Underwater wireless sensor network node positioning method based on matrix completion

Abstract

The application discloses a kind of underwater wireless sensor network node positioning method based on matrix completion, steps are as follows: S1: the Euclidean distance between two different sensor nodes is obtained by TOA ranging method, so as to obtain the Euclidean distance matrix of underwater sensor network node;S2: the Euclidean distance matrix is recovered and completed using the matrix completion algorithm based on non-convex rank approximation, and the distance measurement between all nodes in the network is obtained;S3: the relative coordinates of all nodes underwater are calculated using MDS-MAP algorithm, the relative coordinates of conventional nodes are converted into absolute coordinates by the position of a part of anchor nodes, and the coordinates of conventional nodes are output.The application can not only accurately recover and complete the missing distance matrix, but also effectively handle the influence of Gaussian noise and outlier noise, with good robustness and accuracy.Using the position information of a small number of anchor nodes, the relative position is converted into absolute position, with high node positioning accuracy.

Description

Technical Field

[0001] This invention relates to the field of underwater wireless sensor network technology, and more specifically, to a method for locating nodes in an underwater wireless sensor network based on matrix completion. Background Technology

[0002] Underwater Wireless Sensor Networks (UWSNs), as a key technology for water monitoring, have broad application prospects in fields such as marine exploration, underwater environmental monitoring, underwater target monitoring and tracking, and assisted navigation. Sensor node localization technology plays a crucial role in UWSN applications. Data acquisition with effective node location information is fundamental to data application. To achieve effective acquisition and analysis of underwater resource and environmental data, high-precision underwater sensor node localization technology is essential. Therefore, accurately determining the location of underwater sensor nodes is a key research focus for scholars both domestically and internationally.

[0003] Due to the unique nature of the underwater communication environment, only a subset of nodes, such as submarines, surface buoys, and fixed underwater beacons, can achieve precise location. In UWSNs, these nodes with known locations are called anchor nodes, while other conventional nodes use these anchor nodes as positioning references for communication and location. Because of the difficulty in deployment, the number of underwater anchor nodes is generally small, which increases the difficulty of locating conventional nodes. Furthermore, issues such as water flow or node failures can cause gaps in the underwater sensor network topology, further complicating underwater node location.

[0004] The node localization method based on the MDS algorithm is called the MDS-MAP algorithm. This algorithm is characterized by requiring fewer anchor nodes and achieving higher localization accuracy than general algorithms. The MDS-MAP algorithm requires only 3 anchor nodes in a two-dimensional plane and only 4 anchor nodes in three-dimensional space to locate all nodes in the network, which aligns with the application characteristics of underwater sensor networks and offers significant advantages compared to other algorithms. Generally, this type of node localization technology requires the acquisition of sufficient and accurate distance data; otherwise, the algorithm's localization performance will be severely affected. Due to the limited transmission distance of underwater sensors, partial network connectivity leads to missing distance measurements between many nodes. Furthermore, the complex underwater communication environment exposes distance measurements between nodes to various noise interferences, further reducing the node localization accuracy.

[0005] Due to the complexity of the underwater environment, the deployment of underwater nodes is sparser than that of land nodes, the underwater network structure is uneven, and nodes are difficult to recover, resulting in significant positioning errors for underwater node localization methods based on the MDS-MAP algorithm. The positioning errors of this type of method mainly originate from the following two aspects:

[0006] 1) In the actual process of distance data collection, due to the limitations of the node's own energy status and communication range, it is usually impossible to collect distance information between all nodes, which makes the obtained Euclidean distance matrix often incomplete, thus increasing the difficulty of node localization.

[0007] 2) Distance measurement is inevitably affected by various noise factors, resulting in inaccurate distance data and significant node positioning errors. Typically, Gaussian noise and outlier noise are the main interference factors encountered during distance measurement. Summary of the Invention

[0008] To address the problems of traditional underwater node localization methods requiring a large amount of node distance information and node ranging errors caused by complex underwater environments, this invention provides an underwater wireless sensor network node localization method based on matrix completion, which can effectively improve node localization accuracy.

[0009] To achieve the above-mentioned objectives of this invention, the technical solution adopted is as follows:

[0010] A method for locating nodes in an underwater wireless sensor network based on matrix completion, comprising the following steps:

[0011] S1: Use the TOA ranging method to obtain the Euclidean distance between each pair of different sensor nodes, thereby obtaining the Euclidean distance matrix of the underwater sensor network nodes;

[0012] S2: The Euclidean distance matrix is ​​restored and completed using a matrix completion algorithm based on non-convex rank approximation, thereby obtaining the distance metric between all nodes in the network.

