A method for phase-amplitude error self-calibration of direction of arrival greedy estimation

Abstract

The application discloses a kind of amplitude-phase error self-calibration's wave direction greedy estimation method, comprising: S1: the array received signal model including amplitude-phase error is established;S2: the effective grid size of search grid, iteration stop threshold is calculated;S3: coarse search is carried out on search grid, and the initial wave direction and initial signal corresponding to the maximum projection energy of detection are detected;If the maximum projection energy is lower than iteration stop threshold, then jump to S6;S4: Newton iteration refinement is carried out to initial wave direction, and more accurate continuous angle estimation and signal estimation are obtained;S5: source signal waveform and diagonal calibration matrix are alternately updated, and residual signal is updated accordingly, and current source is eliminated, and return S3;S6: weak source is eliminated and optimized by pruning, and the final wave direction and diagonal calibration matrix estimation are output.The application avoids error transmission, and significantly improves the wave direction estimation precision under unknown array error condition.

Description

Technical Field

[0001] This invention relates to the field of array signal processing and parameter estimation, and in particular to a greedy estimation method for direction of arrival with self-calibration of amplitude and phase error. Background Technology

[0002] Direction of Arrival (DOA) estimation is a core foundational technology in many fields such as radar, sonar, and wireless communication. Classical subspace algorithms perform excellently under ideal array and noise assumptions. However, in practical engineering, array channels inevitably introduce amplitude and phase errors related to array elements due to hardware manufacturing tolerances, component aging, temperature variations, and mutual coupling effects. These errors cause a mismatch between the actual steering vector of the array and the ideal model, severely undermining the orthogonality premise of the subspace method, resulting in a sharp decline in estimation accuracy, the appearance of spurious spectral peaks, or even complete failure.

[0003] To address array error issues, existing technologies mainly fall into two categories: offline calibration and online self-calibration. Offline calibration requires auxiliary sources with known locations in a controlled environment, making it complex to operate and difficult to handle the time-varying characteristics of the working environment. While online self-calibration methods can jointly estimate error parameters and DOA using observation data, most algorithms are either limited to single-source scenarios, have high computational complexity, or require prior knowledge of the number of sources, resulting in insufficient robustness in complex, multi-source, and low signal-to-noise ratio real-world scenarios. In recent years, methods based on sparse reconstruction and compressed sensing have shown high-resolution potential, but they generally do not explicitly model and compensate for array amplitude and phase errors, easily generating a large number of spurious estimates under mismatch conditions. Therefore, there is an urgent need for a practical method that can directly and robustly estimate the DOA of multiple sources and array amplitude and phase errors from noisy observation data without prior independent calibration or knowing the number of sources. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention proposes a greedy DOA estimation method with self-calibrated amplitude and phase errors. The core of this method lies in constructing a "coarse-to-fine" greedy iterative framework, which integrates DOA estimation, signal waveform recovery, and array amplitude and phase error calibration for joint optimization. This method is suitable for high-precision DOA estimation under conditions where the sensor array has unknown amplitude and phase errors.

[0005] The specific technical solution is as follows:

[0006] A greedy direction-of-arrival estimation method with self-calibrated amplitude and phase error includes the following steps:

[0007] S1: Establish an array received signal model that includes amplitude and phase errors, where the amplitude and phase errors are constructed using a diagonal calibration matrix;

[0008] S2: Estimate the effective grid size of the search grid based on the current diagonal calibration matrix, and determine the adaptive iteration stopping threshold accordingly;

[0009] S3: Perform a coarse search on the search grid to detect the initial direction of arrival and initial signal corresponding to the maximum projected energy; determine whether the maximum projected energy at all grid points is lower than the iteration stopping threshold. If yes, jump to S6; otherwise, continue to S4.

