A method for calibrating the shape of a seabed acoustic array based on convex optimization theory

Abstract

The application belongs to the field of underwater information fusion processing, and relates to a seabed sound base array shape calibration method based on convex optimization theory. The method uses a semi-positive programming method to construct a convex optimization problem solving model, takes the element spacing value as a constraint condition of model solving, and finally adopts an interior point method of a convex optimization toolbox to solve and obtain the array shape parameters of the seabed sound base array. The method constructs an array shape calibration problem model considering the unknown emission time of the calibration sound source, the unknown equivalent sound velocity and the element spacing constraint by using the semi-positive programming theory, solves by using the convex optimization toolbox, does not need to set an intermediate parameter, and obtains a more accurate array shape calibration result.

Description

Technical Field

[0001] This invention belongs to the field of underwater information fusion processing and relates to a method for calibrating the configuration of a seabed acoustic array based on convex optimization theory. Background Technology

[0002] A seabed acoustic array (also known as a horizontal array) is an underwater acoustic detection device composed of multiple acoustic detection elements (such as fiber optic hydrophones) arranged at a certain spacing. It enhances the signal-to-noise ratio of the target signal through beamforming technology, enabling the detection of long-range or weak underwater acoustic targets. The spacing d between the array elements is related to the array center operating frequency f. o Closely related, generally f o Based on the radiated noise characteristics of the target being detected, the element spacing *d* of the seabed horizontal array is determined after its assembly (this can be used as prior information). However, during the actual deployment of the seabed horizontal array, the deviation between the actual array shape and the preset shape is unknown due to factors such as the undulating motion of the deployment vessel (affected by sea surface waves), ocean currents, and seabed topography. Inaccurate array parameters will reduce the array gain of beamforming. Studies have shown that if the array shape error exceeds 1 / *10 of the processed signal wavelength, it will result in an array gain loss of more than 1 dB. Therefore, after the seabed horizontal array is deployed, acoustic methods are required for array shape calibration.

[0003] Existing array calibration methods mainly include two categories: regular inversion methods (reference: SEDosso etc., Arrayelement localization for horizontal arrays via Occam's inversion[J]. J. Acoust. Soc. Am. 104, 1998, pp. 846–859) and optimization search methods (reference: He Qi, Gong Zaixiao, Li Fenghua et al. Channel matching array calibration for shallow sea large aperture clock weak synchronization array[J]. Acta Acustica, 48(1), 2023 Vol. 48 No. 1, pp. 5-15; A method and system for horizontal array element position calibration[P], patent application number 202210800346.4, publication date: 2022-09-06). Among them, the regular inversion method requires setting the Lagrange multiplier parameter to control the weight of data fitting and prior information. In practice, this parameter is usually determined by empirical or numerical methods, and it is difficult to obtain its optimal value. The optimization search method generally uses simulated annealing or differential evolution genetic algorithm to perform iterative optimization. These methods rely on the initial value setting, are prone to converge to local optima (which are very different from the true value), and have a large computational load.

[0004] Furthermore, existing array calibration methods treat each array element as an independent node for position estimation, neglecting the prior information of the fixed distance difference between array elements, i.e., the element spacing *d*. When calculating the element spacing based on the estimated array configuration, it can be significantly larger or smaller than the actual element spacing. Physically, this implies that the array is "torn apart" or "overlapping," which is unreasonable for a non-rigid seabed horizontal array with certain bending stress. Therefore, ignoring the element spacing information in array calibration methods leads to inaccurate element position calibration results, and there is still room for improvement in accuracy. Summary of the Invention

[0005] To better utilize the prior information of the element spacing d to improve the array calibration accuracy of the seabed acoustic array, this invention proposes an array calibration method for seabed acoustic arrays based on convex optimization theory. A convex optimization problem solution model is constructed using a semi-positive definite programming method, with the element spacing value as a constraint condition for solving the model. Finally, the array parameters of the seabed acoustic array are obtained by solving the interior point method of the convex optimization toolbox.

[0006] The technical solution adopted in this invention is a method for calibrating the configuration of a seabed acoustic array based on convex optimization theory, which consists of the following steps:

[0007] S1, with the array placement point in the water as the center and R as the radius, draw a circle. The sound source ship tows a mid-to-high frequency broadband sound source to continuously transmit broadband array calibration signals at a fixed period T on the circumference. The seabed acoustic array receives and stores the sound signals throughout the entire process.

