Particle swarm optimization anti-composite noise underwater acoustic sensor network positioning method

Abstract

The invention discloses a particle swarm optimization anti-composite noise underwater acoustic sensor network positioning method, and relates to the field of underwater sensing positioning, and the method comprises the following steps: constructing a distance equation between a node to be positioned and at least four mobile anchor nodes; selecting one of the distance equations as a reference equation, subtracting the reference equation from other distance equations and writing into a matrix form to obtain an equation set; constructing a distance measurement value equation considering an error source; based on the equation set and the distance measurement value equation, minimizing the sum of distance errors as a target function for positioning; and solving the objective function by adopting an improved particle swarm optimization algorithm, and obtaining a positioning result of the node to be positioned. The positioning precision of the method in a composite noise environment is superior to that of an existing comparison algorithm.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of underwater sensing and positioning, and particularly relates to a particle swarm optimization anti-composite noise underwater acoustic sensor network positioning method. BACKGROUND

[0002] As the core infrastructure of ocean environment monitoring, resource exploration and underwater target tracking, the node positioning accuracy of underwater wireless sensor network directly determines the reliability of data collection and task execution. Due to the special physical properties of water medium, electromagnetic waves and light waves face significant attenuation and scattering problems when propagating underwater, and sound waves become the only viable option for underwater positioning technology due to their unique low attenuation characteristics, mature signal processing technology and good economy. The ranging technology based on time of arrival (TOA) is the core method of underwater positioning technology, which is more practical in resource-constrained underwater wireless sensor networks. The TOA technology measures the propagation time of the signal from the beacon node (known position) to the unknown node , and calculates the distance by combining the sound speed c. However, the actual obtained calculation distance will have some errors due to the influence of sound speed stratification, multipath propagation, environmental noise and other factors. The existing technology combines optimization algorithms with TOA technology to compensate for ranging errors, thereby reducing the influence of measurement errors on positioning results.

[0003] Underwater nodes are limited by clock synchronization errors, hardware time delay drift and ocean environment disturbances (such as biological activity, ship noise), and ranging data often contains mixed noise: system constant bias, Gaussian random noise and impulse outliers. Existing positioning algorithms focus on a single error source (such as Gaussian noise or system constant bias), and have not established a unified framework to cooperatively process the above multi-source heterogeneous errors, so it is urgent to build a new positioning framework that takes into account efficiency and robustness. SUMMARY

[0004] In view of the above problems in the prior art, the particle swarm optimization anti-composite noise underwater acoustic sensor network positioning method provided by the present application solves the problem of low positioning accuracy caused by focusing on a single error source in the prior art.

[0005] In order to achieve the above-mentioned application purposes, the technical scheme adopted by the present application is:

[0006] A particle swarm optimization anti-composite noise underwater acoustic sensor network positioning method is provided, which comprises the following steps:

[0007] Constructing a distance equation of the node to be positioned and at least four mobile anchor nodes;

[0008] Select one of the distance equations as a reference equation, subtract the reference equation from the other distance equations, and write them in matrix form to obtain a system of equations;

[0009] Construct a ranging value equation considering error sources;

[0010] Based on the system of equations and the ranging value equation, minimize the sum of distance errors as the objective function of positioning;

[0011] An improved particle swarm optimization algorithm is used to solve the objective function to obtain the positioning result of the node to be positioned;

[0012] The improvement of the particle swarm optimization algorithm includes:

[0013] The inertia weight in the motion equation of the particle in the traditional particle swarm optimization algorithm is replaced by a nonlinear decay inertia weight, the square loss function in the fitness evaluation is replaced by a Huber loss function, and offline calibration is replaced by real-time deviation compensation calibration.

[0014] The method integrates nonlinear decay inertia weight, robust Huber loss function, and real-time system deviation compensation calibration to handle the interference of complex noise encountered in underwater acoustic sensor network positioning. Theoretical analysis and numerical simulation show that the positioning accuracy of the method is better than that of existing comparative algorithms in a complex noise environment. BRIEF DESCRIPTION OF DRAWINGS

[0015] Figure 1 The flowchart of the method is shown in the figure;

[0016] Figure 2 The sensor nodes in the embodiment of the application are randomly distributed in the monitoring space;

[0017] Figure 3 The schematic diagram of the moving target moving along the spiral ascending trajectory in the embodiment of the application is shown in the figure;

[0018] Figure 4 The positioning results under different time measurement deviations in the embodiment of the application are shown in the figure;

