A method for calibrating array amplitude and phase errors based on joint sparse estimation

Abstract

This invention discloses an array amplitude and phase error calibration method based on joint sparse estimation. The method includes: setting a calibration sound source at an unknown far-field direction relative to a linear array of sensors; dividing the observation area of ​​the linear array of sensors into several grid points; correcting the array sampled signal based on the grid points and offsets; constructing an array response signal model; performing joint sparse direction-of-arrival estimation of the grid points and offsets to obtain the direction of arrival of the calibration sound source signal; extending the joint sparse estimation method for solving the direction of arrival of the calibration sound source signal to planar arrays and multi-frequency cross arrays through iterative correction; and completing the array amplitude and phase error calibration using a spatial filtering method based on the estimated direction of arrival of the calibration sound source. This invention solves the beamform attenuation problem caused by existing array amplitude and phase error calibration methods, improves error correction accuracy and efficiency, and broadens the application of error calibration methods in multiple array types.

Description

Technical Field

[0001] This invention relates to the field of phased array three-dimensional imaging sonar technology, and in particular to an array amplitude and phase error calibration method based on joint sparse estimation. Background Technology

[0002] Real-time 3D sonar imaging technology has been widely applied in underwater exploration and other fields in recent years. Phased array 3D imaging sonar systems transmit acoustic pulse signals, receive sonar echo signals through a large planar array, and then use beamforming and real-time image processing techniques to obtain high-resolution underwater 3D images, i.e., beammaps. The receiving sensor elements of the phased array are typically designed and considered to have the same amplitude response and signal processing delay, and the array response signal model is established based on this.

[0003] In real-world scenarios, arrays are affected by factors such as sensor manufacturing precision errors, placement deviations, inconsistent signal conditioning circuits, and temperature stress, resulting in amplitude and phase errors. This leads to signal model mismatch and consequently, beam pattern performance degradation, manifesting as increased sidelobe intensity and main lobe focus shift. This is particularly pronounced in sparse or linear arrays, where the fewer array elements or the higher weighting of some elements in beamforming calculations exacerbate beam pattern attenuation caused by array amplitude and phase errors. If the array's amplitude and phase error factors can be effectively estimated, and the signals received by each transducer can be compensated based on this estimate during subsequent beamforming processing, the phased array 3D camera sonar system can still provide ideal imaging quality even under conditions of array amplitude and phase errors.

[0004] Linear arrays and uniform planar arrays are common array configurations, and their array error calibration methods have been extensively studied. Array error correction methods can be divided into two main categories: active calibration and auto-calibration. Active calibration methods require the use of several active calibration sources with precisely known orientations, while auto-calibration methods, due to the unknown orientations of the calibration sources, usually require simultaneous estimation of the orientations of the calibration sources and the array error parameters. For example, Reference 1 (Direction-of-Arrival Estimation and Sensor Array Error Calibration Based on Blind Signal Separation, 2017, IEEE Signal Processing Letters) provides a direction-of-arrival estimation and sensor array error calibration based on unknown signal separation. It solves for the amplitude error by utilizing the relationship between the diagonal values ​​of the array's received signal covariance matrix, and then performs a dot product operation between the amplitude error-corrected output signal and its conjugate to obtain a covariance matrix independent of the phase error. This covariance matrix is ​​then used for direction-of-arrival estimation (DOA), thus achieving good performance regardless of the magnitude of the phase error. However, since it requires different phase differences between adjacent array elements, it is not suitable for uniform linear arrays, and at least two signals that are spatially angularly separated are required. The computational cost is also a problem that needs to be considered in practical applications.

[0005] Existing array error correction methods require estimation and correction of amplitude and phase errors based on characteristic structures and Toeplitz characteristics. These array error calibration methods mostly rely on array geometry or prior information related to array structure. They have good calibration performance in corresponding array types, but lack versatility across multiple array types.

[0006] Although methods such as spectral peak search, signal subspace, and compressed sensing based on signal spatial domain information can reduce the requirements of array configuration for error calibration methods, they improve the accuracy of direction of arrival (DOA) estimation methods by increasing the grid density of the preset response signal direction. Their computational complexity can reach the third to fourth power of the product of the number of grid points and the number of array elements, resulting in long computational delays in large-scale arrays or high-precision scenarios. Summary of the Invention

[0007] The purpose of this invention is to provide an array amplitude and phase error calibration method based on joint sparse estimation, which solves the beam pattern attenuation problem caused by existing array amplitude and phase error calibration, improves the accuracy and efficiency of error correction, and broadens the application of error calibration methods in multiple array types.