[0008] Let O be the point where the array is placed in the water, and let R be the radius, where R = 3km to 5km. The navigation trajectory S of the sound source calibration vessel is determined accordingly. The sound source vessel tows a mid-to-high frequency broadband sound source that continuously emits a broadband array calibration signal u(t) with a period T, where T = 8s to 12s. Taking a linear frequency modulated signal as an example (but not limited to), u(t) can be expressed as:

[0009] u(t) = A·rect(t / T) p )cos[2π(f c t+0.5γt 2 (1)

[0010] In the formula, A is the signal amplitude, and rect(t / T) p ) indicates that the pulse width is T p The rectangle function, f c γ is the carrier center frequency, and γ is the frequency modulation slope.

[0011] Let t0 be the start time of the sound source calibration ship's launch. After the launch begins, it will launch continuously at a fixed period T. The sound source ship will launch a total of N0 times on the trajectory S, where N0 = 2πR / (v·T), v represents the speed of the sound source calibration ship, v = 1.5m / s to 3m / s. The seabed acoustic array records and stores the received acoustic signals.

[0012] S2, calculate the time-domain correlation waveform set based on the transmitted signal and the array received signal, then determine the time-domain correlation waveform set of the calibration sound source used for subsequent array calibration, extract the peak value of the time-domain correlation waveform set corresponding to the calibration sound source location set as the arrival delay between the calibration sound source and the primitive, and obtain the arrival delay observation set; specifically as follows:

[0013] S2.1, taking t0 as the starting time, the intercepted waveform of the received signal of the primitive element is s with a length of T. i,n (t)=u(t-τ i,n ), i = 1,...,M, n = 1,...,N0, t∈[t0+(n-1)T,t0+nT], i represents the primitive index, M represents the number of primitives, n represents the index of the broadband array calibration signal emitted by the sound source ship, τ i,n =||s n -u i || / c i The time delay difference, s, represents the time delay difference between the sound source ship's emission location and the primitive. n u represents the position of the sound source ship during its nth launch. i Represents the three-dimensional coordinates of the i-th primitive. This represents the two-dimensional coordinates of the i-th primitive on the horizontal plane. x i ,y i These represent the horizontal and vertical coordinates of a two-dimensional coordinate system, respectively. H is the average depth of the element, obtained through actual measurement using a depth sounder. i Let s represent the equivalent propagation speed of the signal received by the i-th primitive in seawater; denoted as s i,n The frequency domain expression of (t) is S i,n (w) can be obtained directly using Fourier transform, where w represents the transformed angular frequency independent variable;

[0014] The spectral response of the matched filter, designed according to the principle of maximum signal-to-noise ratio, is as follows:

[0015]

[0016] Where B = γT p For pulse bandwidth, w o η represents the center angular frequency of the broadband array calibration signal. o This indicates the added time delay that makes the filter physically feasible; the array receives the signal S. i,n(w) The output spectrum after passing through the matched filter is Y i,n (w)=S i,n (w)·H(w), according to the inverse Fourier transform, the time-domain correlation waveform of the output signal after correlation matching through the matched filter is: By iterating through all i and n, the set of time-domain correlated waveforms is obtained;

[0017] S2.2, Calculate the time-domain correlated waveform y in the time-domain correlated waveform set. i,n The signal-to-noise ratio (SNR) of (t), where the SNR is the time-domain correlated waveform y. i,n The dB difference between the correlation peak and the background noise of (t) is used to select time-domain correlation waveforms with a signal-to-noise ratio greater than U dB (the value of U is manually set according to the actual situation, usually set to 6 dB) and with a distance difference fluctuation of less than 30% between adjacent transmission positions on trajectory S. These waveforms form the time-domain correlation waveform set of the calibration sound source used for subsequent array calibration. i,n′ (t), i=1,...,M,n′=1,...,N′}, N′≤N0 represents N′ launches selected from N0 launches;

[0018] S2.3, extract the time delay difference (i.e., arrival delay) t between the maximum peak time and the starting time of each time-domain correlated waveform in the time-domain correlated waveform set of the calibration sound source used for array calibration. i,n′ By iterating through all i and n′, we can obtain the arrival delay observation set {t}. i,n′ The expression i = 1, ..., M, n′ = 1, ..., N′ can be represented as:

[0019]

