A near-field model amplitude and phase error calibration method for the transducer array of a phased array three-dimensional imaging sonar system

Abstract

The present invention discloses a near-field model amplitude and phase error calibration method for a phased array three-dimensional imaging sonar system transducer array, pre-processing the array response signal to obtain a new virtual array response; performing discrete phase transformation on it to obtain a reduced-order array; using fast Fourier transform to process the reduced-order array, roughly estimating the normalized modulation frequency; using three-step iterative calculation to improve the estimation accuracy; using the estimated value of the normalized modulation frequency to demodulate the virtual array response; using fast Fourier transform to process the demodulated array, roughly estimating the normalized angular frequency; using three-step iterative calculation to improve the estimation accuracy; based on the existing estimated value, using a spatial domain matching filter algorithm to estimate the amplitude and phase error factor; using the estimation result to compensate the sampling signal, and finally obtaining a calibrated three-dimensional image through a digital beamforming algorithm. The present invention only uses a calibration source of unknown orientation, without far-field requirements; avoiding a large number of spectrum peak searches, and is suitable for fast calibration of large transducer arrays.

Description

Technical Field

[0001] The invention relates to the technical field of phased array three-dimensional imaging sonar systems, and in particular to a near-field model amplitude and phase error calibration method of a transducer array of a phased array three-dimensional imaging sonar system. Background Art

[0002] The phased array 3D imaging sonar system uses a narrowband acoustic pulse to transmit the entire underwater scene, and uses a 2D uniform rectangular transducer array to receive the backscattered echo signals in the scene to generate array response signals. These array response signals can be processed by beamforming technology and real-time image processing technology to obtain high-resolution underwater 3D images.

[0003] In order to improve the resolution of the image while maintaining a larger detection angle of view, the two-dimensional uniform rectangular transducer array usually has a larger aperture and contains thousands of array elements. Due to the limitations of the processing technology level and the influence of the inevitable device aging factors in actual engineering applications, there is inconsistency in the performance of the hydrophones and signal conditioning circuits of each channel in the receiving array, which leads to amplitude and phase errors in the array, which in turn greatly reduces the imaging quality of the system. In severe cases, it will cause the observation and identification of underwater targets to fail. Therefore, effective calibration of the transducer array of the phased array three-dimensional imaging sonar system is the key to ensuring the detection performance of the system.

[0004] For a phased array 3D imaging sonar system with amplitude and phase errors, if the amplitude and phase error factors of the array can be effectively estimated, and the received signals of each transducer can be compensated based on the estimated results before beamforming processing, ideal imaging quality and detection performance can still be provided.

[0005] From the perspective of error calibration methods, array error calibration technology can be divided into two categories. The first type of calibration method requires the use of several calibration sources with precisely known positions. However, it is difficult to know the precise positions of the calibration sources in advance in the underwater application scenarios of phased array 3D imaging sonar systems, so this type of method is difficult to use. The second type of calibration method does not require the precise position of the calibration source, so it is usually necessary to estimate the position of the calibration source and the error parameters of the array at the same time. This type of method is called a self-calibration method and is more suitable for use in practice.

[0006] Common array error self-calibration methods usually use the far-field model of the array response signal for calibration, which requires the calibration source to be far enough away from the array to ensure the accuracy of the model. Usually, the distance requirement of the far-field model for the calibration source depends on the array aperture. Since the phased array three-dimensional camera sonar system requires a large array aperture to ensure high resolution, the calibration source needs to be placed very far away, which will bring high site costs and reduce the signal-to-noise ratio of the signal received by the array, further reducing the accuracy of the amplitude and phase error calibration.

[0007] If the near-field model of the array response signal is used, the distance requirement of the calibration source can be greatly reduced, and the position estimation of the calibration source is more accurate, which is conducive to improving the accuracy of the array amplitude and phase error calibration. Even if the calibration source meets the far-field conditions, the accuracy of the near-field model is still higher than that of the far-field model, and it still has advantages in the array amplitude and phase error calibration.

