Underwater target electric field positioning method based on particle swarm differential evolution hybrid algorithm

Abstract

The present invention discloses an underwater target electric field positioning method based on a particle swarm differential evolution hybrid algorithm. The differential evolution algorithm DE and the particle swarm optimization algorithm PSO are combined to propose an underwater target electric field positioning method based on a particle swarm differential evolution hybrid algorithm PSODE. ​​The method not only utilizes a three-layer medium electric field radiation model that is closer to the actual positioning scenario, but also integrates multiple algorithms to reduce the risk of falling into a local optimal solution. Dynamic parameters are also adjusted to meet the needs of practical applications, ultimately achieving long-distance and precise positioning of an underwater constant-current electric dipole source.

Description

Technical Field

[0001] The present invention belongs to the technical field of target positioning, and in particular relates to an underwater target electric field positioning method based on a particle swarm differential evolution hybrid algorithm. Background Art

[0002] Underwater target electric field positioning technology uses the electrodes on the positioning device as a signal receiving array to extract and process the electrical signals generated by the target, enabling accurate estimation of the target's spatial position parameters. This technology relies on precise electrode placement and advanced signal processing algorithms, providing new perspectives and solutions for underwater detection.

[0003] Previous research has shown that the electrostatic field of underwater vehicles originates from corrosion and anti-corrosion currents. The potential generated by these currents can still reach tens of nanovolts even at a distance of several kilometers, making it possible to use electric fields for long-range detection and positioning of underwater vehicles. Using electric fields to remotely locate underwater vehicles in shallow waters is equivalent to the problem of locating a constant-current electric dipole source in a stratified ocean environment. Extensive research has been conducted domestically and internationally on models, devices, and algorithms for electric field positioning of constant-current electric dipole sources in marine environments. However, this research still has certain limitations.

[0004] First, when solving the electric field model for an underwater constant-current electric dipole source, most researchers choose infinite or semi-infinite seawater as the positioning scenario. A three-layer medium scenario, considering air, seawater, and the seabed, is rarely chosen. This is primarily because the complexity of the inversion algorithm increases significantly with the number of dielectric layers. However, a three-layer medium model, which is closer to the actual positioning scenario, improves the accuracy of the electric field solution and, in turn, positioning accuracy.

[0005] Secondly, there are two main options for positioning algorithms: field source parameter fitting based on numerical calculations and field source parameter inversion based on intelligent optimization algorithms. The former typically requires fewer measurement points, is less computationally intensive, and has faster operation speeds. However, it also exhibits strong dependence on initial values ​​and limited noise resilience, making it primarily suitable for near-field applications. In contrast, the latter, which incorporates intelligent algorithms, can effectively address the issue of initial value dependence. Despite this, these methods still face challenges such as limited positioning range, susceptibility to local optimal solutions, and low spatial dimensionality. Furthermore, currently, single algorithms struggle to balance global exploration and local exploitation, prone to becoming trapped in local optimal solutions or experiencing slow convergence. To improve the convergence speed of optimization algorithms, enhance global search capabilities, and reduce the risk of becoming trapped in local optimal solutions, combining different algorithms to leverage their strengths has become a breakthrough in current research.

[0006] Third, in practical applications, some environments and positioning parameters may change dynamically. For example, seawater movement causes the position of electric field sensors to constantly shift. In some applications, electric field sensors themselves are even in motion, such as when mounted on underwater vehicles for guidance. These factors increase the number of unknown parameters in the actual positioning process, significantly increasing the difficulty of positioning. In short, existing positioning algorithms struggle to meet the demands of practical applications.

[0007] In summary, in-depth research on underwater electric field positioning related technologies still has important scientific value and engineering significance. Summary of the Invention

[0008] In order to overcome the shortcomings of the existing technology, the present invention provides an underwater target electric field positioning method based on a particle swarm differential evolution hybrid algorithm. The differential evolution algorithm DE and the particle swarm optimization algorithm PSO are combined to propose an underwater target electric field positioning method based on a particle swarm differential evolution hybrid algorithm PSODE. ​​This method not only utilizes a three-layer medium electric field radiation model that is closer to the actual positioning scenario, but also integrates multiple algorithms to reduce the risk of falling into a local optimal solution. It also adjusts dynamic parameters to meet the needs of practical applications, and ultimately realizes the long-distance and precise positioning of an underwater constant current electric dipole source.