[0020] in, Let be the synchronization error, and let be an unknown constant, s. n′ Let n be the coordinates of the position of the sound source ship during its n′th launch. i,n′ This represents the observation noise extracted by time delay;

[0021] S3, the arrival delay observation set {t} obtained from S2 i,n′ The set of primitive arrival delay observations, i = 1, ..., M, n′ = 1, ..., N′, is divided into subsets of primitive arrival delay observations. The difference between these subsets is then calculated to obtain the primitive arrival delay difference observation subset. The details are as follows:

[0022] The arrival time delay observation set {t i,n′ The set i = 1, ..., M, n′ = 1, ..., N′ is divided into primitive arrival delay observation subsets based on the primitive index. (i.e., select a specific i), select the first relevant waveform y. i,1The time delay difference (i.e., arrival delay) between the peak time and the starting time of (t) is t. i,1 For reference, construct a subset of primitive arrival time delay difference observations. Let represent the difference in arrival time delay of the primitive at the i-th primitive and the n′-th transmission, and its expression is as follows:

[0023]

[0024] in The observation noise representing the time delay extraction is usually small and can be ignored; as can be seen from the above formula, the synchronization error... The difference in arrival time of the primitives has been eliminated in the observation of the primitive arrival time delay and does not need to be considered anymore;

[0025] S4, using the primitive arrival time delay difference to observe subsets The equivalent speed of sound in seawater is calculated using the least squares method:

[0026] Define the time delay difference vector of the i-th primitive as follows: The distance norm d between the i-th primitive and the location of the calibration sound source i =[||s1-u i ||,...,||s N′ -u i ||] T ,i=1,...,M, difference operator Among them 1 M-1 This represents an M-1 dimensional column vector of all 1s, and the same applies below;

[0027] Based on equation (4), the observation noise extracted by time delay is ignored. c i Treating it as an unknown, its estimated value can be obtained using the least squares method. The calculation is as follows:

[0028]

[0029] S5, Constructing a model for the array calibration problem; details are as follows:

[0030] Using the least squares criterion, the following array calibration cost function is constructed:

[0031]

[0032] In the above formula, d represents the spacing between primitives;

[0033] Define an operation simplification function Substituting the equivalent speed of sound in equation (5) into equation (6), we get:

[0034]

[0035] The above equation is the solution model for array calibration, which is a non-convex function;

[0036] S6, by relaxing the array calibration problem model constructed in S5, yields a semidefinite programming problem that can be solved by convex optimization:

[0037] Define the distance norm matrix Remember D i The value at row p and column q is D. i,[p,q] , p,q=1,...,N′, optimization variables Let the distance norm d be... i The p-th element of the vector is d i,p ;The semidefinite programming theory is used to relax equation (7), so that the objective function is transformed into a convex function (for the specific relaxation method of convex optimization problem, please refer to the reference: Qi Zhongyong et al., Convex Optimization in Signal Processing and Communication: From Basics to Applications, Electronic Industry Press, 2021, pp. 214-225.), and written in the form of linear matrix inequalities (LMI):

[0038]

[0039] In the above formula, λ is the penalty factor in the cost function, used to improve the model matrix D. i The estimated stability is typically taken in the range of 10. -4 ~10 -6 .

[0040] S7 uses the interior point method of the convex optimization toolbox to solve the semidefinite programming problem and outputs the final calibration results of the seabed acoustic array.

[0041] The interior point method built into convex optimization toolboxes such as Yalmip, SeDuMi, or CVX (for specific operations, please refer to: JFSturm. Using SeDuMi 1.02, a Matlab toolbox for optimization over symmetriccones, Optim. Methods Softw., 11(1-4), 1999, pp. 625-653.) is used to solve equation (8), and the final calibration result of the seabed acoustic array is obtained.