[0010] S4: Refine the initial direction of arrival using Newton iteration to obtain more accurate continuous angle and signal estimates;

[0011] S5: Alternately update the source signal waveform and the diagonal calibration matrix, update the residual signal accordingly, remove the source signal processed in this iteration from the received signal, and return to execute S3;

[0012] S6: By pruning and eliminating spurious sources and optimizing, the final estimated direction of arrival and diagonal calibration matrix are output.

[0013] Further, in S1, the array receiving signal model is specifically as follows: the receiving signal matrix is ​​equal to the diagonal calibration matrix multiplied by the ideal steering matrix and then multiplied by the source signal matrix, and finally the additive white Gaussian noise matrix is ​​added; each diagonal element of the diagonal calibration matrix represents the complex gain of the corresponding array element, which is used to characterize the amplitude and phase error to be estimated for the array element; each column of the ideal steering matrix is ​​a steering vector determined by the corresponding wave direction of arrival.

[0014] Furthermore, in S2, the effective mesh size is calculated as follows:

[0015] Based on the current estimated value of the diagonal calibration matrix, the ideal steering vector is corrected to obtain a set of angle-related corrected steering vectors;

[0016] Calculate the cross-correlation coefficients between the corrected steering vectors corresponding to each point on the search grid, and construct the coherence matrix;

[0017] The ratio of the square of the sum of all eigenvalues ​​of the coherence matrix to the sum of the squares of each eigenvalue is calculated. This ratio is the effective grid size, which is used to replace the nominal total number of grid points in the calculation of the iteration stopping threshold.

[0018] Further, the coarse search in S3 specifically involves: traversing a preset search grid, and for each grid angle, calculating the sum of the energy of the current residual signal projected onto the corrected steering vector corresponding to that angle on all snapshots; taking the grid angle corresponding to its maximum value as the initial direction of arrival estimate detected in this iteration; and obtaining the initial signal estimate based on the initial direction of arrival estimate.

[0019] Further, the Newton iteration refinement in S4 specifically involves: defining an objective function with angle as the variable, which is the projected energy of the current residual signal onto the corresponding corrected steering vector; the new angle estimate is equal to the current angle estimate minus a correction term, where the correction term is the ratio of the sum of the first derivatives of the objective function with respect to the angle to the sum of the second derivatives of the objective function with respect to the angle; updating the signal estimate based on the new angle estimate, and adding the parameter pair consisting of the new angle estimate and the new signal estimates on all snapshots to the current direction of arrival set.

[0020] Furthermore, in step S6, the source signal waveform and the diagonal calibration matrix are alternately updated, and the residual signal is updated accordingly. This specifically includes the following sub-steps:

[0021] (6.1) Fix the currently estimated diagonal calibration matrix and direction of arrival, and update the signal waveforms of all detected sources by solving the least squares problem;

[0022] (6.2) Fix the currently estimated direction of arrival and the updated signal waveform of the detected source, and update the estimated values ​​of the diagonal elements in the diagonal calibration matrix by solving the least squares problem element by element.

[0023] (6.3) Calculate the residual signal for the new round of iteration using the updated source signal and the diagonal calibration matrix.

[0024] Furthermore, the pruning operation in S6 specifically involves: storing all candidate sources detected iteratively into a candidate source set; calculating the total increase in system residual energy after temporarily removing each candidate source; calculating the contribution of each detected source to the overall fitting residual, i.e., calculating the proportion of the energy increase corresponding to each candidate source to the total increase; and identifying candidate sources with a contribution rate lower than a preset contribution rate threshold as false sources and removing them.

[0025] Furthermore, the optimization in S6 specifically involves: for the source signal retained after pruning, performing S4 and S5 alternate updates of the source signal waveform and diagonal calibration matrix multiple times to further converge all parameter estimates.

[0026] A greedy amplitude and phase error self-calibration direction-of-arrival estimation device includes: a memory and one or more processors; the memory stores executable code, and when the one or more processors execute the executable code, they implement the greedy amplitude and phase error self-calibration direction-of-arrival estimation method.