[0009] The technical solutions adopted by the present invention to solve the technical problems are as follows:

[0010] Step 1: Selection and placement of electric field sensors;

[0011] The underwater target is equivalent to a constant current electric dipole source, and the electric field radiated by the constant current electric dipole source is measured using a three-axis electric field sensor. A three-axis electric field sensor consists of six electric field sensor electrodes, which are arranged vertically in pairs.

[0012] Step 2: Measurement of electric field radiated by underwater target;

[0013] Select seven different locations within the constant current electric dipole source positioning area, with the spacing between different locations being greater than 10m and less than 200m. Measure the electric field signals at the seven different locations as the electric field measurement values ​​for the positioning algorithm.

[0014] Step 3: Implementation of underwater constant current electric dipole source positioning algorithm;

[0015] Combining the differential evolution algorithm DE and the particle swarm optimization algorithm PSO, an underwater target electric field positioning method based on the particle swarm differential evolution hybrid algorithm PSODE is adopted to determine the target space coordinates by minimizing the difference between the electric field prediction value and the electric field measurement value.

[0016] The differential evolution algorithm DE and particle swarm optimization algorithm PSO generate their own initial solution sets A and B respectively. The initial solution set represents the initial candidate position set generated by the algorithm at the physical level. Each solution represents a possible three-dimensional coordinate parameter of a constant current electric dipole source. The differential evolution algorithm DE generates a new solution set through mutation, crossover and selection operations. , adaptively adjust the variation factor ;

[0017] The particle swarm optimization algorithm PSO uses the differential evolution algorithm DE to operate the new solution set As input, update the particle velocity and position, and adaptively adjust the inertia weight update function , the particle update formula is:

[0018] (1)

[0019] (2)

[0020] in, is the particle update speed, express Moment The updated particle velocity of each particle, express Moment The particle velocity of each particle; 、 are the individual learning factor and the group learning factor, 、 For interval Random numbers within is the new solution set of differential evolution algorithm DE The A solution, is the first in the particle swarm optimization algorithm PSO solution set B A solution, for time The global optimal solution in The updated particle swarm optimization algorithm PSO solution set ;

[0021] The solution set after the algorithm is updated 、 As the input of the objective function, the objective function values ​​of the differential evolution algorithm DE and the particle swarm optimization algorithm PSO are calculated respectively. and , the expression of the objective function is:

[0022] (3)

[0023] in, is the objective function; is the dynamic weight based on the signal-to-noise ratio, is the robust Huber loss function; For the The electric field prediction value of each electric field sensor, For the The electric field measurement value of the electric field sensor; n represents the number of electric field sensors;

[0024] Calculate the selection probability of differential evolution algorithm DE and particle swarm optimization algorithm PSO respectively, and use random numbers The decision is made to update the solution set, and after iteration until convergence, the optimal solution in the solution set is output, that is, the optimal parameter estimate of the position of the underwater constant current electric dipole source.

[0025] Preferably, the sensitivity of the electric field sensor is better than 1 .

[0026] Preferably, the step 3 is specifically:

[0027] Step 3-1: Use the electric field sensor as the reference system in seawater, select any electric field sensor as the coordinate origin, and use the measurement axis direction of the electric field sensor as the positive direction of the coordinate axis to establish a rectangular coordinate system; define the position vector to be optimized of the constant current electric dipole source ;

[0028] By combining the dynamic weight of the signal-to-noise ratio (SNR) with the Huber loss, the objective function of multi-sensor fusion is constructed, and the positioning problem is transformed into a problem of minimizing the difference between the electric field measurement value and the electric field prediction value. The specific definition of the objective function is:

[0029] (4)

[0030] in, is the robust Huber loss function, which is specifically expressed as:

[0031] (5)

[0032] (6)

[0033] Where, Indicates the The signal-to-noise ratio of the signal received by the electric field sensor, Indicates the The signal-to-noise ratio of the signal received by each electric field sensor; represents the residual, that is, the difference between the predicted and measured electric field values; Represents the threshold parameter, which is used to control the critical point at which the loss function switches from mean square error (MSE) to mean absolute error (MAE);

