Array amplitude-phase error calibration method based on joint sparse estimation

Abstract

The invention discloses an array amplitude-phase error calibration method based on joint sparse estimation. The method comprises the following steps: setting a correction sound source to be positioned in an unknown far-field direction relative to a sensor linear array; the method comprises the following steps: dividing an observation area of a sensor linear array to obtain a plurality of grid points, correcting an array sampling signal based on the grid points and offset, constructing an array response signal model, and performing joint sparse direction-of-arrival estimation of the grid points and the offset to obtain a corrected sound source signal direction-of-arrival; the joint sparse estimation method for solving and correcting the direction of arrival of the sound source signal is popularized to a planar array and a multi-frequency cross array through iterative correction; and on the basis of the estimated corrected sound source direction of arrival, array amplitude-phase error calibration is completed by adopting a spatial filtering method. According to the method, the problem of beam pattern attenuation caused by existing array amplitude phase error calibration is solved, the error correction precision and correction efficiency are improved, and the application range of the error calibration method in multiple array types is widened.

Description

Technical Field

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

[0002] Real-time three-dimensional sonar imaging technology has been widely used in underwater detection and other fields in recent years. The phased array three-dimensional imaging sonar system transmits acoustic pulse signals, receives sonar echo signals through a large planar array, and then uses beamforming technology and real-time image processing technology to obtain high-resolution underwater three-dimensional images, namely beam patterns. The receiving sensor elements of the phased array are usually designed and regarded as having the same amplitude response and signal processing delay, and the array response signal model is also established based on this.

[0003] In real-world scenarios, since the array is affected by factors such as sensor manufacturing accuracy errors, position placement deviations, inconsistent signal conditioning circuits, and temperature stress, there are amplitude and phase errors, which cause signal model mismatch, which in turn leads to beam pattern performance attenuation, sidelobe intensity enhancement, main lobe focus offset and other problems. Especially for sparse arrays or linear arrays, due to the small number of array elements or the large weights of some array elements in the beamforming calculation, the beam pattern attenuation problem caused by the amplitude and phase errors of the array is more serious. If the amplitude and phase error factors of the array can be effectively estimated, and based on the estimation results, the signals received by each transducer are compensated in the subsequent beamforming process, the phased array three-dimensional imaging sonar system will be able to provide ideal imaging quality even in the presence of array amplitude and phase errors.

[0004] As common array configurations, linear arrays and uniform planar arrays have been widely studied for their array error calibration methods. Array error calibration methods can be divided into two categories: active calibration and auto-calibration. Active calibration methods require the use of several active calibration sources with precisely known azimuths, while in auto-calibration methods, since the azimuths of the calibration sources are unknown, it is usually necessary to estimate both the azimuths of the calibration sources and the error parameters of the array. 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 method for direction of arrival estimation and sensor array error calibration based on unknown signal separation. The amplitude error is solved by using the relationship between the diagonal values ​​of the covariance matrix of the array received signal. Then, the output signal after amplitude error correction is point-multiplied with its conjugate to obtain a covariance matrix independent of the phase error, and the covariance matrix is ​​used for direction of arrival estimation (DOA). Therefore, good performance can be obtained regardless of the size of the phase error. However, since the phase differences between adjacent array elements are required to be different, it is not suitable for uniform linear arrays, and at least two signals with far spatial angle separation are required. The amount of calculation required is also an issue that needs to be considered in practical applications.

[0005] Existing array error correction methods need to estimate and correct amplitude and phase errors based on characteristic structures, Toeplitz characteristics, etc. These array error calibration methods mostly rely on array geometric characteristics or prior information related to the array structure. They have good calibration performance in the corresponding array type, but lack versatility for multiple array types.

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

[0007] The purpose of the present invention is to provide an array amplitude and phase error calibration method based on joint sparse estimation, so as to solve the beam pattern attenuation problem caused by the existing array amplitude and phase error calibration, improve the error correction accuracy and correction efficiency, and broaden the application of the error calibration method in multiple array types.