[0042] The beneficial result of this invention is that the method proposed in this invention uses semi-positive definite programming theory to construct a model of the array calibration problem with unknown emission time of the calibration sound source, unknown equivalent sound velocity, and consideration of the element spacing constraint. The model is solved using a convex optimization toolbox, without the need to set intermediate parameters, and more accurate array calibration results are obtained. Attached Figure Description

[0043] Figure 1 This is a flowchart illustrating the implementation of the present invention;

[0044] Figure 2 This is a schematic diagram of the underwater acoustic array calibration scenario proposed in this invention;

[0045] Figure 3 It is a time-domain correlation waveform diagram of the measured data;

[0046] Figure 4 It compares the results of experimental data on array calibration using the method described in this invention and traditional methods;

[0047] Figure 5 It is a comparison of array spacing obtained using the method described in this invention and traditional methods;

[0048] Figure 6 It is the result of actual data orientation detection of the formation obtained by the method described in this invention;

[0049] Figure 7 The result is the measured data line spectrum detection of the array obtained by the method described in this invention. Detailed Implementation

[0050] Figure 1 This is a flowchart illustrating the implementation of the present invention. The technical solution of the present invention includes the following steps:

[0051] The first step is to draw a circle with the array placement point in the water as the center and R as the radius. The sound source ship tows the medium and high frequency broadband sound source to continuously transmit broadband array calibration signals on the circumference with a fixed period T. The seabed acoustic array receives and stores the sound signals throughout the process.

[0052] The second step is to calculate the time-domain correlation waveform set based on the transmitted signal and the array received signal, then determine the time-domain correlation waveform set of the calibration sound source used for subsequent array calibration, extract the peak value of the time-domain correlation waveform set corresponding to the calibration sound source position set as the arrival delay between the calibration sound source and the primitive, and obtain the arrival delay observation set.

[0053] The third step is to divide the arrival delay observation set obtained in the second step into a primitive arrival delay observation subset, and to subtract the primitive arrival delay difference observation subset within the primitive arrival delay subset;

[0054] The fourth step is to use the observation subset with the time delay difference of the primitive arrival to calculate the equivalent speed of sound in seawater using the least squares method;

[0055] Fifth step: Construct a model for the array calibration problem;

[0056] The sixth step is to relax the problem model constructed in the fifth step to obtain a semidefinite programming problem that can be solved by convex optimization.

[0057] The seventh step involves using the interior point method from the convex optimization toolbox to solve the semidefinite programming problem and output the final calibration results of the seabed acoustic array.

[0058] The specific implementation of the present invention was verified using measured data from a sea trial. During the trial, the navigation radius of the sound source calibration ship was R = 3 km, the speed was 2 m / s, and the signal transmission period was T = 8 s.

[0059] Figure 2 This is a schematic diagram of the underwater acoustic array calibration scenario proposed in this invention. Figure 3 This is a time-domain correlation waveform diagram of the measured data. The horizontal axis represents the correlation delay in seconds (s), and the vertical axis represents the element number (unitless). It can be seen that at the location of the calibrated sound source, the received signal from the array elements, after matched filtering, exhibits a significant correlation peak, which can be used to extract the time delay observation.

[0060] Figure 4 The results of the array calibration experiment using the specific implementation method of this invention and the traditional method are compared. The horizontal axis is the x-axis of the rectangular coordinate system, with the unit being "kilometer (km)" and the vertical axis is the y-axis of the rectangular coordinate system, with the unit being "kilometer (km)". As can be seen from the figure, there is a difference in the array element positions estimated by the two methods, indicating that the element spacing constraint proposed in this invention does indeed affect the array calibration results.

[0061] To further compare the array calibration accuracy of the method described in this invention and the traditional method, the array element spacing estimation results are first compared, such as... Figure 5 As shown, the horizontal axis represents the element spacing sequence number (unitless), and the vertical axis represents the spacing value between adjacent elements (meters (m)). Figure 5 It can be seen that the array spacing estimated by the method of this invention satisfies the condition of "less than or equal to the actual spacing," which is consistent with the actual situation (if it were greater than the actual spacing, it would mean that the array was "broken," which is not consistent with reality). Secondly, cooperative target detection experiments were conducted using arrays estimated by different methods. Figure 6 The results show the measured azimuth detection data. The horizontal axis represents the target azimuth in degrees (deg), and the vertical axis represents the time in seconds (s). The target trajectory shown within the box in the figure is the cooperative target. It can be observed that the formation calibrated using the method of this invention has a stronger detection capability, and the target trajectory energy is enhanced by approximately 4.5 dB (at time 223s, the trajectory energy of the traditional method is -13.5 dB, and the trajectory energy of this invention is -9 dB).

[0062] Figure 7The graph shows the measured line spectrum detection results. The horizontal axis represents frequency in Hertz (Hz), and the vertical axis represents time in seconds (s). The line spectrum shown within the box in the graph represents the emission from the cooperative sound source. It can be observed that the array calibrated using the method of this invention has a stronger line spectrum detection capability, with the line spectrum gain increased by approximately 5.43 dB (at time 265s, the line spectrum energy of the traditional method is -13.48 dB, while the trajectory energy of this invention is -8.05 dB).

