Underwater acoustic source positioning method and device based on time difference of arrival measurement model

Abstract

This application relates to an underwater sound source localization method and apparatus based on a time difference of arrival (TDOA) measurement model. The underwater sound source localization method includes: constructing an average sound velocity model for the receiving node of the sound source using the equal area method; calculating the average sound velocity of the receiving node based on its depth using the average sound velocity model; constructing a first estimation observation equation based on the average sound velocity and the TDOA measurement model of the receiving node; calculating a first estimation result of the sound source location based on the first estimation observation equation and the measured value of the sound source location; and performing error compensation based on a second estimation result obtained by correcting for deviations in the first estimation result to obtain a final estimation result of the sound source location. It constructs an average sound velocity model using the equal area method, calculates the estimated sound source location using the obtained average sound velocity, and obtains the sound source location through deviation correction and error compensation, thus achieving accurate localization of underwater sound sources.

Description

Technical Field

[0001] This application relates to the field of underwater positioning technology, and in particular to an underwater sound source positioning method and apparatus based on a time difference of arrival measurement model. Background Technology

[0002] The location of underwater targets (such as submarines, underwater vehicles, and underwater facilities) is a key supporting technology for activities such as marine resource development, military anti-submarine warfare, scientific research, underwater engineering, and search and rescue. Unlike the location of targets on the sea surface and land, due to the strong attenuation effect of seawater on electromagnetic waves and light waves, sound waves become the only effective carrier for underwater information transmission. Therefore, the location of underwater targets mainly relies on underwater acoustic methods.

[0003] Currently, related technologies utilize acoustic beacon networks at known locations to measure distance or direction using the target's acoustic signals, such as the hyperbolic intersection method based on time difference of arrival. However, due to the influence of complex water body temperature, salinity, and pressure distributions, the speed of sound is not constant when propagating in the ocean. Current positioning schemes that rely on the assumption of constant sound speed suffer from low accuracy in locating underwater sound sources.

[0004] There is currently no effective solution to the problem of low accuracy in underwater sound source localization in related technologies. Summary of the Invention

[0005] This embodiment provides an underwater sound source localization method and apparatus based on a time difference of arrival measurement model to solve the problem of low accuracy in underwater sound source localization in related technologies.

[0006] In the first aspect, this embodiment provides an underwater sound source localization method based on a time difference of arrival measurement model, including: constructing an average sound velocity model of the receiving node of the sound source using the equal area method;

[0007] Based on the depth of the receiving node, the average sound speed of the receiving node is calculated using the average sound speed model.

[0008] Based on the average sound speed and the time difference of arrival measurement model of the receiving node, the first estimated observation equation is constructed.

[0009] Based on the first estimation observation equation and the measured value of the sound source location, the first estimation result of the sound source location is calculated;

[0010] Based on the second estimation result obtained by correcting the deviation of the first estimation result, error compensation is performed to obtain the final estimation result of the sound source location.

[0011] In some embodiments, the underwater sound source localization method based on the time difference of arrival measurement model further includes:

[0012] A constant gradient sound velocity profile model is pre-established, and the receiving node of the sound source is set in the constant gradient sound velocity profile model.

[0013] In some embodiments, the calculation of the average sound velocity of the receiving node based on the preset depth of the receiving node using the average sound velocity model includes:

[0014] The depth of the receiving node is input into the average sound speed model to perform an integral operation on the isogradient sound speed profile model, thereby obtaining the average sound speed.

[0015] In some embodiments, the step of performing error compensation based on the second estimation result obtained by bias correction of the first estimation result to obtain the final estimation result of the sound source location includes:

[0016] The first estimation result is corrected for deviation, a second estimation observation equation is constructed, and a second estimation result of the sound source location is calculated.

[0017] Based on the noise term in the second estimation observation equation, an error-compensated observation equation is constructed, and the error-compensated estimation result is calculated; the noise term includes measurement noise and the position error of the receiving node;

[0018] The error-compensated estimation result is superimposed on the second estimation result to obtain the final estimation result of the sound source location.

[0019] In some embodiments, the step of correcting the first estimation result for bias, constructing a second estimation observation equation, and calculating a second estimation result of the sound source location includes:

[0020] The first estimation result is corrected for bias by using the weighted least squares method to obtain the corrected estimation result;

[0021] Substituting the corrected estimation result into the first estimation observation equation, we obtain the second estimation observation equation;

[0022] The second estimation result is calculated based on the second estimation observation equation.

[0023] In some embodiments, calculating the second estimation result based on the second estimation observation equation includes:

[0024] The second estimation result is obtained by solving the second estimated observation equation using the weighted least squares method.

[0025] In some embodiments, the step of constructing an error-compensated observation equation based on the noise term in the second estimated observation equation and calculating the error-compensated estimation result includes:

[0026] Perform a Taylor expansion on the noise term, retain the first-order noise term after the Taylor expansion, and construct the error compensation observation equation.

[0027] Based on the aforementioned error compensation observation equation, the error compensation estimation result is calculated using the weighted least squares method.

[0028] Secondly, this embodiment provides an underwater sound source localization device based on a time difference of arrival measurement model, comprising: a preset module, a first estimation module, and a final estimation module; wherein:

[0029] The preset module is used to construct an average sound velocity model of the receiving node of the sound source using the equal area method; and to calculate the average sound velocity of the receiving node based on the depth of the receiving node using the average sound velocity model.