[0027] A computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the aforementioned greedy estimation method for self-calibrating amplitude and phase errors in direction of arrival.

[0028] The beneficial effects of this invention are:

[0029] (1) Joint estimation and self-calibration: This invention innovatively places DOA estimation and array amplitude and phase error calibration in a unified greedy iterative framework and performs them simultaneously, breaking the traditional process of "calibrating first and then estimating", fundamentally avoiding error propagation and significantly improving the estimation accuracy under unknown array error conditions.

[0030] (2) High precision and super resolution: By combining coarse search with Newton iteration refinement, the global search capability is guaranteed and high precision estimation of continuous angle domain is achieved, breaking through the resolution limit of discrete grid and obtaining super resolution capability beyond Rayleigh limit.

[0031] (3) Adaptive and robust: An adaptive iteration stopping threshold based on the effective grid size is introduced, which reduces the sensitivity to preset parameters (such as grid density); combined with the pruning mechanism, the number of information sources is automatically and accurately estimated without any prior information, and it exhibits strong robustness in low signal-to-noise ratio, multiple information sources and strong error scenarios. Attached Figure Description

[0032] Figure 1 This is a flowchart of the greedy estimation method for amplitude and phase error self-calibration in the direction of arrival in an embodiment of the present invention.

[0033] Figure 2 This is a schematic diagram comparing the estimated value of the calibration matrix with the true value in the simulation experiment of this invention.

[0034] Figure 3 This is a comparison curve of the root mean square error of DOA estimation as a function of signal-to-noise ratio in the simulation experiment of different algorithms in the presence of amplitude and phase errors in the embodiments of the present invention.

[0035] Figure 4 This is a schematic diagram showing the variation of the effective grid size and corresponding threshold with the grid interval in the simulation experiment of this invention.

[0036] Figure 5 This is a schematic diagram comparing the accuracy of the algorithm in estimating the number of information sources before and after the post-pruning operation in the simulation experiment of this invention embodiment.

[0037] Figure 6 This is a schematic diagram of the device for a greedy estimation method for direction of arrival with self-calibration of amplitude and phase error in an embodiment of the present invention. Detailed Implementation

[0038] The present invention will be described in detail below with reference to the accompanying drawings and preferred embodiments. The objectives and effects of the present invention will become clearer as a result. The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0039] like Figure 1 As shown, a greedy estimation method for direction of arrival with self-calibrated amplitude and phase error includes the following steps:

[0040] S1: Establish an array received signal model that includes amplitude and phase errors.

[0041] A uniform linear array of M elements is used to receive K narrowband signals from the far field. Let the direction of arrival of the k-th signal be y = y / k. The complex envelope signal captured by its P snapshots is denoted as the row vector. The array's received signal matrix It can be modeled as (i.e., the expression for the array receiving signal model is):

[0042]

[0043] In the formula, For a diagonal calibration matrix, its diagonal elements This represents the complex gain of the m-th (m=1,2,3,…,M) array element. The magnitude to be estimated. The phase error to be estimated; The ideal steering matrix has its k-th column (k=1,2,3,…,K) as the ideal steering vector. T represents the transpose operation; The source signal matrix; The matrix is ​​an additive white Gaussian noise matrix, with each element independently and identically distributed. .

[0044] To eliminate diagonal calibration matrix With source signal matrix The scale ambiguity between them necessitates the introduction of constraints. In this embodiment, the first array element is fixed as the reference array element, i.e., g1=1.

[0045] S2: Based on the diagonal calibration matrix estimated in the current round, calculate the effective grid size and the adaptive iteration stopping threshold to stabilize the initial detection process. In this embodiment, the adaptive iteration stopping threshold is obtained using the generalized likelihood ratio method. This is specifically achieved through the following sub-steps:

[0046] (2.1) Initialization: Let the initial iteration number k=0, and the initial estimate of the diagonal calibration matrix is ​​as follows: (Identity matrix), initial residual The estimated set of DOAs .

