A three-dimensional underwater wireless sensor network dynamic positioning method

By optimizing the DV-HOP algorithm and improving the HH-VBF protocol, and combining it with the PSR-RBF model, the problems of insufficient positioning accuracy and redundant transmission in underwater wireless sensor networks were solved, and high-precision dynamic positioning and tracking of underwater sensor nodes were achieved.

CN116723478BActive Publication Date: 2026-02-06SHANGHAI MARITIME UNIVERSITY
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Patent Information

Application Number
CN202310923038.5
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2023-07-26
Publication Date
2026-02-06
Estimated Expiration
2043-07-26

AI Technical Summary

Technical Problem

The existing DV-HOP algorithm has insufficient positioning accuracy in underwater wireless sensor networks, and the HH-VBF protocol has multi-path redundant transmission problems and does not fully consider the impact of underwater dynamic environmental factors.

Method used

By employing machine intelligence data and algorithm models, the DV-HOP algorithm is optimized by calculating the hop distance and signal strength of beacon nodes. Combined with the improved HH-VBF routing protocol and PSR-RBF maneuver trajectory prediction model, dynamic positioning and tracking of nodes are achieved.

Benefits of technology

It improves node positioning accuracy, reduces energy consumption, solves routing hole problems and data packet redundancy transmission, and realizes real-time dynamic positioning and tracking of underwater sensor nodes.

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Abstract

The application relates to a three-dimensional underwater wireless sensor network dynamic positioning method, which comprises the following steps: step S1, calculating the minimum hop number and the average hop distance between each unknown node and a beacon node in a three-dimensional underwater wireless sensor network; step S2, converting the signal strength between the unknown node and the beacon node into the communication radius distance between the two, improving the HH-VBF underwater routing protocol, selecting the next hop node and transmitting information by using the improved HH-VBF underwater routing protocol, and calculating the updated minimum hop number; step S3, calculating the average hop distance of each unknown node to the beacon node and optimizing the average hop distance; step S4, calculating the coordinates of the unknown node; and step S5, tracking the target of the unknown node. Compared with the prior art, the application realizes real-time positioning and accurate tracking of unknown sensor nodes in a dynamic three-dimensional underwater environment.
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Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of underwater positioning, in particular to a three-dimensional underwater wireless sensor network dynamic positioning method. BACKGROUND

[0002] Underwater wireless sensor networks (UWSNs) are underwater monitoring network systems composed of sensor nodes with acoustic communication and computing capabilities. These sensor nodes are randomly placed in a three-dimensional area, and the underwater sensor network is more complex than the terrestrial wireless sensor network, mainly relying on underwater acoustic communication for propagation. Due to the erosion of seawater, limited battery energy and difficulty in replacement, and cost constraints, it is not feasible to deploy a large number of AUVs containing GPS positioning. Therefore, a large number of relatively inexpensive underwater sensor nodes can be deployed to collect underwater information to accurately detect abnormal data in the sea. However, due to the influence of factors such as undercurrent and sea wind, the position of each underwater wireless sensor is constantly changing, so it is necessary to automatically detect underwater wireless sensors in real time.

[0003] The hardware equipment required by the range-free positioning technology is simple, and has strong anti-noise ability, low cost and energy consumption. DV-HOP algorithm is one of the representative Range-free algorithms, which is widely applied, easy to expand and has few restrictions. The DV-HOP refers to the distance vector hop method, which is one of a series of distributed positioning algorithms proposed by using the ideas of distance vector routing and GPS positioning, has high positioning accuracy, can meet the requirements of most application scenarios, and is widely favored. The DV-HOP algorithm does not directly measure the distance between nodes, but estimates the coordinates of the nodes by calculating the minimum hop number and the average hop distance between nodes. However, due to the uneven distribution of nodes and different distances between nodes, the traditional DV-HOP algorithm may produce large errors when applied. In addition, the DV-HOP algorithm is mainly used in terrestrial environment and does not consider the influence of underwater noise, waves, wind speed, ships and other factors.

[0004] HH-VBF is an optimized version of the VBF routing protocol, and its idea is to establish a new pipe between the previous hop node and the sink node each time the data packet is forwarded, so that the routing pipe is not fixed, and each node will establish its pipe when transmitting. In addition, HH-VBF can find the relay nodes existing in the network, solve the problem of too few forwarding nodes in the pipe in VBF, and improve the data packet transmission rate. However, HH-VBF still uses the form of flooding for information transmission between nodes, which leads to the problem of multiple path redundant transmission.

