A method for direction estimation of a multi-element stereo hydrophone array

Abstract

The present application relates to the technical field of ultra-short baseline direction measurement data processing, and particularly relates to a direction estimation method of a multi-element stereo hydrophone array. The method approximates sound waves as plane waves and establishes a mathematical relationship between time difference of arrival (TDOA) and a direction vector, takes TDOA as an observation value, calculates a direction vector estimation value according to a weighted least square method, then calculates the equivalent weight of the observation value according to an equivalent weight function, further replaces the original observation value weight array with an equivalent weight array, and recalculates the direction vector according to the weighted least square method, iteratively calculates the equivalent weight and the direction vector, until the difference between the direction vectors of two consecutive times is less than a manually set threshold, and the direction vector is output as the direction of the multi-element stereo hydrophone array. The present application can weaken the influence of the sound ray bending which is not considered in the direction estimation function model, and consider the influence of the array element spacing and the target direction on the direction estimation, thereby improving the accuracy and reliability of the direction estimation of the multi-element stereo hydrophone array.

Description

Technical Field

[0001] The present invention relates to the technical field of ultra-short baseline direction measurement data processing, and in particular to a direction estimation method for a multi-element stereo hydrophone array. Background Art

[0002] The accuracy of direction estimates is one of the primary factors affecting the positioning accuracy of ultra-short baseline and inverse ultra-short baseline positioning systems. Therefore, using the phase difference (PD) or time delay difference (TDD) between hydrophones in a receiving array to estimate direction is a key data processing step in ultra-short baseline direction measurement. Currently, research approaches to improving the accuracy of direction estimates from hydrophone arrays focus on two main areas: first, employing advanced signal processing methods; and second, optimizing the structure of the hydrophone array, particularly designing multi-element stereo hydrophone arrays. The former primarily draws on signal processing techniques from acoustic communication systems, such as adaptive minimum mean square error, recursive least squares, and Fourier transform algorithms to improve phase or time delay estimation accuracy. The latter primarily enhances direction measurement performance by increasing the number of receiving elements (hydrophones) and optimizing the receiving array structure.

[0003] With the increasing 3D and diversified nature of hydrophone receiving arrays, improving direction estimation accuracy solely from a signal processing perspective no longer meets the requirements of these new receiving arrays. This is primarily due to two factors: First, the receiving array structure is a key factor affecting the quality of observation data. For example, under the same measurement environment, the direction-finding accuracy of a planar array depends on the element spacing. Second, different pairs of elements in a 3D array are affected differently by variations in underwater sound velocity. For example, the phase difference or delay difference measured by two vertically spaced elements is affected differently by the bending of the sound line compared to two horizontally spaced elements. For these two reasons, a new direction estimation method suitable for multi-element 3D arrays is needed. Summary of the Invention

[0004] In order to better solve the problem that existing direction estimation methods can no longer meet the direction estimation needs of multi-element stereo hydrophone arrays, the present invention provides a direction estimation method for a multi-element stereo hydrophone array. By adopting the weighted iteration idea in the robust estimation, it can weaken the fact that the function model of direction estimation does not consider the influence of sound line bending, and take into account the influence of array element spacing and target orientation on direction estimation, thereby improving the accuracy and reliability of direction estimation.

[0005] In a first aspect, the present invention provides a method for estimating the direction of a multi-element stereo hydrophone array, comprising:

[0006] Step 1: Obtain the time when each hydrophone in the multi-element stereo hydrophone array receives the acoustic signal, calculate the observation value of the signal received by two adjacent hydrophones, approximate the acoustic wave as a plane wave, and establish a relationship between the direction vector and the observation value;

[0007] Step 2: Based on the relationship in step 1, the identity matrix is ​​used as the observation value weight matrix, and the direction vector estimation is calculated according to the weighted least squares method;

[0008] Step 3: obtaining an observation value residual vector based on the direction vector estimate and the observation vector; wherein the observation vector represents a sequence of observation values ​​arranged in order of hydrophone numbers in the multi-element stereo hydrophone array;

[0009] Step 4: Standardize the observed value residual vector using the median method to obtain a standardized residual vector;

[0010] Step 5: Calculate the equivalent weight of the observation value based on the standardized residual vector through the equivalent weight function to obtain an equivalent weight matrix;

[0011] Step 6: Use the equivalent weight matrix as the new observation value weight matrix and estimate the direction vector according to the least squares method; and calculate whether the iteration condition is met. If it is met, output the direction vector; if not, use the direction vector as the new direction vector estimate and repeat steps 3 to 6.