[0008] To achieve the above-mentioned objectives, an embodiment provides an array amplitude and phase error calibration method based on joint sparse estimation, comprising the following steps:

[0009] The calibration sound source is positioned in an unknown far-field direction relative to the linear array of sensors;

[0010] The observation area of ​​the linear array of the sensor is divided into several grid points. Based on the grid points and the offset, the array sampling signal is corrected, the array response signal model is constructed, and the joint sparse direction of arrival estimation of the grid points and the offset is performed to obtain the corrected sound source signal direction of arrival.

[0011] Through iterative correction, the method for solving the joint sparse estimation of the direction of arrival of the corrected sound source signal is extended to planar arrays and multi-frequency cross arrays.

[0012] Based on the estimated corrected direction of arrival of the sound source, the spatial filtering method is used to complete the array amplitude and phase error calibration.

[0013] In one embodiment, setting the calibration sound source to be located in an unknown far-field direction relative to the sensor linear array includes: for a uniform receiving linear array with M elements, the array center is located at the origin, and the element spacing is d. x A correction source is set relative to the unknown far-field direction of the uniform receiving linear array to generate a response signal.

[0014] In one embodiment, the observation area of ​​the linear array of the sensor is divided into several grid points, including: for an unknown distribution of the target signal, the array observation area is divided into P uniform or non-uniform grid points to replace the continuous signal angle distribution, with each grid point corresponding to an incident signal angle, and the array response signal is represented as follows:

[0015]

[0016] Where x(m) represents the array response signal, s p Let j represent the signal vector, f be the unit imaginary number, and α be the signal frequency. p Let represent the incident signal angle corresponding to grid point p, c be the signal propagation speed in the current medium, and ε be the angle of incidence. m The noise is independent and identically distributed among the array elements m.

[0017] In one embodiment, the correction of the array sampling signal based on grid points and offset includes:

[0018] The grid is extended to a linear array, and an offset is introduced for signal correction, giving it the ability to estimate the direction of arrival (ROA) of off-grid incident signals. The corrected response signal is expressed as:

[0019] X=(A+EΔ)s+ε

[0020] Where A is the observation area matrix, The off-grid angle offset represents the actual angle α′ of the incident signal closest to grid point p. p With at grid point angle α p The difference is T, which represents the transpose operation, and E is the off-grid correction term of the observation area matrix. Since the number of signal samples is much smaller than the number of grid points in practical applications, the signal vector s of the linear array is regarded as a sparse vector, and ε is the noise of the linear array.

[0021] In one embodiment, the joint sparse direction-of-arrival estimation of grid points and offsets includes: to avoid index confusion caused by offsets exceeding limits, the off-grid angle offset should not exceed half of the grid point angle spacing, if the grid points are uniform and the corresponding spacing is 2D. α Then the constraint can be expressed as:

[0022]

[0023] in, The off-grid angle offset represents the actual angle α′ of the incident signal closest to grid point p. p With at grid point angle α p The difference, where P represents the number of grid points;

[0024] make Based on the L2 norm of LASSO theory, the problem of estimating the direction of arrival (DOA) of an array-sampled signal is expressed as:

[0025]

[0026] Wherein, the observation region matrix A∈C M×P C M×P Let E be an M×P matrix, E be the off-network correction term of the observation area matrix, x be the actual response signal of the linear array, and λ||s|| 2，1 The penalty function term to ensure sparsity is s, where s is the incident signal vector at the nearest index, and λ is the regularization parameter. Let d be the square of the L2 norm, for any element d in d. i d is true only if the incident signal at its nearest index is non-zero. i The non-zero value of θ is meaningful, and θ represents the angle between the incident signal at the nearest index;

[0027] Perform a joint sparse estimate on s and d, and let Φ = [A, E] ∈ C. M×2P u = [s T ,d] T ∈C 2P The direction-of-arrival (DOA) estimation problem for array-sampled signals can be further expressed as:

[0028]

[0029] Among them, C M×2P Let C represent an M×2P matrix. 2P Let λ represent a 2P matrix, T denote the transpose operation, and λ||u|| 2，1 To ensure joint sparsity, a penalty function term is used, where u is the joint sparsity estimation term. Iterative optimization is performed based on the joint sparsity estimation term to complete the joint sparse direction of arrival estimation.

[0030] In one embodiment, the iterative solution optimization based on the joint sparsity estimation term includes: on the basis of the fast iterative threshold shrinkage algorithm, adopting Moreau's lower envelope to improve gradient calculation, optimizing the fixed step size to the dynamic gradient descent step size obtained by line search to accelerate iterative convergence, and optimizing the joint sparsity of the direction of arrival estimation problem of the array sampled signal.