[0030] The first estimation module is used to construct a first estimation observation equation based on the average sound speed and the time difference of arrival measurement model of the receiving node; and to calculate a first estimation result of the sound source location based on the first estimation observation equation and the measured value of the sound source location.

[0031] The final estimation module is used to perform error compensation based on the second estimation result obtained by correcting the deviation of the first estimation result, and obtain the final estimation result of the sound source location.

[0032] Thirdly, this embodiment provides an electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the underwater sound source localization method based on the time difference of arrival measurement model described in the first aspect.

[0033] Fourthly, this embodiment provides a storage medium storing a computer program that, when executed by a processor, implements the steps of the underwater sound source localization method based on the time difference of arrival measurement model described in the first aspect.

[0034] Compared with related technologies, the underwater sound source localization method and apparatus based on the time difference of arrival (TDOA) measurement model provided in this embodiment are as follows: First, the underwater sound source localization method based on the TDOA measurement model first constructs an average sound velocity model of the receiving node of the sound source using the equal area method. Second, based on the depth of the receiving node, the average sound velocity of the receiving node is calculated using the average sound velocity model. Then, based on the average sound velocity and the TDOA measurement model of the receiving node, a first estimation observation equation is constructed. Further, based on the first estimation observation equation and the measured value of the sound source location, a first estimation result of the sound source location is calculated. Finally, based on a second estimation result obtained by correcting the deviation of the first estimation result, error compensation is performed to obtain the final estimation result of the sound source location. It constructs an average sound velocity model using the equal area method, equating the complex, depth-dependent, curved propagation of sound rays to straight-line propagation at the average sound velocity. Then, based on the average sound velocity obtained from the average sound velocity model, the estimated sound source location is calculated. After deviation correction and error compensation, the sound source is located, achieving accurate localization of the underwater sound source.

[0035] Details of one or more embodiments of this application are set forth in the following drawings and description to make other features, objects and advantages of this application more readily apparent. Attached Figure Description

[0036] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0037] Figure 1 This is a hardware structure block diagram of a terminal for an underwater sound source localization method based on a time difference of arrival measurement model according to an embodiment of this application.

[0038] Figure 2 This is a flowchart of an underwater sound source localization method based on a time difference of arrival measurement model according to an embodiment of this application;

[0039] Figure 3 This is a preferred flowchart of the underwater sound source localization method based on the time difference of arrival measurement model in this embodiment;

[0040] Figure 4 This is a schematic diagram of a simulation scenario setting for an underwater sound source localization method based on a time difference of arrival measurement model according to an embodiment of this application;

[0041] Figure 5 This is a schematic diagram illustrating the relationship between sound velocity and depth in an underwater sound source localization method based on a time difference of arrival measurement model according to an embodiment of this application.

[0042] Figure 6This is a performance analysis diagram of an underwater sound source localization method based on a time difference of arrival measurement model according to an embodiment of this application;

[0043] Figure 7 This is a structural block diagram of an underwater sound source localization device based on a time difference of arrival measurement model according to an embodiment of this application. Detailed Implementation

[0044] To better understand the purpose, technical solution, and advantages of this application, the application is described and illustrated below in conjunction with the accompanying drawings and embodiments.

[0045] Unless otherwise defined, the technical or scientific terms used in this application shall have the general meaning understood by one of ordinary skill in the art to which this application pertains. Words such as “a,” “an,” “an,” “the,” “the,” and “these” used in this application do not indicate quantitative limitation and may be singular or plural. The terms “comprising,” “including,” “having,” and any variations thereof used in this application are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or device that comprises a series of steps or modules (units) is not limited to the listed steps or modules (units) but may include steps or modules (units) not listed, or may include other steps or modules (units) inherent to these processes, methods, products, or devices. Words such as “connected,” “linked,” and “coupled” used in this application are not limited to physical or mechanical connections but may include electrical connections, whether direct or indirect. “Multiple” used in this application refers to two or more. “And / or” describes the relationship between related objects, indicating that three relationships may exist; for example, “A and / or B” can represent: A alone, A and B simultaneously, and B alone. Normally, the character " / " indicates that the objects before and after it are in an "or" relationship. The terms "first," "second," "third," etc., used in this application are merely to distinguish similar objects and do not represent a specific order of objects.

[0046] The method embodiments provided in this example can be executed on a terminal, computer, or similar electronic device with a certain computing power. For example, it can run on a terminal. Figure 1 This is a hardware structure block diagram of a terminal for an underwater sound source localization method based on a time difference of arrival measurement model, according to an embodiment of this application. Figure 1 As shown, a terminal may include one or more ( Figure 1(Only one is shown) A processor 102 and a memory 104 for storing data. The processor 102 may be, but is not limited to, a processing device such as a microprocessor (MCU) or a programmable logic device (FPGA). The processor 102 includes an algorithm section capable of performing data processing. The terminal may also include a transmission device 106 for communication functions and an input / output device 108. In one example, the input / output device 108 can receive target radiation signals from a sound source sensor and output the location of the target sound source. The sound source sensor is responsible for receiving the radiation signals emitted by the target sound source and converting the raw acoustic signals into electrical signals. The sound source sensor output includes multiple synchronized sound signals or pre-processed arrival time data, which are transmitted to the terminal via wired or wireless means. Those skilled in the art will understand that... Figure 1 The structure shown is for illustrative purposes only and does not limit the structure of the terminal described above. For example, the terminal may also include components that are larger than... Figure 1 The more or fewer components shown, or having the same Figure 1 The different configurations shown are illustrated.