[0047] (2.2) Define the search grid: within the desired azimuth range [θ] min ,θ maxWithin, at fixed angular intervals Divide the search into a uniform grid. , where G is the total number of grid points.

[0048] (2.3) Calculate the effective mesh size G eff : Angle θ for each point in the search grid i The ideal steering vector is corrected using the current diagonal calibration matrix to obtain a set of angle-dependent corrected steering vectors. Calculate the cross-correlation coefficient of the corrected steering vector on the search grid, and construct a G×G coherence matrix. Its elements are:

[0049]

[0050] calculate eigenvalues By analyzing the eigenvalue distribution of the coherence matrix, its participation ratio is calculated, and this participation ratio is the effective mesh size G. eff The expression is as follows:

[0051]

[0052] This value reflects the statistical correlation between grid points, characterizing the effective search dimension for statistical independence, and typically satisfies... This is used to correct the calculation of the iteration stopping threshold, thereby avoiding overly strict thresholds and missed detections caused by excessively dense grids.

[0053] (2.4) Calculate the adaptive iteration stopping threshold :

[0054]

[0055] In the formula, It is the inverse cumulative distribution function of a chi-square distribution with 2P degrees of freedom, where P is the number of degrees of freedom. oe It is the preset overestimation probability (0.01 in this embodiment). This is the estimated noise power.

[0056] S3: Coarse search based on discrete search grid (greedy detection). Specifically implemented through the following operations:

[0057] In the (k+1)th iteration, based on the current residual Detect a new source signal from the currently received signal.

[0058] First, calculate the projected energy at all grid points:

[0059]

[0060] In the formula, yes The t-th column.

[0061] Secondly, the angle of the grid point that maximizes the projected energy of the residual signal is found as the initial angle estimate (i.e., the initial direction of arrival) for the current iteration:

[0062]

[0063] The corresponding initial signal estimate is:

[0064]

[0065] After completing the coarse search, the iteration stopping condition is determined: if the maximum projected energy is less than the iteration stopping threshold, i.e. If the signal does not meet the requirements, the iteration stops and jumps to S6; otherwise, continue executing S4.

[0066] S4: Newton's iterative refinement of the angle, performing local optimization within the continuous angle domain, i.e., refining the coarse estimate. Perform Newton iterations to obtain more accurate continuous angle estimates. This eliminates the "off-grid" error caused by the discrete grid, obtains a more accurate angle estimate, and achieves fast and accurate local convergence of the angle. Specifically, this is achieved through the following sub-steps:

[0067] (4.1) Define the objective function for a single snapshot using the projected energy with angle as the variable:

[0068]

[0069] (4.2) Calculate the first derivative of the objective function and second derivative The correction amount is then calculated based on this. This requires using the first derivative of the correction steering vector with respect to the angle. and second derivative .

[0070] (4.3) Based on the first derivative of the objective function and the two-stage calculation of the correction amount, the Newton update formula is:

[0071]

[0072] This method was used to calculate the refined angle, achieving rapid and accurate local convergence of the angle.

[0073] (4.4) Update the signal estimate using the refined angle, as shown in the following expression:

[0074]

[0075] (4.5) The refined parameters are then compared. Add to the current DOA collection .

[0076] S5: Alternately update the signal and the diagonal calibration matrix. By decomposing the non-convex joint optimization problem into two conditionally convex subproblems (updating the signal and updating the calibration matrix parameters) and solving them alternately, the algorithm ensures that it progresses in the direction of decreasing the joint cost function in each iteration. This is specifically achieved through the following sub-steps:

[0077] (5.1) Update all source signals: fix the currently estimated DOA set. and diagonal calibration matrix The signals of all detected sources are updated in one go using least squares:

[0078]

[0079] (5.2) Update the diagonal calibration matrix: fixed and The gain is updated for each array element. Let... Its m-th action , The m-th line ,but:

[0080]

[0081] In the formula, For a preset, extremely small positive number (such as 10) -6 To ensure numerical stability.

