Position configuration method of seabed acoustic array shape calibration sound source in deep sea environment

Abstract

The invention belongs to the technical field of underwater sound information processing, and relates to a position configuration method of an array calibration sound source of a seabed sound array in a deep sea environment, which comprises the following steps of: constructing a time delay observed quantity model between a calibration sound source and an array element based on a ray sound propagation theory; deriving a relation between an unbiased estimation error lower bound of an array element position and a calibration sound source position, constructing an array calibration performance constraint condition and a calibration source number sparse constraint condition to realize automatic selection of a calibration sound source number, and adopting a positive semidefinite programming technology to solve an optimization configuration problem; compared with a traditional calibration sound source position configuration method, the method adopts the ray acoustic propagation model to model and calibrate the time delay observed quantity between the sound source and the array element, is more in line with the characteristics of the marine environment, and can realize effective compensation of the sound propagation effect.

Description

Technical Field

[0001] The invention belongs to the technical field of underwater acoustic signal processing and relates to a method for configuring the position of a seabed acoustic array array calibration sound source in a deep sea environment. Background Art

[0002] The submarine acoustic array refers to a horizontal acoustic array deployed on the seabed (hereinafter referred to as the acoustic array), which is usually composed of optical fiber or piezoelectric hydrophones, optical signal transmission cables, shore station information processing units and other parts. It uses the method of passively receiving the radiation noise of underwater acoustic targets to achieve the target direction finding or ranging function, and has strong concealment. Therefore, the acoustic array has become an important equipment in the field of marine acoustic research and underwater target detection. In order to give full play to the detection efficiency of the acoustic array, it is very important to obtain the array parameters after its deployment (this process is called array calibration). In the array calibration process, the cooperative acoustic signal is generally emitted by the surface calibration sound source, and each element of the acoustic array receives the acoustic signal, and the time delay difference between the two is used to invert the element position (for specific steps, see the literature: SE Dosso, et.al., Array element localization for horizontal arrays via Occam's inversion. J. Acoust. Soc. Am., vol. 104, no. 2, pp. 846-859, Aug. 1998). Related research on formation calibration mainly focuses on improving the accuracy and robustness of the position inversion algorithm, but there is less research on the position configuration of the calibration sound source.

[0003] The geometric position configuration of the calibration sound source (also called reference node) has a significant impact on the formation calibration result based on the time-delay observation. In fact, the optimal deployment problem of the reference node of the calibration sound source has received extensive attention in the underwater positioning problem, and many optimization methods have been proposed. For example, David et al., for the reference node deployment problem in three-dimensional underwater space, minimized the Cramer-Rao Lower Bound (CRLB) of the node position estimate and gave the optimal deployment scheme of the reference node in different positioning scenarios (D.M. Salinas, et al., Optimal sensor placement for acoustic underwater target positioning with range-only measurements. IEEE J. Oceanic Eng., vol. 41, no. 3, pp. 620–643, 2016). Similarly, Fang Xinpeng et al. studied the optimal deployment of reference nodes under the range-dependent noise model and proposed the optimal position configuration scheme under the fixed distance condition (X. Fang, et al., Sensor placement for underwater source localization with fixed distances. IEEE Geo. and Remote Sens. Lett., vol. 13, no. 3, pp. 1379-1383, 2016). For dynamic positioning scenarios, Yan Weisheng et al. proposed the optimal formation scheme of the main AUV (equipped with high-precision navigation equipment) for the positioning problem of underwater autonomous vehicles (AUVs) (W. Yan et al., Formation optimization for AUV localization with range-dependent measurements noise. IEEE Commu. Lett., vol. 18, no. 9, pp. 1579-1582, 2014).Furthermore, Zhang Yixin et al. studied the optimal deployment method of reference nodes in the AUV positioning problem under the linear sound speed model and proposed a node configuration scheme with stronger environmental adaptability (Y. Zhang, et al., Underwater anchor-AUV localization geometries with an isogradient sound speed profile: A CRLB-based optimality analysis. IEEE Trans. Wireless Commu., vol. 17, no. 12, pp. 8228-8238, 2018). Recently, Zhou Rongyan et al. in China considered the differences in noise variance and equivalent sound speed of different channels in the ocean environment, and optimized the node configuration with the minimum average CRLB trace of all possible target points in the area of ​​interest as the optimization criterion, effectively reducing the positioning error of the positioning system in the ocean sound field (Zhou Rongyan et al. Node configuration method of distributed passive positioning system in ocean sound field. Journal of Acoustics. vol. 45, no. 1, pp. 30-37, 2020). Stan et al. used the downhill simplex and simulated annealing hybrid optimization algorithm to obtain the optimal configuration of the array calibration sound source position, taking the minimization of the array element positioning error as the objective function, and effectively reduced the error in the estimation of the element position (SE Dosso et al., Optimal array element localization. J. Acoust. Soc. Am., vol. 106, no. 6, pp. 3445-3459, 1999). This method optimizes the sound source position under the condition that the number of sound sources is fixed, that is, after the number of calibration sound sources is given, the calibration sound source position is searched and solved by the optimization algorithm. Therefore, only the optimal configuration under the condition of a fixed number of sound sources can be achieved. The main problems with the above method are that it is impossible to automatically set the number of calibration sound sources, and the CRLB of the element position estimate is still not low enough. Summary of the invention

