Method, device and equipment for fusion positioning of underwater target and medium

Abstract

The invention provides a method, a device, equipment and a medium for fusion positioning of an underwater target, and the method aims at the positioning problem of an underwater sensor, constructs a time difference of arrival model which considers node drift and measurement noise at the same time, forms a unified error description, builds an FP positioning model on the basis, and achieves the fusion positioning of an underwater target through a positive semidefinite programming and second-order cone relaxation technology. According to the method, a non-convex problem is converted into a convex optimization expression model, then an interior point method is used for solving to obtain a result matrix, then a positioning initial value is obtained through calculation, and finally a final positioning result is obtained through least square secondary correction. On the premise that hardware complexity and synchronization difficulty are not increased, the influence of position errors of sensor nodes and Gaussian white noise in measurement on positioning performance is effectively restrained, simulation results show that the method is higher in positioning precision and higher in robustness to environment and parameter disturbance, and the method has remarkable engineering application advantages.

Description

Technical Field

[0001] This invention belongs to the field of underwater multi-sensor target localization technology, specifically relating to a method, apparatus, equipment, and medium for fusion localization of underwater targets. Background Technology

[0002] Underwater acoustic sensor networks (UASNs), which use acoustic information as their carrier, offer advantages such as lower cost, convenient covert deployment, and strong adaptability to complex environments, leading to a significant expansion in their application scope in recent years. For positioning requirements of underwater acoustic sensor networks, selectable measurements include: Time of Arrival (TOA), Time Difference of Arrival (TDOA), Angle of Arrival (AOA), and Received Signal Strength (RSS). In complex sea conditions, among existing technologies, TDOA offers better overall cost-effectiveness. It suppresses common bias and transmission time uncertainty through time delay differences between multiple stations, requiring only synchronization between receiving nodes, making it suitable for passive eavesdropping and non-cooperative targets. Meanwhile, the cross-correlation framework focuses on time delay structure information, is less affected by amplitude fluctuations and gain mismatch, and is therefore more robust than RSS. Furthermore, it does not require large arrays, making its engineering complexity and covert deployment capabilities superior to AOA. Although differential processing may incur some SNR overhead, this loss can be effectively compensated for by increasing signal bandwidth, employing robust phase weighting, and introducing geometric redundancy, enabling TDOA to achieve reliable positioning even under underwater conditions of high multipath propagation and weak synchronization. Overall, the positioning system based on TDOA has more comprehensive advantages than systems based on TOA, AOA, or RSS.

[0003] Based on recent research on TDOA, several algorithmic approaches have been proposed. Among them, Maximum Likelihood Estimation (MLE) possesses good statistical properties, but the corresponding optimization often exhibits a non-convex shape, making the actual solution susceptible to local minima. Least Squares (LS) offers advantages in simplicity and computational lightness, but it is prone to significant biases when noise is strong or linearization errors are substantial. However, at present, sensor node drift significantly impacts system performance; especially in underwater acoustic networking, such uncertainties are almost unavoidable and widespread.

[0004] Therefore, this application anticipates a TDOA convex optimization underwater target fusion localization method that considers anchor node drift. Summary of the Invention

[0005] To overcome the problem of unstable underwater acoustic positioning caused by the drift of underwater sensor nodes in the prior art, the present invention provides a method, apparatus, device and medium for fusion positioning of underwater targets.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] In a first aspect, embodiments of this disclosure provide a method for fusing and locating underwater targets, comprising the following steps:

[0008] Step S1: Establish a Cartesian coordinate system as a reference coordinate system in the wireless sensor network, and pre-set multiple sensor nodes with position drift and one target node with unknown position;

[0009] Step S2: Construct the final TDOA measurement model that considers sensor node drift position error and measurement position error, and obtain the TDOA measurement results;

[0010] Step S3: Based on the TDOA measurement results, construct the FP localization model, optimize the FP localization model to obtain the hybrid SD / SOCP model, introduce the second-order cone relaxation method, optimize the hybrid SD / SOCP model to obtain the optimized hybrid SD / SOCP model, introduce a penalty term and penalty coefficient into the optimized hybrid SD / SOCP model for optimization, and obtain the convex optimization expression model.

[0011] Step S4: Process the convex optimization expression model using the interior point method to obtain the result matrix. Restore the result matrix to obtain the initial value matrix. Decompose the eigenvalues ​​of the initial value matrix to obtain the initial positioning values. Use the second to fourth positions of the initial positioning values ​​as the three-dimensional coordinates of the target node, and the fifth to last positions as the distances between the target node and each sensor node.

[0012] Step S5: Based on the three-dimensional coordinates of the target node and the distance between the target node and each sensor node, the least squares method is used to obtain the estimation error, and the final positioning result is obtained based on the estimation error.