[0005] At present, many scholars are researching the positioning of wireless sensor nodes, and on the basis of the traditional DV-HOP improved algorithm based on non-distance measurement, they improve the minimum hop count and the average hop distance. However, for the positioning of dynamic nodes underwater, the consideration of the influence factors of the underwater environment is not sufficient. SUMMARY

[0006] The purpose of the present application is to overcome the defects of the prior art and provide a three-dimensional underwater wireless sensor network dynamic positioning method. Based on the optimization of the non-distance measurement traditional DV-HOP algorithm, the method uses machine intelligence data model and algorithm model to calculate the hop distance of the received multiple beacon nodes, thereby solving the error accumulation problem in the system, reducing the energy consumption, increasing the data security, and significantly improving the positioning accuracy of the nodes.

[0007] The purpose of the present application can be achieved by the following technical solutions:

[0008] The present application provides a three-dimensional underwater wireless sensor network dynamic positioning method, which comprises the following steps:

[0009] Step S1, calculating the minimum hop count and the average hop distance of each unknown node to the beacon node in the three-dimensional underwater wireless sensor network;

[0010] Step S2, converting the signal strength between the unknown node and the beacon node into the communication radius distance between them, improving the HH-VBF underwater routing protocol, wherein HH-VBF refers to hop-by-hop vector forwarding protocol, and using the improved HH-VBF underwater routing protocol to select the next hop node and transmit information, and calculating the updated minimum hop count;

[0011] Step S3, calculating the average hop distance of each unknown node to the beacon node and optimizing the average hop distance;

[0012] Step S4, calculating the coordinates of the unknown node;

[0013] Step S5, target tracking of the node with calculated coordinates.

[0014] Preferably, in step S1, the minimum hop count of each unknown node to the beacon node in the three-dimensional underwater wireless sensor network is calculated, specifically: the beacon node broadcasts its own message in the wireless sensor network, the data packet contains the beacon node ID and the hop count value, the neighbor node receives and records the relevant data, and then forwards the hop count value in the data to its neighbor node, so that all nodes in the wireless sensor network can record the minimum hop count to each beacon node. When the information propagation is completed, all nodes in the wireless sensor network obtain the minimum hop count value to each beacon node.

[0015] Preferably, step S2 includes the following sub-steps:

[0016] Step S21: Based on the characteristic that signal strength varies with distance, convert the signal strength value received by the unknown node between itself and the beacon node into the communication radius distance.

[0017] Step S22: Based on the HH-VBF routing protocol, the Prim algorithm is used to convert the signal strength into the communication radius distance, and the shortest path between each unknown node is calculated. It is determined whether the node is a hole node and the optimal node is selected as the next hop.

[0018] Step S23: Correct the minimum number of hops between the unknown node and each beacon node.

[0019] Preferably, step S21 specifically involves: based on the characteristic that signal strength varies with distance, converting the signal strength value received by the unknown node between itself and the beacon node into the communication radius distance between them, which is 0.25R, 0.5R, 0.75R, and R; where R is the communication radius distance between the unknown node and the beacon node.

[0020] Preferably, step S3 further includes optimizing the average hop distance: by using the weighted summation method of Gaussian radial basis functions, the hop distance of the received multiple beacon nodes is calculated according to the calculation model and the data model to obtain the optimized average hop distance.

[0021] Preferably, the step of calculating the hop distance of multiple received beacon nodes based on the calculation model and data model using a weighted summation method of Gaussian radial basis functions to obtain the optimized average hop distance specifically includes:

[0022] 1) Define the Gaussian function of the Euclidean distance from an unknown node to a beacon node in underwater space, and the corresponding activation function;

[0023] 2) Initialize the center, variance, and weights of the last layer;

[0024] 3) Update the center, width, and weights using the gradient update method;

[0025] 4) Calculate the loss value. If it is within the acceptable range, stop training; otherwise, return to step 2.

[0026] Preferably, step S4 specifically involves the unknown node calculating its own coordinates using the maximum likelihood estimation method based on the recorded average hop distance and minimum hop count to each beacon node.