[0031] In one embodiment, the method for solving the joint sparse estimation of the direction of arrival of the corrected sound source signal is extended to a planar array, including: the planar array has M×N receiving array elements, P beams in the horizontal direction and Q beams in the vertical direction, and based on the estimation of the direction of arrival of the corrected sound source signal in the linear array, the two-dimensional array response is compressed into a vector and the four-dimensional sensing matrix is ​​compressed into a two-dimensional matrix.

[0032] In one embodiment, the method for solving the joint sparse estimation of the direction of arrival of the corrected sound source signal is extended to a multi-frequency cross array, including:

[0033] A three-dimensional imaging effect of an approximate planar array is obtained by plotting beammaps in both the transmission and reception directions, where the number of beams in the transmission direction is P and the number of beams in the reception direction is Q.

[0034] The cross array focuses and transmits a fan-shaped beam at each angle along the transmission direction. The receiving array generates a horizontal beam at the corresponding vertical angle by receiving the echo signal one by one. After traversing the array, P×Q planar beams within the detection range are obtained.

[0035] Based on the planar beamforming results of the cross array, the response signal of the multi-frequency cross array is obtained when multi-frequency transmission occurs.

[0036] In one embodiment, the direction of arrival of the corrected sound source signal after spatial filtering optimization and reconstruction includes:

[0037] The ideal rotation vector is calculated by estimating the direction of arrival of the corrected sound source signal and its intensity.

[0038] Estimate the initial amplitude and phase of the response signal in each sampling snapshot of the direction of arrival of the corrected sound source signal to obtain the actual rotation vector;

[0039] Based on the ideal rotation vector and the actual rotation vector, a spatial filtering method is used to estimate the amplitude and phase error.

[0040] In one embodiment, amplitude and phase error calibration is completed by using root mean square error to quantize beam pattern matching accuracy and amplitude and phase error estimation accuracy.

[0041] Compared with the prior art, the beneficial effects of the present invention include at least the following:

[0042] (1) The problem of estimating the direction of arrival of the corrected sound source is transformed into an optimization problem of solving the corrected sound source signal by reconstructing the array sampled signal. By combining discrete grid points and off-grid offset, an array response signal model is constructed, and the direction of arrival of the response signal is estimated. Based on the compressed sensing method and fast iterative threshold shrinkage algorithm in DOA, the direction of arrival estimation is optimized and solved to obtain the accurate orientation of the response signal, improve the direction estimation performance of the response signal, and balance the computational accuracy and computational complexity.

[0043] (2) Based on the linear array model, an estimation method combining the "iteration-correction" processing framework and the "signal-beam" is proposed, which extends the joint sparse direction of arrival estimation method to application scenarios such as planar arrays and multi-frequency cross arrays, and solves the problem of lack of versatility of existing array calibration methods.

[0044] (3) Spatial filtering is used to optimize amplitude and phase error, which improves the accuracy of amplitude and phase error calibration. Attached Figure Description

[0045] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below.

[0046] Figure 1 A flowchart of an array amplitude and phase error calibration method based on joint sparse estimation provided in an embodiment of the present invention;

[0047] Figure 2 A schematic diagram of the sensor linear array response signal model provided in an embodiment of the present invention;

[0048] Figure 3 A schematic diagram of the sensor planar array response signal model provided in an embodiment of the present invention;

[0049] Figure 4 A schematic diagram of the multi-frequency cross array response signal model provided in an embodiment of the present invention;

[0050] Figure 5A phase error comparison diagram provided in an embodiment of the present invention, wherein Figure 5 In the figure, (a) represents the actual error. Figure 5 (b) in the figure represents the estimation error;

[0051] Figure 6 The root mean square error (RMSE) of array amplitude and phase errors and the standard deviation of amplitude error σ provided for embodiments of the present invention ξ A relationship diagram, in which Figure 6 In the figure, (a) represents the root mean square error of the amplitude and the standard deviation of the amplitude error σ. ξ Relationship diagram, Figure 6 In the figure, (b) represents the root mean square error of the phase and the standard deviation σ of the amplitude error. ξ Relationship diagram;

[0052] Figure 7 The root mean square error (RMSE) and standard deviation of phase error σ of the array amplitude and phase errors provided in the embodiments of the present invention τ A relationship diagram, in which Figure 7 In the figure, (a) represents the root mean square error of the amplitude and the standard deviation of the phase error σ. τ Relationship diagram, Figure 7 In the figure, (b) represents the root mean square error of the phase and the standard deviation of the phase error σ. τ Relationship diagram;

[0053] Figure 8 This is a graph showing the relationship between the root mean square error (RMSE) of array amplitude and phase errors and the signal-to-noise ratio (SNR) provided in an embodiment of the present invention. Figure 8 (a) in the figure shows the relationship between the root mean square error of the amplitude and the signal-to-noise ratio (SNR). Figure 8 (b) in the figure shows the relationship between the root mean square error of the phase and the signal-to-noise ratio (SNR). Detailed Implementation

[0054] To make the objectives, technical solutions, and advantages of this invention clearer, the following description is provided in conjunction with the accompanying drawings and...