[0013] Furthermore, the position coordinates of the sensor node in step S1 for:

[0014] ;

[0015] In the formula, , and These represent the positions of the sensor nodes along the x, y, and z axes in the reference coordinate system. For the first One sensor node; The number of sensor nodes; It is the transpose symbol;

[0016] The location coordinates of the target node whose location is unknown for:

[0017] ;

[0018] In the formula, , and These represent the positions of the target node along the x, y, and z axes in the reference coordinate system.

[0019] Furthermore, obtaining the TDOA measurement result in step S2 includes the following steps:

[0020] Step A1: Each sensor node passively acquires the TDOA measurement value between itself and the target node. After the target node transmits a signal, the sensor node acquires the measurement. The TDOA measurement result without sensor position error acquired by the i-th sensor node includes:

[0021] ;

[0022] In the formula, ; , representing a matrix with zero mean and covariance. Gaussian white noise, Represents an N×N unit diagonal matrix. Represents an N×N matrix of all 1s;

[0023] TDOA measurement results after introducing sensor position error: ;

[0024] Step A2: Construct the model for the i-th sensor node when it has position drift as follows:

[0025] ;

[0026] In the formula, ; This represents the position error of the corresponding sensor node, and the position error vector of the sensor node. It follows a pattern with a mean of zero and a covariance matrix of... The Gaussian distribution, where Represents a 3(N+1)×3(N+1) unit diagonal matrix;

[0027] Step A3: Introduce the model with position drift into the TDOA measurement results without sensor position error to obtain the optimized TDOA measurement model, including:

[0028] ;

[0029] To each and Taylor expansion yields:

[0030] ;

[0031] The position error and measurement error of the sensor node are combined and expressed as follows: ;

[0032] The final TDOA measurement model obtained after merging the representations is as follows: .

[0033] Furthermore, the FP localization model in step S3 includes:

[0034] ;

[0035] ;

[0036] In the formula, k is the coordinate dimension. , For dimension is block matrix; for Zero-dimensional vector for An identity matrix of order 1. for Zero-dimensional matrix; For dimension is block matrix; For the first The position vector of each sensor node for identity matrix of order 1 for Zero-dimensional matrix; For the goal and the first Geometric distance between the sensors; This is a vector representing the distances between the target and each sensor; Distance vector The One component; Let be the target position vector to be estimated; The estimated position vector of the target;

[0037] The covariance matrix of the FP localization model is expressed as: ;

[0038] ;

[0039] In the formula, For TDOA measurement results; The covariance matrix after combining errors. :

[0040] In the formula, ;

[0041] The model was improved based on the final TDOA measurement model. During the improvement, the model was shifted to the left. Squaring both sides of the equation, we get:

[0042] ;

[0043] In the formula, The vector representation is obtained as follows:

[0044] .

[0045] Furthermore, the process of optimizing the FP positioning model in step S3 to obtain the hybrid SD / SOCP model includes:

[0046] After performing equivalent processing on the FP positioning model, we obtain:

[0047] ;

[0048] ;

[0049] ;

[0050] ;

[0051] ;

[0052] In the formula, , Let V be an auxiliary matrix variable, which is a vector. The outer product matrix obtained by multiplying it by its transpose is a symmetric positive semi-definite matrix with rank 1; ; ;

[0053] Discarding the FP localization model after equivalent processing Constraints, introducing new variables and The resulting hybrid SD / SOCP model includes:

[0054] ;

[0055] ;

[0056] ;

[0057] ;

[0058] The optimization of the hybrid SD / SOCP model in step S3 includes:

[0059] ;

[0060] ;

[0061] ;

[0062] ;

[0063] ;

[0064] ;

[0065] In the formula, For matrix The Line 1 Column elements; For the first Sensor node position vectors With matrix element in the first row and first column The product; For matrix Line 2 to Line 3 A column vector consisting of the row and the first column; For matrix The The element in the first column of the row; For the first Sensor node position vectors With matrix No. Line 1 Column elements The product; For matrix The Line 1 Column elements;

[0066] Introducing penalty items and penalty coefficient and from 10 −5 Increase to 10 2 Select the optimal penalty coefficient The value is used to obtain the convex optimization expression model, including:

[0067] ;

[0068] ;

[0069] ;

[0070] ;

[0071] ;

[0072] ;

[0073] In the formula, This is a penalty item; This is the penalty coefficient.

[0074] Furthermore, in step S4, the following steps are adopted: Reconstruct the initial value matrix, where, The result matrix; The value of the first row and first column of the resulting matrix; by... Eigenvalue decomposition yields the resulting matrix and provides initial positioning values. , It is the initial value matrix The subvector formed by the second to fourth components, and suffix subvectors , It is the initial value matrix The subvector formed by the 5th component to the last component, where This indicates that the second to fourth positions represent the three-dimensional coordinates of the target node. This represents the distance between the target node and each sensor node, from the fifth position to the last position.