[0027] Preferably, step S5 includes the following sub-steps:

[0028] Step S51, record the motion trajectory sample of the underwater sensor node;

[0029] Step S52, according to the recorded node coordinate position, use the maneuvering trajectory prediction model to predict the position of the future dynamic node;

[0030] Step S53, use the model predictive controller for underwater dynamic target tracking, the model predictive controller is a process control method for controlling the process while meeting a set of constraints.

[0031] Preferably, the maneuvering trajectory prediction model is a PSR-RBF-based maneuvering trajectory prediction model, and the PSR-RBF is a phase space reconstruction and radial basis function neural network.

[0032] Preferably, in step S52, according to the calculated node coordinate position, the PSR-RBF-based maneuvering trajectory prediction model is used to predict the position of the future dynamic node, specifically:

[0033] First, in the offline training stage, the phase space reconstruction theory is used to process the target maneuvering trajectory time series to determine the optimal embedding dimension and the optimal delay; then, according to the recorded node motion trajectory coordinates, the radial basis function neural network model is trained;

[0034] In the prediction stage, the real-time acquired target data is input into the trained radial basis function neural network model, so as to predict the future motion trajectory of the underwater node, and obtain the predicted coordinate position of the dynamic node.

[0035] Compared with the prior art, the present application has the following advantages:

[0036] 1) The present application introduces a signal strength factor, optimizes the minimum hop value between each beacon node, and makes it more tend to the real value. On the basis of HH-VBF routing protocol, the shortest path between unknown nodes is calculated according to the signal strength converted into communication radius distance, and it is judged whether the node is a hollow node or not, and the optimal node is selected for the next hop, instead of all neighbor nodes. This makes the DV-HOP algorithm more suitable for three-dimensional underwater information propagation, solves the problems of routing hole and excessive redundant forwarding of data packets, increases the network energy consumption and reduces the energy consumption.

[0037] 2) The present application considers the propagation path between nodes, uses the Prim algorithm to calculate the best path of node propagation, obviously reduces the redundancy of node information, reaches the optimal value of communication capacity, and saves the energy consumption.

[0038] 3) The application adopts a weighted summation method of Gaussian radial basis function, calculates the hop distance of the received multiple beacon nodes according to the calculation model and the data model, thereby reducing the error of the average hop distance and uniquely and optimally approximating the average hop distance.

[0039] 4) The application combines the underwater dynamic environment, adopts the improved HH-VBF routing protocol suitable for underwater when propagating information between nodes. Meanwhile, considering that the underwater sensor nodes are non-fixed and change with the water flow, wind direction and movement of ships, the PSR-RBF-based maneuvering trajectory prediction model is adopted to track the positioned dynamic unknown node position, so as to realize the real-time positioning and tracking of the unknown sensor nodes in the dynamic three-dimensional underwater environment. BRIEF DESCRIPTION OF DRAWINGS

[0040] Figure 1 The figure is a flow chart of the method of the application;

[0041] Figure 2 The figure is a topological structure of the underwater wireless sensor network model;

[0042] Figure 3 The figure is a neuron model of the Gaussian radial basis function. DETAILED DESCRIPTION

[0043] The technical solutions in the embodiments of the application will be clearly and completely described below with reference to the drawings in the embodiments of the application. Obviously, the described embodiments are part of the embodiments of the application, rather than all the embodiments of the application. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative work should belong to the protection scope of the application.

[0044] Embodiment 1

[0045] The embodiment provides a three-dimensional underwater wireless sensor network dynamic positioning method, which comprises the following steps:

[0046] Step S1, calculating the minimum hop number and average hop distance of each unknown node to the beacon node in the three-dimensional underwater wireless sensor network, comprising the following sub-steps:

[0047] Step S11, calculating the minimum hop number between each beacon node, the beacon node broadcasts its own message in the wireless sensor network, the data packet contains the beacon node ID and the hop number value, the neighbor node receives and records the related data, and then forwards the hop number value in the data to its neighbor node. In this way, all nodes in the wireless sensor network can record the minimum hop number to each beacon node, and when the information propagation is completed, all nodes in the wireless sensor network obtain the minimum hop number value to each beacon node;

[0048] Step S12, the average hop distance from the unknown node to the beacon node is calculated in the three-dimensional space by using the Euclidean formula, specifically:

[0049]

[0050] Hop ij _pre represents the minimum hop value between the unknown node i and the beacon node j (i≠j), (x i ,y i ,z i ) and (x j ,y j ,z j ) represent the coordinates of the unknown node i and the beacon node j, Hopsize i _pre represents the average hop distance from the unknown node i to the beacon node j.