[0082] After the update, forced To satisfy the reference constraints, a new diagonal calibration matrix estimate is obtained. .

[0083] (5.3) Calculate the new residuals based on the updated source signal and the diagonal calibration matrix:

[0084]

[0085] (5.4) Let k = k + 1, and remove the source signal detected in this round of iteration from the current received signal, and return to S3 to start the next round of iteration detection.

[0086] S6: Pruning and Final Output. When the iteration terminates due to the stopping condition, a set of candidate sources is obtained, denoted as K. cand The process of handling this set of candidate sources includes the following sub-steps:

[0087] (6.1) Calculate the energy contribution: Calculate the cumulative residual energy of all candidate sources. For the c-th candidate source, calculate the residual energy obtained by temporarily removing it from the set and then re-updating the signal and diagonal calibration matrix (i.e., performing S5). Then the contribution of this information source is: .

[0088] (6.2) Normalization and Pruning: Calculate the normalized contribution ratio (i.e., contribution degree) of each source:

[0089]

[0090] Set a contribution threshold η (η=0.01 in this embodiment), if If the source is considered a false source (a false source caused by residual modeling error or noise), it is removed from the estimated DOA set (i.e., pruning is achieved), thereby significantly improving the accuracy and reliability of source number estimation.

[0091] (6.3) Final optimization: For the information sources retained after pruning, execute the loop of S4 and S5 several times (three times in this embodiment) again (only refine the angle and update the parameters alternately, do not perform new detection, that is, execute S4, steps (5.1) and (5.2) in a loop) to make all parameter estimates converge further.

[0092] (6.4) Output: Output the final estimated number of sources. DOA collection Signal matrix and array calibration matrix .

[0093] Through the above steps, this invention achieves high-precision joint estimation and self-calibration of direction of arrival (DOA) under conditions of unknown array amplitude and phase errors. This invention utilizes simulation for testing, and the test results are as follows: Figures 2 to 5 As shown, the simulation results verify the effectiveness and superiority of the proposed method.

[0094] Figure 2 The spatial spectrum estimates obtained sequentially during the algorithm iteration process are three true angles: -40.3°, 40°, and 50°. It can be seen that after three rounds of iteration using the method of this invention, three sharp spectral peaks were finally estimated, with angle estimation results of -40.3°, 40.03°, and 49.98°, proving that the method of this invention has very high angle estimation accuracy.

[0095] Figure 3 The figure shows a comparison between the amplitude and phase values ​​of the array elements estimated by the algorithm and the true values. As can be seen from the figure, the algorithm achieves high-precision amplitude and phase deviation estimation and completes the self-calibration of amplitude and phase errors well during the algorithm iteration process.

[0096] Figure 4 The graph shows the root mean square error (RMSE) of the algorithm's angle estimation accuracy as a function of signal-to-noise ratio (SNR). It compares the Joint Direction of Arrival, Amplitude, and Phase (JDAP) method of this invention with a reference algorithm, which includes Conventional Beamforming (CBF), Multiple Signal Classification (MUSIC), and Multi-snapshot Newtonized Orthogonal Matching Pursuit (MNOMP). The Cramér-Rao Bound (CRB) is also plotted as a benchmark. The graph demonstrates that this invention achieves the highest positioning accuracy.

[0097] Figure 5 Different grid angle intervals The corresponding iteration stopping threshold It can be seen that the iteration stopping threshold proposed in this invention changes more smoothly with the grid angle interval. In scenarios with small grid angle intervals, the iteration stopping threshold is much smaller than the reference threshold, which indirectly proves the necessity of calculating the iteration stopping threshold.