[0004] In order to further optimize the position configuration of the seabed acoustic array formation calibration sound source, the present invention constructs a time delay observation model between the calibration sound source and the array element based on the ray sound propagation theory, derives the relationship between the unbiased estimation error lower bound of the array element position (i.e., the Cramer-Rao lower bound CRLB, for detailed definition, see: Steven M.Kay, Fundamentals of Statistical Signal Processing-Estimation Theory) and the calibration sound source position, constructs formation calibration performance constraints and calibration source number sparse constraints to realize automatic selection of the calibration sound source number, and adopts semi-positive definite programming technology to solve the optimization configuration problem.

[0005] The technical solution of the present invention is divided into the following steps:

[0006] The first step is to construct a time delay observation model between the calibration sound source and the array element:

[0007] Define the three-dimensional space coordinate position of the mth calibration sound source as u m ,v m ,w m They represent the three-dimensional coordinate values ​​of the mth calibration sound source, m = 1, 2, ..., M, M represents the number of calibration sound sources, and the three-dimensional spatial coordinate position of the nth array element is x n ,y n ,z n They represent the three-dimensional coordinate values ​​of the nth array element, n = 1, 2, ..., N, where N represents the number of array elements; the submarine acoustic array is located on the seabed, and the calibration sound source is located near the sea surface (usually within 100 meters below the sea surface). Therefore, z n >w m According to the coordinate definition of the calibration sound source and the array element, the horizontal projection distance between the mth calibration sound source and the nth array element is The propagation delay corresponding to this distance is t m,n Using the ray acoustic propagation model, we can get r m,n and t m,n The expression is as follows:

[0008]

[0009] Where p is the ray path constant, c(z) is the speed of sound at depth z. According to the ray acoustic propagation theory, the ray path constant can be expressed as p = cosθ(z) / c(z), and θ(z) is the ray grazing angle at depth z. From formula (1), it can be seen that the horizontal projection distance r m,n is a function with p as the independent variable, and Newton's iteration method can be used to solve for p. m,n Taylor expansion at p0 gives:

[0010]

[0011] r m,n (p) represents r m,n Taylor expansion at p0, p0 is a value near p, usually |p-p0| does not exceed 1‰; then the iterative update formula of p is:

[0012]

[0013] The calibration sound source transmits cooperative sound signals at a fixed period (assuming no error), but there is a fixed time deviation t0 (unknown constant) between the calibration sound source and the demodulation system of the acoustic array. The time delay observation model between the calibration sound source and the array element can be expressed as:

[0014]

[0015] where n m,n is the delay estimation noise, which usually has a mean of 0 and a variance of Gaussian distribution, represents the noise-free time-delay observation, Represents the estimated value of the delayed observation vector.