Claims

1. A method for calibrating the configuration of a submarine acoustic array based on convex optimization theory, characterized in that, This method consists of the following steps: S1, with the array placement point in the water as the center and R as the radius, draw a circle. The sound source ship tows a mid-to-high frequency broadband sound source to continuously transmit broadband array calibration signals at a fixed period T on the circumference. The seabed acoustic array receives and stores the sound signals throughout the entire process. Let O be the point where the array is placed in the water, and let R be the radius. Use this to determine the navigation trajectory S of the sound source calibration ship. The sound source ship tows a medium-to-high frequency broadband sound source and continuously emits broadband array calibration signals u(t) with a period of T. Let t0 be the start time of the sound source calibration ship's launch. After the launch begins, it will launch continuously at a fixed period T. The sound source ship will launch a total of N0 times on the trajectory S, where N0 = 2πR / (v·T), and v represents the speed of the sound source calibration ship. The seabed acoustic array records and stores the received acoustic signals. S2, calculate the time-domain correlation waveform set based on the transmitted signal and the array received signal, then determine the time-domain correlation waveform set of the calibration sound source used for subsequent array calibration, extract the peak value of the time-domain correlation waveform set corresponding to the calibration sound source location set as the arrival delay between the calibration sound source and the primitive, and obtain the arrival delay observation set; specifically as follows: S2.1, taking t0 as the starting time, the intercepted waveform of the received signal of the primitive element is s with a length of T. i,n (t)=u(t-τ i,n ), i = 1,...,M, n = 1,...,N0, t∈[t0+(n-1)T,t0+nT], i represents the primitive index, M represents the number of primitives, n represents the index of the broadband array calibration signal emitted by the sound source ship, τ i,n =||s n -u i || / c i The time delay difference, s, represents the time delay between the sound source ship's emission location and the primitive. n u represents the position of the sound source ship during its nth launch. i Represents the three-dimensional coordinates of the i-th primitive. This represents the two-dimensional coordinates of the i-th primitive on the horizontal plane. x i ,y i These represent the horizontal and vertical coordinates of a two-dimensional coordinate system, respectively. H is the average depth of the element, obtained through actual measurement using a depth sounder. i Let s represent the equivalent propagation speed of the signal received by the i-th primitive in seawater; denoted as s i,n The frequency domain expression of (t) is S i,n (w) can be obtained directly using Fourier transform, where w represents the transformed angular frequency independent variable; The spectral response of the matched filter designed according to the principle of maximum signal-to-noise ratio is as follows: Where B = γT p Where γ is the pulse bandwidth, γ is the frequency modulation slope, and w o The center angular frequency of the broadband array calibration signal is represented by ηo, which represents the added time delay that makes the filter physically feasible; the array received signal S i,n (w) The output spectrum after passing through the matched filter is Y i,n (w)=S i,n (w)·H(w), according to the inverse Fourier transform, the time-domain correlation waveform of the output signal after correlation matching through the matched filter is: By iterating through all i and n, the set of time-domain correlated waveforms is obtained; S2.2, Calculate the time-domain correlated waveform y in the time-domain correlated waveform set. i,n The signal-to-noise ratio (SNR) of (t), where the SNR is the time-domain correlated waveform y. i,n The dB difference between the correlation peak and the background noise of (t) is used to select time-domain correlation waveforms with a signal-to-noise ratio greater than UdB and with a distance difference fluctuation of less than 30% between adjacent transmission positions on trajectory S to form the time-domain correlation waveform set {y} of the calibration sound source for subsequent array calibration. i,n′ (t), i=1,...,M,n′=1,...,N′}, N′≤N0 represents N′ launches selected from N0 launches; S2.3, Extract the arrival delay t of the maximum peak time and the start time of each time-domain correlated waveform in the time-domain correlated waveform set of the calibration sound source used for array calibration. i,n′ By iterating through all i and n′, we can obtain the arrival delay observation set {t}. i,n′ The expression i = 1, ..., M, n′ = 1, ..., N′ can be represented as: in, Let be the synchronization error, and let be an unknown constant, s. n′ Let n be the coordinates of the position of the sound source ship during its n′th launch. i,n′ This represents the observation noise extracted by time delay; S3, the arrival delay observation set {t} obtained from S2 i,n′ The set of primitive arrival delay observations, i = 1, ..., M, n′ = 1, ..., N′, is divided into subsets of primitive arrival delay observations. The difference between these subsets is then calculated to obtain the primitive arrival delay difference observation subset. The details are as follows: The arrival time delay observation set {t i,n′ The set i = 1, ..., M, n′ = 1, ..., N′ is divided into primitive arrival delay observation subsets based on the primitive index. Select the first relevant waveform y i,1 The arrival time t of the maximum peak time of (t) and the start time i,1 For reference, construct a subset of primitive arrival time delay difference observations. Let represent the difference in arrival time delay of the primitive at the i-th primitive and the n′-th transmission, and its expression is as follows: in This represents the observation noise extracted during time delay, which is negligible. As can be seen from the above formula, the synchronization error... The difference in arrival time of the primitives has been eliminated in the observation of the primitive arrival time delay and does not need to be considered anymore; S4, using the primitive arrival time delay difference to observe subsets The equivalent speed of sound in seawater is calculated using the least squares method: Define the time delay difference vector of the i-th primitive as follows: The distance norm d between the i-th primitive and the location of the calibration sound source i =[||s1-u i ||,...,||s N′ -u i ||] T ,i=1,...,M, difference operator Among them 1 M-1 This represents an M-1 dimensional column vector of all 1s, and the same applies below; Based on equation (4), the observation noise extracted by time delay is ignored. c i Treating it as an unknown, its estimated value can be obtained using the least squares method. The calculation is as follows: S5, Constructing a model for the array calibration problem; details are as follows: Using the least squares criterion, the following array calibration cost function is constructed: In the above formula, d represents the spacing between primitives; Define an operation simplification function Substituting the equivalent speed of sound in equation (5) into equation (6), we get: The above equation is the solution model for array calibration, which is a non-convex function; S6, by relaxing the array calibration problem model constructed in S5, yields a semidefinite programming problem that can be solved by convex optimization: Define the distance norm matrix D i The value at row p and column q is D. i,[p,q] , p,q=1,...,N′, optimization variables Let the distance norm d be... i The p-th element of the vector is d i,p Using semidefinite programming theory to relax equation (7), the objective function is transformed into a convex function and written in the form of a linear matrix inequality: In the above formula, λ is the penalty factor in the cost function, used to improve the model matrix D. i The estimated stability; S7 uses the interior-point method from the convex optimization toolbox to solve the semidefinite programming problem, outputting the final calibration results of the seabed acoustic array: Equation (8) is solved using the built-in interior point method of the Yalmip convex optimization toolbox, yielding the final calibration result of the seabed acoustic array.