[0008] To achieve the above-mentioned object of the invention, an array amplitude and phase error calibration method based on joint sparse estimation is provided in an embodiment, comprising the following steps:

[0009] Set the calibration sound source to be located in the unknown far-field direction relative to the linear array of sensors;

[0010] The observation area of ​​the sensor linear array is divided into several grid points, the array sampling signal is corrected based on the grid points and offsets, the array response signal model is constructed, the joint sparse arrival direction estimation of the grid points and offsets is performed, and the arrival direction of the corrected sound source signal is obtained;

[0011] Through iterative correction, the joint sparse estimation method for solving 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 sound source direction of arrival, the array amplitude and phase error calibration is completed using the spatial domain filtering method.

[0013] In one embodiment, the setting of the correction sound source is located in the unknown far field direction relative to the sensor linear array, including: for a uniform receiving linear array with M array elements, the array center is located at the origin of the coordinate system, and the array element spacing is d x , a correction sound 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 sensors is divided into a plurality of grid points, including: for unknown distribution of target signals, 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 an incident signal angle, and the array response signal is obtained as:

[0015]

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

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

[0018] The grid points are extended to the linear array, and an offset is introduced to correct the signal, so that it has the ability to estimate the direction of arrival of the off-grid incident signal. The corrected response signal is expressed as:

[0019] X=(A+EΔ)s+ε

[0020] Among them, A is the observation area matrix, is the off-grid angle offset, which indicates the actual angle α′ of the incident signal closest to the grid point p p With the angle α at the grid point p , T represents the transpose operation, E is the off-grid correction term of the observation area matrix, and since the number of signal samples in practical applications is far less than the number of grid points, 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 DOA estimation of the grid points and the offset includes: to avoid index confusion caused by the offset crossing the boundary, the off-grid angle offset should not exceed half of the grid 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, is the off-grid angle offset, which indicates the actual angle α′ of the incident signal closest to the grid point p p With the angle α at the grid point p The difference between , P represents the number of grid points;

[0024] make Based on the L2 norm of LASSO theory, the DOA estimation problem of array sampling signal is expressed as:

[0025]

[0026] Among them, the observation area matrix A∈C M×P , C M×P represents an M × P matrix, E is the off-grid correction term of the observation area matrix, x represents the actual response signal of the linear array, λ||s|| 2，1 To ensure the sparsity penalty function, s is the incident signal vector at the nearest index, λ is the regularization parameter, represents the square of the two-norm, for any element d in d i , only when the incident signal at the corresponding nearest index is non-zero, d i The non-zero value of is meaningful, and θ is expressed as the angle of the incident signal at the nearest index;

[0027] Make a joint sparse estimate of s and d, let Φ = [A, E] ∈ C M×2P , u=[s T , d] T ∈C 2P , the DOA estimation problem of array sampling signal is further expressed as:

[0028]

[0029] Among them, C M×2P represents an M×2P matrix, C 2P represents a 2P matrix, T represents a transpose operation, λ||u|| 2，1 In order to ensure the penalty function term of joint sparsity, u is the joint sparsity estimation term; based on the joint sparsity estimation term, iterative solution optimization is performed 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: based on the fast iterative threshold shrinkage algorithm, using the Moreau lower envelope to improve the 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 wave direction estimation problem of the array sampling 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: there are M×N receiving array elements in the planar array, the number of horizontal beams is P, the number of vertical beams is Q, 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 sensor matrix is ​​compressed into a two-dimensional matrix.

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

[0033] The three-dimensional imaging effect of a planar array is obtained by making beam patterns in the transmitting and receiving directions respectively, where the number of beams in the transmitting direction is P and the number of beams in the receiving direction is Q;

[0034] The cross array focuses the transmitted fan-shaped beam at each angle in the transmitting direction, and the receiving array generates a horizontal beam of the corresponding vertical angle by successively receiving the echo signal. After traversal, P×Q plane beam results within the detection range are obtained;

[0035] Based on the plane beam result of the cross array, when multi-frequency transmission is performed, the response signal of the multi-frequency cross array is obtained.