[0012] Furthermore, in step 1, the relationship is:

[0013]

[0014] Among them, δ i,j represents the observed value of the signal received by two adjacent hydrophones, i and j represent the hydrophone numbers in the hydrophone array, t i and t j are the times when hydrophones i and j receive the acoustic signal, c is the underwater sound speed, and p i and p j They represent the position vectors of hydrophones i and j in the hydrophone array, d represents the direction vector of the sound source, and N represents the number of array elements, that is, the number of stereo hydrophones.

[0015] Furthermore, in step 2, the direction vector estimation is calculated according to the weighted least squares method, which is calculated by formula (3):

[0016]

[0017] in, Denotes the direction vector estimation, δ=[δ 1,2 δ 2,3 … δ N-1,N ]T Represents the observation vector, which is composed of all observation values ​​in the multivariate stereo hydrophone array, P represents the observation value weight matrix, ||·|| represents the modulus of the vector, A represents the position coefficient matrix,

[0018]

[0019] Furthermore, in step 3, the observation residual vector is calculated by formula (4):

[0020]

[0021] in, Denotes the direction vector estimation, δ=[δ 1,2 δ 2,3 … δ N-1,N ] T Represents the observation vector, v=[v1 v2 …v N-1 ] T Represents the observation residual vector, A represents the position coefficient matrix,

[0022]

[0023] Furthermore, the step 4 specifically includes:

[0024] Step 401: Calculate the unit weighted mean error using the median method;

[0025] Step 402: Calculate a standardized residual vector using the unit weighted mean error and the observation residual vector.

[0026] Furthermore, in step 401, the unit weighted mean square error is calculated using formula (5):

[0027]

[0028] in, Represents the unit weighted mean error, P i Represents the i-th diagonal element of the observation weight matrix, v i represents the i-th observation residual of the observation residual vector, and med{·} represents the median.

[0029] Furthermore, in step 402, the normalized residual in the normalized residual vector is calculated by formula (6):

[0030]

[0031] in, represents the i-th standardized residual in the standardized residual vector, Denotes the unit weight error, v iRepresents the residual of the i-th observation in the observation residual vector.

[0032] Furthermore, in step 5, the equivalent weight of the observation value is calculated by the IGGIII equivalent weight function, and the calculation formula is as follows:

[0033]

[0034] in, represents the i-th standardized residual in the standardized residual vector, Represents the equivalent weight, which is the i-th diagonal element of the equivalent weight matrix, k0 and k1 represent the manually set parameters, P i Represents the i-th element of the observation weight matrix.

[0035] Furthermore, in step 6, the iteration condition is:

[0036]

[0037] Among them, max(·) means calculating the maximum value of the vector; |·| means taking the absolute value; ε represents the manually set threshold; represents the direction vector calculated for the kth time, Represents the direction vector calculated for the k+1th time.

[0038] In a second aspect, an embodiment of the present invention provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the method for estimating the direction of a multi-element stereo hydrophone array as described above is implemented.

[0039] Beneficial effects of the present invention:

[0040] The present invention approximates acoustic waves as plane waves and establishes a mathematical relationship between the time difference of arrival (TDOA) and the direction vector. TDOA is used as the observation value, and the direction vector estimate is calculated using the weighted least squares method. The equivalent weight of the observation value is then calculated based on the equivalent weight function. The original observation value weight matrix is ​​replaced with the equivalent weight matrix, and the direction vector is recalculated using the weighted least squares method. The equivalent weights and direction vectors are iteratively calculated until the difference between two consecutive direction vector estimates is less than a manually set threshold. The direction vector estimate is then output as the direction of the multi-element stereo hydrophone array. The present invention employs the idea of ​​weighted iteration in robust estimation, which can mitigate the effects of the direction estimation function model that fail to consider the curvature of the sound line, and takes into account the effects of array element spacing and target orientation on the direction estimate, thereby improving the accuracy and reliability of the direction estimate of the multi-element stereo hydrophone array. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1A schematic flow chart of a method for estimating the direction of a multi-element stereo hydrophone array provided in an embodiment of the present invention;