[0019] Figure 5 The error distribution graph when the time measurement deviation is 30 milliseconds in the embodiment of the application is shown in the figure;

[0020] Figure 6 The positioning results under different random deviation variances in the embodiment of the application are shown in the figure;

[0021] Figure 7 The error distribution graph when the random deviation variance is 10 m in the embodiment of the application is shown in the figure;

[0022] Figure 8 The positioning results with different abnormal value deviations in the embodiment of the application are shown in the figure;

[0023] Figure 9 Figure 6 is an error distribution diagram of the abnormal value strength of 5σ in the embodiment of the present application;

[0024] Figure 10 Figure 7 is a comparison of the average positioning error ALE under different models in the embodiment of the present application, and the number of beacon nodes (mobile anchor nodes) is 6 to 11.

[0025] Figure 11 Figure 8 is a positioning result of a mobile node in the embodiment of the present application, and the number of beacon nodes (anchor nodes) is 6.

[0026] Figure 12 Figure 9 is a top view of the embodiment of the present application. Figure 11 Figure 10 is a specific embodiment of the present application. DETAILED DESCRIPTION

[0027] The specific embodiments of the present application are described below to facilitate the understanding of the present application by those skilled in the art, but it should be clear that the present application is not limited to the scope of the specific embodiments, and for those skilled in the art, it is obvious that various changes are within the spirit and scope of the present application defined and determined by the appended claims, and all the inventions utilizing the concept of the present application are within the scope of protection.

[0028] As shown in Figure 1 , the particle swarm optimization anti-composite noise underwater acoustic sensor network positioning method comprises the following steps:

[0029] S1, constructing a distance equation of a node to be positioned and at least 4 mobile anchor nodes;

[0030] S2, selecting one of the distance equations as a reference equation, subtracting the reference equation from the other distance equations and writing them in matrix form to obtain an equation set;

[0031] S3, constructing a ranging value equation considering error sources;

[0032] S4, based on the equation set and the ranging value equation, taking the sum of the distance errors as the objective function of positioning;

[0033] S5, using an improved particle swarm optimization algorithm to solve the objective function to obtain the positioning result of the node to be positioned;

[0034] The improvement of the particle swarm optimization algorithm includes:

[0035] The inertia weight in the motion equation of the particle in the traditional particle swarm optimization algorithm is replaced by a nonlinear decay inertia weight, the square loss function in the fitness evaluation is replaced by a Huber loss function, and the offline calibration is replaced by real-time deviation compensation calibration.

[0036] In this embodiment, the expression for the distance equation between the positioning node and a single moving anchor node is:

[0037]

[0038] Therefore, the expression for the distance equation between the node to be located and at least four moving anchor nodes is:

[0039]

[0040] in The coordinates of the node to be located; For the first The coordinates of each moving anchor node ; For the node to be located and the first The distance between each moving anchor node; For the node to be located and the first The distance between each moving anchor node.

[0041] The above distance equations are simplified by eliminating quadratic terms, with the first equation as the baseline, and the remaining equations subtracted from the baseline equation:

[0042]

[0043] Written in matrix form, it is ,in:

[0044]

[0045] The superscript T indicates the transpose of the matrix.

[0046] In this embodiment, the ranging value of underwater acoustic positioning is affected by multiple error sources. The expression of the ranging value equation considering the error sources is as follows:

[0047]

[0048] in Indicates the node to be located and the first The measured distance of each moving anchor node; Is the node to be located and the first The actual distance of each moving anchor node , This indicates the actual location of the node to be located. Indicates the first The actual location of each moving anchor node; Indicates systematic bias; Indicates the first Gaussian random noise of a moving anchor node; Indicates the first Outlier noise from a moving anchor node.

[0049] The optimal solution X for the positioning optimization problem of underwater acoustic wireless sensor networks based on TOA ranging technology can be obtained by minimizing the sum of distance errors. The expression for minimizing the sum of distance errors is:

[0050]

[0051] in This represents minimizing the sum of distance errors; This indicates finding the minimum value; This indicates the location result of the node to be located; Indicates the first The actual location of each moving anchor node; Indicates the node to be located and the first The actual distance between each moving anchor node; N is the total number of moving anchor nodes.

[0052] Traditional Particle Swarm Optimization (PSO) algorithms achieve multi-dimensional space search through a swarm cooperation mechanism, and their dynamic behavior is defined by position-velocity update rules. Let the target search space be... If the particle swarm size is M, then the equation of motion for the i-th particle in the t-th iteration is:

[0053]

[0054] in, This is the optimal position in the particle's history. Let W be the group's historical optimal position, W be the inertia weight, and c1 and c2 be fixed learning factors. This is a random disturbance term.