[0008] The near-field model of the array response signal is more complex than the far-field model. The array error self-calibration method using the far-field model is usually difficult to directly apply to the near-field model. Most of the existing near-field model amplitude and phase error calibration methods use spectrum peak search to determine the location of the calibration source, which is widely used in linear arrays. For a phased array three-dimensional imaging sonar system containing thousands of array elements, the computational burden of such methods is very large, which is not conducive to field application. Summary of the invention

[0009] In view of the above, the purpose of the present invention is to provide a near-field model amplitude and phase error calibration method for a phased array three-dimensional imaging sonar system transducer array. The method only requires the placement of a calibration source of unknown orientation, and does not require any prior information on array characteristics to obtain a higher amplitude and phase error calibration accuracy. The calibration source does not need to meet the far-field condition, which reduces the demand for a large site. The orientation of the calibration source is quickly estimated by using two different three-step iterative calculations, which avoids complicated iterations and a large number of spectral peak searches. The method has a small amount of calculation and is suitable for on-site calibration of large transducer arrays in phased array three-dimensional imaging sonar systems.

[0010] The technical solution provided by the embodiment is:

[0011] A method for calibrating the amplitude and phase errors of a near-field model of a transducer array of a controlled array three-dimensional imaging sonar system comprises the following steps:

[0012] (1) Preprocess the array response signal of the two-dimensional transducer array to obtain a virtual two-dimensional array response R x and R y ;

[0013] (2) Respectively respond to the two-dimensional array R x and R y Perform discrete phase transformation to obtain a two-dimensional sinusoidal signal Y x and Y y ;

[0014] (3) For the two-dimensional sinusoidal signal Y x and Y y Perform a 2D Fast Fourier Transform to get an initial estimate of the normalized modulation rate and

[0015] (4) Based on initial estimates and The frequency estimate is obtained by three-step iterative calculation and

[0016] (5) Using frequency estimates and Respectively respond to the two-dimensional array R x and R y Demodulate and obtain a two-dimensional array Z x and Z y ;

[0017] (6) For the two-dimensional array Z x and Z y Perform a 2D Fast Fourier Transform to get an initial estimate of the normalized modulation rate and

[0018] (7) Based on initial estimates and The frequency estimate is obtained by three-step iterative calculation and

[0019] (8) Based on frequency estimates The amplitude and phase error factors of each transducer channel in the transducer array are estimated using the spatial domain matched filtering algorithm;

[0020] (9) The amplitude and phase error factors are used to compensate the complex sampling signals of each transducer channel. Finally, a digital beamforming algorithm is used to obtain a three-dimensional imaging sonar beam that has been calibrated for amplitude and phase errors.

[0021] Compared with the prior art, the present invention has the following beneficial technical effects:

[0022] The near-field model amplitude and phase error calibration method provided by the present invention uses only one calibration source of unknown orientation, and does not require prior information about the amplitude and phase characteristics of the transducer array. The calibration source does not need to meet the far-field condition, which reduces the demand for large sites. The orientation of the calibration source is quickly estimated by using two different three-step iterative calculations, which avoids complicated iterations and a large number of spectrum peak searches. The present invention can simultaneously obtain estimates of the amplitude and phase errors of up to thousands of transducer channels in a phased array three-dimensional imaging sonar system, and the estimation accuracy is higher than the amplitude and phase error calibration method using a far-field model, which can effectively improve the beam pattern performance of the phased array three-dimensional imaging sonar system. Therefore, the present invention is suitable for on-site calibration of the transducer array of a phased array three-dimensional imaging sonar system, and improves the imaging quality and detection performance of the three-dimensional imaging sonar system when there is an array amplitude and phase error. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] 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 will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0024] Figure 1 A schematic diagram of a near-field signal model of a phased array three-dimensional imaging sonar system transducer array provided by an embodiment;

[0025] Figure 2 A schematic flow chart of a method for calibrating near-field model amplitude and phase errors of a phased array three-dimensional imaging sonar system transducer array provided by an embodiment;

[0026] Figure 3 A beam pattern of a phased array three-dimensional imaging sonar system in the presence of array amplitude and phase errors provided by an embodiment;

[0027] Figure 4 An embodiment provides a beam pattern of a phased array three-dimensional imaging sonar system after compensating the received signals of each transducer channel using the amplitude and phase error calibration method of the present invention in the presence of array amplitude and phase errors.