[0047] The memory 104 can be used to store computer programs, such as application software programs and modules, like the computer program corresponding to the underwater sound source localization method based on the time difference of arrival measurement model in this embodiment, as well as the storage of input and output data. The processor 102 executes various functional applications and data processing by running the computer programs stored in the memory 104, thereby implementing the above-described method. The memory 104 may include high-speed random access memory, and may also include non-volatile memory, such as one or more magnetic storage devices, flash memory, or other non-volatile solid-state memory. In some instances, the memory 104 may further include memory remotely located relative to the processor 102, and these remote memories can be connected to the terminal via a network. Examples of such networks include, but are not limited to, the Internet, corporate intranets, local area networks, mobile communication networks, and combinations thereof.

[0048] The transmission device 106 is used to receive or send data via a network. This network includes a wireless network provided by the terminal's communication provider. In one example, the transmission device 106 includes a Network Interface Controller (NIC), which can connect to other network devices via a base station to communicate with the Internet. In another example, the transmission device 106 can be a Radio Frequency (RF) module used for wireless communication with the Internet.

[0049] This embodiment provides an underwater sound source localization method based on a time difference of arrival measurement model. Figure 2This is a flowchart of an underwater sound source localization method based on a time difference of arrival measurement model according to an embodiment of this application, as follows: Figure 2 As shown, the process includes the following steps:

[0050] Step S210: Construct the average sound velocity model of the receiving node of the sound source using the equal area method.

[0051] In real-world acoustic positioning scenarios, the speed of sound is not uniformly distributed in space due to variations in seawater temperature and salinity, or temperature gradients in the air, causing the sound wave propagation path to bend. If the assumption of a globally constant speed of sound is still adopted, treating sound waves as propagating in a straight line, it will introduce sound source positioning errors. To address this issue, this embodiment uses the equal-area method to model the sound speed field.

[0052] The equal-area method is an effective modeling strategy for reasonably simplifying complex sound velocity fields. The core idea is that when a sound wave propagates from a sound source to a receiving node, its main energy traverses a certain spatial region between the two. The equal-area method transforms the problem of propagation along a curved path into the problem of propagation along a straight path at a certain average sound velocity. This average sound velocity is not a simple arithmetic average, but is determined by area-weighted integration based on the true sound velocity profile of the region near the line connecting the sound source and the receiving node. The average sound velocity model constructed based on the time-of-arrival measurement model is a set of functional relationships with the positions of the sound source and the receiving node as independent variables. For each receiving node, the model outputs a corresponding average sound velocity value, which can be expressed as a calculation formula or a lookup table.

[0053] Step S220: Based on the depth of the receiving node, the average sound speed of the receiving node is calculated using the average sound speed model.

[0054] Specifically, given that the location of the sound source is known or given, the coordinates of the sound source and the coordinates of each receiving node are input into the average sound velocity model constructed in step S210. Combined with the pre-acquired environmental sound velocity profile data, the average sound velocity value reflecting the acoustic characteristics of the actual propagation path can be calculated for each receiving node. This calculation process is based on the integration principle of the time difference of arrival measurement model, and automatically completes the weighted average of the sound velocity along the propagation path between the sound source and the receiving node through the average sound velocity model.

[0055] Step S230: Based on the average speed of sound and the time difference of arrival measurement model of the receiving node, the first estimated observation equation is constructed.

[0056] Specifically, the Time Difference of Arrival (TDOA) measurement model is a mathematical model used in sound source localization systems to establish the relationship between the location of a sound source and the time difference in signal arrival at different receiving nodes. The basic principle of the TDOA measurement model is that the signal emitted by the sound source propagates through a medium, and because the distance between each receiving node and the sound source is different, the time it takes for the signal to arrive at each node is also different. By measuring the time difference of the same signal arriving at any two nodes, an observation equation can be constructed with the sound source location as the unknown.

[0057] Based on the average speed of sound calculated in the preceding steps, and combined with the time difference of arrival measurement model, the first estimated observation equation can be constructed as follows:

[0058] ;

[0059] in, The location of the sound source to be estimated is defined as follows: the unknown parameter vector is defined as follows: , A three-dimensional spatial coordinate vector representing the sound source; It is the inner product of the sound source coordinate vectors, and its value is equal to the square of the distance from the sound source to the origin of the spatial coordinate system; This represents the true geometric distance from the sound source to the reference receiving node. This refers to the error in the receiving node's position. In one embodiment, s1 can be set as the reference node. The formula for the coefficient matrix h1 is:

[0060] ;

[0061] Here, h1 is a column vector composed of known observation data, including noisy measurements. Write in vector form s i Let represent the coordinate vector of the known position of the i-th receiving node. It is the dot product of the node position vectors, representing the square of the distance from the receiving node to the origin, c. i Let G1 represent the average speed of sound from the sound source to the i-th receiving node. The formula for the coefficient matrix G1 is:

[0062] ;

[0063] Here, G1 is an M-1 row, 3 column matrix, where M represents the total number of receiving nodes and M-1 represents the number of independent TDOA observations. Taking the first receiving node as a reference, the remaining M-1 nodes are paired with the first receiving node to form observation pairs; each row of the matrix corresponds to one such observation pair. The formula for the coefficient matrix C1 is:

[0064] ;

[0065] Where, diag[] represents a diagonal matrix. This represents the actual distance from the sound source to the Mth receiving node. The local average sound velocity or ambient background sound velocity at the Mth receiving node is obtained through a sound velocity profile. The formula for the coefficient matrix D1 is:

[0066] ;

[0067] in, The degree of first-order impact of a small change in the reference node position s1 on its own computational complexity. This represents the initial distance or related quantity calculated based on the calibration position s1.