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

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

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

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

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

[0041] Compared with the prior art, the present invention has the following beneficial effects:

[0042] (1) The problem of estimating the direction of arrival of the correction sound source is converted into an optimization problem of reconstructing the correction sound source signal through array sampling signal reconstruction. The array response signal model is constructed by combining discrete grid points with off-grid offsets to estimate the direction of arrival of the response signal. The direction of arrival estimation is optimized and solved based on the compressed sensing method in DOA and the fast iterative threshold shrinkage algorithm to obtain the precise azimuth of the response signal, improve the performance of the response signal direction estimation, and take into account both the calculation accuracy and the calculation complexity.

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

[0044] (3) Spatial domain filtering is used to optimize the amplitude and phase errors, thereby improving the accuracy of amplitude and phase error calibration. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art are briefly introduced below.

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

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

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

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

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

[0051] Figure 6 The root mean square error (RMSE) and amplitude error standard deviation σ of the array amplitude and phase error provided in the embodiment of the present invention are ξ The relationship diagram, where Figure 6 (a) is the root mean square error of the amplitude and the standard deviation of the amplitude error σ ξ The relationship diagram, Figure 6 (b) is the RMS error of phase and the standard deviation of amplitude error σ ξ Relationship diagram;

[0052] Figure 7 The root mean square error (RMSE) of the array amplitude and phase error and the phase error standard deviation σ provided in the embodiment of the present invention are τ A relationship diagram, where Figure 7 (a) is the root mean square error of the amplitude and the standard deviation of the phase error σ τ The relationship diagram, Figure 7 (b) is the phase root mean square error and the phase error standard deviation σ τ Relationship diagram;

[0053] Figure 8 A relationship diagram of the root mean square error (RMSE) of the array amplitude and phase error and the signal-to-noise ratio (SNR) provided in an embodiment of the present invention, wherein Figure 8 (a) is the relationship between the root mean square error of the amplitude and the signal-to-noise ratio (SNR). Figure 8 (b) in the figure is the relationship between the root mean square error of the phase and the signal-to-noise ratio (SNR). DETAILED DESCRIPTION

[0054] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the following is a

[0055] The present invention is further described in detail in the following examples. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not limit the scope of protection of the present invention.

[0056] In order to ensure accurate estimation of the response signal azimuth, the embodiment provides an array amplitude and phase error calibration method based on joint sparse estimation, which sets the correction sound source in an unknown far-field direction relative to the sensor array, and converts the direction of arrival estimation problem of the correction sound source into an optimization problem of solving the correction sound source signal by reconstructing the array sampling signal, constructs an array response signal model, and proposes a joint sparse direction of arrival estimation method (DOA) combining discrete grid points in the response signal direction with continuous offset, taking into account both calculation accuracy and complexity; then, the method is extended to uniform and sparse planar arrays and multi-frequency cross arrays through iterative correction solutions, thereby improving the scenario applicability of the method; and spatial domain filtering is used to correct the influence of the array phase error on the DOA, thereby improving the error correction accuracy.

[0057] like Figure 1 As shown, an array amplitude and phase error calibration method based on joint sparse estimation provided in an embodiment 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 the embodiment, the correction sound source is located in the unknown far-field direction relative to the linear array of sensors, and the problem of estimating the direction of arrival of the correction sound source is converted into an optimization problem of solving the correction sound source signal by reconstructing the array sampling signal. Figure 2 As shown, a uniform receiving linear array with M array elements is located at the origin of the coordinate system. The array element spacing is d. x , and the array element with serial number m is positioned For a signal incident at an angle α in the array far field (from target reflection or correction source emission), the ideal response signal of array element m is x o (m) is:

[0060]

[0061] Among them, ω represents the signal strength value, j is a unit imaginary number, is the time domain initial phase offset of the corrected sound source signal, f represents the signal frequency, c is the propagation speed of the signal in the current medium, ε m is the independent and identically distributed noise of array element m.