[0028] Figure 5 An embodiment provides Figure 2 and Figure 3 In θ a =Comparison of beam patterns under -10° section. DETAILED DESCRIPTION

[0029] To make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific implementation methods described herein are only used to explain the present invention and do not limit the scope of protection of the present invention.

[0030] Figure 2 The present invention is a flow chart of a method for calibrating the near-field model amplitude and phase error of a phased array three-dimensional imaging sonar system transducer array provided by an embodiment. Figure 2 As shown, the near-field model amplitude and phase error calibration method provided in the embodiment includes the following steps:

[0031] Step 1: preprocess the sampled snapshot signals corresponding to the k array responses of the two-dimensional transducer array to obtain a virtual two-dimensional array response R x and R y .

[0032] In the embodiment, the transducer array of the phased array three-dimensional imaging sonar system is a large M×N two-dimensional uniform rectangular array, the horizontal spacing and vertical spacing of each transducer in the rectangular array are equal, and M and N are generally natural numbers greater than 40. For example, M=N=50, the array element spacing is λ / 2, and λ is the wavelength of the sound wave.

[0033] In the embodiment, the array response signal is regarded as a near-field signal model, and the amplitude and phase error calibration method uses only one calibration source with unknown position, and the calibration source emits a continuous narrowband sinusoidal signal, and the calibration source does not need to meet the far-field condition. In the near-field model, the position of the calibration source is given by (θ a ,θ e ,r) three parameters are determined, among which, θ a is the range angle corresponding to the calibration source orientation, θ e is the elevation angle corresponding to the calibration source azimuth, and r is the distance between the calibration source and the transducer array. Figure 1 As shown, the first channel is taken as the coordinate origin, and the azimuth angle θ of the calibration source is a =-10° upward viewing angleθ e =-20°, distance r = 10m; amplitude factor ρ of the transducer array i and the phase factor ψ i They satisfy the following normal distribution respectively: A set of amplitude and phase factors are randomly generated, with the first channel as the reference channel, i.e., ρ1=1, ψ1=0; the signal-to-noise ratio of the array response signal is 20 dB, and the number of sampling snapshots K is 200.

[0034] In the embodiment, for the kth snapshot, the array response signal is a two-dimensional frequency modulation signal, which is expressed as:

[0035]

[0036] Among them, X k (m,n) is the complex sampling signal of the (m,n)th transducer channel in the kth sampling snapshot, where m and n represent the transducer index in the horizontal and vertical directions, respectively;

[0037] Normalized angular frequency is defined as: u1 = 2πd x sinθ a / λ; v1=2πd y sinθ e / λ; the normalized modulation rate is defined as: u2 = -π(d x cosθ a ) 2 / λr;v2=-π(d y cosθ e ) 2 / λr;

[0038] ξ k (m,n) is complex multiplicative noise, including amplitude and phase error factors; ε k (m,n) is the additive noise of the array response; d x is the horizontal spacing between adjacent transducers; d y is the vertical spacing between adjacent transducers; j is the imaginary unit; λ is the carrier wavelength.

[0039] In an embodiment, preprocessing the array response signal includes:

[0040] First, the array response signal X corresponding to the kth sampling snapshot is k Perform the following calculations:

[0041]

[0042] Then, for K R kx and R ky Superimpose them respectively to obtain two virtual two-dimensional array responses R x and R y :

[0043]

[0044] The superscript H represents the conjugate transpose operation.

[0045] Step 2: Response R to the two-dimensional array x and R y Perform discrete phase transformation to obtain a two-dimensional sinusoidal signal Y x and Y y .

[0046] In the embodiment, the two-dimensional array response R x and R y It is a two-dimensional frequency modulated signal, which is reduced to a two-dimensional sinusoidal signal Y using discrete phase transform x and Y y , where the discrete phase transform operation is:

[0047]

[0048]

[0049] Where M and N represent the number of transducers in the horizontal and vertical directions, respectively, and m1 and m2 represent the R x In the horizontal and vertical directions, n1 and n2 represent the index of R y Index in horizontal and vertical direction, symbol Indicates rounding down, and the symbol * indicates the conjugate operation of array elements.