[0034] Considering the three-layer ocean environment consisting of air, seawater, and seabed, a single three-axis electric field sensor is used to collect electric field data at different locations within the target positioning area, and the x, y, and z components of the electric field intensity at each location are obtained. Assuming that seawater is a uniform and isotropic medium, and its conductivity parameters remain constant in time and space; the dielectric constant and conductivity of each layer of medium are respectively 、 , , subscripts 1, 2, and 3 represent air, seawater, and seabed, respectively. is the depth of seawater, in m;

[0035] The electric field model of a constant current electric dipole source radiating in three parallel stratified media of air, seawater and seabed is used to solve the predicted electric field values ​​at seven locations. The specific expression is:

[0036] (7)

[0037] Where, is the predicted electric field value obtained by any electric field sensor, in V / m; Represents the electric dipole moment of the constant current electric dipole, the coefficient 、 The expression is:

[0038] (8)

[0039] (9)

[0040] In the formula, the mirror transformation matrices corresponding to the air-seawater interface and the seawater-seabed interface are , is the unit normal vector of the seawater-air interface, and its direction is from seawater to air. is the unit normal vector of the seawater-seabed interface, with its direction pointing from seawater to seabed; the matrix 、 、 、 is the electric field intensity transfer matrix at point M, and the specific calculation formula is:

[0041] (10)

[0042] Where, express The model, 、 、 、 represents the position vector of any field point relative to the constant current electric dipole group in the model. Different subscripts represent the mirror electric dipole group formed by the underwater constant current electric dipole source mirroring back and forth between the air-seawater interface and the seawater-seabed interface. The integer ; is the identity matrix;

[0043] Step 3-2: Generate the initial solution sets of differential evolution algorithm DE and particle swarm optimization algorithm PSO respectively; the solution set represents the initial candidate position set generated by the algorithm, and each solution represents a possible three-dimensional coordinate parameter of the constant current electric dipole source; the initial solution set A of differential evolution algorithm DE = , the initial solution set B of particle swarm optimization algorithm PSO= ;

[0044] Perform mutation, crossover, and selection operations on the differential evolution algorithm DE solution set to generate a new solution set = , the specific expression of the mutation process is as follows:

[0045] (11)

[0046] in, is the solution after mutation, 、 and is a randomly selected solution individual from the solution set, It represents the mutation factor update function at time t, and its expression is as follows:

[0047] (12)

[0048] in, is the maximum value of the variation factor, is the minimum value of the variation factor, Indicates the maximum number of iterations;

[0049] Will Substitute each solution into the formula , calculate the minimum value of the objective function of the differential evolution algorithm DE ;

[0050] Step 3-3: Set the solution of differential evolution algorithm DE Input the particle swarm optimization algorithm PSO as the input to the particle swarm update formula of the particle swarm optimization algorithm PSO, and update the speed and position of the population as follows:

[0051] (13)

[0052] (14)

[0053] in, The update formula is as follows:

[0054] (15)

[0055] in, is the maximum value of the inertia weight, is the minimum value of inertia weight;

[0056] Particle Swarm Optimization Algorithm PSO Solution Set Substitute each solution into the formula Calculate the minimum objective function value of the particle swarm optimization algorithm PSO ;

[0057] Step 3-4: Compare and The size of the target function is selected as the global minimum value. ; Calculate the selection probability of differential evolution algorithm DE and the selection probability of the particle swarm optimization algorithm PSO :

[0058] (16)

[0059] (17)

[0060] Where, and The calculation formulas are:

[0061] (18)

[0062] (19)

[0063] Step 3-5: Generate interval Random numbers between ,if , select the differential evolution algorithm DE and update the solution set according to step 3-2; if , then select the particle swarm optimization algorithm PSO and update the solution set according to step 3-3;

[0064] Step 3-6: Determine whether the maximum number of iterations has been reached. If not, continue to update the solution set according to step 3-5; if it has been reached, compare and ,like , then the solution set after the nth update of the DE algorithm is selected As the result of the positioning algorithm; otherwise, the solution set after the nth update of the PSO algorithm As a result of the localization algorithm, the solution set contains the optimal position estimation parameters of the constant current electric dipole source.

[0065] A computer program enables a computer to execute the above-mentioned underwater target electric field positioning method.

[0066] An electronic device comprises: a processor and a memory; the memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory, so that the electronic device performs the above-mentioned underwater target electric field positioning method.

[0067] A computer-readable storage medium stores a computer program, which implements the above-mentioned underwater target electric field positioning method when executed by a processor.