[0062] Assume that the array has phase and amplitude errors (phase errors), and the amplitude error of array element m is denoted by ξ m , the phase error is τ m , then the actual response signal of array element m is for:

[0063]

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

[0065] S2. Divide the observation area of ​​the linear array of sensors into several grid points, correct the array sampling signal based on the grid points and offsets, build an array response signal model, perform joint sparse arrival direction estimation of the grid points and offsets, and obtain the corrected sound source signal arrival direction.

[0066] In the 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 grid division, s p represents the signal vector, j is a unit imaginary number, f represents the signal frequency, α p represents the incident signal angle corresponding to the grid point p, c is the propagation speed of the signal in the current medium, ε m is the independent and identically distributed noise of array element m.

[0069] By extending the grid points to a linear array, the actual response signal of the linear array can be expressed in the matrix form x = As + ε:

[0070]

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

[0072] In the embodiment, a continuous correction term is introduced to optimize the off-grid model so that it has the ability to estimate the direction of arrival of the off-grid incident signal. The corrected response signal is expressed as:

[0073] X=(A+EΔ)s+ε (5)

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

[0075]

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

[0077]

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

[0079] make Based on the L2 norm of LASSO theory, the DOA estimation problem of array sampling signal is expressed as:

[0080]

[0081] Among them, the observation area matrix A∈C M×P , C M×P represents an M × P matrix, E is the off-grid correction term of the observation area matrix, x represents the actual response signal of the linear array, λ||s|| 2，1 To ensure the sparsity penalty function, s is the incident signal vector at the nearest index, λ is the regularization parameter, represents the square of the two-norm. Furthermore, the penalty function term λ||s|| 2，1 Defined as:

[0082]

[0083] in, represents the L2 norm of the signal vector at the grid point p. For any element d in d i , only when the incident signal at the corresponding nearest index is non-zero, d i Non-zero values ​​of are meaningful, and θ is expressed as the angle of the incident signal at the nearest index.

[0084] Based on the correlation between s and d, a joint sparse estimation is performed on s and d instead of solving them iteratively. Let Φ = [A, E] ∈ C M ×2P , u=[s T , d]T ∈C 2P , the DOA estimation problem of array sampling signal is further expressed as:

[0085]

[0086] Among them, C M×2P represents an M×2P matrix, C 2P represents a 2P matrix, T represents a transpose operation, λ||u|| 2，1 To ensure the penalty function term of joint sparsity, u is the joint sparsity estimation term; further, the sparse penalty function term of the joint estimation term u is defined as:

[0087]

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

[0089] Based on the joint sparsity of the joint estimation term u, formula (10) can be regarded as a sparse linear inverse problem and solved by a targeted optimized linear inverse problem method. Based on the traditional fast iterative threshold hand shrinkage algorithm (FISTA), the gradient calculation is improved according to the Moreau lower envelope to address the joint sparsity characteristics, and 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 joint sparse estimation method for solving the corrected sound source signal arrival direction is extended to planar arrays and multi-frequency cross arrays.

[0091] like Figure 3 As shown in the figure, unlike linear arrays, planar arrays have beam resolution in both horizontal and vertical dimensions. For a uniform receiving planar array, it contains M×N receiving array elements, with azimuth and elevation angles α and β respectively, P beams in the horizontal direction, and Q beams in the vertical direction. For array element (m, n), the center of the array is located at the origin of the coordinate system, and the array element positions are 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 (α p , β q ) direction, the planar array element response signal x(m, n) can be expressed as follows:

[0093]

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

[0095] like Figure 4 As shown, in the embodiment, the wave direction estimation of the corrected sound source signal is extended to a multi-frequency cross array, and a three-dimensional imaging effect similar to a planar array is obtained by performing beamforming in the transmitting and receiving directions. x ,d y The equally spaced array has the following transmitting elements and receiving positions: d y (n) = (n-1)d y .