[0068] Step S240: Based on the first estimated observation equation and the measured value of the sound source location, calculate the first estimated result of the sound source location.

[0069] Specifically, based on the constructed linearized equations ,in To account for the residual terms that include noise and error, a weighting matrix W1 is introduced. This weighting matrix is ​​the inverse of the residual covariance matrix, and its function is to assign different weights to observation equations with different reliability. Observations with smaller residual variances have larger weights and greater influence in the estimation. Based on this, the weighted least squares method is used to solve for the location of the sound source to be estimated. The calculation formula is as follows:

[0070] ;

[0071] in, for The optimal estimate is obtained. Compared to ordinary least squares, the weighted least squares method can effectively suppress the interference of observations with large errors, improve the accuracy and stability of the initial estimate, and provide a higher quality initial solution for subsequent calculations.

[0072] Step S250: Based on the second estimation result obtained by correcting the deviation of the first estimation result, error compensation is performed to obtain the final estimation result of the sound source location.

[0073] Specifically, firstly, to address the systematic biases introduced in the first estimation result due to model linearization and sound velocity approximation, a second estimation observation equation is constructed and solved using the weighted least squares method to obtain a second estimation result after bias correction of the first estimation result. Based on this, considering the influence of measurement noise and receiver node position errors that have not been completely eliminated in the observation equation, an error compensation observation equation is constructed to estimate the residual random and systematic errors in the second estimation result and calculate the corresponding error compensation amount. Finally, this error compensation amount is superimposed on the second estimation result to correct the sound source position, thereby obtaining a final estimation result that is closer to the true value and has better statistical characteristics. This multi-stage progressive estimation strategy can progressively peel off and compensate for errors of different natures.

[0074] Compared to related technologies, conventional approaches typically rely on pre-deployed acoustic beacon arrays with accurate coordinates. They calculate the target's location by detecting the acoustic signals radiated by the target and extracting the time difference, phase, or azimuth information of its arrival at different nodes. However, the hyperbolic intersection localization method based on time difference of arrival faces challenges in real-world marine environments. The seawater medium is not homogeneous or static; its acoustic characteristics are influenced by multiple physical factors, including temperature stratification, salinity gradients, depth and pressure variations, and ocean currents. This results in a complex and dynamic distribution of sound speed across three-dimensional space and time. During actual propagation, sound waves refract due to changes in the sound speed profile, causing the propagation path to bend. This leads to systematic deviations in the ranging relationship derived from straight-line propagation and constant sound speed, resulting in low accuracy in current underwater sound source localization methods.

[0075] Steps S210 to S250 above involve: first, constructing an average sound velocity model for the receiving nodes of the sound source using the equal-area method; second, calculating the average sound velocity of the receiving nodes based on their depth using the average sound velocity model; further, constructing a first estimation observation equation based on the average sound velocity and the time difference of arrival measurement model of the receiving nodes; then, calculating a first estimation result of the sound source location based on the first estimation observation equation and the measured value of the sound source location; finally, performing error compensation based on a second estimation result obtained by correcting the deviation of the first estimation result to obtain the final estimation result of the sound source location. This method constructs an average sound velocity model using the equal-area method, transforming the complex, depth-dependent, curved propagation of sound rays into equivalent straight-line propagation at the average sound velocity. Compared to existing technologies, it does not rely on the assumption of a constant sound velocity, but instead determines the corresponding average sound velocity based on the depth of each receiving node, obtains the estimated sound source location from the average sound velocity, and then obtains the sound source location through deviation correction and error compensation, thus achieving accurate positioning of underwater sound sources.

[0076] Optionally, in one embodiment, the underwater sound source localization method based on the time difference of arrival measurement model may further include: pre-establishing an isogradient sound velocity profile model and setting a receiving node for the sound source in the isogradient sound velocity profile model.

[0077] Firstly, based on typical ocean hydrological conditions or measured statistical patterns, a constant-gradient sound velocity profile model can be established, where the sound velocity varies linearly with depth. Mathematically, this model can be expressed as c = az + b, where z represents depth, a is the sound velocity gradient, and b is the sound velocity value at the sea surface or a reference depth. This mathematical expression effectively characterizes the common vertical stratification of sound velocity in the ocean, providing a foundation for subsequent calculations of the equivalent average sound velocity.

[0078] After completing the sound velocity profile modeling, a receiver node array needs to be deployed and configured within the target water area. In this embodiment, typically M receiver nodes are set within a depth range of 0 meters to 1000 meters, and their specific locations are set as follows: The receivers can be randomly distributed or optimally deployed within a certain spatial range (e.g., within a horizontal region and a depth range) according to mission requirements to form an observation network with good geometric configuration. The coordinate vector s of the known position of each receiver node... i The measured data will be used as known input. Based on this, an isogradient sound velocity profile model will be established, which is based on the sound velocity profile and the node distribution. This isogradient sound velocity profile model correlates the sound source location, node location, and sound velocity profile with the measured time difference of arrival.

