Robust synthetic aperture direction finding algorithm based on spatial filtering and alternating iteration

Abstract

The present application belongs to synthetic aperture antenna array signal processing field, specifically, it is a kind of robust synthetic aperture direction finding algorithm based on space filtering and alternating iteration, which can overcome the influence of phase noise and array moving deviation and improve angle estimation precision, comprising, first, constructing global data matrix by using mobile platform array receiving signal;Then, based on local data, the coarse estimation value of angle and phase error is obtained;Then, the MVDR space filter is constructed by using coarse estimation parameter, and the single target signal is extracted to realize multi-target decoupling;Then, the single target signal is alternately iterated for fine estimation, and the parameter is updated by one-dimensional local search and algebraic mapping;Finally, according to the convergence condition, the reconstructed filter is returned to continue iteration, or the high-precision angle fine estimation value is output, the present application avoids multi-dimensional joint search, and realizes robust high-precision direction finding under non-ideal condition.

Description

Technical Field

[0001] This invention belongs to the field of synthetic aperture antenna array signal processing. Specifically, it is a robust synthetic aperture direction finding algorithm based on spatial filtering and alternating iteration that can overcome the influence of phase noise and array movement deviation and improve the angle estimation accuracy by expanding the array aperture through synthetic aperture. Background Technology

[0002] In direction-finding systems, the accuracy of direction finding directly depends on the physical aperture size of the antenna array. Increasing the array aperture can effectively narrow the beamwidth and improve direction-finding accuracy. However, in engineering practice, according to the Nyquist sampling theorem, simply increasing the number of physical array elements to expand the aperture leads to increased costs and also increases the burden on the mounting platform. To address this inherent contradiction between direction-finding accuracy and physical size, the introduction of synthetic aperture technology provides an effective solution.

[0003] Synthetic aperture technology (SAP) utilizes the platform's mobility, performing multiple samples during movement to convert accumulated temporal gain into spatial gain. This technique effectively expands the array aperture without increasing the number of antennas, thereby improving direction-finding accuracy. However, in practical applications, phase noise inherent in the receiving system and positional offsets caused by incomplete array movement make it difficult to meet ideal SAP conditions. This phase noise and positional deviations lead to manifold mismatch in the array's received signal, preventing the system from completing SAP processing and ultimately resulting in incorrect signal angle estimation. Summary of the Invention

[0004] This invention addresses the manifold mismatch problem caused by phase noise and positional deviation when performing angle estimation for passive synthetic aperture arrays. It proposes a robust synthetic aperture direction finding algorithm based on spatial filtering and alternating iteration. This algorithm represents phase noise and positional deviation as phase errors, reconstructs the signal form, obtains coarse estimates of angle and phase error from the received signal through two-dimensional parameter estimation, extracts single-target signals using spatial filtering and alternating iteration techniques, updates the phase error value through local high-density search and algebraic mapping, and achieves high-precision angle estimation under phase error conditions through multiple iterations.

[0005] This invention achieves its purpose through the following measures: A robust synthetic aperture direction finding algorithm based on spatial filtering and alternating iteration is characterized by the following steps: Step 1: Utilize a mobile platform equipped with an antenna array to receive far-field space target signals; Step 2: Obtain a rough estimate of the angle and phase error values; Step 3: Extract the single target signal using spatial filtering with the global data matrix; Step 4: Combining alternating iteration with precise estimation to update angle and phase errors; Step 5: Repeat the iteration until the system converges or the maximum number of iterations is reached; Step three, which involves using the global data matrix to perform spatial filtering to extract the single-target signal, specifically involves: Step 3-1: Combine The received signals are stacked column by column to construct a global data matrix. With global data covariance matrix : (8), (9), Step 3-2: Utilize the obtained angle value With phase error set Reconstruction Equivalent space steering vector : (10), Step 3-3: Receiving data from multiple targets Extract The components are introduced into a minimum variance distortionless response (MVDR) beamformer to construct a spatial filtering weight vector. The beamformer constraint criterion is: fix the desired target direction gain to 1, minimize the total filter power, and create nulls in the array beam in the direction of the interference signal, i.e.: (11), Steps 3-4: Utilize For global data matrix Perform filtering: (12); In step four, the angle and phase errors are updated iteratively and alternately as follows: Step 4-1: Estimate the signal using a single target and By performing cross-correlation calculations, the true steering vector, including phase error, can be obtained. Approximate estimate : (13) Step 4-2: Approximate guide vector Classified as A subvector, denoted as By calculating the relationship between each sub-vector and... Inner product, constructing the angle of arrival One-dimensional cost function : (14) Step 4-3: In the coarse estimate Perform a one-dimensional local fine search within the neighborhood. Make the cost function... The angle that represents the maximum value is the angle under this iteration. Angle Precision Estimation ; Step 4-4: Obtain a precise angle estimate Then, the phase error value is directly updated using algebraic relationships. Substituting the guide vector yields and with Perform inner product and extract scalar. : (15) Steps 4-5: Since there is no positional deviation or phase noise at the initial moment, the first... Time period and By performing conjugate multiplication and extracting the phase through cross multiplication, the estimated value of the phase correction factor for each segment can be determined. : (16).