[0098] Corresponding to the aforementioned embodiments of the greedy direction-of-arrival estimation method with self-calibration of amplitude and phase errors, the present invention also provides embodiments of a greedy direction-of-arrival estimation device with self-calibration of amplitude and phase errors.

[0099] like Figure 6 As shown in the figure, an embodiment of the present invention provides a greedy estimation method for amplitude and phase error self-calibration of direction of arrival, which includes a memory and one or more processors. The memory stores executable code, and when the one or more processors execute the executable code, they are used to implement the greedy estimation method for amplitude and phase error self-calibration of direction of arrival in the above embodiment.

[0100] The embodiments of the amplitude and phase error self-calibration greedy direction-of-arrival estimation device of the present invention can be applied to any device with data processing capabilities, such as a computer. The device embodiments can be implemented in software, hardware, or a combination of both. Taking software implementation as an example, as a logical device, it is formed by the processor of any data processing device loading the corresponding computer program instructions from non-volatile memory into memory for execution. From a hardware perspective, such as... Figure 6 The diagram shown is a hardware structure diagram of any device with data processing capabilities, where the amplitude and phase error self-calibration greedy estimation device for direction of arrival is located. (Except for...) Figure 6 In addition to the processor, memory, network interface, and non-volatile memory shown, any data processing device in the embodiment may also include other hardware depending on the actual function of the data processing device, which will not be described in detail here.

[0101] The specific implementation process of the functions and roles of each unit in the above device can be found in the implementation process of the corresponding steps in the above method, and will not be repeated here.

[0102] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of the present invention according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0103] This invention also provides a computer-readable storage medium storing a program thereon, which, when executed by a processor, implements the wave direction-of-arrival greedy estimation method for amplitude and phase error self-calibration described in the above embodiments.

[0104] The computer-readable storage medium can be an internal storage unit of any data processing device described in any of the foregoing embodiments, such as a hard disk or memory. The computer-readable storage medium can also be an external storage device, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc., equipped on the device. Furthermore, the computer-readable storage medium can include both internal storage units of any data processing device and external storage devices. The computer-readable storage medium is used to store the computer program and other programs and data required by the data processing device, and can also be used to temporarily store data that has been output or will be output.

[0105] It will be understood by those skilled in the art that the above descriptions are merely preferred examples of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and equivalent substitutions made within the spirit and principles of the invention should be included within the scope of protection of the invention.

Claims

1. A method of phase error self-calibration for DOA greedy estimation, characterized in that, Includes the following steps: S1: Establish an array received signal model that includes amplitude and phase errors, where the amplitude and phase errors are constructed using a diagonal calibration matrix; S2: Estimate the effective grid size of the search grid based on the current diagonal calibration matrix, and determine the adaptive iteration stopping threshold accordingly; S3: Perform a coarse search on the search grid to detect the initial direction of arrival and initial signal corresponding to the maximum projected energy; determine whether the maximum projected energy at all grid points is lower than the iteration stopping threshold. If yes, jump to S6; otherwise, continue to S4. S4: Refine the initial direction of arrival using Newton iteration to obtain more accurate continuous angle and signal estimates; S5: Alternately update the source signal waveform and the diagonal calibration matrix, update the residual signal accordingly, remove the source signal processed in this iteration from the received signal, and return to execute S3; S6: By pruning and eliminating spurious sources and optimizing, the final estimated direction of arrival and diagonal calibration matrix are output.

2. The amplitude and phase error self-calibrated direction of arrival greedy estimation method of claim 1, wherein, In S1, the array receiving signal model is specifically as follows: the receiving signal matrix is ​​equal to the diagonal calibration matrix multiplied by the ideal steering matrix, then multiplied by the source signal matrix, and finally the additive white Gaussian noise matrix is ​​added; each diagonal element of the diagonal calibration matrix represents the complex gain of the corresponding array element, which is used to characterize the amplitude and phase error to be estimated for that array element; each column of the ideal steering matrix is ​​a steering vector determined by the corresponding wave direction of arrival.