[0079] In this embodiment, by constructing an isogradient sound speed profile model, the excessive reliance of the traditional closed-loop weighted least squares algorithm on the assumption of constant sound speed or prior depth information can be effectively overcome.

[0080] In addition, in one embodiment, the average sound speed of the receiving node is calculated based on the preset depth of the receiving node using an average sound speed model, including: inputting the depth of the receiving node into the average sound speed model, and performing an integral operation on the isogradient sound speed profile model to obtain the average sound speed.

[0081] Using the known depths of the sound source and the receiving node, an average sound velocity model is input, which automatically determines the depth range covered by the sound wave propagation path. Then, the pre-constructed average sound velocity model is invoked. Internally, this model, based on the principle of equal area, performs integration and weighted averaging on a pre-established isogradient sound velocity profile within this depth range. A customized average sound velocity is calculated for each path from the sound source to a specific node. The formula for the average sound velocity is:

[0082] ;

[0083] Where z is the target depth. Let be the depth of the i-th receiving node, a be the sound speed gradient, and b be the sound speed at the sea surface.

[0084] Therefore, by combining the average sound speed, the theoretical value of TDOA for each node can be obtained. The expression for the theoretical value of TDOA is:

[0085] ;

[0086] in, This is the actual location of the receiving node, while the actual measured value... and theoretical value The relationship is , The measurement noise vector is given, and the measurement noise follows a Gaussian distribution with a mean of zero and a covariance matrix.

[0087] By performing path integration on the sound velocity profile in this embodiment, the complex spatially varying sound velocity field is transformed into an equivalent average sound velocity, thereby fundamentally correcting the error introduced by the bending propagation of sound waves and laying an accurate data foundation for subsequent sound source localization.

[0088] In one embodiment, based on a second estimation result obtained by correcting for deviations in the first estimation result, error compensation is performed to obtain a final estimation result of the sound source location, including:

[0089] The first estimation result is corrected for deviation, a second estimation observation equation is constructed, and the second estimation result of the sound source location is calculated. Based on the noise term in the second estimation observation equation, an error compensation observation equation is constructed, and the error compensation estimation result is calculated. The noise term includes measurement noise and the position error of the receiving node. The error compensation estimation result is superimposed on the second estimation result to obtain the final estimation result of the sound source location.

[0090] After obtaining the initial estimate of the sound source location, a two-stage progressive optimization process, including bias correction and error compensation, is used to improve the accuracy and reliability of the final positioning result. First, the initial estimate contains biases due to model linearization and sound velocity equivalence processing. Therefore, a second estimation observation equation is reconstructed based on the initial estimate and the bias. This equation, by incorporating propagation geometry or introducing higher-order correction terms, effectively reduces model errors caused by linear approximation. Subsequently, the weighted least squares method is used to solve this equation, yielding a second estimate with corrected bias. This result is theoretically closer to the true location of the sound source, but it does not completely eliminate the influence of random errors during measurement.

[0091] Since the second estimation result is still constrained by two main types of random errors—measurement noise of the receiving node regarding signal arrival time and calibration error of the receiving node's own spatial position—an independent error-compensated observation equation is constructed to suppress the influence of these errors. The comprehensive deviation caused by the error to the current position estimation is calculated using least-squares estimation; this is the error-compensated estimation result. Finally, the calculated error-compensated estimation result is superimposed on the second estimation result to correct the sound source location, ultimately outputting a final sound source localization estimate with enhanced accuracy and robustness.

[0092] In one embodiment, the first estimation result is corrected for bias, a second estimation observation equation is constructed, and a second estimation result of the sound source location is calculated, including:

[0093] The first estimation result is corrected for bias by using weighted least squares to obtain the corrected estimation result; the corrected estimation result is substituted into the first estimation observation equation to obtain the second estimation observation equation; the second estimation result is calculated based on the second estimation observation equation.

[0094] Systematic bias correction of the first estimation result using weighted least squares is a key step in improving positioning accuracy. In this embodiment, the first estimation result is first... Consider it as a bias The approximate solution, that is, let Substituting this into the first estimation measurement equation, a formula is constructed using the deviation quantity. The new observation equation for the unknown vector is called the second estimated observation equation. This equation has the form: Among them, let The weighted least squares method is applied again to the equation to solve it. This allows us to obtain the optimal estimate of the deviation. Finally, the correction amount... Superimposed on the first estimation result, we obtain The result.

[0095] By constructing and solving the second estimation observation equation with the deviation as the unknown quantity in this embodiment, the first-order error introduced by the linearization approximation of the model is corrected, thereby improving the consistency and accuracy of the sound source location estimation.

[0096] In one embodiment, calculating the second estimation result based on the second estimated observation equation includes: solving the second estimated observation equation using the weighted least squares method to calculate the second estimation result.

[0097] Corrected and deviation The corrected sound source location vector can be obtained by adding the first N components of the two vectors. Specifically, the corrected sound source location vector... The formula is:

[0098] ;

[0099] in, Represents from vector Extract the first to Nth elements, where N represents the spatial dimension. For example, when N is 3, it represents three-dimensional space. Represents the deviation vector Extract the first N elements. This bias vector contains the amount of correction needed to the position estimate.