[0075] Furthermore, obtaining the final positioning result in step S5 includes the following steps:

[0076] Step B1: Based on Obtain the target node position and each sensor node distance , In the formula, True value of the target location With each sensor The distance;

[0077] Step B2: Distance exist That is Taylor expansion at this point yields:

[0078] ;

[0079] Step B3: Use the least squares method to calculate the distance after Taylor expansion. The modeling yielded the following:

[0080] ;

[0081] ;

[0082] Step B4: Use vector representation to obtain the least squares localization model from the modeling results of step B3:

[0083] ;

[0084] in:

[0085] ;

[0086] ;

[0087] ;

[0088] ;

[0089] Obtain the weighted matrix for: ;

[0090] Step B5: Based on the weighting matrix The final positioning result is obtained. include:

[0091] ;

[0092] .

[0093] In a second aspect, embodiments of this disclosure provide a system for fusing the location of underwater targets, comprising:

[0094] The initialization unit is configured to: establish a Cartesian coordinate system as a reference coordinate system in the wireless sensor network, and pre-set multiple sensor nodes with position drift and one target node with unknown position;

[0095] The measurement unit is configured to: construct the final TDOA measurement model that considers the sensor node drift position error and the measurement position error, and obtain the TDOA measurement results;

[0096] The optimization unit is configured to: construct an FP localization model based on the TDOA measurement results, optimize the FP localization model to obtain a hybrid SD / SOCP model, introduce a second-order cone relaxation method to optimize the hybrid SD / SOCP model to obtain an optimized hybrid SD / SOCP model, and introduce a penalty term and penalty coefficient into the optimized hybrid SD / SOCP model for optimization to obtain a convex optimization expression model.

[0097] The decomposition unit is configured to: process the convex optimization expression model using the interior point method to obtain a result matrix, restore the result matrix to obtain an initial value matrix, decompose the eigenvalues ​​of the initial value matrix to obtain the initial positioning value, and use the second to fourth positions of the initial positioning value as the three-dimensional coordinates of the target node, and the fifth to the last position as the distance between the target node and each sensor node.

[0098] The output unit is configured to: obtain the estimation error using the least squares method based on the three-dimensional coordinates of the target node and the distance between the target node and each sensor node, and obtain the final positioning result based on the estimation error.

[0099] In a third aspect, embodiments of this disclosure provide an electronic device, characterized in that the electronic device comprises:

[0100] At least one processor; and,

[0101] The memory is communicatively connected to the at least one processor; wherein,

[0102] The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the method for fusion positioning of underwater targets.

[0103] In a fourth aspect, embodiments of this disclosure provide a non-transitory computer-readable storage medium, characterized in that the non-transitory computer-readable storage medium stores computer instructions for causing the computer to perform the method for fusion positioning of underwater targets.

[0104] The beneficial effects of this invention are:

[0105] This invention provides a method, apparatus, device, and medium for fusion positioning of underwater targets. This method addresses the underwater sensor positioning problem. First, it constructs a time-of-arrival (TOA) model that simultaneously considers node drift and measurement noise, forming a unified error description. Based on this, a FP positioning model is established. Through semidefinite programming and second-order cone relaxation techniques, the non-convex problem is transformed into a convex optimization expression model. Then, the interior-point method is used to solve for the result matrix, which is then used to calculate the initial positioning value. Finally, the final positioning result is obtained through least-squares quadratic correction. This method, through the organic connection of steps S1 to S5, tightly integrates error modeling, convex optimization, and the least-squares method. Without increasing hardware complexity or synchronization difficulty, it effectively suppresses the impact of sensor node position errors and Gaussian white noise in measurements on positioning performance. Simulation results show that the overall performance of this method is superior to existing convex optimization methods and least-squares methods based on TOA, with higher positioning accuracy and stronger robustness to environmental and parameter disturbances, demonstrating significant advantages in engineering applications. Attached Figure Description

[0106] Figure 1 A flowchart illustrating a method for fusing and locating underwater targets according to an embodiment of this disclosure is shown;

[0107] Figure 2 The diagram shows a comparison of the mean square error as the covariance of the measurement noise increases, under the condition that the covariance of the node position error is 1 in the embodiments of this disclosure.

[0108] Figure 3 This embodiment of the present disclosure illustrates a measurement where the covariance of the noise is 10. -3 Under the condition of increasing node position error, a comparison chart of the mean square error changes;

[0109] Figure 4 This disclosure illustrates an embodiment where the covariance of the measured noise is 10. -3 And, under the condition that the covariance of the node position error is 1, the mean square error changes as the number of nodes increases.