3. The greedy estimation method for direction of arrival with self-calibrated amplitude and phase error according to claim 1, characterized in that, In S2, the effective mesh size is calculated as follows: Based on the current estimated value of the diagonal calibration matrix, the ideal steering vector is corrected to obtain a set of angle-related corrected steering vectors; Calculate the cross-correlation coefficients between the corrected steering vectors corresponding to each point on the search grid, and construct the coherence matrix; The ratio of the square of the sum of all eigenvalues ​​of the coherence matrix to the sum of the squares of each eigenvalue is calculated. This ratio is the effective grid size, which is used to replace the nominal total number of grid points in the calculation of the iteration stopping threshold.

4. The amplitude and phase error self-calibrated direction of arrival greedy estimation method of claim 1, wherein, The coarse search in S3 specifically involves: traversing a preset search grid; for each grid angle, calculating the sum of the energy of the current residual signal projected onto the corrected steering vector corresponding to that angle on all snapshots; taking the grid angle corresponding to its maximum value as the initial direction of arrival estimate detected in this iteration; and obtaining the initial signal estimate based on the initial direction of arrival estimate.

5. The amplitude and phase error self-calibrated direction of arrival greedy estimation method of claim 1, wherein, The Newton iteration refinement in S4 specifically involves: defining an objective function with angle as the variable, which is the projected energy of the current residual signal onto the corresponding corrected steering vector; the new angle estimate is equal to the current angle estimate minus a correction term, where the correction term is the ratio of the sum of the first derivatives of the objective function with respect to the angle to the sum of the second derivatives of the objective function with respect to the angle; updating the signal estimate based on the new angle estimate, and adding the parameter pair consisting of the new angle estimate and the new signal estimates on all snapshots to the current direction of arrival set.

6. The amplitude and phase error self-calibrated direction of arrival greedy estimation method of claim 1, wherein, In step S6, the source signal waveform and the diagonal calibration matrix are alternately updated, and the residual signal is updated accordingly. This specifically includes the following sub-steps: (6.1) Fix the currently estimated diagonal calibration matrix and direction of arrival, and update the signal waveforms of all detected sources by solving the least squares problem; (6.2) Fix the currently estimated direction of arrival and the updated signal waveform of the detected source, and update the estimated values ​​of the diagonal elements in the diagonal calibration matrix by solving the least squares problem element by element. (6.3) Calculate the residual signal for the new round of iteration using the updated source signal and the diagonal calibration matrix.

7. The amplitude and phase error self-calibrated direction of arrival greedy estimation method of claim 1, wherein, The pruning operation in S6 is specifically as follows: all candidate sources detected iteratively are stored in the candidate source set, and the total increase in the system residual energy is calculated after temporarily removing each candidate source. Calculate the contribution of each detected information source to the overall fitting residual, that is, calculate the proportion of the energy increase corresponding to each candidate information source to the total increase; determine the candidate information sources with the contribution value below the preset contribution value threshold as false sources and remove them.

8. The amplitude and phase error self-calibrating direction of arrival greedy estimation method of claim 1, wherein, The optimization in S6 specifically involves: for the source signal retained after pruning, performing S4 and S5 alternately to update the source signal waveform and diagonal calibration matrix multiple times, so that all parameter estimates converge further.

9. A phase error self-calibrating direction of arrival greedy estimation apparatus, characterized in that, include: Memory and one or more processors; The memory stores executable code, and when the one or more processors execute the executable code, they are used to implement the wave direction greedy estimation method for amplitude and phase error self-calibration as described in any one of claims 1 to 8.

10. A computer readable storage medium characterized by, It stores a program that, when executed by a processor, implements the greedy estimation method for amplitude and phase error self-calibration of direction of arrival as described in any one of claims 1 to 8.

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