[0013] S3: Calculate the relative coordinates of all underwater nodes using the MDS-MAP algorithm, convert the relative coordinates of regular nodes to absolute coordinates using the positions of some anchor nodes, and output the coordinates of regular nodes.

[0014] Preferably, S1 is as follows:

[0015] The Euclidean distance between sensor node i and sensor node j is obtained using the TOA ranging method. During the positioning period T, node i receives broadcast data packets from node j.

[0016] Node i calculates the Euclidean distance between node i and node j based on the sending and receiving times of the received data packets. The calculation formula is as follows:

[0017] d ij =V×(t2-t1) (1)

[0018] Where, d ij t1 is the Euclidean distance between node i and node j; V is the speed of sound propagation; t1 is the time to send the data packet; t2 is the time to receive the data packet.

[0019] After calculating the Euclidean distance from node i to node j, the Euclidean distance d is then... ij The Euclidean distance matrix of the underwater sensor network nodes is obtained by transmitting the data from the buoy nodes to the shore-based base station.

[0020]

[0021] Where n represents the number of nodes in the underwater wireless sensor network, and EDM represents the Euclidean distance matrix.

[0022] Furthermore, the data packet includes a node identifier, a positioning period marker, and a transmission time;

[0023] The node labels are sorted and set before the network nodes are deployed;

[0024] The aforementioned positioning period is used to determine whether a data packet belongs to the current positioning period. If it does not belong to the current positioning period, it is discarded and listening continues; otherwise, node i updates the data packet.

[0025] The sending time refers to the time when node j sends the data packet.

[0026] Preferably, in step S2, a matrix completion algorithm based on non-convex rank approximation is used to restore and complete the Euclidean distance matrix, as follows:

[0027] The Euclidean distance matrix is ​​decomposed to obtain a low-rank matrix containing distance data and a sparse matrix containing outlier noise; the low-rank matrix is ​​approximated by the nuclear norm, and the sparse matrix is ​​approximated by the l1 norm.

[0028] The restoration and completion of the Euclidean distance matrix can then be modeled as follows:

[0029]

[0030] Where D represents the complete Euclidean distance matrix, E represents the noise matrix, S represents the observation distance matrix, Ω represents the set of indices of known elements in the observation distance matrix S, and P Ω Let ||| represent the projection operator. *Let λ denote the nuclear norm of the matrix, λ denote the Lagrange multiplier, and |||1 denote the l1 norm of the matrix.

[0031] Secondly, a non-convex rank function is introduced to replace the nuclear norm to approximate the original rank function, resulting in a non-convex rank function approximation model.

[0032] Then, the proposed non-convex rank function approximation model is solved using the alternating direction multiplier method to obtain a complete and noise-free Euclidean distance matrix.

[0033] Furthermore, the introduction of a non-convex rank function to replace the nuclear norm to approximate the original rank function yields a non-convex rank function approximation model, as detailed below:

[0034] The nuclear norm in equation (3) is relaxed by using a non-convex regularization term based on the Laplace function, and equation (3) is transformed into a smaller-scale optimization problem using the idea of ​​matrix factorization:

[0035]

[0036] Among them, |V| γ It is a non-convex function; U and V both represent an n×r matrix, where r represents the rank of matrix D, when U T When U = I, D = UV;

[0037] Treating equation (4) as a separable convex programming problem, the augmented Lagrangian form of equation (4) is:

[0038]

[0039] Where Λ represents the linearly constrained Lagrange operator, <·,·> represents the matrix inner product operation, and μ>0 represents the penalty parameter. The F-norm of a matrix is ​​denoted by .