[0110] Figure 5 A diagram of an apparatus for a method of fusing and locating underwater targets according to an embodiment of the present disclosure is shown. Detailed Implementation

[0111] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0112] To address the issue of unstable underwater acoustic positioning caused by underwater sensor node drift. Figure 1 A flowchart 100 of a method for fusing and locating underwater targets according to an embodiment of this disclosure is shown, as follows: Figure 1 As shown, it includes the following steps:

[0113] In step S101, a Cartesian coordinate system is established in the wireless sensor network as a reference coordinate system, and multiple sensor nodes with position drift and a target node with unknown position are preset.

[0114] Specifically, the position coordinates of the sensor node in step S101 for:

[0115] ;

[0116] In the formula, , and These represent the positions of the sensor nodes along the x, y, and z axes in the reference coordinate system. For the first One sensor node; The number of sensor nodes; It is the transpose symbol;

[0117] The location coordinates of the target node whose location is unknown for:

[0118] ;

[0119] In the formula, , and These represent the positions of the target node along the x, y, and z axes in the reference coordinate system.

[0120] Next, proceed to step S102.

[0121] In step S102, a final TDOA measurement model considering sensor node drift position error and measurement position error is constructed, and the TDOA measurement result is obtained.

[0122] Specifically, obtaining the TDOA measurement result in step S102 includes the following steps:

[0123] Step A1: Each sensor node passively acquires the TDOA measurement value between itself and the target node. After the target node transmits a signal, the sensor node acquires the measurement. The TDOA measurement result without sensor position error acquired by the i-th sensor node includes:

[0124] ;

[0125] In the formula, ; , representing a matrix with zero mean and covariance. Gaussian white noise, Represents an N×N unit diagonal matrix. Represents an N×N matrix of all 1s;

[0126] TDOA measurement results after introducing sensor position error: ;

[0127] Step A2: Construct the model for the i-th sensor node when it has position drift as follows:

[0128] Yan Yongsheng, Wang Yibo, Lin Chenxi, Wang Haiyan ;

[0129] In the formula, ; This represents the position error of the corresponding sensor node, and the position error vector of the sensor node. It follows a pattern with a mean of zero and a covariance matrix of... The Gaussian distribution, where Represents a 3(N+1)×3(N+1) unit diagonal matrix;

[0130] Step A3: Introduce the model with position drift into the TDOA measurement results without sensor position error to obtain the optimized TDOA measurement model, including:

[0131] ;

[0132] To each and Taylor expansion yields:

[0133] ;

[0134] The position error and measurement error of the sensor node are combined and expressed as follows: ;

[0135] The final TDOA measurement model obtained after merging the representations is as follows: ;

[0136] Next, proceed to step S103.

[0137] In step S103, based on the TDOA measurement results, an FP localization model is constructed, and the FP localization model is optimized to obtain a hybrid SD / SOCP model. A second-order cone relaxation method is introduced to optimize the hybrid SD / SOCP model to obtain an optimized hybrid SD / SOCP model. A penalty term and penalty coefficient are introduced into the optimized hybrid SD / SOCP model for optimization to obtain a convex optimized expression model.

[0138] Specifically, the FP localization model in step S103 includes:

[0139] First, in order to model the FP positioning model, we first shift to the left. Squaring both sides of the equation gives the result;

[0140] ;

[0141] Specifically, this involves calculating the covariance matrix of the FP positioning model. ,Will The vector representation is obtained as follows:

[0142] ;

[0143] Then, the covariance matrix of the FP localization model in step S103 is... Preliminary calculations include calculating the covariance matrix after combining errors. :

[0144] .

[0145] Finally, the FP positioning model is derived:

[0146] ;

[0147] ;

[0148] In the formula, k is the coordinate dimension. , For dimension is block matrix; for Zero-dimensional vector for An identity matrix of order 1. for Zero-dimensional matrix; For dimension is block matrix; For the first The position vector of each sensor node for identity matrix of order 1 for Zero-dimensional matrix; For the goal and the first Geometric distance between the sensors; This is a vector representing the distances between the target and each sensor; Distance vector The One component; Let be the target position vector to be estimated; The estimated position vector of the target;

[0149] The covariance matrix of the FP localization model is expressed as: ;

[0150] ;

[0151] In the formula, This is the TDOA measurement result.