[0016] The second step is to calculate the unbiased estimate error lower bound (Cramer-Rao lower bound CRLB) of the array primitive position:

[0017] The noise-free time-delay observation vector f is defined as:

[0018]

[0019] The superscript T indicates the transpose operation, f m represents the time delay observation vector between the mth calibration sound source and all array elements.

[0020] The delay estimation noise vector n is defined as:

[0021]

[0022] where n m Denotes the time-delay observation f m The corresponding delay estimation noise vector.

[0023] Define the covariance matrix R of n n and n m The covariance matrix R n ] m They are:

[0024]

[0025] Ε[·] means to find the expectation, I MN represents the MN-dimensional identity matrix, I N Represents the N-dimensional unit matrix; the parameters that need to be estimated in array calibration include the array element position coordinates b n and a fixed time deviation t0, these variables to be estimated are stacked into a vector x, expressed as follows:

[0026] x T =[x1,y1,z1,...,x N ,yN ,z N ,t0] (9)

[0027] Define the Gaussian distribution observation information matrix F(x) (this matrix can be used as the performance measure of the formation calibration in the third step), the element [F(x)] in the i-th row and j-th column of F(x) i,j = (Assume that the covariance of the delay estimation error is independent of the parameters to be estimated. For the solution method, see Steven M.Kay, Fundamentals of Statistical Signal Processing-Estimation Theory):

[0028]

[0029] where x i and x j Respectively represent the i-th and j-th elements of vector x, i≠j.

[0030] Set an M-dimensional Boolean variable w to implement observation selection (i.e., calibrate the configuration of the sound source position): w = [w1, w2, ..., w M ] T ∈{0,1} M , w m Represents the value of the mth element of a Boolean variable, {0,1} M It means that the value of all M elements of this Boolean variable can only be 0 or 1. Then we have (The additive property of the information matrix is ​​used, see Steven M. Kay, Fundamentals of Statistical Signal Processing-Estimation Theory) m (x) represents the observation information matrix corresponding to the mth calibration sound source: Therefore, the calculation of the observation information matrix F(x) can be transformed into the calculation of the observation information matrix F corresponding to the mth calibration sound source: m (x), and calculate F m The key to (x) is to calculate the time delay observation f between the mth calibration sound source and all array elements. m The partial derivatives with respect to the parameter vector x to be estimated.

[0031] Next, we will calculate F in detail. m The partial derivatives contained in (x) are:

[0032] Known Then we have:

[0033]

[0034] The reason why the partial derivative of the third equation above is 0 is that r m,n With parameter z n is irrelevant;

[0035] In addition, from formula (1), we can get:

[0036]

[0037] From formula (2), we can get:

[0038]

[0039] Comparing formulas (12) and (13), we can obtain the following relationship:

[0040]

[0041] According to the chain rule of partial derivatives, and using the results of formulas (11)-(14), we can get:

[0042]

[0043] Similarly, we can get:

[0044]

[0045] Below Solve (parameter z n is the upper limit of the integral, so calculate This is a problem of integral differentiation with parameter variables, and is solved using the theorem of differentiation under the integral sign. Refer to Chapter 15 of the book "Mathematical Analysis - Volume 2" by Chen Jixiu et al.). From formula (2), we can get:

[0046]

[0047] From formula (1), we can get:

[0048]

[0049] According to formula (18), we can know:

[0050]

[0051] Substituting equation (19) into equation (17), we can obtain The expression is:

[0052]

[0053] Finally, from formula (5) we can see Therefore, there is

[0054] Based on the above partial derivative results, the observation information matrix of formula (10) can be calculated. In fact, The partial derivatives involved in the calculation of include: (equal to 1), formulas (15), (16), and (20) give the calculation results of these partial derivatives.

[0055] According to parameter estimation theory (see Steven M.Kay, Fundamentals of Statistical Signal Processing-Estimation Theory), it is assumed that the unbiased estimator of the array calibration parameter vector x to be estimated in formula (9) is Its covariance matrix is but The relationship with the information matrix F(x) should satisfy:

[0056]

[0057] where ≥ 0 means the matrix is ​​positive semidefinite. Therefore, the covariance matrix The lower limit (Cramé-Rao lower bound CRLB) is F -1 (x).