[0040] Furthermore, the proposed non-convex rank function approximation model is solved using the alternating direction multiplier method, as follows:

[0041] The alternating direction multiplier method is used to iteratively solve equation (5), and its basic iterative formula is shown below:

[0042]

[0043]

[0044]

[0045]

[0046] μ k+1 =min(ρμk ,μ max (10)

[0047] Where ρ>1 is a constant, and k represents the current iteration number;

[0048] Step D1: To update U, keep V, E, and Λ unchanged, and transform equation (6) into its equivalent form:

[0049]

[0050] Where P = S + Λ k / ρ k ; Assumption (PE) k V=AΣB T A and B are matrices (PE) k If V has left and right singular value vectors, then the solution to U is:

[0051] U k+1 =AB T (12)

[0052] Step D2: Solve for V according to equation (13):

[0053]

[0054] Step D3: Solve for E according to equation (14):

[0055] E k+1 =sgn(W k )·max{|W k |-λ / μ k ,0} (14)

[0056] in, sgn(·) is the sign function;

[0057] Step D4: Update the Lagrange multiplier Λ according to equation (9) k+1 ;

[0058] Step D5: Update parameter μ according to equation (10) k+1 ;

[0059] Step D6: Determine Is it true? If true, output the following: To finally restore the completed Euclidean distance matrix; otherwise, return to step D1; where ε represents the tolerable error.

[0060] Preferably, the relative coordinates of all underwater nodes are calculated using the MDS-MAP algorithm, and the specific steps are as follows:

[0061] First, calculate the bicentered similarity matrix G of the restored and completed Euclidean distance matrix:

[0062]

[0063] in, J represents the centralized matrix, I represents the identity matrix, n represents the number of all nodes in the underwater wireless sensor network, and D represents the restored Euclidean distance matrix.

[0064] Then perform singular value decomposition on the bicentered similarity matrix G:

[0065] [A,Σ,B]=svd(G) (16)

[0066] Where Σ represents the diagonal matrix obtained by singular value decomposition of matrix G, svd() represents the singular value decomposition operation, and A and B represent two orthogonal matrices obtained by singular value decomposition of matrix G.

[0067] Finally, calculate the relative coordinate matrix R of the nodes:

[0068]

[0069] Where, r n Represents the relative coordinates of the nth node; d represents the dimension of the node coordinates, and T represents the matrix transpose operation.

[0070] Furthermore, by converting the relative coordinates of regular nodes to absolute coordinates using the positions of a subset of anchor nodes, the coordinates of the regular nodes are output, as follows:

[0071] First, calculate the coordinate transformation matrix Q of the anchor node:

[0072]

[0073] Where Q1 represents the rotation matrix, Q2 represents the mirror matrix, m represents the number of anchor nodes, and t m Represents the absolute coordinates of the m-th node;

[0074] Then convert the relative coordinates of the regular nodes to absolute coordinates:

[0075] t i =Q(r) i -r1)+t1,i=m+1,…,n (19)

[0076] The final output is the coordinates of the regular node {t} i |t m+1 ,t m+2 ,...,t n}

[0077] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the matrix completion-based underwater wireless sensor network node localization method.

[0078] A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the steps of the underwater wireless sensor network node localization method based on matrix completion are implemented.

[0079] The beneficial effects of this invention are as follows:

[0080] This invention addresses the problems of missing and noise-contaminated distance data in underwater wireless sensor networks by employing a matrix completion algorithm based on non-rank approximation to restore and complete the Euclidean distance matrix. This algorithm not only accurately restores and completes the missing distance matrix but also effectively handles the effects of Gaussian noise and outlier noise, exhibiting good robustness and accuracy.

[0081] This invention addresses the problem of low node positioning accuracy caused by the small number and uneven distribution of anchor nodes and large iteration errors in underwater wireless sensor networks. Based on the restored and completed complete Euclidean distance matrix, this invention uses the MDS-MAP algorithm to calculate the relative positions of regular nodes, and then uses the position information of a small number of anchor nodes to convert the relative positions into absolute positions, resulting in high node positioning accuracy. Attached Figure Description

[0082] Figure 1 This is a schematic diagram of an underwater wireless sensor network structure.

[0083] Figure 2 This is a flowchart of the steps of the underwater wireless sensor network node localization method based on matrix completion of the present invention.

[0084] Figure 3 This is a schematic diagram of the network topology.

[0085] Figure 4 This is a schematic diagram of EDM completion error.

[0086] Figure 5 This is a schematic diagram of node positioning error.