[0100] In this embodiment, the weighted least squares method is used to optimally solve the second estimated observation equation. Considering the different reliability of each observation, a second estimation result with smaller bias is obtained.

[0101] Furthermore, in one embodiment, an error-compensated observation equation is constructed based on the noise term in the second estimated observation equation, and the error-compensated estimation result is calculated, including: performing a Taylor expansion on the noise term, retaining the first-order noise term after the Taylor expansion, and constructing the error-compensated observation equation; and calculating the error-compensated estimation result using the weighted least squares method based on the error-compensated observation equation.

[0102] By using actual TDOA measurements Decomposed into theoretical truth values With measurement noise The summation is then performed, and a first-order Taylor expansion is applied to the theoretical truth value at some operating point (i.e., the current estimate). After expansion, it will be expressed as an approximation based on the current estimate. This is added to the sum of first-order bias terms caused by various error sources. Specifically, the first-order Taylor expansion of the TDOA observation equation is:

[0103] ;

[0104] in, It is the sound speed gradient error term. It is the partial derivative of TDOA with respect to gradient a. It is the estimation error of the sound speed gradient 'a'; It is the reference sound speed error term. It is the partial derivative of TDOA with respect to gradient b. It is the estimation error of the reference sound speed b; This is the sound source location error term. It is TDOA for gradient gradient vector, This is the estimation error of the sound source location; This is the receiver node position error term. It is TDOA for the position s of the i-th node. i gradient vector, This represents the calibration error at the position of the i-th node. Subsequently, the first-order noise term is retained and written in matrix form:

[0105] ;

[0106] Where h2 consists of the residual between the actual measured value and the calculated value based on the current estimate, the specific calculation formula is as follows:

[0107] G2 is the coefficient matrix of the estimation error of the sound source location. Each row corresponds to the transpose of the gradient vector of the TDOA formula. G2 associates the sound source location error with the observation residual. The specific calculation formula is as follows:

[0108] ;

[0109] ;

[0110] D2 is the coefficient matrix of the node position error, and the specific calculation formula is as follows:

[0111] ;

[0112] E2 is the coefficient matrix of the sound velocity gradient error, and the specific calculation formula is as follows:

[0113] ;

[0114] F2 is the coefficient matrix of the reference sound speed error, and the specific calculation formula is as follows:

[0115] ;

[0116] Solving by using the weighted least squares algorithm The optimal estimation result for:

[0117] ;

[0118] in, , It is the TDOA observation noise covariance matrix. It is the covariance matrix of the prior uncertainty of the sound source location. This is the uncertainty covariance matrix of the sound velocity gradient parameters. The final estimation result obtained is... for:

[0119] ;

[0120] in, It is the corrected sound source position vector.

[0121] Figure 3 This is a preferred flowchart of the underwater sound source localization method based on the time difference of arrival measurement model in this embodiment, as shown below. Figure 3 As shown, the underwater sound source localization method based on the time difference of arrival measurement model includes the following steps:

[0122] Step S301: Establish an isogradient sound velocity profile model.

[0123] Step S302: Deploy and mark the receiving nodes.

[0124] Step S303: Construct an average sound velocity model using the equal area method, and calculate the average sound velocity of each receiving node based on the average sound velocity model.

[0125] Step S304: Construct the first estimated measurement equation based on the average sound speed and time difference of arrival measurement model of the receiving node.

[0126] Step S305: Using the weighted least squares method, the first estimation result is calculated based on the measured value of the sound source location.

[0127] Step S306: Treat the first estimation result as an approximate solution with bias, substitute it into the first estimation observation equation, and derive the second estimation observation equation with the bias as the unknown quantity.

[0128] Step S307: Apply the weighted least squares method to solve the second estimated observation equation to obtain the optimal estimate of the bias.

[0129] Step S308: The optimal estimate of the deviation is superimposed with the first estimate to obtain the second estimate.

[0130] Step S309: For the noise term in the second estimation observation equation, construct the error compensation observation equation and calculate the error compensation estimation result.

[0131] Step S310: The error compensation estimation result is superimposed on the second estimation result to obtain the final estimation result of the sound source location.

[0132] In steps S301 to S310 above, this embodiment calculates the equivalent average sound velocity using the equal area method, transforming the complex sound ray bending propagation problem into an equivalent constant sound velocity model. A closed-form coarse estimate of the sound source location is then directly obtained using the weighted least squares method, completely eliminating the dependence on initial iteration values. Subsequently, using the coarse estimate as the Taylor expansion point, an accurate isogradient sound velocity profile propagation model is introduced to construct a linear observation equation regarding the sound source location deviation. The weighted least squares method is then used again for system error compensation and precise estimation. This allows the underwater sound source localization method based on the time difference of arrival measurement model in this embodiment to effectively compensate for the sound ray bending effect without requiring initial grazing angles and initial position values. Furthermore, it overcomes the problems of traditional iterative algorithms being prone to divergence due to sensitivity to initial values, and the inaccurate localization caused by the constant sound velocity model neglecting the sound velocity profile. This achieves an underwater localization method that combines high robustness, high accuracy, and high computational efficiency.