[0096] In the cross array, the number of beams in the horizontal direction is P, and the number of beams in the vertical direction is Q. The conventional cross array focuses the transmitted fan-shaped beam at each angle in the transmitting direction (here defined as the vertical direction). The receiving array generates a horizontal beam of the corresponding vertical angle by successively receiving the corresponding vertical direction echo signal. After traversing and scanning the complete vertical direction, P×Q plane beam results within the detection range are obtained.

[0097] When transmitting at multiple frequencies, the signal response s of the qth beam in the vertical angle direction is T (q) is expressed as:

[0098]

[0099] Among them, w t (n) is the nth transmitting array element weight, f q is the corresponding transmission frequency, β q is the corresponding pitch angle.

[0100] The mth element of the receiving array is at f q The signal component x(m, f q ) can be derived as:

[0101]

[0102] Where p in formula (14) represents the horizontal beam, q represents the vertical beam, ρ is the calibration target reflection coefficient, and δ pq It is the index coefficient of whether there is a target in the corresponding two-dimensional angle index direction, α p It represents the incident signal angle corresponding to the horizontal beam, and h(m, p, q) represents a signal component in the plane beam.

[0103] S4. Based on the estimated corrected sound source arrival direction, the array amplitude and phase error calibration is completed using the spatial domain filtering method.

[0104] In the embodiment, the process of estimating the amplitude and phase errors according to the spatial matched filter is:

[0105] First, the direction and strength of the correction signal are obtained according to the direction of arrival estimation method, and the ideal rotation vector γ′ is calculated mn :

[0106]

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

[0108] After determining the final estimated direction of arrival of the corrected sound source, the initial amplitude phase of the response signal of the direction of arrival of the corrected sound source in each sampling snapshot is estimated to be expressed as:

[0109]

[0110] Among them, ω l Indicates the response signal strength value, It is the time domain initial phase offset of the corrected sound source signal, H refers to the conjugate transpose operation, x1 represents the response signal response, and MN represents M×N receiving array elements.

[0111] Furthermore, relative to the ideal rotation vector γ′ mn For the actual rotation vector γm n If there is an influence of array amplitude and phase errors, the amplitude and phase of the response signal can be removed from the array response, and the average of the multi-shot calculation results is taken:

[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 by element, which is Specifically, it can be expressed as follows:

[0114]

[0115] Among them, ξ mn represents the amplitude error of the array element (m, n), τ mn represents the phase error of the array element (m, n), ∠ represents the angle calculation; the array amplitude error vector has a mean of 1 and a variance of Gaussian distribution The phase error vector has zero mean and variance is Gaussian distribution

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

[0117]

[0118] Among them, RMSE BP Represents the root mean square error of the beam pattern, RMSE ξ Represents the root mean square error of amplitude, RMSE τ represents the phase root mean square error, BP represents the actual beam pattern, BP′ represents the optimized beam pattern, represents the actual amplitude, ξ′ represents the optimized amplitude, represents the actual phase, τ′ represents the optimized phase, LP represents the number of beam pattern samples, and LM represents the number of signal samples.

[0119] In order to better demonstrate the technical effect, the present invention designs a series of experiments for illustration.

[0120] The calibration performance experiment of the planar receiving array uses an array with 50×50 array elements arranged in equal spacing, and the array element spacing d=2.5mm. The calibration sound source signal frequency f is located in the array far field (10°, -20°). Additive Gaussian noise is used, the noise ratio (SNR) is 20dB, and the number of signal samples L=1000. In the experiment, the beam pattern is normalized with the main lobe intensity of the ideal array beam.

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

[0122] Table 1 Actual and estimated values ​​of some amplitude and phase errors

[0123]

[0124]

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

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

[0127] The experiment compares the three-step iteration method (TSI) in uniform planar array calibration, where JSC is the array amplitude and phase error calibration method based on joint sparse estimation (Joint SparseCalibration) provided by the present invention. The JSC method and the TSI method are different in σ τ =0.25rad, SNR = 20dB, error estimation accuracy and amplitude error standard deviation σ ξ The relationship is as Figure 6 As shown in Figure 2, since the array amplitude error has little effect on the signal angle estimation in the response signal DOA estimation stage, the RMSE of the two calibration methods is ξ and RMSE τ remains essentially stable when the array amplitude changes. ξ Increase, JSC method RMSE ξ The curve has a slight upward trend, but is generally lower than the result of the TSI method. ξ Average RMSE in the scenario ξ This is 42% lower than the TSI method.