[0055] Traditional PSO with fixed inertia weights leads to an imbalance between global exploration and local exploitation capabilities, making it difficult to adapt to the dynamic optimization requirements under complex error environments. The expression for the nonlinear decaying inertia weights proposed in this embodiment is as follows:

[0056]

[0057] in This represents the nonlinear decaying inertia weight corresponding to the t-th iteration; and These represent the upper and lower bounds of the nonlinear decaying inertia weight, respectively. This indicates the number of iterations to terminate the transition phase, with a value of 120. This is the decay rate control factor. , , .

[0058] Traditional squared loss functions are highly sensitive to outliers, leading to localization results being dominated by abnormal ranging data. This embodiment introduces the Huber loss function to reconstruct the fitness evaluation criterion. The expression for the Huber loss function is:

[0059]

[0060] in The value of Huber's loss function; Indicates the node to be located and the first Distance residuals of each moving anchor node , Indicates the node to be located and the first The measured distance of each moving anchor node. This indicates the actual location of the node to be located. Indicates the first The actual location of each moving anchor node; For threshold parameters, , , This represents the estimator of the absolute deviation of the median. This represents the medain function.

[0061] Practical ranging systems often suffer from time-varying offset errors (such as clock skew). Traditional methods rely on offline calibration, which is difficult to adapt to dynamic environments. This embodiment proposes a real-time offset compensation calibration method:

[0062] First, calculate the deviation observations:

[0063]

[0064] Next, perform an EWMA (Exponentially Weighted Moving Average) update:

[0065]

[0066] The effective window length of EWMA is determined by β, where β is generally taken as 0.8.

[0067] The deviation estimate is fed back to the ranging data preprocessing stage:

[0068]

[0069] in For the t-th iteration The distance measurement value corrected for each moving anchor node; Indicates the node to be located and the first The measured distance of each moving anchor node; This represents the estimated value of the constant deviation in underwater positioning at the t-th iteration; denotes the bias observation at the tth iteration; denotes the measured distance between the node to be located and the tth mobile anchor node at the tth iteration; denotes the measured distance between the node to be located and the tth mobile anchor node at the tth iteration; denotes the current global optimal positioning location at the tth iteration; denotes the measured distance between the node to be located and the tth mobile anchor node at the tth iteration; denotes the true position of the tth mobile anchor node.

[0070] In this embodiment, the measured distance data needs to be processed as follows:

[0071] Raw data acquisition: collect raw ranging values from devices such as underwater acoustic sensors ;

[0072] Bias real-time estimation: calculate the bias at the current time using historical error data through the Exponential Moving Average (EMMA) method ;

[0073] Compensation correction: subtract the raw from the raw to obtain the corrected ;

[0074] Robust error calculation: input the corrected into the Huber loss function to calculate the error between the current particle position and ;

[0075] Closed-loop optimization feedback: input the corrected into the fitness function for calculation, and through particle swarm iteration optimization of the node position to be measured, the new error data is updated to form a closed-loop correction mechanism of measurement-compensation-optimization-recompensation, continuously improving the positioning accuracy.

[0076] Based on the above improvement strategies, in the process of solving the objective function, the motion equation of the ith particle at the tth iteration of the improved particle swarm optimization algorithm is:

[0077]

[0078] where denotes the motion speed of the ith particle at the t+1th iteration; denotes the nonlinear decay inertia weight corresponding to the tth iteration; denotes the motion speed of the ith particle at the tth iteration; and are learning factors; and are random disturbance items between 0 and 1; is the historical optimal position of the ith particle; is the position of the i-th particle solved in the t-th iteration; is the position of the i-th particle solved in the t+1-th iteration; is the historical optimal position of the particle swarm; is the fitness function; is the regularization coefficient; represents the estimation of the constant bias in the t-th iteration in underwater positioning; the position of the particle is the positioning result of the node to be positioned. The value of is 0.1.

[0079] In the specific implementation process, in order to verify the effect of the method, the embodiment further gives the design and execution process of the verification experiment.