2. A method for calibrating the configuration of a submarine acoustic array based on convex optimization theory according to claim 1, characterized in that: In S1, the radius R is 3km to 5km.

3. A method for calibrating the configuration of a submarine acoustic array based on convex optimization theory according to claim 1, characterized in that: In S1, the high-frequency broadband sound source continuously emits broadband array calibration signals with a period of T = 8s to 12s.

4. A method for calibrating the configuration of a submarine acoustic array based on convex optimization theory according to claim 1, characterized in that: In S1, when the broadband array calibration signal is a linear frequency modulated signal, u(t) can be expressed as: u(t)=A·rect(t / T p )cos[2π(f c t+0.5γt 2 )](1) In the formula, A is the signal amplitude, and rect(t / T) p ) indicates that the pulse width is T p The rectangle function, f c γ is the carrier center frequency, and γ is the frequency modulation slope.

5. A method for calibrating the configuration of a submarine acoustic array based on convex optimization theory according to claim 1, characterized in that: In S1, the speed of the sound source calibration ship is v = 1.5m / s to 3m / s.

6. A method for calibrating the configuration of a submarine acoustic array based on convex optimization theory according to claim 1, characterized in that: In S2.2, U is set to 6dB.

7. A method for calibrating the configuration of a submarine acoustic array based on convex optimization theory according to claim 1, characterized in that: In S6, the penalty factor λ in the cost function ranges from 10. -4 ~10 -6 .

8. A method for calibrating the configuration of a submarine acoustic array based on convex optimization theory according to claim 1, characterized in that: In S7, the convex optimization toolbox can also be SeDuMi or CVX.

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