[0055] The embodiments further illustrate the present invention in detail. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not limit the scope of protection of the invention.

[0056] To ensure accurate estimation of the direction of arrival (DOA) of the response signal, this embodiment provides an array amplitude and phase error calibration method based on joint sparse estimation. The method involves setting the correction source to an unknown far-field direction relative to the sensor array and transforming the DOA estimation problem of the correction source into an optimization problem of reconstructing the correction source signal from the array sampled signals. This constructs an array response signal model and proposes a joint sparse DOA estimation method combining discrete grid points and continuous offsets of the response signal direction, balancing computational accuracy and complexity. The method is then extended to uniform and sparse planar arrays and multi-frequency cross arrays through iterative correction, improving its applicability to various scenarios. Finally, spatial filtering is used to correct the impact of array phase error on DOA, enhancing error correction accuracy.

[0057] like Figure 1 As shown in the embodiment, an array amplitude and phase error calibration method based on joint sparse estimation is provided, which includes the following steps:

[0058] S1. Set the calibration sound source to be located in the unknown far-field direction relative to the linear array of sensors.

[0059] In this embodiment, the direction of arrival (DOA) estimation problem of the correction sound source is transformed into an optimization problem of reconstructing the correction sound source signal through array sampling signals, with the correction sound source located in an unknown far-field direction relative to the linear array of sensors. Figure 2 As shown, a uniform receiving linear array with M elements is centered at the origin. Let the element spacing be d. x Position the array element with index m as... For a signal incident at an angle α in the far field of the array (from a target reflection or a correction source), the ideal response signal x of array element m is... o (m) is:

[0060]

[0061] Where ω represents the signal strength value, and j is the imaginary unit. It corrects the initial phase shift of the sound source signal in the time domain, where f represents the signal frequency, c is the signal propagation speed in the current medium, and ε... m The noise is independent and identically distributed among the array elements m.

[0062] Assuming the array has phase and amplitude errors (phase error), the amplitude error of array element m is denoted as ξ. m The phase error is τ m Then the actual response signal of array element m for:

[0063]

[0064] in Represents the signal vector, amplitude error ξm It follows a Gaussian distribution with a mean of 1, and the phase error τ m It follows a zero-mean Gaussian distribution.

[0065] S2. The observation area of ​​the linear array of the sensor is divided into several grid points. Based on the grid points and the offset, the array sampling signal is corrected, the array response signal model is constructed, and the joint sparse direction of arrival estimation of the grid points and the offset is performed to obtain the corrected sound source signal direction of arrival.

[0066] In this embodiment, when the target signal distribution is unknown, the array observation area is divided into P uniform or non-uniform grid points to replace the continuous signal angle distribution. Each grid point corresponds to a candidate incident signal angle, and the array response signal x(m) is expressed as:

[0067]

[0068] Where x(m) represents the array response signal after gridding, s p Let j represent the signal vector, f be the unit imaginary number, and α be the signal frequency. p Let represent the incident signal angle corresponding to grid point p, c be the signal propagation speed in the current medium, and ε be the angle of incidence. m The noise is independent and identically distributed among the array elements m.

[0069] Extending the lattice to a linear array, the actual response signal of the linear array can be expressed in matrix form as x = As + ε:

[0070]

[0071] Wherein, the response vector x in the linear array L ∈C M The observation region matrix A∈C M×P Observation area matrix C M×P An element in the array is represented as A mp = a(m, p), signal vector s∈C P Since the number of signal samples is far less than the number of grid points in practical applications, the signal vector s of a linear array is regarded as a sparse vector.