[0133] Figure 4 This is a schematic diagram of a simulation scenario setting for an underwater sound source localization method based on a time difference of arrival measurement model according to an embodiment of this application. Figure 4 A three-dimensional coordinate system is used, where the vertical axis (z-axis) represents depth in meters, with a scale ranging from 0 to 1000 meters, clearly defining the vertical span of the water column. The horizontal axes include the x-axis and y-axis, both in meters. Figure 4 middle" “★” indicates the location of the receiving node sensor, and “★” indicates the location of the sound source. Figure 5 This is a schematic diagram illustrating the relationship between sound velocity and depth in an underwater sound source localization method based on a time difference of arrival measurement model, according to an embodiment of this application. Figure 5 The horizontal axis represents the speed of sound, in meters per second, and the vertical axis represents depth, in meters. (Combined) Figure 4 and Figure 5 In one embodiment, the information sets the relationship between sound speed and depth as follows: Set the sound source location as... Set the locations of 8 receiving nodes They are respectively , , , , , , , .

[0134] Figure 6 This is a performance analysis diagram of an underwater sound source localization method based on a time difference of arrival measurement model according to an embodiment of this application. Figure 6 The x-axis represents the variance of the time-of-arrival measurement noise. The values ​​are expressed in decibels (dB), with the ordinate representing the root mean square error (RMSE) in meters. The underwater sound source localization method (AveTe) based on the time difference of arrival (TDOA) model in this application exhibits a negative correlation between its localization accuracy and noise variance, and its RMSE approaches the theoretically optimal Cramer-Rao lower bound (CRLB), demonstrating that this method has near-theoretical estimation efficiency in environments with non-uniform sound speeds. In contrast, traditional algorithms based on the constant sound speed assumption, including the Two-stage Weighted Least Squares with Constant soundspeed (TWLS-C) algorithm and the Direct Navigation Solution for Positioning (DNSP), fail to approach the CRLB under all noise levels, validating the necessity of sound speed gradient modeling. Furthermore, although the (AveTe-GN) scheme, which uses the results of the underwater sound source localization method based on the time difference of arrival measurement model of this application as the initial value of the Gauss-Newton method, can eventually approximate CRLB, it requires a higher low-noise threshold, reflecting that the iterative method is more sensitive to noise. In contrast, the underwater sound source localization method based on the time difference of arrival measurement model of this application can provide a stable and near-optimal solution under moderate noise conditions, demonstrating its comprehensive advantages in accuracy and robustness.

[0135] Figure 7 This is a structural block diagram of an underwater sound source locator 70 based on a time difference of arrival measurement model according to an embodiment of this application, as shown below. Figure 7 As shown, the underwater sound source localization device 70 based on the time difference of arrival measurement model includes: a preset module 72, a first estimation module 74, and a final estimation module 76; wherein: the preset module 72 is used to construct an average sound velocity model of the receiving node of the sound source using the equal area method; and calculate the average sound velocity of the receiving node based on the depth of the receiving node using the average sound velocity model; the first estimation module 74 is used to construct a first estimation observation equation based on the average sound velocity and the time difference of arrival measurement model of the receiving node; and calculate a first estimation result of the sound source location based on the first estimation observation equation and the measured value of the sound source location; the final estimation module 76 is used to perform error compensation based on a second estimation result obtained by deviation correction of the first estimation result, and obtain a final estimation result of the sound source location.

[0136] The device provided in this embodiment improves upon traditional positioning methods that rely on the assumption of a constant sound velocity or accurate prior depth information. The underwater sound source positioning device based on the time difference of arrival (TDOA) measurement model dynamically constructs and calculates the average sound velocity through a preset module, overcoming the sound wave bending effect caused by spatial variations in sound velocity. Furthermore, it performs preliminary positioning through a first estimation module, followed by a two-step optimization process of deviation correction and error compensation through a final estimation module. This ultimately improves the overall accuracy, robustness, and engineering practicality of sound source positioning in complex underwater environments.

[0137] It should be noted that the above modules can be functional modules or program modules, and can be implemented through software or hardware. For modules implemented through hardware, the above modules can reside in the same processor; or the above modules can be located in different processors in any combination.

[0138] This embodiment also provides an electronic device including a memory and a processor, the memory storing a computer program and the processor being configured to run the computer program to perform the steps in any of the above method embodiments.

[0139] Optionally, the electronic device may further include a transmission device and an input / output device, wherein the transmission device is connected to the processor and the input / output device is connected to the processor.

[0140] Optionally, in this embodiment, the processor can be configured to perform the following steps via a computer program:

[0141] S1, using the equal area method, construct the average sound velocity model of the receiving node of the sound source;

[0142] S2, based on the depth of the receiving node, calculates the average sound velocity of the receiving node using the average sound velocity model;

[0143] S3. Based on the average speed of sound and the time difference of arrival measurement model of the receiving node, the first estimated observation equation is constructed.

[0144] S4. Based on the first estimated observation equation and the measured value of the sound source location, the first estimated result of the sound source location is calculated.

[0145] S5. Based on the second estimation result obtained by correcting the deviation of the first estimation result, error compensation is performed to obtain the final estimation result of the sound source location.

[0146] It should be noted that the specific examples in this embodiment can refer to the examples described in the above embodiments and optional implementations, and will not be repeated in this embodiment.