[0128] Figure 7 Shows that in σ ξ =0.2, SNR = 20dB, array error estimation accuracy and phase error standard deviation σ τ The relationship between ξ ~RMSE ξ The experimental results are similar, σ τ When the RMSE increases ξ The change is not obvious. τ When the amplitude estimation error of the proposed JSC method is less than 0.55 rad, it is better than that of the TSI method. τWhen it is greater than 0.55rad, it is slightly higher than the result of TSI method, but its average RMSE g is 3.056×10 -3 , which is about 6% lower than the average estimation bias of the TSI method.

[0129] The standard deviation of the amplitude error σ ξ =0.2, phase error standard deviation σ τ =0.25rad, the relationship between the array response signal SNR and the amplitude and phase error estimation accuracy is shown in Figure 8 As can be seen from the figure, unlike the previous amplitude and phase error experimental results, the RMSE of the amplitude error estimation is strongly correlated with the SNR, especially in the case of low SNR. ξ The increase is one order of magnitude. This is because when the SNR is low, the noise signal strength is close to the response signal strength, which makes it difficult to accurately estimate the DOA stage, affecting the calibration accuracy. When the SNR is ≥ ≥ 20dB, the proposed JSC method can achieve higher estimation accuracy and is better than the TSI method. As for the phase error estimation accuracy, both methods are relatively stable when the SNR is ≥ ≥ 20dB. When the SNR is further reduced, the estimation accuracy will decrease slightly. Except for the extreme case of 0dB, the performance of the JSC method is better than that of the TSI.

[0130] The array amplitude and phase error calibration method based on joint sparse estimation provided by the present invention can effectively solve the beam pattern attenuation problem caused by the existing array amplitude and phase errors. Compared with the existing error calibration method, the present invention can improve the error correction accuracy and correction efficiency, no longer rely on prior information related to the array geometric characteristics and array structure, and improves the scenario applicability of the error calibration method.

[0131] The specific implementation methods described above provide a detailed description of the technical solutions and beneficial effects of the present invention. It should be understood that the above is only the most preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, supplements and equivalent substitutions made within the scope of the principles of the present invention should be included in 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 comprises the following steps: Set the calibration sound source to be located in the unknown far-field direction relative to the linear array of sensors; The observation area of ​​the sensor linear array is divided into several grid points, the array sampling signal is corrected based on the grid points and offsets, the array response signal model is constructed, the joint sparse arrival direction estimation of the grid points and offsets is performed, and the arrival direction of the corrected sound source signal is obtained; Through iterative correction, the joint sparse estimation method for solving 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 sound source direction of arrival, the array amplitude and phase error calibration is completed using the spatial domain filtering method.

2. The array amplitude and phase error calibration method based on joint sparse estimation according to claim 1, characterized in that: The setting correction sound source is located in the unknown far field direction relative to the sensor linear array, including: for a uniform receiving linear array with M array elements, the array center is located at the origin of the coordinates, and the array element spacing is d x , a correction sound 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 observation area of ​​the linear array of sensors is divided into a number of grid points, including: for unknown distribution of target signals, 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 an incident signal angle, and the array response signal is obtained as: Where x(m) represents the array response signal, s p represents the signal vector, j is a unit imaginary number, f represents the signal frequency, α p represents the incident signal angle corresponding to the grid point p, c is the propagation speed of the signal in the current medium, ε m is the independent and identically distributed noise of array element m.