[0051] Step S2, the signal strength between the unknown node and the beacon node is converted into the communication radius distance between the two, and the HH-VBF underwater routing protocol is improved, wherein HH-VBF refers to hop-by-hop vector forwarding protocol, the improved HH-VBF underwater routing protocol is used for next hop node selection and information transmission, and the updated minimum hop count is calculated, including the following sub-steps:

[0052] Step S21, since the nodes are randomly and non-uniformly deployed in the underwater area, the distances between the unknown nodes located within the communication radius of the beacon node and the beacon node are different, so they cannot all be recorded as 1 hop, otherwise it will cause a large error when calculating the coordinates of the unknown node. Considering that the node positioning error is mainly caused by the selection of hop value 1, according to the characteristics that the signal strength changes with the distance, the signal strength value between the unknown node and the beacon node received by the unknown node is converted into the communication radius distance between the two, which are 0.25R, 0.5R, 0.75R and R respectively, so as to reduce the positioning error; wherein R is the communication radius distance of the node.

[0053] Step S22, the HH-VBF routing protocol is an optimization of the VBF routing protocol, and its idea is to establish a vector line segment between the source node and the Sink node, and extend a pipe outward with the vector as the center line, only the underwater nodes in the pipe can participate in data packet forwarding. However, this protocol has the disadvantages of data propagation in a flooding manner and fixed routing pipe. In order to solve this problem, the HH-VBF routing protocol improves the pipe fixing aspect, and its idea is to establish a new pipe between the last hop node and the Sink node each time the data packet is forwarded, and redefine the forwarding factor:

[0054]

[0055] In the formula, R is the communication radius distance of the node, d is the distance between nodes, and theta is the included angle between the target node vector and the sending node vector.

[0056] The optimization of the HH-VBF routing protocol to VBF is that the routing pipe is not fixed, and each node establishes its own pipe when transmitting, however, the protocol still propagates in a flooding manner, resulting in excessive redundant forwarding of data packets and increasing network energy consumption. In order to solve this problem, the present application is improved on the basis of the HH-VBF routing protocol. The shortest path between each unknown node is calculated according to the signal strength converted into the communication radius distance by using the Prim algorithm, and it is judged whether the node is a void node or not, and the next hop is selected by selecting the optimal node instead of all neighbor nodes, so that the DV-HOP algorithm is more suitable for the propagation of three-dimensional underwater information, solves the routing void problem, and reduces the consumption of energy.

[0057] Step S23, by correcting the minimum hop number between the unknown node and each beacon node, the minimum hop number value from the unknown node to the beacon node can be calculated more accurately, and even if the minimum hop number is not an integer, accurate results can be obtained.

[0058] Step S3, the average hop distance of each unknown node to the beacon node is calculated, and the expression is:

[0059]

[0060] In the formula, Hop ij _act represents the updated minimum hop number value between the unknown node i and the beacon node j (i≠j), (x i ,y i ,z i ) and (x j ,y j ,z j ) represent the coordinates of the unknown node i and the beacon node j, and Hopsize i _act represents the average hop distance of the updated unknown node i to the beacon node j.

[0061] Step S4, the unknown node calculates its own coordinates by using the maximum likelihood estimation method according to the recorded hop distance to each beacon node, which specifically includes:

[0062]

[0063] In the formula, the coordinates of the unknown node P are (X, Y, Z), and the coordinates of the beacon node are (X i , Y i , Z i ); after expansion, it is written as a matrix AX=b, which is specifically:

[0064]

[0065]

[0066]

[0067] It can be concluded that:

[0068] X = (A T A) -1 A T b (8)

[0069] The coordinates of the unknown nodes can be obtained from formula (8).