[0068] A chip includes: a processor for calling and running a computer program from a memory, so that a device equipped with the chip executes the above-mentioned underwater target electric field positioning method.

[0069] A computer program product includes a computer storage medium storing a computer program, wherein the computer program includes instructions executable by at least one processor, and when the instructions are executed by the at least one processor, the above-mentioned underwater target electric field positioning method is implemented.

[0070] The beneficial effects of the present invention are as follows:

[0071] The present invention realizes high-precision target positioning in shallow sea environments through the collaborative optimization of the PSO and DE algorithms and dynamic parameter adjustment. The experiment of the present invention equates the underwater target to a constant-current electric dipole source. From the results of multiple experiments, this method can more accurately realize the positioning of the underwater constant-current electric dipole source. Its technical solution establishes a complete positioning algorithm process by integrating the shallow sea three-layer medium electric field radiation model and the PSODE hybrid optimization algorithm, and has been verified through a large number of computer simulations. Through the method proposed by the present invention, engineers and researchers can realize long-distance target positioning when the target position is unknown, which significantly improves the practical level of underwater electric field positioning technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 Flow chart of the method of the present invention;

[0073] Figure 2 This is a schematic diagram of positioning the underwater constant current electric dipole source of the present invention;

[0074] Figure 3 It is the convergence curve diagram of the objective function of the present invention;

[0075] Figure 4This is a diagram showing the three-dimensional positioning results of an underwater constant-current electric dipole source using the PSODE algorithm according to an embodiment of the present invention. DETAILED DESCRIPTION

[0076] The present invention will be further described below with reference to the accompanying drawings and examples.

[0077] In order to meet the needs of electric field positioning of underwater targets in actual application scenarios, the present invention equates the underwater target to a constant-current electric dipole source. Aiming at the electric field positioning problem of the constant-current electric dipole source underwater in shallow water, an underwater target electric field positioning method based on the particle swarm differential evolution hybrid algorithm (PSODE) is proposed based on the electric field radiation model of the constant-current electric dipole source in a three-layer medium. Through multi-algorithm collaborative optimization and dynamic parameter adjustment, the long-distance and high-precision positioning performance of the underwater constant-current electric dipole source in a shallow sea environment is achieved.

[0078] This paper combines multi-algorithm collaborative optimization and dynamic parameter adjustment to propose an underwater target electric field localization method based on a hybrid particle swarm differential evolution (PSODE) algorithm. This method can achieve high-precision, long-range localization of underwater constant-current electric dipole sources in shallow water environments. Simulations validate the effectiveness of the localization algorithm.

[0079] The main contents of the present invention are:

[0080] (1) Selection and placement of electric field sensors: The underwater target is equivalent to a constant current electric dipole source, and the electric field radiated by the constant current electric dipole source is measured using a three-axis electric field sensor. A three-axis electric field sensor consists of six electric field sensor electrodes, which are placed vertically in pairs. This placement can measure the components of the electric field strength along the x-axis, y-axis, and z-axis. Based on the needs of long-distance positioning, a sensor with a sensitivity better than 1 electric field sensor.

[0081] (2) Measurement of electric field radiated by underwater targets: Seven different locations are selected within the constant current electric dipole source positioning area. The spacing between different locations is required to be greater than 10m and less than 200m. The electric field signals are measured at the seven different locations as the electric field measurement values ​​of the positioning algorithm.

[0082] (3) Implementation of underwater constant current electric dipole source positioning algorithm: In order to achieve long-distance and high-precision positioning of underwater constant current electric dipole sources in shallow sea environments, the present invention proposes a positioning strategy based on the PSODE hybrid optimization algorithm, whose core goal is to determine the target space coordinates by minimizing the difference between the electric field prediction value and the measured value. In view of the problems that the traditional DE algorithm is prone to premature convergence and the PSO algorithm has insufficient local search capabilities, the present invention takes the strengths of the differential evolution algorithm (DE) and the particle swarm optimization algorithm (PSO) and proposes an underwater target electric field positioning method based on the particle swarm differential evolution hybrid algorithm (PSODE). Through multi-algorithm collaborative optimization and dynamic parameter adjustment, the algorithm convergence characteristics can be effectively improved and the risk of falling into a local optimal solution can be reduced. The overall steps of the PSODE positioning algorithm are as follows:

[0083] DE and PSO algorithms generate their own initial solution sets A and B respectively. The solution set here represents the initial candidate position set generated by the algorithm at the physical level. Each solution represents a possible three-dimensional coordinate parameter of the constant current electric dipole source. DE algorithm generates new solution sets through mutation, crossover and selection operations. , adaptively adjust the variation factor .