[0042] Figure 2 A schematic diagram of the structure of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0043] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly described below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0044] An embodiment of the present invention provides a method for estimating the direction of a multi-element stereo hydrophone array, comprising:

[0045] Step 1: Obtain the time when each hydrophone in the multi-element stereo hydrophone array receives the acoustic signal, and calculate the observation value of the received signal of two adjacent hydrophones.

[0046] Approximate the sound wave as a plane wave and establish the relationship between the direction vector and the observation value:

[0047]

[0048] Among them, δ i,j represents the observed value of the received signal of two adjacent hydrophones, that is, the time difference of arrival TDOA; i and j represent the hydrophone numbers in the hydrophone array, t i and t j are the times when hydrophones i and j receive the acoustic signal, c is the underwater sound speed, and p i and p j They represent the position vectors of hydrophones i and j in the hydrophone array respectively, d is a unit vector, representing the direction vector of the sound source, and N represents the number of array elements, that is, the number of stereo hydrophones.

[0049] Step 2: Based on the relationship in step 1, use the identity matrix as the observation value weight matrix and calculate the direction vector estimate according to the weighted least squares method.

[0050] Specifically, the position coefficient matrix composed of the position coefficient vectors is calculated by equation (1):

[0051]

[0052] Where A represents the position coefficient matrix.

[0053] Compute an estimate of the direction vector using the weighted least squares method:

[0054]

[0055] in, Denotes the direction vector estimation, δ=[δ 1,2 δ 2,3 …δ N-1,N ] T represents the observation vector, which is composed of all the observations in the multivariate stereo hydrophone array, P represents the observation weight matrix, ||·|| represents the modulus of the vector, and A represents the position coefficient matrix, which is composed of the position coefficient vector. It should be noted that the purpose of normalization in formula (3) is to prevent numerical calculation errors from causing the modulus of the calculated direction vector to be different from 1.

[0056] Step 3: Obtain an observation value residual vector based on the direction vector estimate and the observation vector; wherein the observation vector represents a sequence of observation values ​​arranged in the order of the hydrophone numbers in the multivariate stereo hydrophone array.

[0057] Specifically, the estimated value of the observation is obtained by calculating the direction vector estimation and the position coefficient matrix, and the estimated value is added to the observation vector to obtain the residual vector of the observation value;

[0058] The observation residual vector is calculated using formula (4):

[0059]

[0060] Where v=[v1 v2 … v N-1 ] T represents the observation residual vector.

[0061] Step 4: Use the median method to standardize the observation residual vector to obtain the standardized residual vector.

[0062] Step 401: Calculate the unit weighted mean error of the observation vector using the median method.

[0063] Specifically, the unit weighted mean error is calculated by formula (5)

[0064]

[0065] in, Represents the unit weighted mean error, P i Represents the i-th diagonal element of the observation weight matrix, v i represents the i-th observation residual of the observation residual vector, and med{·} represents the median.

[0066] Step 402: Calculate a standardized residual vector using the unit weighted mean error and the observation residual vector.

[0067] Specifically, the standardized residual in the standardized residual vector is calculated by formula (6):

[0068]

[0069] in, represents the i-th standardized residual in the standardized residual vector, Denotes the unit weight error, v i Represents the residual of the i-th observation in the observation residual vector.

[0070] Step 5: Calculate the equivalent weight of the observation value through the equivalent weight function based on the standardized residual vector to obtain the equivalent weight matrix.