[0072] In this embodiment, a continuous correction term is introduced to optimize the off-grid model, enabling it to estimate the direction of arrival (ROA) of the off-grid incident signal. The corrected response signal is expressed as follows:

[0073] X=(A+EΔ)s+ε (5)

[0074] in, The off-grid angle offset represents the actual angle α′ of the incident signal closest to grid point p. p With at grid point angle αp The difference, where T denotes the transpose operation, and E is the off-network correction term of the observation area matrix, is derived as follows by first-order Taylor expansion of E:

[0075]

[0076] In this embodiment, after correction, compressed sensing is used for constraint optimization to construct an array response signal model. To avoid index confusion caused by offset exceeding the limit, the off-grid angle offset should not exceed half of the grid point angle spacing. If the grid points are uniform and the corresponding spacing is 2D... α Then the constraint can be expressed as:

[0077]

[0078] in, The off-grid angle offset represents the actual angle α′ of the incident signal closest to grid point p. p With at grid point angle α p The difference, where P represents the number of grid points;

[0079] make Based on the L2 norm of LASSO theory, the problem of estimating the direction of arrival (DOA) of an array-sampled signal is expressed as:

[0080]

[0081] Wherein, the observation region matrix A∈C M×P C M×P Let E be an M×P matrix, E be the off-network correction term of the observation area matrix, x be the actual response signal of the linear array, and λ||s|| 2，1 The penalty function term to ensure sparsity is s, where s is the incident signal vector at the nearest index, and λ is the regularization parameter. Let λ represent the square of the L2 norm, and further, the penalty function term λ||s|| 2，1 Defined as:

[0082]

[0083] in, The L2 norm of the signal vector at lattice point p is given by the expression for any element d in d. i d is true only if the incident signal at its nearest index is non-zero. i The non-zero value of θ is meaningful, and θ represents the angle between the incident signal at the nearest index.

[0084] Based on the correlation between s and d, a joint sparse estimation of s and d is performed instead of alternating iterative solutions. Let Φ = [A, E] ∈ C. M ×2P u = [s T ,d]T ∈C 2P The direction-of-arrival (DOA) estimation problem for array-sampled signals can be further expressed as:

[0085]

[0086] Among them, C M×2P Let C represent an M×2P matrix. 2P Let λ represent a 2P matrix, T denote the transpose operation, and λ||u|| 2，1 To guarantee the joint sparsity, a penalty function term is given, where u is the joint sparsity estimate; further, the sparse penalty function term of the joint estimate u is defined as:

[0087]

[0088] in, Let L2 norm be the joint estimate of lattice point p. The L2 norm represents the joint estimate of the grid point and the off-grid angle offset.

[0089] Based on the joint sparsity of the joint estimation term u, Equation (10) can be regarded as a sparse linear inverse problem, which can be solved by a targeted optimization method for linear inverse problems. Based on the traditional Fast Iterative Threshold Hand Shrinkage (FISTA) algorithm, the gradient calculation is improved according to Moreau's lower envelope to address the joint sparsity characteristics. The fixed step size is optimized to the dynamic gradient descent step size obtained by line search to accelerate iterative convergence.

[0090] S3. Through iterative correction, the method for solving the joint sparse estimation of the direction of arrival of the corrected sound source signal is extended to planar arrays and multi-frequency cross arrays.

[0091] like Figure 3 As shown, unlike linear arrays, planar arrays possess beam resolution in both horizontal and vertical dimensions. For a uniform receiving planar array, containing M×N receiving elements, with azimuth and elevation angles of α and β respectively, P horizontal beams and Q vertical beams, for element (m, n), the array center is located at the origin, and the element positions are as follows: and A calibration sound source is set relative to the unknown far-field direction of the planar array to generate a calibration response signal.

[0092] For from (α) p ,β q The response signal of a planar array element, x(m, n), incident in the direction of the incident signal can be represented as follows:

[0093]

[0094] In formula (12), p represents the horizontal beam, q represents the vertical beam, and s pq Represents the signal vector, α p β represents the incident signal angle corresponding to the horizontal beam. q ε represents the incident signal angle corresponding to the vertical beam. mn The noise is independent and identically distributed for the array elements (m, n); further, to facilitate matrix calculation, the two-dimensional array response is compressed into a vector x∈C. MN The four-dimensional sensing matrix is ​​compressed into a two-dimensional matrix A∈C MN×PQ Two-dimensional matrix C MN×PQ An element in the array is represented as A mnpq =a(m,n,p,q), the general formula for calculating a planar array matrix is ​​x = As + ε.

[0095] like Figure 4 As shown, in this embodiment, the method for estimating the direction of arrival (DOA) of the corrected sound source signal is extended to a multi-frequency cross array. By performing beamforming in both the transmission and reception directions, a three-dimensional imaging effect approximating a planar array is obtained. For array element spacing d... x d y The equally spaced array has the following transmitting and receiving positions: d y (n)=(n-1)d y .

[0096] In a cross array, the number of horizontal beams is P and the number of vertical beams is Q. A conventional cross array focuses and transmits fan-shaped beams at each angle along the transmission direction (here defined as the vertical direction). The receiving array generates horizontal beams at the corresponding vertical angles by successively receiving the corresponding vertical echo signals. After traversing and scanning the entire vertical direction, P×Q planar beams within the detection range are obtained.