[0084] The PSO algorithm takes the new solution set after the DE algorithm is operated As input, update the particle velocity and position, and adaptively adjust the inertia weight update function The main particle update formula is:

[0085]

[0086]

[0087] The updated solution set 、 As the input of the objective function, the objective function values ​​of DE and PSO algorithms are calculated respectively and , the expression of the objective function is:

[0088]

[0089] in, The core function is to guide the optimization algorithm to search for the target position by quantifying the difference between the predicted value and the measured value of the electric field. is the dynamic weight based on the signal-to-noise ratio, is the robust Huber loss function. For the The electric field prediction value of each electric field sensor is calculated and generated by the electric field radiation model of a constant current electric dipole source in a three-layer medium. is the measured value of the electric field.

[0090] Calculate the selection probability of DE and PSO algorithms respectively, and use random numbers The decision is made to update the solution set. After iteration until convergence, the optimal solution in the solution set is output, which is the optimal parameter estimate of the position of the underwater constant current electric dipole source.

[0091] The flow chart of the particle swarm differential evolution hybrid algorithm (PSODE) is as follows Figure 1 As shown, the technical solution adopted is divided into the following six steps:

[0092] Step 1: First, take the electric field sensor as the reference system in the seawater, select any electric field sensor as the coordinate origin, and use the measurement axis direction of the electric field sensor as the positive direction of the coordinate axis to establish a rectangular coordinate system. Then, define the position vector to be optimized of the constant current electric dipole source .

[0093] The present invention combines the dynamic SNR weight with the Huber loss to construct the objective function of multi-sensor fusion, transforming the positioning problem into a problem of minimizing the difference between the electric field measurement value and the electric field prediction value. The specific definition of the objective function is:

[0094]

[0095] in, is the robust Huber loss function, which is specifically expressed as:

[0096]

[0097]

[0098] Where, The Huber loss function is the weight of the current electric field sensor's signal-to-noise ratio relative to the total signal-to-noise ratio. It can determine the contribution of high-SNR data and enhance the robustness of the algorithm. The Huber loss function combines the mean squared error (MSE) and mean absolute error (MAE) loss functions to overcome their shortcomings. Using MSE for small errors and MAE for large errors effectively reduces the algorithm's sensitivity to outliers when dealing with regression problems.

[0099] formula middle, For the The electric field measurement value of each electric field sensor is input through the electric field sensor; For the The predicted electric field values ​​of each electric field sensor are calculated using a three-layer medium electric field radiation model. This serves as a basis for iteratively estimating the parameters of the underwater constant current electric dipole source. The calculation of the predicted electric field strength value of the constant current electric dipole source is specifically given below:

[0100] like Figure 2 As shown, considering the three-layer ocean environment composed of air, seawater and seabed, a single three-axis electric field sensor is used to collect electric field data at different positions within the target positioning area to obtain the x, y and z components of the electric field strength at each position. The conductivity in seawater is affected by many factors, including the composition and concentration of electrolytes, temperature, pressure, etc. For the convenience of research, the present invention assumes that seawater is a uniform isotropic medium and its conductivity parameters remain constant in time and space. The dielectric constant and conductivity of each layer of medium are respectively 、 , subscripts 1, 2, and 3 represent air, seawater, and seabed, respectively. is the depth of seawater in meters.

[0101] The electric field model of a constant current electric dipole source radiating in three parallel stratified media of air, seawater, and seabed is used to solve the predicted electric field values ​​at seven locations. The specific expression is:

[0102]

[0103] Among them, the coefficient 、 The expression is:

[0104]

[0105]

[0106] matrix 、 、 、 The calculation formula is:

[0107]

[0108] Step 2: Generate initial solution sets for differential evolution (DE) and particle swarm optimization (PSO) respectively. The solution set specifically represents the initial candidate position set generated by the algorithm, and each solution represents a possible three-dimensional coordinate parameter of the constant current electric dipole source. DE initial solution set A = , PSO initial solution set B= .