[0071] Specifically, the equivalent weight of the observation value is calculated by the IGGⅢ equivalent weight function, and the calculation formula is as follows:

[0072]

[0073] in, represents the i-th standardized residual in the standardized residual vector, represents the equivalent weight, which is the i-th diagonal element of the equivalent weight matrix, and k0 and k1 represent manually set parameters.

[0074] Step 6: Use the equivalent weight matrix as the new observation value weight matrix and estimate the direction vector according to the least squares method; and calculate whether the iteration condition is met. If it is met, output the direction vector; if not, use the direction vector as the new direction vector estimate and repeat steps 3 to 6.

[0075] Specifically, the equivalent weight matrix is ​​used as the new observation weight matrix (i.e. ), and re-estimate the direction vector according to the least squares formula (3), and calculate whether the iteration condition is met. If it is met, the direction vector is output as the final estimated direction. If it is not met, the direction vector is used as the new direction vector estimation, and steps 3 to 6 are repeated until the iteration condition is met and the direction is output;

[0076] The iteration conditions are:

[0077]

[0078] Among them, max(·) is the maximum value of the calculated vector; |·| is the absolute value; ε>0 is the manually set threshold; the superscript is the iteration number, represents the direction vector calculated for the kth time, Represents the direction vector calculated for the k+1th time.

[0079] An embodiment of the present invention provides a new direction estimation method that takes into account the characteristics of sound ray curvature and the receiving array structure. By approximating the sound wave as a plane wave and establishing a mathematical relationship between the time difference of arrival (TDOA) and the direction vector, the TDOA is used as the observation value, and the direction vector estimate is calculated using the weighted least squares method. The equivalent weights of the observation value are then calculated based on an equivalent weight function. The original observation value weight matrix is ​​then replaced with the equivalent weight matrix, and the direction vector is recalculated using the weighted least squares method. The equivalent weights and direction vector are iteratively calculated until the difference between two consecutive direction vector estimates is less than a manually set threshold. The direction vector estimate is then output as the direction of the multi-element stereo hydrophone array. This method utilizes the weighted iteration approach used in robust estimation to mitigate the effects of sound ray curvature that are not considered in the direction estimation function model. It also takes into account the effects of array element spacing and target orientation on the direction estimate, thereby improving the accuracy and reliability of direction estimation for the multi-element stereo hydrophone array.

[0080] like Figure 2 As shown, an embodiment of the present invention further provides an electronic device, comprising: a processor 201, a communications interface 202, a memory 203, and a communication bus 204, wherein the processor 201, the communications interface 202, and the memory 203 communicate with each other via the communication bus 204. The processor 201 can call the logic instructions in the memory 203 to execute the method in the above embodiment, which includes:

[0081] Step 1: Obtain the time when each hydrophone in the multi-element stereo hydrophone array receives the acoustic signal, calculate the observation value of the signal received by two adjacent hydrophones, approximate the acoustic wave as a plane wave, and establish the relationship between the direction vector and the observation value;

[0082] Step 2: Based on the relationship in step 1, use the identity matrix as the observation value weight matrix and calculate the direction vector estimate according to the weighted least squares method;

[0083] Step 3: Obtain an observation value residual vector based on the direction vector estimate and the observation vector; wherein the observation vector represents a sequence of observation values ​​arranged in the order of the hydrophone numbers in the multivariate stereo hydrophone array;

[0084] Step 4: Use the median method to standardize the observation residual vector to obtain the standardized residual vector;

[0085] Step 5: Calculate the equivalent weight of the observation value through the equivalent weight function based on the standardized residual vector to obtain the equivalent weight matrix;

[0086] Step 6: Use the equivalent weight matrix as the new observation value weight matrix and estimate the direction vector according to the least squares method; and calculate whether the iteration condition is met. If it is met, output the direction vector; if not, use the direction vector as the new direction vector estimate and repeat steps 3 to 6.