[0058] The third step is to establish the relationship between the formation calibration performance metric and the Cramer-Rao lower bound:

[0059] The performance requirements of the calibrated sound source location configuration are determined by the parameter estimation error By constraining the error, the error can be limited to a circular error range:

[0060] Pr(‖ε||2≤R e )≥P e (twenty two)

[0061] where Pr(·) represents the probability, ||ε||2 represents the second norm of the parameter estimation error ε, and R e represents the upper bound of the parameter estimation error ε, P e Indicates the parameter estimation error ε2 norm size in R e The probability of R e and P e Together they constrain the need for calibration accuracy.

[0062] According to Chebyshev inequality, the following relationship can be established (refer to TMCover and JA Thomas, Elements of Information Theory. New York, NY, USA: Wiley, 2012.):

[0063]

[0064] tr{} means finding the trace of a matrix.

[0065] Based on formula (23), the following expression is further obtained:

[0066]

[0067] In order to satisfy inequalities (22) and (24) at the same time, according to the A-Optimality criterion (see DJ Torrieri, "Statistical theory of passive systems", IEEE Trans. Aerosp. Electron. Syst. Vol. 20, no. 2, pp. 183-198, Mar. 1984.), it is required that:

[0068]

[0069] Assuming the equality in formula (21) holds, we have When the minimum eigenvalue of F(x) is λ min (F(x)), then The maximum eigenvalue of 3N+1 is the number of elements of vector x. According to formula (25), we have Right now

[0070]

[0071] λ eig represents the lower bound of the minimum eigenvalue of F(x), and K=3N+1 represents the number of parameters to be estimated.

[0072] So far, the formation calibration performance metric and the Cramer-Rao lower bound (i.e., λ eig ). In order to satisfy the constraint condition of formula (26), it means that every eigenvalue of the observation information matrix F(x) must be greater than λ eig , so the following linear matrix inequality can be established (using the additive property of the information matrix):

[0073]

[0074] Denotes that the matrix is ​​positive definite, I 3N+1 represents the identity matrix of dimension 3N+1, 0 3N+1 represents an all-zero matrix with a dimension of 3N+1. Equation (27) is the performance constraint for calibrating the sound source position configuration.

[0075] The fourth step is to solve the calibration sound source position configuration parameters:

[0076] The calibration sound source position configuration problem can be described as: Under the premise of satisfying the array calibration performance constraint of formula (27), determine the minimum value and position of the calibration sound source. To this end, the l1 norm (the sum of the absolute values ​​of each element of the vector) is used to minimize the number of calibration sound sources, so there is no need to fix the number of calibration sound sources in advance. Combined with the performance constraint of formula (27), the following calibration sound source position configuration problem model is established:

[0077]

[0078] in Represents an M-dimensional real space, vector is an estimate of w (i.e., the configuration of the calibration sound source position), and the value of each element determines whether the corresponding sound source is selected. In order to keep the calibration sound source position configuration problem model expressed in equation (28) solvable, w in the above equation m The value is limited to a real number between 0 and 1. A calibration sound source grid is defined in the array deployment area (the grid spacing is determined according to actual needs, such as 500m), and each grid point represents the possible configuration position of the calibration sound source. The built-in interior point method of convex optimization toolboxes such as Yalmip, SeDuMi or CVX is used to solve equation (28) (for specific operations, please refer to the literature: JF Sturm. Using SeDuMi1.02, a Matlab toolbox for optimization oversymmetric cones, Optim. Methods Softw., 11 (1-4), 1999, pp. 625-653.), and the final calibration sound source position configuration result is obtained as follows: In formula (28), The value range of the solution is a real number between 0 and 1, and whether the mth calibration sound source is selected is {0, 1} (i.e. w m ), so the threshold θ is taken Perform rounding operation. The calibration sound source position is selected when When θ=0.5, the calibration sound source position is discarded. So far, the calibration sound source position configuration parameters have been completed. The solution.