[0152] The process of optimizing the FP localization model in step S103 to obtain the hybrid SD / SOCP model includes:

[0153] After performing equivalent processing on the FP positioning model, we obtain:

[0154] ;

[0155] ;

[0156] ;

[0157] ;

[0158] ;

[0159] In the formula, , Let V be an auxiliary matrix variable, which is a vector. The outer product matrix obtained by multiplying it by its transpose is a symmetric positive semi-definite matrix with rank 1; ; ;

[0160] The FP localization model after equivalent processing is non-convex, but quasi-convex. The rank-1 constraint is also non-convex. In this embodiment, the constraint is discarded in the FP localization model after equivalent processing. Constraints, introducing new variables and The resulting hybrid SD / SOCP model includes:

[0161] ;

[0162] ;

[0163] ;

[0164] ;

[0165] The optimization of the hybrid SD / SOCP model in step S103 includes:

[0166] ;

[0167] ;

[0168] ;

[0169] ;

[0170] ;

[0171] ;

[0172] In the formula, For matrix The Line 1 Column elements; For the first Sensor node position vectors With matrix element in the first row and first column The product; For matrix Line 2 to Line 3 A column vector consisting of the row and the first column; For matrix The The element in the first column of the row; For the first Sensor node position vectors With matrix No. Line 1 Column elements The product; For matrix The Line 1 Column elements;

[0173] Introducing penalty items and penalty coefficient and from 10 −5 Increase to 10 2 Select the optimal penalty coefficient The value is used to obtain the convex optimization expression model, including:

[0174] ;

[0175] ;

[0176] ;

[0177] ;

[0178] ;

[0179] ;

[0180] In the formula, This is a penalty item; This is the penalty coefficient.

[0181] Next, proceed to step S104.

[0182] In step S104, the interior point method is used to process the convex optimization expression model to obtain the result matrix. The result matrix is ​​restored to obtain the initial value matrix. The eigenvalues ​​of the initial value matrix are decomposed to obtain the initial positioning values. The second to fourth positions of the initial positioning values ​​are used as the three-dimensional coordinates of the target node, and the fifth to the last position are used as the distances between the target node and each sensor node.

[0183] Specifically, in step S104, the following steps are adopted: Reconstruct the initial value matrix, where, The result matrix; The value of the first row and first column of the resulting matrix; by... Eigenvalue decomposition yields the resulting matrix and provides initial positioning values. , It is the initial value matrix The subvector formed by the second to fourth components, and suffix subvectors , It is the initial value matrix The subvector formed by the 5th component to the last component, where This indicates that the second to fourth positions represent the three-dimensional coordinates of the target node. This represents the distance between the target node and each sensor node, from the fifth position to the last position.

[0184] Next, proceed to step S105.

[0185] In step S105, based on the three-dimensional coordinates of the target node and the distance between the target node and each sensor node, the least squares method is used to obtain the estimation error, and the final positioning result is obtained based on the estimation error.

[0186] Specifically, obtaining the final positioning result in step S105 includes the following steps:

[0187] Step B1: Based on Obtain the target node position and each sensor node distance , In the formula, True value of the target location With each sensor The distance;

[0188] Step B2: Distance exist That is Taylor expansion at this point yields:

[0189] ;

[0190] Step B3: Use the least squares method to calculate the distance after Taylor expansion. The modeling yielded the following:

[0191] ;

[0192] ;

[0193] Step B4: Represent the modeling results from Step B3, i.e., the two equations in Step B3, using vector representation to obtain the least squares localization model:

[0194] ;

[0195] in:

[0196] ;

[0197] ;

[0198] ;

[0199] ;

[0200] Obtain the weighted matrix for: ;

[0201] Step B5: Based on the weighting matrix The final positioning result is obtained. include:

[0202] ;

[0203] .

[0204] In this embodiment, simulation experiments are used to verify the feasibility, effectiveness, and superior positioning performance of this embodiment. It is assumed that the wireless sensor network has N = 16 sensor nodes and one target node, and all sensor nodes and the target node are randomly deployed in a two-dimensional space of 50 × 50 square meters.

[0205] Figure 2Figure 2 shows a comparison of the mean square error (MSE) changes as the covariance of measurement noise increases, obtained by the method provided in this embodiment, the convex optimization target localization method in existing related technologies, and the weighted least squares method in existing related technologies, under the condition that the covariance of the node position error is 1. As can be seen from Figure 2, as the covariance of measurement noise increases, the MSE of all methods shows an upward trend, while the method provided in this embodiment consistently outperforms the other methods, indicating that the method provided in this embodiment has stronger robustness and higher positioning accuracy.

[0206] Figure 3 This shows that the covariance of the measured noise is... Under the given conditions, a comparison chart is shown of the changes in the root mean square error of the Cramer-Rao lower bound obtained by the method provided in this embodiment, the convex optimization target localization method in existing related technologies, and the weighted least squares method in existing related technologies as the node position error increases. From Figure 4 As can be seen, the MSE of all methods increases with the increase of node position error, and the method provided in this embodiment consistently outperforms other methods.