[0097] During multi-frequency transmission, the signal response s in the vertical angular direction of the q-th beam T (q) is represented as:

[0098]

[0099] Among them, w t (n) represents the weight of the nth transmitting element, f q For the corresponding transmission frequency, β q This corresponds to the pitch angle.

[0100] The m-th element of the receiving array in f q Frequency signal component x(m, f) q This can be deduced as:

[0101]

[0102] In formula (14), p represents the horizontal beam, q represents the vertical beam, ρ is the reflection coefficient of the calibrated target, and δ pq It is an indicator coefficient, α, indicating whether there is a target in the corresponding two-dimensional angular index direction. p The angle of the incident signal corresponding to the horizontal beam is represented by h(m, p, q), and h(m, p, q) represents a certain signal component in the plane beam.

[0103] S4. Based on the estimated corrected direction of arrival of the sound source, the spatial filtering method is used to complete the array amplitude and phase error calibration.

[0104] In this embodiment, the process of estimating the amplitude and phase error based on the spatially matched filter is as follows:

[0105] First, the direction and intensity of the correction signal are obtained using the direction-of-arrival estimation method, and then the ideal rotation vector γ′ is calculated. mn :

[0106]

[0107] Where γ′mn represents the ideal rotation vector of M×N receiver array elements. This represents the direction angle of the ideal rotation vector. The pitch angle represents the ideal rotation vector.

[0108] After determining the direction of arrival (DOA) of the finally estimated corrected sound source, the initial amplitude and phase of the response signal in each sampling snapshot for estimating the DOA of the corrected sound source are expressed as:

[0109]

[0110] Where, ω l Indicates the response signal strength value. It corrects the initial phase shift of the sound source signal in the time domain. H refers to the conjugate transpose operation, x1 represents the response signal response, and MN represents M×N receiver array elements.

[0111] Furthermore, relative to the ideal rotation vector γ′ mn In other words, the actual rotation vector γm n If there are array amplitude and phase errors, the results can be obtained by removing the amplitude and phase of the response signal from the array response and then averaging the results from multiple calculations.

[0112]

[0113] Therefore, the amplitude and phase error vector of the array can be obtained by dividing the actual rotation vector γ by the ideal rotation vector γ′ element-wise, which is: Specifically, it can be represented as follows:

[0114]

[0115] Where, ξ mn τ represents the amplitude error of the array element (m, n). mn The phase error of array element (m, n) is represented by ∠, and the angle calculation is represented by ∠. The array amplitude error vector follows a function with a mean of 1 and a variance of 1. Gaussian distribution The phase error vector follows a zero mean and a variance of . Gaussian distribution

[0116] To quantify the performance of the method, the common root mean square error (RMSE) index is used to quantify the beam pattern matching accuracy and amplitude and phase error estimation accuracy. The definitions of each index are as follows:

[0117]

[0118] Among them, RMSE BP The root mean square error (RMSE) of the beam pattern is represented by this value. ξ The root mean square error (RMSE) represents the magnitude error. τ BP represents the root mean square error of the phase, BP represents the actual beam pattern, and BP′ represents the optimized beam pattern. ξ' represents the actual amplitude, and ξ′ represents the optimized amplitude. τ′ represents the actual phase, LP represents the optimized phase, and LM represents the number of beam pattern samples.

[0119] To better demonstrate the technical effects, this invention includes a series of experiments for illustration.

[0120] The planar receiver array calibration performance experiment used a 50×50 array with equally spaced elements, with an element spacing d = 2.5 mm. The frequency f of the calibrated sound source signal was located in the far field (10°, -20°) of the array. Additive Gaussian noise was used, with a noise ratio (SNR) of 20 dB and a signal sample size L = 1000. In the experiment, the beam pattern was normalized to the main lobe intensity of the ideal array beam.

[0121] Actual and estimated values ​​of phase error are as follows Figure 5 (a) and Figure 5 As shown in (b) in the figure, the actual and estimated values ​​of some amplitude and phase errors are shown in Table 1.

[0122] Table 1 shows the actual and estimated values ​​of some amplitude and phase errors.

[0123]

[0124]

[0125] In this embodiment, to further explore the performance of the proposed array amplitude and phase error calibration method based on joint sparse estimation under various conditions, the influence of key factors such as amplitude error, phase error and signal-to-noise ratio of response signal on calibration accuracy was compared and analyzed.