[0080] In the simulation, the beacons (mobile anchor nodes) and unknown nodes (nodes to be positioned) are jointly deployed in a 1000m×1000m×1000m cubic space. The positioning scene can be divided into static positioning and dynamic positioning, which respectively simulate underwater stationary targets (underwater fixed defense instruments) and underwater mobile targets (AUVs in the ocean). The unknown nodes (whose coordinates need to be calculated by the positioning algorithm) and sensor nodes (i.e. anchor nodes, used to position the unknown nodes) are randomly deployed in the entire cubic monitoring space, and the specific network architecture is as shown in Figure 2 , wherein the blue circles and orange pentagrams respectively represent beacon nodes and unknown nodes. The underwater mobile target moves along a spiral ascending trajectory in the monitoring space, as shown in Figure 3 . According to the modeling of mixed noise, the distance measurement error is composed of constant bias, random noise and outlier noise. Unless otherwise specified, the constant bias in the simulation is 10m by default, the variance of the random noise is 5m by default, and the amplitude of the outlier noise is 2 .

[0081] For the evaluation of positioning accuracy, the positioning error and the average positioning error are used as evaluation indexes, and the specific calculation formula definitions are as follows:

[0082] Positioning error:

[0083] Average positioning error:

[0084] Wherein, T represents the discrete time in mobile positioning; is the calculated coordinate of the unknown node; is the actual coordinate of the unknown node; is the calculated coordinate of the unknown node changing with time in mobile positioning; is the actual coordinate of the unknown node changing with time in mobile positioning. ​

[0085] First, the positioning accuracy of the four algorithms was compared and verified under different intensities of three types of interference (clock measurement deviation, random noise, and outlier noise). From Figure 4 As can be seen, the ARBC-PSO algorithm (this method) exhibits the best positioning accuracy. Among them, the ARBC-PSO and CFS algorithms can effectively handle interference from clock measurement deviations, and their positioning accuracy remains stable as the interference intensity increases. In contrast, the PSO and LS algorithms are sensitive to interference from time measurement deviations, and their accuracy (ALE) increases linearly, with PSO showing the steepest slope. Figure 6 The results show that all four algorithms exhibit good noise resistance under low-level random noise interference. While the ALE (Advanced Level Error) of all algorithms generally increases linearly with increasing random noise intensity, the ALE is more gradual compared to the LS and CFS algorithms, particularly in ARBC-PSO. Similarly, from... Figure 8 As can be seen, with the increase of outlier noise intensity, the ARBC-PSO algorithm has the best positioning accuracy and a relatively gentle trend of change. Figure 5 , Figure 7 and Figure 9 The error distribution of each algorithm in the data shows that, under the interference of three different biases, the ARBC-PSO algorithm has the smallest error and the most concentrated error distribution, demonstrating excellent noise resistance and positioning performance.

[0086] Next, simulations were conducted to verify the four algorithms under different beacon node densities and distributions, demonstrating the algorithms' localization performance in tracking moving nodes. From... Figure 10 As can be seen, under the basic condition of random beacon deployment, the point-to-point average positioning error (ALE) of the four algorithms generally decreases with the increase of the number of beacon nodes. Among them, the ALE of the PSO-like algorithms (original PSO and ARBC-PSO algorithms) decreases more stably, indicating that the positioning accuracy of the PSO-like algorithms is positively correlated with the number of beacon nodes. Figure 11 and Figure 12 The simulation demonstrated the localization of a target node moving along a spiral ascent trajectory using four different algorithms. Figure 12 yes Figure 11 The top-down views of these two figures show that the calculated trajectory located by the ARBC-PSO algorithm best matches the actual target trajectory. This demonstrates that the ARBC-PSO model possesses excellent tracking and localization capabilities for mobile nodes in UASNs and good noise resistance to underwater composite noise.

[0087] In conclusion, this invention addresses the interference of complex noise encountered in underwater acoustic sensor network localization by integrating nonlinear decaying inertial weights, a robust Huber loss function, and real-time system bias compensation calibration. Theoretical analysis and numerical simulations demonstrate that this method achieves superior localization accuracy compared to existing algorithms in environments with complex noise.

Claims

1. A particle swarm optimization anti-composite noise underwater acoustic sensor network positioning method, characterized in that, The method comprises the following steps: constructing a distance equation of a to-be-positioned node and at least four mobile anchor nodes; selecting one of the distance equations as a reference equation, subtracting the reference equation from the other distance equations, and writing the distance equations in a matrix form to obtain an equation group; constructing a ranging value equation considering error sources; based on the equation group and the ranging value equation, taking minimization of a sum of distance errors as a positioning objective function; solving the objective function by using an improved particle swarm optimization algorithm to obtain a positioning result of the to-be-positioned node; wherein the improvement of the particle swarm optimization algorithm comprises: replacing an inertia weight in a motion equation of a particle in a traditional particle swarm optimization algorithm with a nonlinear decay inertia weight, replacing a square loss function in fitness evaluation with a Huber loss function, and replacing offline calibration with real-time deviation compensation calibration.