[0070] Step S5, target tracking is performed on the nodes whose coordinates are calculated, specifically including the following sub-steps:

[0071] Step S51, record the motion trajectory samples of the underwater sensor nodes, specifically: according to the coordinates (x t , y t , z t ) of the nodes calculated in S5, record the moving trajectory of all nodes in a period of time, at time t = 1, 2,..., n, the coordinates of the nodes at time t are X n = (x tn , y tn , z tn ).

[0072] Step S52, according to the recorded coordinate positions of the nodes, use the PSR-RBF-based maneuvering trajectory prediction model to predict the future position of the dynamic nodes, wherein the PSR-RBF is phase space reconstruction and radial basis neural network. Specifically:

[0073] First, in the offline training stage, according to the phase space reconstruction theory, the optimal embedding dimension and the optimal delay are determined for the target maneuvering trajectory time series; then, according to the recorded motion trajectory coordinates X k = [X k , X k-1 ,..., K k+1-m ], the best radial basis prediction model is trained;

[0074] In the prediction stage, the received target data obtained in real time is input into the trained radial basis neural network model, so as to predict the future motion trajectory of the underwater node, and the predicted coordinate position of the dynamic node is obtained;

[0075] Step S53, dynamic target underwater tracking using a model predictive controller, which is a process control method for controlling a process while satisfying a set of constraints. Specifically, in the actual underwater dynamic target tracking process, the control increment is taken as the state quantity of the objective function, and the optimization objective function is constructed as:

[0076]

[0077] wherein N p is the prediction horizon, N c is the control horizon, and Q and R are weight matrices; the first term reflects the ability of the underwater wireless sensor node to track the dynamic target, and the second term reflects the requirement for smooth changes in the control quantity.

[0078] Embodiment 2

[0079] The difference between this embodiment and Embodiment 1 is that:

[0080] According to formula (3), the average hop distance from the unknown node to the beacon node is calculated, which is only an estimation of the position of the unknown node. When the hop number is larger, the estimation error will also be larger. In order to reduce the error of the average hop distance, the step S3 of this embodiment further includes optimizing the average hop distance. By using a Gaussian radial basis function, the hop distances from the unknown node to the beacon node received are weighted and summed to reduce the error of the average hop distance, so as to obtain the optimized average hop distance. Specifically, it includes:

[0081] 1) defining a Gaussian function of the Euclidean distance from any node in the underwater space to the beacon node, corresponding to the activation function;

[0082] The Gaussian function of the Euclidean distance from any node in the underwater space to the beacon node is defined as:

[0083]

[0084] wherein r is the distance from any point in the space to the beacon node;

[0085] corresponding to the activation function expression:

[0086]

[0087] wherein X n represents the position coordinates (x n , y n , z n ) of the unknown node, and X p is the input data of a group of neurons [X1, X2,..., X n ], and c iis the weight of node i, c is the center of the Gaussian function, and σ is the variance of the Gaussian function, which can be used to adjust the influence radius;

[0088] 2) Initialize the center, variance and the last layer weight:

[0089]

[0090] where p is the total number of hidden layer neurons, j is the index of hidden layer neurons, i is the index of input neurons, and max i, min i are the minimum / maximum values of all input information of the i-th feature in the training set;

[0091]

[0092] where c max is the maximum distance between selected centers, and h is the number of hidden layer nodes;

[0093] 3) Update the center, width and weight using gradient update method:

[0094] The center, width and adjustment weight parameters are adaptively adjusted to the optimal values through learning, and the iterative calculation is as follows:

[0095]

[0096]

[0097]

[0098] where W kj (t) is the adjustment weight between the k-th output neuron and the j-th hidden layer neuron at the t-th iteration calculation; c ji (t) is the center component of the j-th hidden layer neuron for the i-th input neuron at the t-th iteration calculation; d ji (t) is the width corresponding to the center c ji (t); and η is the learning factor;

[0099] 4) Calculate the loss value, and if it is within the acceptable range, stop training, otherwise return to 2):

[0100]

[0101] where E is the evaluation of error, O lk is the expected output value of the k-th output neuron at the l-th input sample; and y lk is the network output value of the k-th output neuron at the l-th input sample.

[0102] The above merely illustrates the specific embodiments of the present application, but the protection scope of the present application is not limited thereto, and any skilled person in the art can easily think of various equivalent modifications or replacements within the technical range disclosed by the present application, and these modifications or replacements shall be covered within the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.