[0087] Figure 6 This is a schematic diagram of the actual positioning effect of the node. Detailed Implementation

[0088] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0089] Example 1

[0090] The network structure of the underwater wireless sensor networks (UWSNs) considered in this embodiment is as follows: Figure 1 As shown, it mainly consists of buoy nodes, anchor nodes, and conventional nodes. Buoy nodes are nodes deployed on the water surface, equipped with GPS receivers, enabling them to locate themselves using GPS signals and communicate with shore-based base stations to transmit relevant data. Anchor nodes are a type of UWSN with strong computing power; these nodes can obtain their location information by directly communicating with buoy nodes, thus achieving self-positioning. Conventional nodes are a type of underwater node with weaker computing power and lower energy consumption. These nodes typically cannot directly obtain their own location information and require positioning algorithms to calculate their coordinates.

[0091] The underwater node localization method based on matrix completion proposed in this invention mainly includes three stages: Euclidean Distance Matrix (EDM) construction stage, Euclidean distance matrix completion stage, and node localization stage, as detailed below. Figure 2 As shown, an underwater wireless sensor network node localization method based on matrix completion is described, and the method includes the following steps:

[0092] S1: Use the TOA ranging method to obtain the Euclidean distance between each pair of different sensor nodes, thereby obtaining the Euclidean distance matrix of the underwater sensor network nodes;

[0093] S2: The Euclidean distance matrix is ​​restored and completed using a matrix completion algorithm based on non-convex rank approximation, thereby obtaining the distance metric between all nodes in the network.

[0094] S3: Calculate the relative coordinates of all underwater nodes using the MDS-MAP algorithm, convert the relative coordinates of regular nodes to absolute coordinates using the positions of some anchor nodes, and output the coordinates of regular nodes.

[0095] In a specific embodiment, S1 is as follows:

[0096] The Euclidean distance between sensor node i and sensor node j is obtained using the TOA ranging method. During the positioning period T, node i receives broadcast data packets from node j.

[0097] Node i calculates the Euclidean distance between node i and node j based on the sending and receiving times of the received data packets. The calculation formula is as follows:

[0098] d ij =V×(t2-t1) (1)

[0099] Where, d ij t1 is the Euclidean distance between node i and node j; V is the speed of sound propagation; t1 is the time to send the data packet; t2 is the time to receive the data packet.

[0100] After calculating the Euclidean distance from node i to node j, the Euclidean distance d is then... ij The Euclidean distance matrix of the underwater sensor network nodes is obtained by transmitting the data from the buoy nodes to the shore-based base station.

[0101]

[0102] Where n represents the number of nodes in the underwater wireless sensor network, and EDM represents the Euclidean distance matrix.

[0103] In this embodiment, the data packet includes a node identifier, a positioning period marker, and a transmission time;

[0104] See Table 1 for details:

[0105] Table 1 Data packets for underwater sensor nodes

[0106] Node label (j) <![CDATA[Positioning cycle marker (T n )]]> <![CDATA[Transmission time t1]]>

[0107] The node labels are sorted before the network nodes are deployed; that is, the nodes are sorted before the network nodes are deployed.

[0108] The aforementioned positioning period is used to determine whether a data packet belongs to the current positioning period. If it does not belong to the current positioning period, it is discarded and listening continues; otherwise, node i updates the data packet.

[0109] The sending time refers to the time when node j sends the data packet.

[0110] In a specific embodiment, S2, a matrix completion algorithm based on non-convex rank approximation is used to restore and complete the Euclidean distance matrix, as follows:

[0111] Based on the low-rank property of the Euclidean distance matrix (EDM), we consider decomposing the original EDM into a low-rank matrix and a sparse matrix. Therefore, the Euclidean distance matrix is ​​decomposed to obtain a low-rank matrix containing distance data and a sparse matrix containing outlier noise; the low-rank matrix is ​​approximated using the nuclear norm, and the sparse matrix is ​​approximated using the l1 norm.

[0112] The restoration and completion of the Euclidean distance matrix can then be modeled as follows:

[0113]

[0114] Where D represents the complete Euclidean distance matrix, E represents the noise matrix, S represents the observation distance matrix, Ω represents the set of indices of known elements in the observation distance matrix S, and P Ω Represents the projection operator; || || * Let λ denote the nuclear norm of the matrix, λ denote the Lagrange multiplier, and |||1 denote the l1 norm of the matrix.

[0115] Secondly, a non-convex rank function is introduced to replace the nuclear norm to approximate the original rank function, resulting in a non-convex rank function approximation model;

[0116] Then, the proposed non-convex rank function approximation model is solved using the alternating direction multiplier method to obtain a complete and noise-free Euclidean distance matrix.