[0147] Furthermore, in conjunction with the underwater sound source localization method based on the time difference of arrival (TDOA) measurement model provided in the above embodiments, this embodiment can also provide a storage medium for implementation. This storage medium stores a computer program; when executed by a processor, the computer program implements any of the underwater sound source localization methods based on the TDOA measurement model described in the above embodiments.

[0148] It should be understood that the specific embodiments described herein are merely illustrative of the application and not intended to limit it. All other embodiments derived by those skilled in the art based on the embodiments provided in this application without inventive effort are within the scope of protection of this application.

[0149] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties.

[0150] Obviously, the accompanying drawings are merely some examples or embodiments of this application. Those skilled in the art can apply this application to other similar situations based on these drawings without any creative effort. Furthermore, it is understood that although the work done in this development process may be complex and lengthy, for those skilled in the art, certain design, manufacturing, or production modifications made based on the technical content disclosed in this application are merely conventional technical means and should not be considered as insufficient disclosure of this application.

[0151] The term "embodiment" in this application refers to a specific feature, structure, or characteristic described in connection with an embodiment that may be included in at least one embodiment of this application. The appearance of this phrase in various places in the specification does not necessarily imply the same embodiment, nor does it imply that it is mutually exclusive with or independent of other embodiments. It will be clearly or implicitly understood by those skilled in the art that the embodiments described in this application may be combined with other embodiments without conflict.

[0152] The above embodiments merely illustrate several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of patent protection. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the appended claims.

Claims

1. A method for locating underwater sound sources based on a time difference of arrival (TDOA) measurement model, characterized in that, include: The average sound velocity model of the receiving node of the sound source is constructed using the equal area method. Based on the depth of the receiving node, the average sound speed of the receiving node is calculated using the average sound speed model. Based on the average sound speed and the time difference of arrival measurement model of the receiving node, the first estimated observation equation is constructed. Based on the first estimation observation equation and the measured value of the sound source location, the first estimation result of the sound source location is calculated; Based on the second estimation result obtained by correcting the deviation of the first estimation result, error compensation is performed to obtain the final estimation result of the sound source location.

2. The underwater sound source localization method based on the time difference of arrival measurement model according to claim 1, characterized in that, Also includes: A constant gradient sound velocity profile model is pre-established, and the receiving node of the sound source is set in the constant gradient sound velocity profile model.

3. The underwater sound source localization method based on the time difference of arrival measurement model according to claim 2, characterized in that, The average sound velocity of the receiving node is calculated based on the preset depth of the receiving node using the average sound velocity model, including: The depth of the receiving node is input into the average sound speed model to perform an integral operation on the isogradient sound speed profile model, thereby obtaining the average sound speed.

4. The underwater sound source localization method based on the time difference of arrival measurement model according to claim 1, characterized in that, The second estimation result, obtained by correcting the deviation of the first estimation result, is used to compensate for errors and obtain the final estimation result of the sound source location, including: The first estimation result is corrected for deviation, a second estimation observation equation is constructed, and a second estimation result of the sound source location is calculated. Based on the noise term in the second estimation observation equation, an error-compensated observation equation is constructed, and the error-compensated estimation result is calculated; the noise term includes measurement noise and the position error of the receiving node; The error-compensated estimation result is superimposed on the second estimation result to obtain the final estimation result of the sound source location.

5. The underwater sound source localization method based on the time difference of arrival measurement model according to claim 4, characterized in that, The step of correcting the first estimation result for bias, constructing a second estimation observation equation, and calculating a second estimation result of the sound source location includes: The first estimation result is corrected for bias by using the weighted least squares method to obtain the corrected estimation result; Substituting the corrected estimation result into the first estimation observation equation, we obtain the second estimation observation equation; The second estimation result is calculated based on the second estimation observation equation.

6. The underwater sound source localization method based on the time difference of arrival measurement model according to claim 5, characterized in that, The step of calculating the second estimation result based on the second estimation observation equation includes: The second estimation result is obtained by solving the second estimated observation equation using the weighted least squares method.

7. The underwater sound source localization method based on the time difference of arrival measurement model according to claim 4, characterized in that, The step of constructing an error-compensated observation equation based on the noise term in the second estimated observation equation and calculating the error-compensated estimation result includes: Perform a Taylor expansion on the noise term, retain the first-order noise term after the Taylor expansion, and construct the error compensation observation equation. Based on the aforementioned error compensation observation equation, the error compensation estimation result is calculated using the weighted least squares method.

8. An underwater acoustic source localization device based on a time difference of arrival measurement model, characterized in that, include: The module consists of a preset module, a first estimation module, and a final estimation module; wherein: The preset module is used to construct an average sound velocity model of the receiving node of the sound source using the equal area method; and to calculate the average sound velocity of the receiving node based on the depth of the receiving node using the average sound velocity model. The first estimation module is used to construct a first estimation observation equation based on the average sound speed and the time difference of arrival measurement model of the receiving node; and to calculate a first estimation result of the sound source location based on the first estimation observation equation and the measured value of the sound source location. The final estimation module is used to perform error compensation based on the second estimation result obtained by correcting the deviation of the first estimation result, and obtain the final estimation result of the sound source location.

9. An electronic device comprising a memory and a processor, characterized in that, The memory stores a computer program, and the processor is configured to run the computer program to perform the underwater sound source localization method based on the time difference of arrival measurement model as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the underwater sound source localization method based on the time difference of arrival measurement model as described in any one of claims 1 to 7.

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