[0050] Step 3: respectively analyze the two-dimensional sinusoidal signal Y x and Y y Perform a 2D Fast Fourier Transform to get an initial estimate of the normalized modulation rate and

[0051] In the embodiment, in order to obtain an initial estimate of the normalized modulation rate, the two-dimensional sinusoidal signal Y x and Y y Perform a two-dimensional fast Fourier transform, search for the maximum value of the two-dimensional fast Fourier transform spectrum, and convert Y x The horizontal angular frequency and Y y The vertical angular frequencies corresponding to the maximum values ​​of the spectrum are divided by and After that, it is used as an initial estimate of the normalized modulation rate in the raw array response and

[0052] In the embodiment, for the two-dimensional sinusoidal signal Y x and Y y When performing a two-dimensional fast Fourier transform, Y x and Y y L x ×L x and L y ×L y A two-dimensional matrix signal, where: In order to use fast algorithms to obtain higher computational efficiency in the two-dimensional fast Fourier transform (2D-FFT transform) calculation process, when L x or L y When Y is not a power of 2, it is necessary to calculate x and Y y The zero padding operation is performed to make its length reach the nearest integer power of 2, which is conducive to the fast implementation of 2D-FFT, such as L x If it is 31, add a 0 to make its length 32, which is 2 to the fifth power. Search for Y x and Y y The index corresponding to the maximum value in the spectrum of is and Y x and Y y They are all complex conjugate symmetric arrays, so the absolute values ​​of the angular frequencies corresponding to the maximum values ​​of the spectrum in the horizontal and vertical directions are equal, but the signs are opposite (Z x and Z y (The same is true). and Satisfy the following form: where p and q are Y x and Y y The frequency index value corresponding to the maximum value of the spectrum in the horizontal and vertical directions.

[0053] The two-dimensional sinusoidal signal Y in the embodiment x and Y y The relationship between the maximum value of the spectrum and the normalized modulation frequency is as follows: After conversion, an initial estimate of the normalized modulation rate can be obtained and

[0054] Step 4: Based on the initial estimate and The frequency estimate is obtained by three-step iterative calculation and

[0055] In the embodiment, a three-step iterative calculation is used to obtain the frequency estimate and include:

[0056] (4-1) Let i = 1, Using equations (6) and (7) to obtain the frequency estimate

[0057]

[0058]

[0059] in,

[0060]

[0061]

[0062]

[0063]

[0064]

[0065]

[0066] (4-2) Let i = 2, Using equations (6) and (7) to obtain the frequency estimate

[0067] (4-3) Let i = 3, M3 = M, N3 = N, and use equations (6) and (7) to obtain the frequency estimate

[0068] Step 5: Use frequency estimates and Respectively respond to the two-dimensional array R x and R y Demodulate and obtain a two-dimensional array Z x and Z y .

[0069] In the embodiment, the frequency estimation value is used and Respectively respond to the two-dimensional array R x and R y The demodulation operation is:

[0070]

[0071]

[0072] Among them, m1 and m2 represent R x In the horizontal and vertical directions, n1 and n2 represent the index of R y Index in horizontal and vertical direction.

[0073] Step 6: For the two-dimensional array Z x and Z y Perform a 2D Fast Fourier Transform to get an initial estimate of the normalized modulation rate and

[0074] In the embodiment, in order to obtain an initial estimate of the normalized angular frequency (u1, v1), the two-dimensional array Z is respectively x and Z y Perform a two-dimensional fast Fourier transform, search for the maximum value of the two-dimensional fast Fourier transform spectrum, and set Z x The horizontal angular frequency corresponding to the maximum value of the spectrum and the Z y The vertical angular frequency corresponding to the maximum value of the spectrum is used as the initial estimate of the normalized angular frequency in the original array response. and

[0075] In the two-dimensional array Z x and Z y When performing a two-dimensional fast Fourier transform, Z x and Z y They are two-dimensional arrays of M×M and N×N, respectively. In order to use fast algorithms to obtain higher computational efficiency in the two-dimensional fast Fourier transform (2D-FFT transform) calculation process, when M or N is not a power of 2, Z needs to be calculated. x and Z yThe zero padding operation is performed to make its length reach the nearest integer power of 2, which is conducive to the fast implementation of 2D-FFT. The initial normalized angular frequency and Satisfy the following form: where p and q are Z x and Z y The index value corresponding to the maximum value of the spectrum.