[0006] Step one of this invention specifically involves: defining the existence of... The far-field narrowband signal, the first The signal is Its angle of incidence is Let the physical array be Linear array, element spacing is The platform is fast Move, proceed Sub-synthetic aperture, sampling interval is Considering phase noise and positional deviation, the first in the array The array element in the first The actual received signal from the subsynthetic aperture is represented as follows: (1), in, For the signal wavelength, The signal carrier frequency; Indicates signal In the The phase noise of the subsynthesized form satisfies , This is for accumulated phase noise; Indicates the array at the The positional error of the secondary synthesized aperture is defined as follows: ; It is additive white Gaussian noise. Phase noise and position deviation are unified into phase error, and a signal is defined. In the The phase error of the secondary synthesized aperture is Its expression is: (2), p. The array receives the signal during sub-synthetic aperture: (3), in, It is a signal vector; This is the array noise vector; For array manifold matrix, This is the equivalent guiding vector for array movement; Let represent the phase error matrix. In this case, the array manifold vectors differ from the manifold vectors without phase error, which is called the manifold mismatch problem.

[0007] Step two of this invention involves a coarse estimation of the angle and phase error values, specifically: Step 2-1: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require and Perform simultaneous operations to construct Its expression is: (4), Step 2-2: For the matrix Eigenvalue decomposition is performed on the covariance matrix to obtain the noise subspace. With noise subspace projection matrix , Divide the matrix into four equal subarrays: (5), Steps 2-3: Based on the real target guidance vector and The orthogonality of the property makes Construct the cost function : (6); Steps 2-4: First, determine the search using a coarse grid. Angle set of signals Let the partial derivatives Solve After extracting its phase, the first... Phase error estimate : (7), By traversal It can provide a coarse estimate of the signal angle and correction factor, providing global initialization parameters for subsequent algorithms.

[0008] In step five of this invention, the evaluation of the system's iterative convergence conditions and the output of the final estimation result are specifically as follows: Step 5-1: Targeting the space By processing all signals according to steps three and four, the global angle estimation set after a single iteration can be obtained. With global correction bias estimation set Calculate the parameters updated in this iteration and the parameters from the previous iteration (i.e., ...). and The sum of the absolute values ​​of the changes between ) : (17); Step 5-2: Set the system's convergence threshold as follows And set the maximum allowed number of iterations as Sum of the absolute values ​​of the changes in the iterative parameters With threshold Comparison: like or the number of iterations has reached If the system has reached convergence, the iteration loop stops, and the current parameter set is output. As a signal angle estimate; like And the current iteration count has not been reached. If the system has not yet converged, then the system parameter set is determined to be... and Replacement parameter set and And return to step three, using and Constructing the guiding vector Spatial domain filter weight vector Then continue the cyclical process of steps four and five until the convergence condition is met.