[0109] Perform mutation, crossover, and selection operations on the DE solution set to generate a new solution set = , the specific expression of the mutation process is as follows:

[0110]

[0111] in, is the solution after mutation, 、 and is a randomly selected solution individual from the solution set, is the mutation factor update function, and its expression is as follows:

[0112]

[0113] Mutation factors involved in the mutation process , is the key factor affecting the solution set update. The value should be as large as possible, which means expanding the search range of the solution set. As the evolution process proceeds, The value should be small, and the algorithm switches from global search to local search to achieve accurate optimization.

[0114] Solution set generated by DE algorithm ,Will Substitute each solution into the formula , calculate the minimum value of the objective function of the DE algorithm .

[0115] Step 3: Update the solution set of DE algorithm Input the PSO algorithm as the input to the PSO algorithm particle swarm update formula and update the population speed and position as follows:

[0116]

[0117]

[0118] Among them, the inertia weight An adaptive parameter adjustment strategy is adopted, and a linear decreasing strategy is adopted to meet the algorithm requirements. The update formula is as follows:

[0119]

[0120] The new PSO solution set Substitute each solution into the formula Calculate the minimum objective function value of the PSO algorithm .

[0121] Step 4: Compare and The size of the objective function is selected as the global minimum value. ; Further, the selection probability of the DE algorithm is calculated according to the following formula and the selection probability of the PSO algorithm :

[0122]

[0123]

[0124] Where, and The calculation formula is:

[0125]

[0126]

[0127] Step 5: Generate interval Random numbers between ,if , select the DE algorithm and update its solution set according to step 2. If , then use the PSO algorithm and update the solution set according to step three.

[0128] Step 6: Repeat the above steps to determine whether the maximum number of iterations has been reached. If not, continue to update the solution set according to step 5; if it has been reached, compare and ,like , then select As a result of the positioning algorithm; otherwise, As a result of the localization algorithm, the solution set contains the optimal position estimation parameters of the constant current electric dipole source.

[0129] Example:

[0130] In order to verify the effectiveness of the underwater target electric field positioning method based on the particle swarm differential evolution hybrid algorithm (PSODE) proposed in this paper, theoretical simulation verification was carried out, taking the underwater constant current electric dipole source positioning as an example.

[0131] Simulation conditions:

[0132] (1) Environmental parameters: air conductivity , seawater conductivity , seabed conductivity , the depth of seawater is 50 m.

[0133] (2) Electric field sensor deployment: A single three-axis electric field sensor moves along a straight line and passes through 7 different positions. The coordinates of the electric field sensors at the 7 positions are A m、B m、C m、O m、D m、E m, G m.

[0134] (3) Target parameter setting: The actual position of the constant current electric dipole source is m, electric dipole moment is 500 A m. The parameter vector to be optimized for the constant current electric dipole source is In the PSODE algorithm iteration, the parameters do not have initial values ​​set, only the optimization range is set. The optimization ranges of the parameters are: , , , the above units are all in the International System of Units.

[0135] (4) PSODE algorithm parameter setting: Let the initial solution set size =200, maximum number of iterations is 120, the crossover probability =0.9, learning factor 、 is 0.25, inertia weight range , Factor of variation range ,in , , , .

[0136] (5) Noise model: superimposed electric field measurement error and pink noise. Electric field measurement value of positioning algorithm for:

[0137]

[0138] in, is the noise vector of pink noise, is the measurement accuracy of the electric field sensor, here we take V / m. is the error percentage, which is 20% in the simulation. is the electric field value radiated by the constant current electric dipole source in the three-layer medium electric field model.

[0139] Simulation results verification:

[0140] (1) Figure 3 The iterative convergence curve of the PSODE positioning algorithm is shown. The objective function value decreases rapidly and reaches stability within 30 iterations. The algorithm converges very quickly, demonstrating a balanced global search and local exploitation capabilities. The final result is close to 0, indicating that the algorithm successfully approaches the global optimal solution, verifying the accuracy of the model and the effectiveness of the optimization strategy.

[0141] (2) Under the above conditions, the PSODE positioning algorithm of the present invention is used to complete 10 source parameter inversions and take the average value. The positioning effect and error are as follows: Figure 4 As shown, the real coordinates of the target are m, the true distance is 2174.95 m, and the coordinates of the average estimated position are m, the average estimated distance is 2126 m. After calculation, the positioning error is only 2.5%. The estimated positions are closely clustered around the theoretical positions. The point cloud is evenly distributed without significant outliers, indicating the stability of the algorithm in complex environments. It can achieve accurate positioning of long-distance targets under low signal-to-noise ratio conditions.