[0117] In a specific embodiment, the introduction of a non-convex rank function to replace the nuclear norm to approximate the original rank function yields a non-convex rank function approximation model, as detailed below:

[0118] Since the nuclear norm in equation (3) is not the best approximation of the matrix rank, it is difficult to obtain an exact solution to the model. Therefore, this embodiment considers using a non-convex rank function to replace the nuclear norm, and proposes a matrix reconstruction model based on the non-convex rank approximation. This model uses a non-convex regularization term based on the Laplace function (called the γ function) to relax the nuclear norm in equation (3), and uses the idea of ​​matrix decomposition to transform equation (3) into a smaller-scale optimization problem:

[0119]

[0120] Among them, |V| γ It is a non-convex function; U and V both represent an n×r matrix, where r represents the rank of matrix D, when U T When U = I, D = UV;

[0121] This is because the rank of matrix D in equation (3) is r, and the size of matrix D is n×n, while the sizes of matrices U and V are n×r respectively. When U T When U = I, D = UV T Since r is much smaller than n, matrix D can be decomposed into two smaller matrices, U and V, for solution.

[0122] Treating equation (4) as a separable convex programming problem, the augmented Lagrangian form of equation (4) is:

[0123]

[0124] Where Λ represents the linearly constrained Lagrange operator, <·,·> represents the matrix inner product operation, and μ>0 represents the penalty parameter. The F-norm of a matrix is ​​denoted by .

[0125] In this embodiment, "approximation" means "approximate" or "replacement." The original rank function is an l0 norm, which is difficult to solve. The conventional approach is to use the nuclear norm to replace the l0 norm to calculate an approximate solution to the problem. However, this embodiment uses a non-convex rank function in equation (4). γ The l0 norm is used to replace the l0 norm to calculate an approximate solution to the problem. The non-convex function approximation model described in this embodiment is shown in equation (5).

[0126] In a specific embodiment, the proposed non-convex function approximation model is solved using the alternating direction multiplier method, as follows:

[0127] The alternating direction multiplier method is used to iteratively solve equation (5), and its basic iterative formula is shown below:

[0128]

[0129]

[0130]

[0131]

[0132] μ k+1 =min(ρμ k ,μ max (10)

[0133] Where ρ>1 is a constant, and k represents the current iteration number;

[0134] Step D1: To update U, keep V, E, and Λ unchanged, and transform equation (6) into its equivalent form:

[0135]

[0136] Where P = S + Λ k / ρ k ; Assumption (PE) k V=AΣB T A and B are matrices (PE) k If V has left and right singular value vectors, then the solution to U is:

[0137] U k+1 =AB T (12)

[0138] Step D2: Solve for V according to equation (13):

[0139]

[0140] Step D3: Solve for E according to equation (14):

[0141] E k+1 =sgn(W k )·max{|W k |-λ / μ k ,0} (14)

[0142] in, sgn(·) is the sign function;

[0143] In this embodiment, equation (14) can be optimized by using the classic orthogonal Procrusters technique.

[0144] Step D4: Update the Lagrange multiplier Λ according to equation (9) k+1 ;

[0145] Step D5: Update parameter μ according to equation (10) k+1 ;

[0146] Step D6: Determine Is it true? If true, output the following: To finally restore the completed Euclidean distance matrix, otherwise return to step D1; where ε represents the tolerable error.

[0147] Based on the matrix completion method using the non-convex rank approximation described above, the complete Euclidean distance matrix (EDM) is recovered, which allows us to obtain the distance metrics between all nodes in the network. Then, the MDS-MAP algorithm can be used to calculate the relative coordinates of all underwater nodes. The specific steps are as follows:

[0148] First, calculate the bicentered similarity matrix G of the restored and completed Euclidean distance matrix:

[0149]

[0150] in, J represents the centralized matrix, I represents the identity matrix, n represents the number of all nodes in the underwater wireless sensor network, and D represents the restored Euclidean distance matrix.

[0151] Then perform singular value decomposition on the bicentered similarity matrix G:

[0152] [A,Σ,B]=svd(G) (16)

[0153] Where Σ represents the diagonal matrix obtained by singular value decomposition of matrix G, svd() represents the singular value decomposition operation, and A and B represent two orthogonal matrices obtained by singular value decomposition of matrix G.