[0076] Step 7: Based on the initial estimate and The frequency estimate is obtained by three-step iterative calculation and

[0077] In the embodiment, a three-step iterative calculation is used to obtain the frequency estimation value and include:

[0078] (7-1) Let i = 1, Using equations (17) and (18) to obtain the frequency estimate

[0079]

[0080]

[0081] in,

[0082]

[0083]

[0084]

[0085]

[0086] (7-2) Let i = 2, Using equations (17) and (18) to obtain the frequency estimate

[0087] (7-3) Let i = 3, M3 = M, N3 = N, and use equations (17) and (18) to obtain the frequency estimate

[0088] Step 8: Estimate the value based on the frequency The amplitude and phase error factors of each transducer channel in the transducer array are estimated using the spatial domain matched filtering algorithm.

[0089] In an embodiment, the amplitude and phase error factors of each transducer channel in the transducer array are estimated using a spatial domain matched filtering algorithm, including:

[0090] (8-1) Using frequency estimates Calculate the calibration source amplitude in the kth sampling snapshot:

[0091]

[0092] in, is the theoretical steering vector corresponding to the orientation of the previous estimation result, x(k) is the column vector of the array response in the kth snapshot;

[0093] (8-2) Using equation (24), calculate the real steering vector affected by amplitude and phase disturbances

[0094]

[0095] (8-3) The amplitude and phase error vector is calculated using formula (25), that is, the amplitude and phase error factor of each transducer channel is obtained:

[0096]

[0097] in, Represents an element-wise division operation on a vector.

[0098] Step 9, using the amplitude and phase error factors to compensate the complex sampling signals of each transducer channel, and finally using a digital beamforming algorithm to obtain a three-dimensional imaging sonar beam that has been calibrated for amplitude and phase errors.

[0099] In the embodiment, the Chebyshev weighting method is adopted in the beam forming algorithm, and the maximum value of the side lobe of the beam pattern is -30dB.

[0100] After the amplitude and phase error factors of the transducer array are obtained, the amplitude and phase error factors are stored inside the phased array 3D imaging sonar system. When the phased array 3D imaging sonar system works normally, the amplitude and phase error factors of the complex sampling signals x(t) in each transducer channel are first compensated. The compensated complex sampling signals are: Then, the compensated complex sampled signal x c (t) Perform beamforming processing.

[0101] Table 1 shows the true values ​​of some amplitude factors in this embodiment and the estimated values ​​obtained by using the method of the present invention; Table 2 shows the true values ​​of some phase factors in this embodiment and the estimated values ​​obtained by using the method of the present invention.

[0102] Table 1

[0103]

[0104] Table 2

[0105]

[0106] It can be seen from Table 1 and Table 2 that the method of the present invention can estimate the amplitude factor and phase factor of each transducer channel more accurately.

[0107] like Figure 3 As shown in the figure, due to the existence of the array amplitude and phase errors, the sidelobe peak value in the two-dimensional beam pattern of the phased array three-dimensional imaging sonar system without amplitude and phase error calibration reaches about -23dB, and the overall intensity of the sidelobe beam is significantly greater than the design value of -30dB. After the amplitude and phase errors are calibrated by the method of the present invention, the two-dimensional beam pattern obtained by the phased array three-dimensional imaging sonar system is as follows: Figure 4 shown. Figure 5 The comparison of the θ before and after calibration is shown in a = -10° section beam pattern, the sidelobe peak of the two-dimensional beam pattern after the amplitude and phase error calibration of the present invention is controlled below -30dB. Therefore, the calibrated phased array three-dimensional imaging sonar system still effectively guarantees the performance of the two-dimensional beam pattern despite the array error.