Claims

1. A dynamic positioning method for a three-dimensional underwater wireless sensor network, characterized in that, The method comprises the following steps: Step S1, calculating the minimum hop number of each unknown node to the beacon node in the three-dimensional underwater wireless sensor network and the average hop distance; Step S2, converting the signal strength between the unknown node and the beacon node into the communication radius distance therebetween, improving the HH-VBF underwater routing protocol, wherein the HH-VBF refers to the hop-by-hop vector forwarding protocol, selecting the next hop node and transmitting information by using the improved HH-VBF underwater routing protocol, and calculating the updated minimum hop number, comprising the following sub-steps: Step S21, converting the signal strength value between the unknown node and the beacon node received by the unknown node into the communication radius distance therebetween according to the characteristic that the signal strength varies with the distance; Step S22, on the basis of the HH-VBF routing protocol, using the Prim algorithm to calculate the shortest path between each unknown node according to the signal strength converted into the communication radius distance, judging whether the node is a void node, and selecting the optimal node as the next hop; Step S23, correcting the minimum hop number between the unknown node and each beacon node; Step S3, calculating the average hop distance of each unknown node to the beacon node and optimizing the average hop distance; The optimization of the average hop distance specifically comprises: calculating the hop distance of the received multiple beacon nodes according to the calculation model and the data model by using the weighted summation method of the Gaussian radial basis function, so as to obtain the optimized average hop distance; The calculation of the hop distance of the received multiple beacon nodes according to the calculation model and the data model by using the weighted summation method of the Gaussian radial basis function, so as to obtain the optimized average hop distance, specifically comprises: 1) defining the Gaussian function of the Euclidean distance of the unknown node to the beacon node in the underwater space, and the corresponding activation function; 2) initializing the center, variance and last layer weight; 3) updating the center, width and weight by using the gradient update method; 4) calculating the loss value, and stopping training if the loss value is within the acceptable range, otherwise returning to 2); Step S4, calculating the coordinates of the unknown node; Step S5, performing target tracking on the node with the calculated coordinates.

2. The method of claim 1, wherein, The minimum hop number of each unknown node to the beacon node in the three-dimensional underwater wireless sensor network in step S1 is specifically: the beacon node broadcasts its own message in the wireless sensor network, the data packet contains the beacon node ID and the hop number value, the neighbor node receives and records the relevant data, and then forwards the hop number value in the data to its neighbor node, so that all nodes in the wireless sensor network can record the minimum hop number to each beacon node. When the information propagation is completed, all nodes in the wireless sensor network obtain the minimum hop number value to each beacon node.

3. The method of claim 1, wherein, Step S21 specifically comprises: converting the signal strength value between the unknown node and the beacon node received by the unknown node into the communication radius distance therebetween according to the characteristic that the signal strength varies with the distance, which is 0.25R, 0.5R, 0.75R and R; wherein R is the communication radius distance between the beacon node.

4. The method of claim 1, wherein, The step S4 is specifically: the unknown node calculates its own coordinate by using maximum likelihood estimation method according to the recorded average hop distance and minimum hop number to the beacon node.

5. The method of claim 1, wherein, The step S5 includes the following sub-steps: Step S51, record the motion trajectory sample of the underwater sensor node; Step S52, predict the position of the future dynamic node by using a maneuvering trajectory prediction model according to the recorded node coordinate position; Step S53, use a model predictive controller for underwater dynamic target tracking, wherein the model predictive controller is a process control method for controlling the process while meeting a set of constraint conditions.

6. The method of claim 5, wherein, The maneuvering trajectory prediction model is a PSR-RBF-based maneuvering trajectory prediction model, and the PSR-RBF is a phase space reconstruction and radial basis function neural network.

7. The method of claim 6, wherein, In the step S52, the position of the future dynamic node is predicted by using the PSR-RBF-based maneuvering trajectory prediction model according to the calculated node coordinate position, which specifically includes: First, in the offline training stage, the phase space reconstruction theory is used to process the target maneuvering trajectory time series to determine the optimal embedding dimension and the optimal delay; then, the radial basis function neural network model is trained according to the recorded node motion trajectory coordinates; In the prediction stage, the real-time acquired target data is input into the trained radial basis function neural network model, so as to predict the future motion trajectory of the underwater node and obtain the predicted coordinate position of the dynamic node.

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