[0142] (3) To verify the superiority of the PSODE hybrid optimization algorithm proposed in this paper, experimental simulations were conducted on the traditional particle swarm optimization (PSO) and differential evolution (DE) algorithms under the same conditions. The positioning errors are shown in Table 1. The table compares the performance differences of the three algorithms in three key error indicators, fully demonstrating that the PSODE algorithm proposed in this paper has significant advantages in positioning accuracy, noise resistance, and convergence efficiency. Its innovative design provides a reliable technical solution for high-precision target detection in complex marine environments.

[0143] Table 1 Comparison of errors of different positioning algorithms

[0144]

[0145] According to the implementation examples, it can be considered that the underwater target electric field positioning method based on the particle swarm differential evolution hybrid algorithm (PSODE) proposed in the present invention can achieve accurate positioning of long-distance targets in shallow sea environments.

Claims

1. A method for underwater target electric field positioning based on a particle swarm differential evolution hybrid algorithm, characterized in that: The steps include: Step 1: Selection and placement of electric field sensors; The underwater target is equivalent to a constant current electric dipole source, and the electric field radiated by the constant current electric dipole source is measured using a three-axis electric field sensor. A three-axis electric field sensor consists of six electric field sensor electrodes, which are arranged vertically in pairs; Step 2: Measurement of electric field radiated by underwater target; Select seven different locations within the constant current electric dipole source positioning area, with the spacing between different locations being greater than 10m and less than 200m. Measure the electric field signals at the seven different locations as the electric field measurement values ​​for the positioning algorithm. Step 3: Implementation of underwater constant current electric dipole source positioning algorithm; Combining the differential evolution algorithm DE and the particle swarm optimization algorithm PSO, an underwater target electric field positioning method based on the particle swarm differential evolution hybrid algorithm PSODE is adopted to determine the target space coordinates by minimizing the difference between the electric field prediction value and the electric field measurement value. The differential evolution algorithm DE and the particle swarm optimization algorithm PSO generate their own initial solution sets A and B respectively. The initial solution set represents the initial candidate position set generated by the algorithm at the physical level. Each solution represents a possible three-dimensional coordinate parameter of a constant current electric dipole source. The differential evolution algorithm DE generates a new solution set A′ through mutation, crossover and selection operations, and adaptively adjusts the mutation factor F. The particle swarm optimization algorithm PSO takes the new solution set A′ after the differential evolution algorithm DE operation as input, updates the particle speed and position, and adaptively adjusts the inertia weight update function w(t). The particle update formula is: V i (k+1)=w(t)·V i (k)+c1·r1·(X′ i,de (k)-X i,pso (k))+c2·r2·(G best (k)-X i,pso (k)) (1) X′ i,pso (k)=X i,pso (k)+V i (k+1) (2) Among them, V i is the particle update speed, V i (k+1) represents the updated particle velocity of the i-th particle at time t+1, V i (k) represents the particle velocity of the i-th particle at time t; c1 and c2 are the individual learning factor and the group learning factor respectively, r1 and r2 are random numbers in the interval [0,1], X′ i,de (k) is the i-th solution in the new solution set A′ of the differential evolution algorithm DE, X i,pso (k) is the i-th solution in the particle swarm optimization algorithm PSO solution set B, G best (k) is X at time k i,pso The global optimal solution in (k), X′ i,pso (k) is the updated particle swarm optimization algorithm PSO solution set B′; The updated solution sets A′ and B′ are used as the input of the objective function, and the objective function values ​​h of the differential evolution algorithm DE and the particle swarm optimization algorithm PSO are calculated respectively. de and h pso , the expression of the objective function is: Where h(X) is the objective function; ω i is the dynamic weight based on the signal-to-noise ratio, L Huber (.) is the robust Huber loss function; E model,i is the electric field prediction value of the i-th electric field sensor, E means,i is the electric field measurement value of the i-th electric field sensor; n represents the number of electric field sensors; Calculate the selection probability of differential evolution algorithm DE and particle swarm optimization algorithm PSO respectively, and use the random number N rand The decision is made to update the solution set, and after iteration until convergence, the optimal solution in the solution set is output, that is, the optimal parameter estimate of the position of the underwater constant current electric dipole source.