[0154] Finally, calculate the relative coordinate matrix R of the nodes:

[0155]

[0156] Where, r n Represents the relative coordinates of the nth node; d represents the dimension of the node coordinates, and T represents the matrix transpose operation.

[0157] In one specific embodiment, the relative coordinates of regular nodes are converted to absolute coordinates by using the positions of a subset of anchor nodes, and the coordinates of the regular nodes are output, as follows:

[0158] First, calculate the coordinate transformation matrix Q of the anchor node:

[0159]

[0160] Where Q1 represents the rotation matrix, Q2 represents the mirror matrix, m represents the number of anchor nodes, and t m Represents the absolute coordinates of the m-th node;

[0161] Then convert the relative coordinates of the regular nodes to absolute coordinates:

[0162] t i =Q(r) i -r1)+t1,i=m+1,…,n (19)

[0163] The final output is the coordinates of the regular node {t} i |t m+1 ,t m+2 ,...,t n}

[0164] This embodiment addresses the problem of missing and noise-contaminated distance measurement data in underwater wireless sensor networks. The invention proposes a low-rank matrix completion model based on non-convex rank approximation. This model can not only accurately recover and complete missing distance matrices but also effectively handle the effects of Gaussian noise and outlier noise, exhibiting good robustness and accuracy.

[0165] This embodiment addresses the problem of low node positioning accuracy caused by the small number and uneven distribution of anchor nodes and large iteration errors in underwater wireless sensor networks. Based on the restored and completed complete Euclidean distance matrix, the present invention uses the MDS-MAP algorithm to calculate the relative positions of regular nodes, and then uses the position information of a small number of anchor nodes to convert the relative positions into absolute positions, which has high node positioning accuracy.

[0166] To verify the effectiveness of the proposed underwater wireless sensor node localization method (NRAM) based on matrix completion, it is assumed that all sensor nodes in the network model are equipped with pressure sensors. The depth information of the underwater nodes is obtained through these pressure sensors, thereby utilizing two-dimensional planar techniques to solve the problem of node localization in underwater three-dimensional space. This invention considers... Figure 3 The network topology shown is as follows. Figure 3 As shown, 100 sensor nodes are evenly distributed in a 100*100m area. 2 Within the square monitoring area, five anchor nodes are placed at the four corners and the center of the monitoring area, while the remaining 95 regular nodes are randomly and evenly distributed within the square monitoring area.

[0167] To investigate the algorithm's performance under noise interference conditions, this invention examines its performance under simultaneous Gaussian noise and outlier noise. The experimental results are compared with several state-of-the-art methods, including localization algorithms based on Online Robust Matrix Completion (ORMC), Matrix Completion with Column Outliers and Sparse Noise (MCOS), Matrix Decomposition via Truncated Nuclear Norm and a Sparse Regularizer (TNNSR), and Semidefinite Relaxation Localization (SDRL). The simulation platform for this invention is configured as follows: Windows 10 64-bit operating system, Intel(R) Core(TM) i7-7700k 4.20GHz CPU, 16GB RAM, and MATLAB R2022a simulation software. All simulations were run 100 times, and their average value was taken as the final result.

[0168] To effectively evaluate algorithm performance, the two evaluation metrics selected in this invention are defined as follows:

[0169] (1) Average Completion Error (ACE):

[0170]

[0171] Where D represents the actual complete EDM, This indicates the restored and completed EDM.

[0172] (2) Average Localization Error (ALE):

[0173]

[0174] Where X represents the actual node coordinate matrix, This represents the estimated node coordinate matrix.

[0175] This invention assumes that the distance information acquisition process is simultaneously affected by Gaussian noise and outlier noise. In the experiment, Gaussian noise with a mean of 0 and a variance of 100, as well as outlier noise with values ​​between 500 and 1000, are added simultaneously. The proportion of outlier noise is set to 1%. Figure 4 and Figure 5 The EDM completion error and node localization error of five algorithms under the influence of mixed noise are presented respectively.

[0176] like Figure 4 As shown, both NRAM and ORMC algorithms exhibit good matrix completion performance under mixed noise conditions, effectively smoothing Gaussian noise and handling interference from outlier noise. Specifically, both ORMC and NRAM algorithms achieve a stable matrix completion error of 0.02m at an observation rate of 0.3. In contrast, the SDRL algorithm only reaches a matrix completion error of 0.02m at an observation rate of 0.7, and the MCOS algorithm only reaches 0.02m at an observation rate of 0.9. The TNNSR algorithm still exhibits a significant completion error at an observation rate of 0.9. While ORMC achieves nearly the same matrix completion accuracy as NRAM when the observation rate is greater than 0.3, its performance is significantly worse than NRAM when the observation rate is below 0.2. Experimental results demonstrate that the proposed NRAM algorithm effectively handles the effects of mixed noise and maintains high matrix completion accuracy even at low observation rates.