[0079] The beneficial effects of the present invention are:

[0080] 1. Compared with the traditional calibration sound source position configuration method, the present invention adopts the ray acoustic propagation model to model the time delay observation between the calibration sound source and the array element, which is more in line with the characteristics of the marine environment and can achieve effective compensation for the sound propagation effect.

[0081] 2. The present invention uses the l1 norm (the sum of the absolute values ​​of each element of the vector) to minimize the number of calibration sound sources, which can minimize the number of calibration sound sources and improve the efficiency of formation calibration sea trials (i.e., the sound source transmission positions are optimized to a minimum). BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 It is a flow chart of the implementation of the present invention;

[0083] Figure 2 The figures are the results of numerical simulation experiments using the specific implementation methods of the present invention: (a) is the simulation scene and the sound source selection when the mean square error of the measurement is 0.15 cm; (b) is the simulation scene and the sound source selection when the mean square error of the measurement increases to 15 cm.

[0084] Figure 3 This is the performance comparison result between the present invention and the traditional algorithm under different measurement mean square errors. DETAILED DESCRIPTION

[0085] Figure 1 It is a flow chart of the implementation of the present invention. The specific implementation method includes the following steps:

[0086] The first step is to construct a time delay observation model between the calibration sound source and the array element.

[0087] The second step is to calculate the unbiased estimate error lower bound (Cramer-Rao lower bound) of the array element position.

[0088] The third step is to establish the relationship between the formation calibration performance metric and the Cramer-Rao lower bound.

[0089] The fourth step is to construct and solve the calibration sound source position configuration problem.

[0090] Figure 2 It is the result of a numerical simulation experiment using a specific implementation of the present invention. The simulation experiment scenario is designed as follows: there are 123 seabed acoustic array elements to be calibrated in the scenario, which are randomly distributed at a depth of around 1500m, with an array element spacing of 1.75m and arranged in a rectangular plane; there are a total of 361 sound source positions to be selected for calibration near a depth of 15m above the water surface, arranged in a circle with a radius of 250m, and the center of the circle is the same as the geometric center of the underwater acoustic array plane; the effective sound speed in the water uses the measured sound speed profile of the Indian Ocean, which varies around 1500m / s; the distance measurement noise mean square error varies from 0.15cm to 15cm. The sound sources under each measurement noise mean square error are selected through simulation as follows Figure 2 shown. Figure 2 (a) is the calibration sound source configuration when the mean square error of the distance measurement noise is 0.15 cm: when the measurement error is small, only four surface calibration sound sources, symmetrically distributed at equal intervals, can provide position calibration that meets the performance requirements for the 123 underwater array elements; Figure 2 (b) is the sound source selection when the mean square error of the distance measurement noise is 15cm: Figure 2 (a) It is found that as the measurement noise increases, the number of sound sources needs to be increased to meet the calibration requirements of the underwater acoustic array elements. From the distribution of sound source positions, the geometric shape of the selected sound sources is related to the geometric shape of the underwater sensor node to be located.

[0091] Figure 3 It is the CRLB when the calibration sound source selected by the method of the present invention and the calibration sound source selected by the traditional method (random selection) is used for array calibration. It can be seen that the CRLB of the algorithm of the present invention is 11.9 dB lower than the CRLB of the traditional algorithm on average, and the CRLB of both increases with the increase of noise. Therefore, the configuration of the calibration sound source according to the present invention can achieve the underwater acoustic array calibration requirements set by the user using the minimum number of calibration sound sources.