[0009] The robust direction-finding algorithm proposed in this invention, operating under phase error, achieves accurate single-signal extraction through spatial filtering and transforms multi-dimensional parameter joint estimation into local one-dimensional search and algebraic mapping calculation through alternating iteration. This invention effectively overcomes the manifold mismatch problem caused by system phase noise and array movement deviation in practical reconnaissance environments, achieving high-precision target direction finding and providing a reliable solution for the engineering application of single-platform synthetic aperture technology in complex electromagnetic environments. Attached Figure Description

[0010] Appendix Figure 1 This is a flowchart illustrating the present invention.

[0011] Appendix Figure 2 This is a schematic diagram of the target angle-phase error in Embodiment 1 of the present invention, wherein the number of array elements is 10, SNR=10dB, single synthesized aperture is 500, the number of snapshots is 500, and the angle is 10 ... The array movement distance is 0.5m, the element movement deviation is 0.025m to the right, and the phase noise is... The phase error is approximately .

[0012] Appendix Figure 3 This is a schematic diagram of the target angle-phase error in Embodiment 1 of the present invention, wherein the number of array elements is 10, SNR=10dB, single synthesized aperture is [value missing], number of snapshots is 500, number of signals is 14, and the angle is uniformly distributed [value missing]. The array movement distance is 0.5m, the element movement deviation is 0.025m to the right, and the phase noise is uniformly distributed. Phase error phase The values ​​are distributed as follows: .

[0013] Appendix Figure 4 This section compares the theoretical computational cost of Embodiment 1 of the present invention with that of the comparison algorithm as a function of the number of snapshots. , , , , , , , , , .

[0014] Table 1 shows the theoretical computational cost of Embodiment 1 of the present invention and the comparison algorithm.

[0015] Appendix Figure 5 To illustrate the variation of the RMSE (Relative Mean Squared Error) of the angle estimation for a stationary array with the input signal-to-noise ratio in Embodiment 1 of the present invention, five incoherent signals were set, with the signal angles... Evenly distributed in The aperture was synthesized in a single step and in two steps, with a snapshot count of 500.

[0016] Appendix Figure 6 To illustrate the variation of the RMSE (Relative Mean Squared Error) of the angle estimation for a stationary array with the number of snapshots in Embodiment 1 of the present invention, five incoherent signals were set, with signal angles... Evenly distributed in The pore size was synthesized in a single attempt and in two attempts, with an SNR of 5dB. Detailed Implementation

[0017] The present invention will be further described below with reference to the accompanying drawings and embodiments: Example

[0018] This example proposes a robust synthetic aperture direction finding algorithm based on spatial filtering and alternating iteration. The specific steps are as follows: Figure 1 As shown, the first step involves using a mobile platform equipped with an antenna array to receive far-field spatial target signals: Existing in the defined space The far-field narrowband signal, the first The signal is Its angle of incidence is Let the physical array be... Linear array, element spacing is The platform is fast. Move, proceed Sub-synthetic aperture, sampling interval is Considering phase noise and positional deviation, the first in the array The array element in the first The actual received signal from the subsynthetic aperture is represented as follows: (1), in, For the signal wavelength, The signal carrier frequency; Indicates signal In the The phase noise of the subsynthesized form satisfies , This is for accumulated phase noise; Indicates the array at the The positional error of the secondary synthesized aperture is defined as follows: ; It is additive white Gaussian noise.

[0019] Phase noise and position deviation are unified into phase error, and a signal is defined. In the The phase error of the secondary synthesized aperture is Its expression is: (2), No. The array receives the signal during sub-synthetic aperture: (3), in, It is a signal vector; This is the array noise vector; For array manifold matrix, This is the equivalent guiding vector for array movement; Let represent the phase error matrix. In this case, the array manifold vector differs from the manifold vector without phase error, a problem known as manifold mismatch.

[0020] Step 2: Coarse estimation of angle and phase error values. Step 2 includes the following steps: (1) and Perform simultaneous operations to construct Its expression is: (4), (2) For the matrix Eigenvalue decomposition is performed on the covariance matrix to obtain the noise subspace. With noise subspace projection matrix . Divide the matrix into four equal subarrays: (5), (3) Based on the real target guidance vector and The orthogonality of the property makes Construct the cost function : (6), (4) First determine the coarse grid search. Angle set of signals Let the partial derivatives Solve After extracting its phase, the first... Phase error estimate

[0021] (7), By traversal It can provide a coarse estimate of the signal angle and correction factor, providing global initialization parameters for subsequent algorithms.