[0207] Figure 4 This shows that the covariance of the measured noise is... Under the condition that the covariance of the node position error is 1, the method provided in this embodiment, as well as the convex optimization target localization method and the weighted least squares method in the existing related technologies, show the change of the root mean square error of the Cramer-Rao lower bound as the number of nodes increases. The positioning accuracy of the method provided in this embodiment is always higher than that of the other two algorithms.

[0208] The simulation results show that the method provided in this embodiment has good performance and can well meet the requirements of high positioning accuracy.

[0209] A second embodiment of the present invention provides a system for fusion positioning of underwater targets, comprising:

[0210] The initialization unit is configured to: establish a Cartesian coordinate system as a reference coordinate system in the wireless sensor network, and pre-set multiple sensor nodes with position drift and one target node with unknown position;

[0211] The measurement unit is configured to: construct the final TDOA measurement model that considers the sensor node drift position error and the measurement position error, and obtain the TDOA measurement results;

[0212] The optimization unit is configured to: construct an FP localization model based on the TDOA measurement results, optimize the FP localization model to obtain a hybrid SD / SOCP model, introduce a second-order cone relaxation method to optimize the hybrid SD / SOCP model to obtain an optimized hybrid SD / SOCP model, and introduce a penalty term and penalty coefficient into the optimized hybrid SD / SOCP model for optimization to obtain a convex optimization expression model.

[0213] The decomposition unit is configured to: process the convex optimization expression model using the interior point method to obtain a result matrix, restore the result matrix to obtain an initial value matrix, decompose the eigenvalues ​​of the initial value matrix to obtain the initial positioning value, and use the second to fourth positions of the initial positioning value as the three-dimensional coordinates of the target node, and the fifth to the last position as the distance between the target node and each sensor node.

[0214] The output unit is configured to: obtain the estimation error using the least squares method based on the three-dimensional coordinates of the target node and the distance between the target node and each sensor node, and obtain the final positioning result based on the estimation error.

[0215] The third embodiment of the present invention also provides an electronic device, the electronic device comprising:

[0216] At least one processor; and,

[0217] The memory is communicatively connected to the at least one processor; wherein,

[0218] The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the fusion positioning method for underwater targets according to any of the foregoing embodiments.

[0219] The fourth embodiment of the present invention also provides a non-transitory computer-readable storage medium storing computer instructions for causing the computer to execute the method for fusion positioning of underwater targets as described in any of the foregoing embodiments.

[0220] The fifth embodiment of the present invention also provides a computer program product, which includes a computing program stored on a non-transitory computer-readable storage medium. The computer program includes program instructions that, when executed by a computer, cause the computer to perform the method for fusion positioning of underwater targets according to any of the foregoing embodiments.

[0221] Figure 5The illustration shows a method or device 1000 implementing an embodiment of the present invention. In some embodiments, more or fewer devices may be included than illustrated. In some embodiments, it may be implemented using a single or multiple devices. In some embodiments, it may be implemented using cloud-based or distributed devices.

[0222] like Figure 5 As shown, device 1000 includes a processor 1001, which can perform various appropriate operations and processes based on programs and / or data stored in read-only memory (ROM) 1002 or programs and / or data loaded from storage portion 1008 into random access memory (RAM) 1003. Processor 1001 may be a multi-core processor or may contain multiple processors. In some embodiments, processor 1001 may include a general-purpose main processor and one or more special coprocessors, such as a central processing unit (CPU), graphics processing unit (GPU), neural network processor (NPU), digital signal processor (DSP), etc. Various programs and data required for the operation of device 1000 are also stored in RAM 1003. Processor 1001, ROM 1002, and RAM 1003 are interconnected via bus 1004. Input / output (I / O) interface 1005 is also connected to bus 1004.

[0223] The processor and memory described above are used together to execute programs stored in the memory. When the program is executed by a computer, it can implement the methods, steps, or functions described in the above embodiments.

[0224] The following components are connected to I / O interface 1005: an input section 1006 including a keyboard, mouse, touchscreen, etc.; an output section 1007 including a cathode ray tube (CRT), liquid crystal display (LCD), etc., and speakers, etc.; a storage section 1008 including a hard disk, etc.; and a communication section 1009 including a network interface card such as a LAN card, modem, etc. The communication section 1009 performs communication processing via a network such as the Internet. A drive 1010 is also connected to I / O interface 1005 as needed. A removable medium 1011, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., is installed on drive 1010 as needed so that computer programs read from it can be installed into storage section 1008 as needed. Figure 5 The diagram only shows a portion of the components and does not imply that the device 1000 only includes... Figure 5 The components shown.