4. The array amplitude and phase error calibration method based on joint sparse estimation according to claim 1, characterized in that: The correction of array sampling signals based on grid points and offsets includes: The grid points are extended to the linear array, and an offset is introduced to correct the signal, so that it has the ability to estimate the direction of arrival of the off-grid incident signal. The corrected response signal is expressed as: X=(A+EΔ)s+ε Among them, A is the observation area matrix, is the off-grid angle offset, which indicates the actual angle α′ of the incident signal closest to the grid point p p With the angle α at the grid point p , T represents the transpose operation, E is the off-grid correction term of the observation area matrix, and since the number of signal samples in practical applications is far less than the number of grid points, the signal vector s of the linear array is regarded as a sparse vector, and ε is the noise of the linear array.

5. The array amplitude and phase error calibration method based on joint sparse estimation according to claim 1, characterized in that: The joint sparse DOA estimation of the grid points and offsets includes: to avoid index confusion caused by offset out of bounds, the off-grid angle offset should not exceed half of the grid angle spacing. If the grid points are uniform and the corresponding spacing is 2D α , then the constraint can be expressed as: in, is the off-grid angle offset, which indicates the actual angle α′ of the incident signal closest to the grid point p p With the angle α at the grid point p The difference between , P represents the number of grid points; make Based on the L2 norm of LASSO theory, the DOA estimation problem of array sampling signal is expressed as: Among them, the observation area matrix A∈C M×P , C M×P represents an M × P matrix, E is the off-grid correction term of the observation area matrix, x represents the actual response signal of the linear array, λ||s|| 2，1 To ensure the sparsity penalty function, s is the incident signal vector at the nearest index, λ is the regularization parameter, represents the square of the two-norm, for any element d in d i , only when the incident signal at the corresponding nearest index is non-zero, d i The non-zero value of is meaningful, and θ is expressed as the angle of the incident signal at the nearest index; Make a joint sparse estimate of s and d, let Φ = [A, E] ∈ C M×2P , u=[s T , d] T ∈C 2P , the DOA estimation problem of array sampling signal is further expressed as: Among them, C M×2P represents an M×2P matrix, C 2P represents a 2P matrix, T represents a transpose operation, λ||u|| 2,1 In order to ensure the penalty function term of joint sparsity, u is the joint sparsity estimation term; based on the joint sparsity estimation term, iterative solution optimization is performed to complete the joint sparse direction of arrival estimation.

6. The array amplitude and phase error calibration method based on joint sparse estimation according to claim 5, characterized in that: The iterative solution optimization based on the joint sparsity estimation term includes: based on the fast iterative threshold shrinkage algorithm, using the Moreau lower envelope to improve the gradient calculation, optimizing the fixed step size to the dynamic gradient descent step size obtained by line search to accelerate the iterative convergence, and optimizing the joint sparsity of the wave direction estimation problem of the array sampling signal.

7. 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 a planar array, including: there are M×N receiving array elements in the planar array, the number of horizontal beams is P, the number of vertical beams is Q, 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 sensor matrix is ​​compressed into a two-dimensional matrix.

8. The array amplitude and phase error calibration method based on joint sparse estimation according to claim 1, characterized in that: The joint sparse estimation method for solving the direction of arrival of the corrected sound source signal is extended to a multi-frequency cross array, comprising: The three-dimensional imaging effect of a planar array is obtained by making beam patterns in the transmitting and receiving directions respectively, where the number of beams in the transmitting direction is P and the number of beams in the receiving direction is Q; The cross array focuses the transmitted fan-shaped beam at each angle in the transmitting direction, and the receiving array generates a horizontal beam of the corresponding vertical angle by successively receiving the echo signal. After traversal, P×Q plane beam results within the detection range are obtained; Based on the plane beam result of the cross array, when multi-frequency transmission is performed, the response signal of the multi-frequency cross array is obtained.

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

10. The array amplitude and phase error calibration method based on joint sparse estimation according to claim 9, characterized in that: The amplitude and phase error calibration is completed by using the root mean square error to quantify the beam pattern matching accuracy and the amplitude and phase error estimation accuracy.

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