[0108] In summary, the near-field model amplitude and phase error calibration method of the phased array three-dimensional imaging sonar system transducer array provided in the embodiment adopts a narrow-band calibration source with unknown azimuth to estimate the amplitude and phase error of the array; using the estimated amplitude and phase error, the phased array three-dimensional imaging sonar system can still provide good detection performance under the condition of the existence of array amplitude and phase error.

[0109] 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 near-field model amplitude and phase error calibration method for a phased array three-dimensional imaging sonar system transducer array, characterized in that: The following steps are involved: (1) Preprocess the array response signal of the two-dimensional transducer array to obtain a virtual two-dimensional array response R x and R y ; (2) Respectively respond to the two-dimensional array R x and R y Perform discrete phase transformation to obtain a two-dimensional sinusoidal signal Y x and Y y ; (3) For the two-dimensional sinusoidal signal Y x and Y y Perform a 2D Fast Fourier Transform to get an initial estimate of the normalized modulation rate and (4) Based on initial estimates and The frequency estimate is obtained by three-step iterative calculation and include: (4-1) Let i = 1, Using equations (1) and (2) to obtain the frequency estimate in, (4-2) Let i = 2, Using equations (1) and (2) to obtain the frequency estimate (4-3) Let i = 3, M3 = M, N3 = N, and use equations (1) and (2) to obtain the frequency estimate Where M and N represent the number of transducers in the horizontal and vertical directions, respectively, and m1 and m2 represent the R x In the horizontal and vertical directions, n1 and n2 represent the index of R y Indexes in horizontal and vertical directions; (5) Using frequency estimates and Respectively respond to the two-dimensional array R x and R y Demodulate and obtain a two-dimensional array Z x and Z y ; (6) For the two-dimensional array Z x and Z y Perform a 2D Fast Fourier Transform to get an initial estimate of the normalized modulation rate and (7) Based on initial estimates and The frequency estimate is obtained by three-step iterative calculation and (8) Based on frequency estimates The amplitude and phase error factors of each transducer channel in the transducer array are estimated using the spatial domain matched filtering algorithm; (9) The amplitude and phase error factors are used to compensate the complex sampling signals of each transducer channel. Finally, a digital beamforming algorithm is used to obtain a three-dimensional imaging sonar beam that has been calibrated for amplitude and phase errors.

2. The near-field model amplitude and phase error calibration method of the phased array three-dimensional imaging sonar system transducer array according to claim 1 is characterized in that: In step (1), the array response signal is regarded as a near-field signal model. A calibration source with unknown orientation is used, and the calibration source emits a continuous narrow-band sinusoidal signal. The calibration source does not need to meet the far-field condition, but the near-field model is also applicable under the far-field condition. For the kth sampling snapshot, the array response signal is expressed as: Among them, X k (m, n) is the complex sampling signal of the (m, n)th transducer channel in the kth sampling snapshot, where m and n represent the transducer indexes in the horizontal and vertical directions, respectively; Normalized angular frequency is defined as: u1 = 2πd x sinθ a / λ; v1=2πd y sinθ e / λ; the normalized modulation rate is defined as: u2 = -π(d x cosθ a ) 2 / λr;v2=-π(d y cosθ e ) 2 / λr;θ a ,θ e , r are the three parameters for calibrating the source orientation, θ a is the range angle corresponding to the calibration source orientation, θ e is the elevation angle corresponding to the calibration source orientation, r is the distance between the calibration source and the transducer array; ξ k (m, n) is complex multiplicative noise, including amplitude and phase error factors; ε k (m, n) is the additive noise of the array response; d x is the horizontal spacing between adjacent transducers; d y is the vertical spacing between adjacent transducers; j is the imaginary unit; λ is the carrier wavelength.