[0177] Depend on Figure 5It can be seen that the node localization error and matrix completion error results of the five algorithms are similar. Under the influence of mixed noise, the node localization error of the NRAM algorithm proposed in this invention can reach 1.5m at an observation rate of 0.1. Under the same conditions, the localization errors of TNNSR, ORMC, MCOS, and SDRL algorithms are 4.8m, 3.6m, 4.5m, and 3.5m, respectively. Experimental results show that the NRAM algorithm proposed in this invention can effectively handle the interference of Gaussian noise and outlier noise, and can still achieve good matrix completion results even with a low data observation rate, thus obtaining high node localization accuracy.

[0178] Figure 6 The final positioning results of 100 sensor nodes are shown. Solid triangles represent the actual positions of anchor nodes, hollow circles represent the actual positions of regular nodes, and solid dots represent the positions of regular nodes calculated using the positioning method proposed in this invention. In this experiment, the observation rate of distance data was 0.3, the mean Gaussian noise was 0, the variance was 100, and the proportion of outlier noise was 1%. Figure 6 As shown, the solid points can generally fall within the hollow circles with relatively high accuracy. The results indicate that, even with missing sampling data and noise contamination, the matrix completion-based positioning method proposed in this invention can achieve accurate positioning of sensor nodes.

[0179] In summary, the underwater node localization algorithm based on matrix completion proposed in this invention can not only effectively handle the noise effects in complex underwater environments, but also maintain high positioning accuracy and good robustness even when underwater nodes are randomly arranged, the network structure is uneven, there are few anchor nodes, and the network area is large.

[0180] Example 2

[0181] A computer device includes 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 steps of the underwater wireless sensor network node localization method based on matrix completion as described in Embodiment 1.

[0182] Example 3

[0183] A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the steps of the underwater wireless sensor network node localization method based on matrix completion as described in Embodiment 3 are implemented.

[0184] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the claims of the present invention.

Claims

1. A method for underwater wireless sensor network node localization based on matrix completion, characterized in that: The method includes the following steps: S1: Use the TOA ranging method to obtain the Euclidean distance between each pair of different sensor nodes, thereby obtaining the Euclidean distance matrix of the underwater sensor network nodes; S2: The Euclidean distance matrix is ​​restored and completed using a matrix completion algorithm based on non-convex rank approximation, thereby obtaining the distance metric between all nodes in the network. S2 uses a matrix completion algorithm based on non-convex rank approximation to restore and complete the Euclidean distance matrix, as follows: The Euclidean distance matrix is decomposed to obtain a low-rank matrix including distance data and a sparse matrix including outlier noise; the low-rank matrix is approximated by a nuclear norm, and the sparse matrix is approximated by a l 1 norm 1 norm The restoration and completion of the Euclidean distance matrix can then be modeled as follows: (3) in, D Represents the complete Euclidean distance matrix. E Represents the noise matrix. S Ω represents the observation distance matrix. S The set of known indices of elements in the set. Represents the projection operator. , Indicates Lagrange multipliers, Representing a matrix l 1-norm; Secondly, a non-convex rank function is introduced to replace the nuclear norm to approximate the original rank function, resulting in a non-convex rank function approximation model; Then, the proposed non-convex rank function approximation model is solved using the alternating direction multiplier method to obtain a complete and noise-free Euclidean distance matrix; The method of introducing a non-convex rank function to approximate the original rank function instead of the nuclear norm is described below, resulting in a non-convex rank function approximation model: The nuclear norm in equation (3) is relaxed by using a non-convex regularization term based on the Laplace function, and equation (3) is transformed into a smaller-scale optimization problem using the idea of ​​matrix factorization: (4) in, It is a non-convex function; U and V Both represent one matrix, r Representation matrix D The rank, when satisfying hour, D = UV ; Treating equation (4) as a separable convex programming problem, the augmented Lagrangian form of equation (4) is: (5) in, Represents the linearly constrained Lagrange operator. This represents the matrix inner product operation. Indicates the penalty parameter, F Norm; S3: Calculate the relative coordinates of all underwater nodes using the MDS-MAP algorithm, convert the relative coordinates of regular nodes to absolute coordinates using the positions of some anchor nodes, and output the coordinates of regular nodes.