Claims

1. A method for configuring the position of a seabed acoustic array array calibration sound source in a deep sea environment, characterized by: The method is divided into the following steps: The first step is to construct a time delay observation model between the calibration sound source and the array element: Define the three-dimensional space coordinate position of the mth calibration sound source as u m ,v m ,w m They represent the three-dimensional coordinate values ​​of the mth calibration sound source, m = 1, 2, ..., M, M represents the number of calibration sound sources, and the three-dimensional spatial coordinate position of the nth array element is x n ,y n ,z n represents the three-dimensional coordinate value of the nth array element, n = 1, 2, ..., N, N represents the number of array elements; the seabed acoustic array is located on the seabed, and the calibration sound source is located near the sea surface, so z n >w m According to the coordinate definition of the calibration sound source and the array element, the horizontal projection distance between the mth calibration sound source and the nth array element is: The propagation delay corresponding to this distance is t m,n Represents; using the ray acoustic propagation model, we can get r m,n and t m,n The expression is as follows: Where p represents the ray path constant, c(z) represents the speed of sound at depth z; according to the ray acoustic propagation theory, the ray path constant is expressed as p = cosθ(z) / c(z), and θ(z) represents the ray grazing angle at depth z; From formula (1), we can see that the horizontal projection distance r m,n is a function with p as the independent variable, and Newton's iteration method can be used to solve p; m,n Taylor expansion at p0 gives: r m,n (p) represents r m,n Taylor expansion at p0, p0 is a value near p; then the iterative update formula of p is: The calibration sound source emits cooperative sound signals at a fixed period, but there is a fixed time deviation t0 between the calibration sound source and the demodulation system of the acoustic array. The time delay observation model between the calibration sound source and the array element can be expressed as: where n m,n is the delay estimation noise, represents the noise-free time-delay observation, represents the estimated value of the delayed observation vector; The second step is to calculate the lower bound of the unbiased estimate error of the array element position: The noise-free time-delay observation vector f is defined as: The superscript T indicates the transpose operation, f m represents the time delay observation vector between the mth calibration sound source and all array elements; The delay estimation noise vector n is defined as: where n m Denotes the time-delay observation f m The corresponding delay estimation noise vector; Define the covariance matrix R of n n and n m The covariance matrix R n ] m They are: Ε[·] means to find the expectation, I MN represents the MN-dimensional identity matrix, I N Represents the N-dimensional unit matrix; the parameters that need to be estimated in array calibration include the array element position coordinates b n and a fixed time deviation t0, these variables to be estimated are stacked into a vector x, expressed as follows: x T =[x1,y1,z1,...,x N ,y N ,z N ,t0] (9) Define the Gaussian distribution observation information matrix F(x), the element in the i-th row and j-th column of F(x) [F(x)] i,j for: where x i and x j Respectively represent the i-th and j-th elements of vector x, i≠j; Set an M-dimensional Boolean variable w to implement observation selection: w = [w1, w2, ..., w M ] T ∈{0,1} M , w m Represents the value of the mth element of a Boolean variable, {0,1} M It means that the value of all M elements of this Boolean variable can only be 0 or 1; then F m (x) represents the observation information matrix corresponding to the mth calibration sound source: Therefore, the calculation of the observation information matrix F(x) can be transformed into the calculation of the observation information matrix F corresponding to the mth calibration sound source: m (x), and calculate F m The key to (x) is to calculate the time delay observation f between the mth calibration sound source and all array elements. m The partial derivative of the estimated parameter vector x; Next, we will calculate F in detail. m The partial derivatives contained in (x) are: Known Then we have: The reason why the partial derivative of the third equation above is 0 is that r m,n With parameter z n is irrelevant; In addition, from formula (1), we can get: From formula (2), we can get: Comparing formulas (12) and (13), we can obtain the following relationship: According to the chain rule of partial derivatives, and using the results of formulas (11)-(14), we can get: Similarly, we can get: Below Solve; from formula (2), we can get: From formula (1), we can get: According to formula (18), we can know: Substituting equation (19) into equation (17), we can obtain The expression is: Finally, from formula (5) we can see Therefore, there is Based on the above partial derivative results, the observation information matrix of formula (10) can be calculated; in fact, The partial derivatives involved in the calculation of include: Formulas (15), (16), and (20) give the calculation results of these partial