[0022] Step 3: Extract the single target signal by spatial filtering using the global data matrix. Step 3 includes the following steps: (1) There will be a total of The received signals are stacked column by column to construct a global data matrix. With global data covariance matrix : (8), (9), (2) Using angle values With phase error set Reconstruction Equivalent space steering vector : (10), (3) To receive data from multiple targets Extract The components are introduced into a minimum variance distortionless response (MVDR) beamformer to construct a spatial filtering weight vector. The beamformer constraint criterion is: fix the desired target direction gain to 1, minimize the total filter power, and create a null in the direction of the interference signal in the array beam, i.e.: (11), (4) Utilization For global data matrix Perform filtering: (12) Step 4: Update the angle and phase errors through alternating iterations. Step 4 includes the following steps: (1) Using a single target to estimate the signal and By performing cross-correlation calculations, the true steering vector, including phase error, can be obtained. Approximate estimate : (13) (2) Approximate guiding vector Classified as A subvector, denoted as By calculating the relationship between each sub-vector and... Inner product, constructing the angle of arrival One-dimensional cost function : (14) (3) In the rough estimate Perform a one-dimensional local fine search within the neighborhood. Make the cost function... The angle that represents the maximum value is the angle under this iteration. Angle Precision Estimation .

[0023] (4) Obtaining precise angle estimation Then, the phase error value is directly updated using algebraic relationships. Substituting the guide vector yields and with Perform inner product and extract scalar. : (15) (5) Since there is no positional deviation or phase noise at the initial moment, the first Time period and By performing conjugate multiplication and extracting the phase through cross multiplication, the estimated value of the phase correction factor for each segment can be determined. : (16) Step 5: Evaluate the system's iterative convergence conditions and output the final estimation results. Step 5 includes the following steps: (1) Regarding the space that exists By processing all signals in steps three and four, the global angle estimation set after a single iteration can be obtained. With global correction bias estimation set Calculate the parameters updated in this iteration and the parameters from the previous iteration (i.e., ...). and The sum of the absolute values ​​of the changes between ) : (17).

[0024] (2) Set the system's convergence threshold as And set the maximum allowed number of iterations as Sum of the absolute values ​​of the changes in the iteration parameters With threshold Comparison: like or the number of iterations has reached If the system reaches convergence, the iteration loop stops. The current parameter set is then output. As a signal angle estimate.

[0025] like And the current iteration count has not been reached. If the system has not yet converged, then the system parameter set is considered to be... and Replacement parameter set and And return to step three, using and Constructing the guiding vector Spatial domain filter weight vector Then, continue the cyclical process from step four to step five until the convergence condition is met.

[0026] The performance of this example can be illustrated through the following simulation: 1. Simulation conditions To demonstrate the effectiveness and feasibility of the proposed algorithm, computer simulation was used to verify its function and performance, and a comparative analysis was conducted with a static uniform array. The synthetic aperture array parameters were configured as follows: carrier frequency f0 = 3 GHz, frequency offset Δf = 1 kHz, and the spacing between the transmitting and receiving antenna elements was 0.05 m.

[0027] 2. Simulation content and results Simulation 1 assumes the presence of P=2 far-field targets in space, with M=10 array elements, a signal-to-noise ratio of 10dB, and 500 snapshots. To effectively analyze the angle estimation of the algorithm, the target angle and phase error values ​​are preset to (32°, 55.3°) and (41°, 36.95°), respectively; the target angle estimation is as follows... Figure 2 As shown.

[0028] from Figure 2 As can be seen, the algorithm proposed in this invention can effectively estimate the angle and phase errors of multiple targets, thereby achieving the purpose of accurate direction finding; at the same time, the actual position of the target and the estimated position highly coincide.

[0029] Simulation 2 assumes the presence of P = 14 far-field targets in space, with M = 10 array elements, a signal-to-noise ratio of 10 dB, and 500 snapshots. To effectively analyze the angle estimation performance of the algorithm, the target angles are uniformly distributed across... The phase error values ​​are distributed in ; Target angle estimation situation as follows Figure 3 As shown.