[0126] A uniform planar array of 30×30 elements is used, with an array spacing d = 2.5 mm. The calibration sound source is placed at the far field (20°, 20°) of the array. By default, the amplitude error standard deviation σ is... ξ =0.2 phase error standard deviation σ τ =0.25rad, SNR=20dB. In the experiment, 100 independent experiments were performed under each experimental condition to eliminate the influence of chance, and the results were averaged.

[0127] The experiment compared the three-step iterative method (TSI) in uniform planar array calibration, where JSC is the array amplitude and phase error calibration method based on joint sparse estimation provided in this invention. The JSC and TSI methods differ in σ... τ When the amplitude is 0.25 rad and the standard deviation of the amplitude error is 20 dB, the accuracy of the error estimation is related to the standard deviation of the amplitude error σ. ξ Relationship such as Figure 6 As shown. Since the array amplitude error has a relatively small impact on the signal angle estimation during the DOA estimation stage of the response signal, the RMSE of the two calibration methods is relatively low. ξ and RMSE τ It remains essentially stable as the array amplitude changes. With σ ξ Increase, JSC method RMSE ξ The curves showed a slight upward trend, but overall remained lower than the results obtained using the TSI method, with its total σ... ξ Average RMSE in the scenario ξ It is 42% lower than the TSI method.

[0128] Figure 7 It shows that in σ ξ Under the conditions of 0.2 and SNR = 20dB, the accuracy of array error estimation and the standard deviation of phase error σ τ The relationship with ρ. ξ ~RMSE ξ The experimental results are similar, σ τ RMSE increases ξ The change is not significant. In σ τ When the amplitude estimation error is less than 0.55 rad, the proposed JSC method outperforms the TSI method; when σ τAfter exceeding 0.55 rad, the result is slightly higher than that of the TSI method, but its average RMSE is lower. g 3.056×10 -3 The average estimation bias is about 6% lower than that of the TSI method.

[0129] In the standard deviation of amplitude error σ ξ =0.2, phase error standard deviation σ τ Under the condition of 0.25 rad, the relationship between the array response signal SNR and the accuracy of amplitude and phase error estimation is shown in the figure. Figure 8 As shown in the figure, unlike the previous experimental results for amplitude and phase errors, the RMSE of amplitude error estimation is strongly correlated with SNR, especially under low SNR conditions. ξ This represents an order of magnitude increase. This is because at lower SNR levels, the noise signal strength is already close to the response signal strength, making accurate estimation of the DOA stage more difficult and affecting calibration accuracy. When SNR ≥ 20dB, the proposed JSC method achieves higher estimation accuracy and outperforms the TSI method. Regarding phase error estimation accuracy, both methods are relatively stable when SNR ≥ 20dB. As SNR further decreases, the estimation accuracy slightly declines. Except for the extreme case of 0dB, the JSC method outperforms the TSI method.

[0130] The array amplitude and phase error calibration method based on joint sparse estimation provided by this invention can effectively solve the beam pattern attenuation problem caused by existing array amplitude and phase errors. Compared with existing error calibration methods, this invention can improve the accuracy and efficiency of error correction, and no longer relies on prior information related to array geometry and array structure, thus improving the applicability of the error calibration method in various scenarios.