2. The particle swarm optimization anti-composite noise underwater acoustic sensor network positioning method according to claim 1, characterized in that, An expression of the distance equation of the to-be-positioned node and the at least four mobile anchor nodes is: ； wherein is the coordinate of the node to be positioned; is the coordinate of the th mobile anchor node, ; is the distance between the node to be positioned and the th mobile anchor node; is the distance between the node to be positioned and the th mobile anchor node.

3. The particle swarm optimization anti-composite noise underwater acoustic sensor network positioning method according to claim 2, characterized in that, An expression of the equation group is: ； wherein: ； a superscript T represents a transpose of a matrix.

4. The particle swarm optimization anti-composite noise underwater acoustic sensor network positioning method according to claim 1, characterized in that, An expression of the ranging value equation considering error sources is: ； wherein denotes a measured distance of the node to be localized to the th mobile anchor node; is the true distance of the node to be localized to the th mobile anchor node, , denotes the true position of the node to be localized, denotes the true position of the th mobile anchor node; denotes a systematic bias; denotes a Gaussian random noise of the th mobile anchor node; denotes an outlier noise of the th mobile anchor node.

5. The particle swarm optimization anti-composite noise underwater acoustic sensor network positioning method according to claim 1, characterized in that, An expression of the minimization of the sum of the distance errors is: ； wherein denotes minimizing the sum of distance errors; denotes finding the minimum; denotes the positioning result of the node to be positioned; denotes the real position of the th mobile anchor node; denotes the real distance between the node to be positioned and the th mobile anchor node; N is the total number of mobile anchor nodes.

6. The particle swarm optimization anti-composite noise underwater acoustic sensor network positioning method according to claim 5, characterized in that, An expression of the nonlinear decay inertia weight is: ； wherein denotes the nonlinear damping inertia weight corresponding to the tth iteration; and denote the upper and lower bounds of the nonlinear damping inertia weight, respectively; denotes the number of iterations at the end of the transition phase, which takes the value 120; is the damping rate control factor.

7. The particle swarm optimization anti-composite noise underwater acoustic sensor network positioning method according to claim 5, characterized in that, An expression of the Huber loss function is: ； wherein is a Huber loss function value; denotes a ranging residual of the node to be localized to the th mobile anchor node, , denotes a measured distance of the node to be localized to the th mobile anchor node, denotes a true position of the node to be localized, denotes a true position of the th mobile anchor node; is a threshold parameter, , , denotes a median absolute deviation estimator, denotes a medain function.

8. The particle swarm optimization anti-composite noise underwater acoustic sensor network positioning method according to claim 5, characterized in that, An expression of the real-time deviation compensation calibration is: ； ； ； wherein is the corrected range value for the tth iteration for the th mobile anchor node; denotes the measured distance of the node to be localized to the th mobile anchor node; denotes the estimate of the constant bias in the tth iteration for underwater localization; denotes the bias observation for the tth iteration; denotes the measured distance of the node to be localized to the th mobile anchor node in the tth iteration; denotes the current globally optimal localization position at the tth iteration; denotes the true position of the th mobile anchor node; is a constant.

9. The particle swarm optimization anti-composite noise underwater acoustic sensor network positioning method according to claim 5, characterized in that, In a process of solving the objective function by using the improved particle swarm optimization algorithm, a motion equation of an i th particle in a t th iteration is: ； wherein denotes the motion velocity of the i-th particle at the t+1-th iteration; denotes the non-linear damping inertia weight corresponding to the t-th iteration; denotes the motion velocity of the i-th particle at the t-th iteration; and is a learning factor; and is a random perturbation term between 0 and 1; is the historical optimal position of the i-th particle; is the position of the i-th particle obtained at the t-th iteration; is the position of the i-th particle obtained at the t+1-th iteration; is the historical optimal position of the particle swarm; is a fitness function; is a regularization coefficient; denotes the estimation of the constant bias in the underwater positioning at the t-th iteration; the position of the particle is the positioning result of the node to be positioned.

10. The particle swarm optimization anti-composite noise underwater acoustic sensor network positioning method according to claim 9, characterized in that, the value of 0.1.

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