3. The near-field model amplitude and phase error calibration method of the phased array three-dimensional imaging sonar system transducer array according to claim 2 is characterized in that: Preprocess the array response signal, including: First, the array response signal X corresponding to the kth sampling snapshot is k Perform the following calculations: Then, for K R kx and R ky Superimpose them respectively to obtain two virtual two-dimensional array responses R x and R y : The superscript H represents the conjugate transpose operation.

4. The near-field model amplitude and phase error calibration method of the phased array three-dimensional imaging sonar system transducer array according to claim 1, characterized in that: In step (2), the two-dimensional array response R x and R y It is a two-dimensional frequency modulated signal, which is reduced to a two-dimensional sinusoidal signal Y using discrete phase transform x and Y y , where the discrete phase transform operation is: Among them, the symbol Indicates rounding down, and the symbol * indicates the conjugate operation of array elements.

5. The near-field model amplitude and phase error calibration method of the phased array three-dimensional imaging sonar system transducer array according to claim 1, characterized in that: In step (3), the two-dimensional sinusoidal signal Y x and Y y Perform a two-dimensional fast Fourier transform, search for the maximum value of the two-dimensional fast Fourier transform spectrum, and convert Y x The horizontal angular frequency and Y y The vertical angular frequencies corresponding to the maximum values ​​of the spectrum are divided by and After that, it is used as an initial estimate of the normalized modulation rate in the raw array response and In step (6), the two-dimensional array Z is x and Z y Perform a two-dimensional fast Fourier transform, search for the maximum value of the two-dimensional fast Fourier transform spectrum, and set Z x The horizontal angular frequency corresponding to the maximum value of the spectrum and the Z y The vertical angular frequency corresponding to the maximum value of the spectrum is used as the initial estimate of the normalized angular frequency in the original array response. and 6. The near-field model amplitude and phase error calibration method of the phased array three-dimensional imaging sonar system transducer array according to claim 5, characterized in that: For a two-dimensional sinusoidal signal Y x and Y y When performing a two-dimensional fast Fourier transform, Y x and Y y L x ×L x and L y ×L y A two-dimensional matrix signal, where: When L x or L y When Y is not a power of 2, it is necessary to calculate x and Y y Perform a zero-padding operation to make its length reach the nearest integer power of 2; In the two-dimensional array Z x and Z y When performing a two-dimensional fast Fourier transform, Z x and Z y They are two-dimensional arrays of M×M and N×N, respectively. When M or N is not a power of 2, Z needs to be calculated. x Perform zero-padding operation on Zy to make its length reach the nearest integer power of 2.

7. The near-field model amplitude and phase error calibration method of the phased array three-dimensional imaging sonar system transducer array according to claim 1, characterized in that: In step (5), the frequency estimate is used and Respectively respond to the two-dimensional array R x and R y The demodulation operation is: Among them, m1 and m2 represent R x In the horizontal and vertical directions, n1 and n2 represent the index of R y Index in horizontal and vertical direction.

8. The near-field model amplitude and phase error calibration method of the phased array three-dimensional imaging sonar system transducer array according to claim 1, characterized in that: In step (7), a three-step iterative calculation is used to obtain the frequency estimate and include: (7-1) Let i = 1, Using equations (16) and (17) to obtain the frequency estimate in, (7-2) Let i = 2, Using equations (16) and (17) to obtain the frequency estimate (7-3) Let i = 3, M3 = M, N3 = N, and use equations (16) and (17) to obtain the frequency estimate 9. The near-field model amplitude and phase error calibration method of the phased array three-dimensional imaging sonar system transducer array according to claim 1, characterized in that: In step (8), the amplitude and phase error factors of each transducer channel in the transducer array are estimated using a spatial domain matched filtering algorithm, including: (8-1) Using frequency estimates Calculate the calibration source amplitude in the kth sampling snapshot: in, is the theoretical steering vector corresponding to the orientation of the previous estimation result, x(k) is the column vector of the array response in the kth snapshot; (8-2) Using equation (23), calculate the real steering vector affected by amplitude and phase disturbances (8-3) The amplitude and phase error vector is calculated using equation (24), that is, the amplitude and phase error factor of each transducer channel is obtained: in, Represents an element-wise division operation on a vector.

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