derivatives; According to parameter estimation theory, it is assumed that the unbiased estimator of the parameter vector x to be estimated for array calibration in formula (9) is Its covariance matrix is but The relationship with the information matrix F(x) should satisfy: where _0 means that the matrix is ​​positive semidefinite; therefore, the covariance matrix The lower limit is F -1 (x); The third step is to establish the relationship between the formation calibration performance metric and the Cramer-Rao lower bound: The performance requirements of the calibrated sound source location configuration are determined by the parameter estimation error By constraining the error, the error can be limited to a circular error range: Pr(||ε||2≤R e )≥P e (22) where Pr(·) represents the probability, ||ε||2 represents the second norm of the parameter estimation error ε, and R e represents the upper bound of the parameter estimation error ε, P e Indicates the parameter estimation error ε2 norm size in R e The probability of R e and P e Together they constrain the need for calibration accuracy; According to Chebyshev inequality, the following relationship is established: tr{} means finding the trace of the matrix; Based on formula (23), the following expression is further obtained: In order to satisfy inequalities (22) and (24) simultaneously, according to the A-Optimality criterion, it is required that: Assuming the equality in formula (21) holds, we have When the minimum eigenvalue of F(x) is λ min (F(x)), then The maximum eigenvalue of 3N+1 is the number of elements of vector x; according to formula (25), we have Right now λ eig represents the lower bound of the minimum eigenvalue of F(x), K=3N+1 represents the number of parameters to be estimated; So far, the relationship between the array calibration performance metric and the Cramer-Rao lower bound is obtained; in order to satisfy the constraint condition of equation (26), it means that every eigenvalue of the observation information matrix F(x) must be greater than λ eig , so the following linear matrix inequality can be established: Denotes that the matrix is ​​positive definite, I 3N+1 represents the identity matrix of dimension 3N+1, 0 3N+1 represents an all-zero matrix with a dimension of 3N+1. Equation (27) is the performance constraint condition for calibrating the sound source position configuration; The fourth step is to solve the calibration sound source position configuration parameters: The calibration sound source position configuration problem can be described as: under the premise of satisfying the formation calibration performance constraint of formula (27), determine the minimum value and position of the calibration sound source; for this purpose, the l1 norm is used to minimize the number of calibration sound sources, so there is no need to fix the number of calibration sound sources in advance; combined with the performance constraint of formula (27), the following calibration sound source position configuration problem model is established: 0≤w m ≤1,m=1,...,M in Represents an M-dimensional real space, vector is the estimated value of w, and the value of each element determines whether the corresponding sound source is selected; in order to keep the calibration sound source position configuration problem model expressed in equation (28) solvable, w in the above equation m The value is limited to a real number between 0 and 1. A calibration sound source grid is defined in the array deployment area, and each grid point represents a possible configuration position of the calibration sound source. The built-in interior point method of the Yalmip convex optimization toolbox is used to solve equation (28) to obtain the final calibration sound source position configuration result: In formula (28), The value range of the solution is a real number between 0 and 1, and whether the mth calibration sound source is selected is defined by {0, 1}, so the threshold θ is taken for Perform rounding operation; when The calibration sound source position is selected when , the calibration sound source position is discarded; so far, the calibration sound source position configuration parameters are completed. The solution.

2. The method for arranging the position of the seabed acoustic array calibration sound source in a deep sea environment according to claim 1, characterized in that: In formula (3), |p-p0| does not exceed 1‰.

3. The method for arranging the position of the seabed acoustic array calibration sound source in a deep sea environment according to claim 1, characterized in that: Delay estimation noise n m,n The mean is 0 and the variance is Gaussian distribution.

4. The method for arranging the position of the seabed acoustic array calibration sound source in a deep sea environment according to claim 1, characterized in that: The calibration sound source grid spacing is set at 500m.

5. The method for arranging the position of the seabed acoustic array calibration sound source in a deep sea environment according to claim 1, characterized in that: Threshold θ=0.

5.

6. The method for arranging the position of the seabed acoustic array calibration sound source in a deep sea environment according to any one of claims 1 to 5, characterized in that: The convex optimization toolbox is SeDuMi or CVX.

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