[0131] The specific embodiments described above illustrate the technical solution and beneficial effects of the present invention in detail. It should be understood that the above description is only the most preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, additions, and equivalent substitutions made within the scope of the principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calibrating array amplitude and phase errors based on joint sparse estimation, characterized in that, The array amplitude and phase error calibration method includes the following steps: The calibration sound source is positioned in an unknown far-field direction relative to the linear array of sensors; The observation area of ​​the linear array of the sensor is divided into several grid points, including the distribution of the target signal which is unknown. The continuous signal angle distribution is replaced by dividing the array observation area into P uniform or non-uniform grid points, with each grid point corresponding to an incident signal angle. The array response signal is then expressed as: ,in, Indicates the array response signal. Represents a signal vector. For imaginary numbers, Indicates signal frequency. Representing grid points The corresponding incident signal angle, The speed at which the signal propagates in the current medium. For array element Independent and identically distributed noise; correction of the array sampled signal based on grid points and offsets, including: expanding the grid points to a linear array and introducing offsets for signal correction, so that it has the ability to estimate the direction of arrival of off-grid incident signals. The corrected response signal is expressed as: ,in, For the observation area matrix, , This represents the off-grid angle offset, indicating the distance from the grid point. The most recent incident signal actual angle and at grid point angle The difference, where T represents the transpose operation. This is the off-grid correction term for the observation area matrix. Since the number of signal samples is far less than the number of grid points in practical applications, the signal vector of the linear array... Treat it as a sparse vector. To address the noise in the linear array, a model of the array response signal is constructed, and joint sparse direction-of-arrival estimation of the grid points and offsets is performed. This includes: to avoid index confusion caused by offsets exceeding limits, the off-grid angle offset should not exceed half of the grid point angle spacing. If the grid points are uniform and the corresponding spacing is... Then the constraint can be expressed as: ,in, This represents the off-grid angle offset, indicating the distance from the grid point. The most recent incident signal actual angle and at grid point angle The difference, where P represents the number of grid points; make Based on the L2 norm of LASSO theory, the problem of estimating the direction of arrival (DOA) of an array-sampled signal is expressed as: Among them, the observation area matrix , express The matrix, This is the off-network correction term for the observation region matrix. This represents the actual response signal of the linear array. To ensure sparsity, a penalty function term is applied. Let the incident signal vector be at the nearest index. For regularization parameters, Denotes the square of the L2 norm, for any element Only when the incident signal at its corresponding nearest index is non-zero, Non-zero values ​​are meaningful. It represents the angle between the incident signals at the nearest index; right and Perform joint sparsity estimation, let , The direction-of-arrival (DOA) estimation problem for array-sampled signals can be further expressed as: ,in, express The matrix, Let T denote a matrix, and T denote the transpose operation. To ensure joint sparsity, a penalty function term is applied. This is the joint sparsity estimation term; based on the joint sparsity estimation term, iterative optimization is performed to complete the joint sparse direction of arrival estimation and obtain the corrected sound source signal direction of arrival. Through iterative correction, the method for solving the joint sparse estimation of the direction of arrival of the corrected sound source signal is extended to planar arrays and multi-frequency cross arrays. Based on the estimated corrected direction of arrival of the sound source, the spatial filtering method is used to complete the array amplitude and phase error calibration.

2. The array amplitude and phase error calibration method based on joint sparse estimation according to claim 1, characterized in that, The setting of the correction sound source to be located in an unknown far-field direction relative to the sensor linear array includes: for a uniform receiving linear array with M elements, the array center is located at the origin, and the element spacing is... A correction source is set relative to the unknown far-field direction of the uniform receiving linear array to generate a response signal.

3. The array amplitude and phase error calibration method based on joint sparse estimation according to claim 1, characterized in that, The aforementioned iterative solution optimization based on joint sparsity estimation term includes: on the basis of the fast iterative threshold shrinkage algorithm, adopting Moreau lower envelope to improve gradient calculation, optimizing the fixed step size to the dynamic gradient descent step size obtained by line search to accelerate iterative convergence, and optimizing the joint sparsity of the direction of arrival estimation problem of array sampled signals.

4. The array amplitude and phase error calibration method based on joint sparse estimation according to claim 1, characterized in that, The aforementioned method for solving the joint sparse estimation of the direction of arrival of the corrected sound source signal is extended to planar arrays, including: the planar array contains There are 1 receiving array element with P horizontal beams and Q vertical beams. Based on the direction of arrival estimation of the corrected sound source signal in the linear array, the two-dimensional array response is compressed into a vector, and the four-dimensional sensing matrix is ​​compressed into a two-dimensional matrix.

5. The array amplitude and phase error calibration method based on joint sparse estimation according to claim 1, characterized in that, The method for solving the joint sparse estimation of the direction of arrival of the corrected sound source signal is extended to multi-frequency cross arrays, including: A three-dimensional imaging effect of an approximate planar array is obtained by plotting beammaps in both the transmission and reception directions, where the number of beams in the transmission direction is P and the number of beams in the reception direction is Q. The cross array focuses and transmits a fan-shaped beam at each angle along the transmission direction. The receiving array generates a horizontal beam at the corresponding vertical angle by receiving the echo signal one by one. After traversing the array, P×Q planar beams within the detection range are obtained. Based on the planar beamforming results of the cross array, the response signal of the multi-frequency cross array is obtained when multi-frequency transmission occurs.

6. The array amplitude and phase error calibration method based on joint sparse estimation according to claim 1, characterized in that, The method of using spatial filtering to calibrate array amplitude and phase errors includes: The ideal rotation vector is calculated by estimating the direction of arrival of the corrected sound source signal and its intensity. Estimate the initial amplitude and phase of the response signal in each sampling snapshot of the direction of arrival of the corrected sound source signal to obtain the actual rotation vector; Based on the ideal rotation vector and the actual rotation vector, a spatial filtering method is used to estimate the amplitude and phase error.

7. The array amplitude and phase error calibration method based on joint sparse estimation according to claim 6, characterized in that, Amplitude and phase error calibration is completed by quantifying beam pattern matching accuracy and amplitude and phase error estimation accuracy using root mean square error quantization.

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