[0225] The systems, devices, modules, or units described in the above embodiments can be implemented by a computer or its associated components. The computer may be, for example, a mobile terminal, smartphone, personal computer, laptop computer, in-vehicle human-machine interface device, personal digital assistant, media player, navigation device, game console, tablet computer, wearable device, smart TV, Internet of Things system, smart home, industrial computer, server, or a combination thereof.

[0226] Although not shown, in this embodiment of the invention, a computer-readable storage medium is provided having a computer program / instructions stored thereon, which, when executed by a processor, implements the method for fusion positioning of underwater targets as described in the embodiment.

[0227] Storage media in embodiments of the present invention include articles that are permanent and non-permanent, removable and non-removable, capable of storing information by any method or technology. Examples of storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic magnetic disk storage or other magnetic storage devices, or any other non-transfer medium that can be used to store information accessible by a computing device.

[0228] Although not shown, embodiments of the present invention also provide a computer program product, including: a computer program / instructions that, when executed by a processor, implement the method for fusion positioning of underwater targets as described in the embodiments.

[0229] The methods, programs, systems, apparatuses, etc., in embodiments of the present invention can be executed or implemented in one or more networked computers, or practiced in a distributed computing environment. In the embodiments of this specification, in these distributed computing environments, tasks can be performed by remote processing devices connected via a communication network.

Claims

1. A method for fusing and locating underwater targets, characterized in that, Includes the following steps: Step S1: Establish a Cartesian coordinate system as a reference coordinate system in the wireless sensor network, and pre-set multiple sensor nodes with position drift and one target node with unknown position; Step S2: Construct the final TDOA measurement model that considers sensor node drift position error and measurement position error, and obtain the TDOA measurement results; Step S3: Based on the TDOA measurement results, construct the FP localization model, optimize the FP localization model to obtain the hybrid SD / SOCP model, introduce the second-order cone relaxation method, optimize the hybrid SD / SOCP model to obtain the optimized hybrid SD / SOCP model, introduce a penalty term and penalty coefficient into the optimized hybrid SD / SOCP model for optimization, and obtain the convex optimization expression model. Step S4: Process the convex optimization expression model using the interior point method to obtain the result matrix. Restore the result matrix to obtain the initial value matrix. Decompose the eigenvalues ​​of the initial value matrix to obtain the initial positioning values. Use the second to fourth positions of the initial positioning values ​​as the three-dimensional coordinates of the target node, and the fifth to last positions as the distances between the target node and each sensor node. Step S5: Based on the three-dimensional coordinates of the target node and the distance between the target node and each sensor node, the least squares method is used to obtain the estimation error, and the final positioning result is obtained based on the estimation error.

2. The method for fusion positioning of underwater targets according to claim 1, characterized in that, The position coordinates of the sensor node in step S1 for: ； In the formula, , and These represent the positions of the sensor nodes along the x, y, and z axes in the reference coordinate system. For the first One sensor node; The number of sensor nodes; It is the transpose symbol; The location coordinates of the target node whose location is unknown for: ； In the formula, , and These represent the positions of the target node along the x, y, and z axes in the reference coordinate system.

3. The method for fusion positioning of underwater targets according to claim 1, characterized in that, When obtaining the TDOA measurement result in step S2, the following steps are included: Step A1: Each sensor node passively acquires the TDOA measurement value between itself and the target node. After the target node transmits a signal, the sensor node acquires the measurement. The TDOA measurement result without sensor position error acquired by the i-th sensor node includes: ； In the formula, ; , representing a matrix with zero mean and covariance. Gaussian white noise, Represents an N×N unit diagonal matrix. Represents an N×N matrix of all 1s; TDOA measurement results after introducing sensor position error: ; Step A2: Construct the model for the i-th sensor node when it has position drift as follows: ； In the formula, ; This represents the position error of the corresponding sensor node, and the position error vector of the sensor node. It follows a pattern with a mean of zero and a covariance matrix of... The Gaussian distribution, where Represents a 3(N+1)×3(N+1) unit diagonal matrix; Step A3: Introduce the model with position drift into the TDOA measurement results without sensor position error to obtain the optimized TDOA measurement model, including: ； To each and Taylor expansion yields: ； The position error and measurement error of the sensor node are combined and expressed as follows: ; The final TDOA measurement model obtained after merging the representations is as follows: .