[0030] from Figure 3 As can be seen, the algorithm proposed in this invention can effectively estimate the angle and phase errors of multiple targets with more than the number of array elements, thereby achieving the purpose of accurate direction finding; at the same time, the actual position of the target and the estimated position highly coincide.

[0031] Simulation 3 examines the computational efficiency of the proposed algorithm and the classical algorithm for calculating the angle and phase error of the target signal under different snapshots. The number of snapshots is set to... From the theoretical computational complexity (as shown in Table 1), Figure 4 The computational efficiency is evaluated using an equivalent method.

[0032] As can be seen from Table 1, the computational efficiency of the algorithm of this invention is higher than that of the traditional algorithm.

[0033] Table 1

[0034] Simulation 4: To compare and analyze the performance of the algorithm proposed in this invention, the minimum root mean square error (RMSE) was used as the evaluation index. The results of each performance experiment were statistical averages of 500 Monte Carlo simulations. The RMSE for the target signal angle estimate was defined as follows: (18).

[0035] The impact of signal-to-noise ratio on the performance of this invention and stationary array angle estimation was investigated, where there are P=5 far-field targets, M=10 array elements, and the target angles are uniformly distributed. The phase error values ​​are distributed in The signal-to-noise ratio ranged from -10dB to 10dB, and the number of snapshots was 500. Single-shot and double-shot aperture synthesis were used respectively. The results are as follows: Figure 5 As shown.

[0036] from Figure 5 As can be seen, after synthesizing the aperture, the array estimation accuracy is better than that of the static array. The algorithm proposed in this invention can effectively overcome the negative impact of phase error and improve the direction finding accuracy.

[0037] Simulation 5 further discusses the impact of snapshot count on the performance of the algorithm proposed in this invention. To ensure consistency of the experiments, the simulation parameters are the same as in Simulation 4, and single-shot and double-shot aperture synthesis are performed respectively. The results are as follows: Figure 6 As shown.

[0038] from Figure 6 As can be seen from the results, Simulation 5 has the same conclusion as Simulation 4, namely, the angle estimation performance of the algorithm proposed in this invention is better than the angle estimation result of the static array.

[0039] This invention innovatively proposes a robust direction-finding technique based on spatial filtering and alternating iteration. It efficiently separates the complex problem of joint estimation of multiple targets and multi-dimensional parameters into a single target. Unlike traditional multi-parameter joint search techniques, the new method extracts the target signal by constructing an adaptive spatial filtering weight vector. Furthermore, since spatial filtering achieves multi-signal decoupling, the new method alternately searches for the target angle and generalized phase error through local one-dimensional high-density search and algebraic mapping, avoiding phase spectrum peak search calculations through algebraic decoupling. This method meets the engineering requirements of high precision, strong robustness, and low computational complexity in non-ideal electromagnetic environments, providing strong theoretical support for the lightweighting, engineering, and practical application of single-platform synthetic aperture direction-finding equipment.