[0087] In addition, when the logic instructions in the above-mentioned memory 203 are implemented in the form of a software functional unit and sold or used as an independent product, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0088] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method for estimating the direction of a multi-element stereo hydrophone array, characterized in that: include: Step 1: Obtain the time when each hydrophone in the multi-element stereo hydrophone array receives the acoustic signal, calculate the observation value of the signal received by two adjacent hydrophones, approximate the acoustic wave as a plane wave, and establish a relationship between the direction vector and the observation value; wherein the relationship is: Among them, δ i,j represents the observed value of the signal received by two adjacent hydrophones, i and j represent the hydrophone numbers in the hydrophone array, t i and t j are the time when hydrophone i and j receive the acoustic signal, c is the underwater sound speed, p i and p j denote the position vectors of hydrophones i and j in the hydrophone array, d denotes the direction vector of the sound source, and N denotes the number of array elements, i.e., the number of stereo hydrophones; Step 2: Based on the relationship in step 1, the identity matrix is ​​used as the observation value weight matrix, and the direction vector estimation is calculated according to the weighted least squares method; Step 3: obtaining an observation value residual vector based on the direction vector estimate and the observation vector; wherein the observation vector represents a sequence of observation values ​​arranged in order of hydrophone numbers in the multi-element stereo hydrophone array; Step 4: Standardize the observed value residual vector using the median method to obtain a standardized residual vector; Step 5: Calculate the equivalent weight of the observation value based on the standardized residual vector through the equivalent weight function to obtain an equivalent weight matrix; Step 6: Use the equivalent weight matrix as the new observation value weight matrix and estimate the direction vector according to the least squares method; and calculate whether the iteration condition is met. If it is met, output the direction vector; if not, use the direction vector as the new direction vector estimate and repeat steps 3 to 6.

2. The method for estimating the direction of a multi-element stereo hydrophone array according to claim 1, wherein: In step 2, the direction vector estimate is calculated using the weighted least squares method, using formula (3): in, Denotes the direction vector estimation, δ=[δ 1,2 δ 2,3 …δ N-1,N ] T represents the observation vector, which is composed of all observation values ​​in the multivariate stereo hydrophone array, P represents the observation value weight matrix, ||·|| represents the modulus of the vector, A represents the position coefficient matrix, 3. The method for estimating the direction of a multi-element stereo hydrophone array according to claim 1, wherein: In step 3, the observation residual vector is calculated using formula (4): in, Denotes the direction vector estimation, δ=[δ 1,2 δ 2,3 …δ N-1,N ] T Represents the observation vector, v=[v1 v2…v N-1 ] T Represents the observation residual vector, A represents the position coefficient matrix, 4. The method for estimating the direction of a multi-element stereo hydrophone array according to claim 1, wherein: The step 4 specifically includes: Step 401: Calculate the unit weighted mean error using the median method; Step 402: Calculate a standardized residual vector using the unit weighted mean error and the observation residual vector.

5. The method for estimating the direction of a multi-element stereo hydrophone array according to claim 4, wherein: In step 401, the unit weighted mean error is calculated using formula (5): in, Represents the unit weighted mean error, P i Represents the i-th diagonal element of the observation weight matrix, v i represents the i-th observation residual of the observation residual vector, and med{·} represents the median.

6. The method for estimating the direction of a multi-element stereo hydrophone array according to claim 4, wherein: In step 402, the normalized residual in the normalized residual vector is calculated using formula (6): in, represents the i-th standardized residual in the standardized residual vector, Denotes the unit weight error, v i Represents the residual of the i-th observation in the observation residual vector.

7. The method for estimating the direction of a multi-element stereo hydrophone array according to claim 1, wherein: In step 5, the equivalent weight of the observation value is calculated using the IGGIII equivalent weight function. The calculation formula is as follows: in, represents the i-th standardized residual in the standardized residual vector, Represents the equivalent weight, which is the i-th diagonal element of the equivalent weight matrix, k0 and k1 represent the manually set parameters, P i Represents the i-th element of the observation weight matrix.

8. The method for estimating the direction of a multi-element stereo hydrophone array according to claim 1, wherein: In step 6, the iteration condition is: Among them, max(·) means calculating the maximum value of the vector; |·| means taking the absolute value; ε represents the manually set threshold; represents the direction vector calculated for the kth time, Represents the direction vector calculated for the k+1th time.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the method according to any one of claims 1 to 8 is implemented.

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