4. The method for fusion positioning of underwater targets according to claim 1, characterized in that, The FP localization model in step S3 includes: ； ； In the formula, k is the coordinate dimension. , For dimension is block matrix; for Zero-dimensional vector for An identity matrix of order 1. for Zero-dimensional matrix; For dimension is block matrix; For the first The position vector of each sensor node for identity matrix of order 1 for Zero-dimensional matrix; For the goal and the first Geometric distance between the sensors; This is a vector representing the distances between the target and each sensor; Distance vector The One component; Let be the target position vector to be estimated; The estimated position vector of the target; The covariance matrix of the FP localization model is expressed as: ; ； In the formula, For TDOA measurement results; The covariance matrix after combining errors. : In the formula, ; The model was improved based on the final TDOA measurement model. During the improvement, the model was shifted to the left. Squaring both sides of the equation, we get: ； In the formula, The vector representation is obtained as follows: 。 5. The method for fusion positioning of underwater targets according to claim 1, characterized in that, The process of optimizing the FP localization model in step S3 to obtain the hybrid SD / SOCP model includes: After performing equivalent processing on the FP positioning model, we obtain: ； ； ； ； ； In the formula, , Let V be an auxiliary matrix variable, which is a vector. The outer product matrix obtained by multiplying it by its transpose is a symmetric positive semi-definite matrix with rank 1; ; ; Discarding the FP localization model after equivalent processing Constraints, introducing new variables and The resulting hybrid SD / SOCP model includes: ； ； ； ； The optimization of the hybrid SD / SOCP model in step S3 includes: ； ； ； ； ； ； In the formula, For matrix The Line 1 Column elements; For the first Sensor node position vectors With matrix element in the first row and first column The product; For matrix Line 2 to Line 1 A column vector consisting of the row and the first column; For matrix The The element in the first column of the row; For the first Sensor node position vectors With matrix No. Line 1 Column elements The product; For matrix The Line 1 Column elements; Introducing penalty items and penalty coefficient and from 10 −5 Increase to 10 2 Select the optimal penalty coefficient The value is used to obtain the convex optimization expression model, including: ； ； ； ； ； ； In the formula, This is a penalty item; This is the penalty coefficient.

6. The method for fusion positioning of underwater targets according to claim 1, characterized in that, The method used in step S4 Reconstruct the initial value matrix, where, The result matrix; The value of the first row and first column of the resulting matrix; by... Eigenvalue decomposition yields the resulting matrix and provides initial positioning values. , It is the initial value matrix The subvector formed by the second to fourth components, and suffix subvectors , It is the initial value matrix The subvector formed by the 5th component to the last component, where This indicates that the second to fourth positions represent the three-dimensional coordinates of the target node. This represents the distance between the target node and each sensor node, from the fifth position to the last position.

7. The method for fusion positioning of underwater targets according to claim 1, characterized in that, When obtaining the final positioning result in step S5, the following steps are included: Step B1: Based on Obtain the target node position and each sensor node distance , In the formula, True value of the target location With each sensor The distance; Step B2: Distance exist That is Taylor expansion at this point yields: ； Step B3: Use the least squares method to calculate the distance after Taylor expansion. The modeling yielded the following: ； ； Step B4: Use vector representation to obtain the least squares localization model from the modeling results of step B3: ； in: ； ； ； ； Obtain the weighted matrix for: ; Step B5: Based on the weighting matrix The final positioning result is obtained. include: ； 。 8. A system for fusion positioning of underwater targets, characterized in that, The method for fusing and locating underwater targets according to any one of claims 1-7 includes: The initialization unit is configured to: establish a Cartesian coordinate system as a reference coordinate system in the wireless sensor network, and pre-set multiple sensor nodes with position drift and one target node with unknown position; The measurement unit is configured to: construct the final TDOA measurement model that considers the sensor node drift position error and the measurement position error, and obtain the TDOA measurement results; The optimization unit is configured to: construct an FP localization model based on the TDOA measurement results, optimize the FP localization model to obtain a hybrid SD / SOCP model, introduce a second-order cone relaxation method to optimize the hybrid SD / SOCP model to obtain an optimized hybrid SD / SOCP model, and introduce a penalty term and penalty coefficient into the optimized hybrid SD / SOCP model for optimization to obtain a convex optimization expression model. The decomposition unit is configured to: process the convex optimization expression model using the interior point method to obtain a result matrix, restore the result matrix to obtain an initial value matrix, decompose the eigenvalues ​​of the initial value matrix to obtain the initial positioning value, and use the second to fourth positions of the initial positioning value as the three-dimensional coordinates of the target node, and the fifth to the last position as the distance between the target node and each sensor node. The output unit is configured to: obtain the estimation error using the least squares method based on the three-dimensional coordinates of the target node and the distance between the target node and each sensor node, and obtain the final positioning result based on the estimation error.

9. An electronic device, characterized in that, The electronic device includes: At least one processor; and, The memory is communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the method for fusion positioning of an underwater target as described in any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium stores computer instructions for causing the computer to perform the method for fusion positioning of an underwater target as described in any one of claims 1 to 7.

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