2. The underwater wireless sensor network node localization method based on matrix completion according to claim 1, characterized in that: S1, as detailed below: Using the TOA ranging method to obtain sensor nodes i To sensor node j The Euclidean distance, during the positioning cycle T Inside, node i Received node j Broadcast data packets; node i The node is calculated based on the sending time and receiving time of the received data packet. i and nodes j The Euclidean distance between them is calculated using the following formula: (1) in, d ij It is a node i With nodes j The Euclidean distance between them; V It is the speed of sound signal propagation; t 1 represents the time it took to send the data packet; t 2 represents the time the data packet was received; node i Calculate the distance to the node j After determining the Euclidean distance, the Euclidean distance is... d ij The Euclidean distance matrix of the underwater sensor network nodes is obtained by transmitting the data from the buoy nodes to the shore-based base station. (2) in, n This indicates the number of nodes in an underwater wireless sensor network. This represents the Euclidean distance matrix.

3. The underwater wireless sensor network node localization method based on matrix completion according to claim 2, characterized in that: The data packet includes a node identifier, a positioning period marker, and a transmission time; The node labels are sorted and set before the network nodes are deployed; The aforementioned positioning period is used to determine whether a data packet belongs to the current positioning period. If it does not belong to the current positioning period, it is discarded, and listening continues; otherwise, the node... i Update data package; The aforementioned sending time, node j The time it takes to send data packets.

4. The underwater wireless sensor network node localization method based on matrix completion according to claim 1, characterized in that: The proposed non-convex rank function approximation model is solved using the alternating direction multiplier method, as detailed below: The alternating direction multiplier method is used to iteratively solve equation (5), and its basic iterative formula is shown below: (6) (7) (8) (9) (10) in, It is a constant. k Indicates the current iteration number; Step D1: For updating U ,save V , E , Without changing the equation, we can transform equation (6) into its equivalent form: (11) in, ; Assumption , A and B Each is a matrix If the left and right singular value vectors are then U The solution is: (12) Step D2: Solve according to equation (13) V : (13) Step D3: Solve according to equation (14) E : (14) in, , It is a symbolic function; Step D4: Update the Lagrange multipliers according to equation (9) ; Step D5: Update the parameters according to equation (10) ; Step D6: Determine Is it true? If true, output the following: To finally restore the completed Euclidean distance matrix; otherwise, return to step D1; where, This indicates the tolerable error.

5. The underwater wireless sensor network node localization method based on matrix completion according to claim 1, characterized in that: The relative coordinates of all underwater nodes were calculated using the MDS-MAP algorithm. The specific steps are as follows: First, calculate the bicentered similarity matrix of the restored and completed Euclidean distance matrix. G : (15) in, , J Represents a centered matrix. I Represents the identity matrix. n This indicates the total number of nodes in the underwater wireless sensor network. D This represents the Euclidean distance matrix for restoration and completion. Then, for the bi-centered similarity matrix G Perform singular value decomposition: (16) in, Representation matrix G The diagonal matrix obtained through singular value decomposition This represents the singular value decomposition operation. A and B Representation matrix G Two orthogonal matrices obtained through singular value decomposition; Finally, calculate the relative coordinate matrix of the nodes. R : (17) in, Indicates the first n The relative coordinates of each node; , d The dimension representing the node coordinates. T This represents the matrix transpose operation.

6. The underwater wireless sensor network node localization method based on matrix completion according to claim 5, characterized in that: The relative coordinates of regular nodes are converted to absolute coordinates by using the positions of a subset of anchor nodes, and the coordinates of the regular nodes are then output, as follows: First, calculate the coordinate transformation matrix of the anchor node. Q : (18) in, Represents the rotation matrix. Represents a mirror matrix. m Indicates the number of anchor nodes. ; Then convert the relative coordinates of the regular nodes to absolute coordinates: (19) The final output is the coordinates of the regular nodes. .

7. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the underwater wireless sensor network node localization method based on matrix completion as described in any one of claims 1 to 6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, it implements the steps of the underwater wireless sensor network node localization method based on matrix completion as described in any one of claims 1 to 6.

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