Claims

1. A robust synthetic aperture direction finding algorithm based on spatial filtering and alternating iteration, characterized in that, Includes the following steps: Step 1: Utilize a mobile platform equipped with an antenna array to receive far-field space target signals; Step 2: Obtain a rough estimate of the angle and phase error values; Step 3: Extract the single target signal using spatial filtering with the global data matrix; Step 4: Combining alternating iteration with precise estimation to update angle and phase errors; Step 5: Repeat the iteration until the system converges or the maximum number of iterations is reached; Step three, which involves using the global data matrix to perform spatial filtering to extract the single-target signal, specifically involves: Step 3-1: Combine The received signals are stacked column by column to construct a global data matrix. With global data covariance matrix : （8）， （9）， Step 3-2: Utilize the obtained angle value With phase error set Reconstruction Equivalent space steering vector : （10）， Step 3-3: Receiving data from multiple targets Extract The components are introduced into a minimum variance distortionless response (MVDR) beamformer to construct a spatial filtering weight vector. The beamformer constraint criterion is: fix the desired target direction gain to 1, minimize the total filter power, and create nulls in the array beam in the direction of the interference signal, i.e.: （11）， Steps 3-4: Utilize For global data matrix Perform filtering: （12）； In step four, the angle and phase errors are updated iteratively and alternately as follows: Step 4-1: Estimate the signal using a single target and By performing cross-correlation calculations, the true steering vector, including phase error, can be obtained. Approximate estimate : （13）， Step 4-2: Approximate guide vector Classified as A subvector, denoted as By calculating the relationship between each sub-vector and... Inner product, constructing the angle of arrival One-dimensional cost function : （14）， Step 4-3: In the coarse estimate Perform a one-dimensional local fine search within the neighborhood. Make the cost function... The angle that represents the maximum value is the angle under this iteration. Angle Precision Estimation ; Step 4-4: Obtain a precise angle estimate Then, the phase error value is directly updated using algebraic relationships. Substituting the guide vector yields and with Perform inner product and extract scalar. : （15）， Steps 4-5: Since there is no positional deviation or phase noise at the initial moment, the first... Time period and By performing conjugate multiplication and extracting the phase through cross multiplication, the estimated value of the phase correction factor for each segment can be determined. : （16）。 2. The robust synthetic aperture direction finding algorithm based on spatial filtering and alternating iteration as described in claim 1, characterized in that, Step one specifically involves defining the existence of space. The far-field narrowband signal, the first The signal is Its angle of incidence is Let the physical array be Linear array, element spacing is The platform is fast Move, proceed Sub-synthetic aperture, sampling interval is Considering phase noise and positional deviation, the first in the array The array element in the first The actual received signal from the subsynthetic aperture is represented as follows: （1）， in, For the signal wavelength, The signal carrier frequency; Indicates signal In the The phase noise of the subsynthesized form satisfies , This is for accumulated phase noise; Indicates the array at the The positional error of the secondary synthesized aperture is defined as follows: ; It is additive white Gaussian noise. Phase noise and position deviation are unified into phase error, and a signal is defined. In the The phase error of the secondary synthesized aperture is Its expression is: （2）， No. The array receives the signal during sub-synthetic aperture: （3）， in, It is a signal vector; This is the array noise vector; For array manifold matrix, This is the equivalent guiding vector for array movement; Let represent the phase error matrix. In this case, the array manifold vectors differ from those without phase error, which is called the manifold mismatch problem.

3. The robust synthetic aperture direction finding algorithm based on spatial filtering and alternating iteration as described in claim 2, characterized in that, Step two involves a rough estimation of the angle and phase error values, specifically: Step 2-1: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] and Perform simultaneous operations to construct Its expression is: （4）， Step 2-2: For the matrix Eigenvalue decomposition is performed on the covariance matrix to obtain the noise subspace. With noise subspace projection matrix , Divide the matrix into four equal subarrays: （5）， Steps 2-3: Based on the real target guidance vector and The orthogonality of the property makes Construct the cost function : （6）； Steps 2-4: First, determine the search using a coarse grid. Angle set of signals Let the partial derivatives Solve After extracting its phase, the first... Phase error estimate : （7）， By traversal It can provide a coarse estimate of the signal angle and correction factor, providing global initialization parameters for subsequent algorithms.

4. The robust synthetic aperture direction finding algorithm based on spatial filtering and alternating iteration as described in claim 3, characterized in that, Step five involves evaluating the system's iterative convergence conditions and outputting the final estimation results as follows: Step 5-1: Targeting the space By processing all signals according to steps three and four, the global angle estimation set after a single iteration can be obtained. With global correction bias estimation set Calculate the parameters updated in this iteration and the parameters from the previous iteration (i.e., ...). and The sum of the absolute values ​​of the changes between ) : (17); Step 5-2: Set the system's convergence threshold as follows And set the maximum allowed number of iterations as Sum of the absolute values ​​of the changes in the iterative parameters With threshold Comparison: like or the number of iterations has reached If the system has reached convergence, the iteration loop stops, and the current parameter set is output. As a signal angle estimate; like And the current iteration count has not been reached. If the system has not yet converged, then the system parameter set is determined to be... and Replacement parameter set and And return to step three, using and Constructing the guiding vector Spatial domain filter weight vector Then continue the cyclical process of steps four and five until the convergence condition is met.

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