the off-grid processing mechanism in the mobile synthetic aperture system: only by expanding the aperture through motion can improve the physical resolution, but if the grid mismatch problem is not solved, the system performance will still touch the grid ceiling; the combination of MSVA and OGSBL can break through the physical aperture limit and mathematical grid limit at the same time, and realize the synergistic gain. Overall, the method of this patent shows the best estimation performance under different number of synthetic pulses.

[0079] The specific examples described in this patent application are intended to be illustrative only and are not intended to limit the scope of the application. Various modifications, substitutions, and alternatives to the described specific examples can be made by those skilled in the art without departing from the spirit and scope of the application or the scope of the claims.

Claims

1. A high-precision DOA estimation method based on a mobile synthetic virtual array, applicable to uniform linear arrays mounted on a mobile platform, wherein the array comprises... There are array elements, and the spacing between the array elements is... ,in , The signal wavelength; the platform moves at a constant speed along the array axis. Motion, radar system acquisition The pulse cycle is The echo data is characterized by: The high-precision DOA estimation method based on a moving synthetic virtual array includes the following steps: Step 1: Place the uniform linear array in The data received within each pulse period are vectorized, stacked, and rearranged to construct a dimension of... observation matrix ,in The equivalent number of array elements, For the number of snapshots; Step 2: Calculate the first... pulse moment Spatial displacement of the platform relative to its initial position And for each possible signal direction Calculate the additional phase increment caused by the platform displacement. ,in , , Number of signal sources; Step 3: Divide the airspace angular range into A grid of uniformly spaced points Grid spacing is For each grid point Construct dictionary matrix The first of the matrix Listed as: ,in, Represents the Kronecker product. The physical guide vector for the stationary array; Step 4: Construct the derivative matrix The first of the matrix Listed as: ,in, express right The first-order partial derivative; Step 5: Introduce the deviation error vector It is initialized as a vector of all zeros, and the maximum number of iterations is set. and convergence threshold Initialize noise accuracy and its hyperparameters ; Step Six: Using the synthesized dictionary matrix and observation matrix The correlation mapping yields the signal power vector. The initial value; Step 7: Begin the iteration process, at the... In this iteration, the corrected perception matrix is ​​calculated. Calculate the posterior covariance matrix. With the The posterior mean vector of each snapshot ,in, Represents a diagonal matrix consisting of corresponding elements, with superscripts. Indicates the first In the next iteration, the superscript -1 and These represent matrix inversion and conjugate transpose, respectively. Step 8: Based on the posterior mean obtained in Step 7 and posterior covariance From the formula Update signal power vector ,in express The first in One element, Represents the posterior covariance matrix The first on the diagonal One element, To take the square of the modulus; Step Nine: According to the formula Update noise accuracy ,in The total observation dimension of the data. It is the data fitting error. Represents the L2 norm. It is the error expectation correction term introduced by the uncertainty in signal estimation. Represents the trace of a matrix; Step 10: Select signal power The largest Each index constitutes a support set. Constructing information about off-grid error linear equation system The updated value of the off-scale error is obtained by solving this system of linear equations, and the value greater than 1 is set to 1. The terms are restricted to boundary values, where, The coefficient matrix, It is a constant vector; Step 11: According to the formula Calculate the signal power vector relative rate of change ;like Less than the convergence threshold Or the number of iterations reaches If the iteration fails, proceed to step eleven; otherwise, return to step seven to continue the next iteration. Step 12: Calculate the spatial spectrum based on the posterior mean matrix, search for the grid angle corresponding to the spectral peak, and then... Calculate the final DOA estimate, where, for The index corresponding to the maximum value The preset grid angle corresponding to this index. This is the optimal deviation error correction amount corresponding to the index, i.e., the iteration termination value.

2. The high-precision DOA estimation method based on a moving synthetic virtual array as described in claim 1, characterized in that: The specific process of vectorizing and stacking the received data in step one is as follows: A1: Note For the first Take a quick picture, the first one Within the nth pulse cycle, by the first The complex signal received by each physical array element, among which , , ; A2: For each snapshot ,Will Acquired within one pulse cycle The metadata of each physical array is concatenated according to the pulse time sequence, constructing a dimension of... Equivalent observation column vector ; A3: Sort the equivalent observation column vectors corresponding to all snapshots by time sequence number. Arranged horizontally in sequence, the final result is a dimension of Equivalent observation matrix .

3. The high-precision DOA estimation method based on a moving synthetic virtual array as described in claim 1, characterized in that: The signal power vector mentioned in step six The calculation process is as follows: B1: Calculation dimension is Intermediate correlation matrix ; B2: The intermediate correlation matrix Each complex element in the expression is replaced with its modulus. B3: According to the formula The real energy distribution is subjected to an arithmetic mean along the time snapshot dimension, and the resulting mean vector is the signal power vector. The initial value.

4. The high-precision DOA estimation method based on a moving synthetic virtual array as described in claim 1, characterized in that: In step ten, the coefficient matrix and constant vector The construction method is as follows: coefficient matrix The element constant vector The element ,in, The support set index represents the signal power filtered. Location of potential signal sources For matrix The column vectors, Re denotes the conjugate operation for complex numbers, and Re denotes the operation of taking the real part.

5. The high-precision DOA estimation method based on a moving synthetic virtual array as described in claim 1, characterized in that: In step twelve, the The estimation process is as follows: According to the formula Calculate each grid point The spatial power spectrum vector is obtained by arranging the average power across all snapshots in index order. ,exist The search value with the largest value A peak, and the The grid indices corresponding to the peak values ​​are denoted as follows: .

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