2. The underwater target electric field positioning method based on the particle swarm differential evolution hybrid algorithm according to claim 1 is characterized in that: The sensitivity of the electric field sensor is better than 3. The underwater target electric field positioning method based on the particle swarm differential evolution hybrid algorithm according to claim 1 is characterized in that: The step 3 is specifically as follows: Step 3-1: Use the electric field sensor as the reference system in seawater, select any electric field sensor as the coordinate origin, and use the measurement axis direction of the electric field sensor as the positive direction of the coordinate axis to establish a rectangular coordinate system; define the position vector to be optimized of the constant current electric dipole source as X = [x0, y0, z0]; By combining the dynamic weight of the signal-to-noise ratio (SNR) with the Huber loss, the objective function of multi-sensor fusion is constructed, and the positioning problem is transformed into a problem of minimizing the difference between the electric field measurement value and the electric field prediction value. The specific definition of the objective function is: Among them, L Huber (.) is the robust Huber loss function, which is specifically expressed as: Where, SNR i Represents the signal-to-noise ratio of the signal received by the i-th electric field sensor, SNR k represents the signal-to-noise ratio of the signal received by the kth electric field sensor; r represents the residual, that is, the difference between the electric field prediction value and the electric field measurement value; δ represents the threshold parameter, which is used to control the critical point at which the loss function switches from the mean square error (MSE) to the mean absolute error (MAE); Considering the three-layer ocean environment consisting of air, seawater, and seabed, a single three-axis electric field sensor is used to collect electric field data at different locations within the target positioning area, and the x, y, and z components of the electric field intensity at each location are obtained. Assuming that seawater is a uniform and isotropic medium, and its conductivity parameters remain constant in time and space; the dielectric constant and conductivity of each layer of medium are ε respectively. i , σ i , i=1,2,3, subscripts 1, 2, 3 represent air, seawater and seabed respectively; The electric field model of a constant current electric dipole source radiating in three parallel stratified media of air, seawater and seabed is used to solve the predicted electric field values ​​at seven locations. The specific expression is: Where, E Model is the predicted electric field value obtained by any electric field sensor, in V / m; P represents the electric dipole moment of the constant current electric dipole, and the expressions of the coefficients η1 and η2 are: In formula (7), the mirror transformation matrices corresponding to the air-seawater interface and the seawater-seabed interface are Q1=Q2=I-2n1n2, n1 is the unit normal vector of the seawater-air interface, and its direction is from seawater to air, and n2 is the unit normal vector of the seawater-seabed interface, and its direction is from seawater to seabed; the matrix is the electric field intensity transfer matrix at point M, and the specific calculation formula is: In the formula, R represents the modulus of R, R (2m) 、R (2m+1) 、R (2k-1) 、R (2k) represents the position vector of any field point relative to the constant current electric dipole group in the model. Different subscripts represent the mirror electric dipole groups formed by the underwater constant current electric dipole source mirroring back and forth between the air-seawater interface and the seawater-seabed interface. Integers m = 0, 1, 2, …, k = 1, 2, 3, …; I is the unit matrix; Step 3-2: Generate the initial solution set of differential evolution algorithm DE and particle swarm optimization algorithm PSO respectively; the solution set represents the initial candidate position set generated by the algorithm, and each solution represents a possible three-dimensional coordinate parameter of the constant current electric dipole source; the initial solution set of differential evolution algorithm DE Particle swarm optimization algorithm PSO initial solution set B = Perform mutation, crossover, and selection operations on the differential evolution algorithm DE solution set to generate a new solution set The specific expression of the mutation process is as follows: U i (g)=X p1 (g)+F(t)·(X p2 (g)-X p3 (g)) (11) Among them, U i (g) is the solution after mutation, X p1 (g), X p2 (g) and X p3 (g) is a randomly selected solution individual from the solution set, and F(t) represents the mutation factor update function at time t, which is expressed as follows: Among them, F max is the maximum value of the variation factor, F min is the minimum value of the variation factor, N max Indicates the maximum number of iterations; Substitute each solution in A′ into formula (4) to calculate the minimum value h of the objective function of the differential evolution algorithm DE de ; Step 3-3: Input the solution set A′ of the differential evolution algorithm DE into the particle swarm optimization algorithm PSO as the input in the particle swarm update formula of the particle swarm optimization algorithm PSO, and update the speed and position of the population as follows: V i (k+1)=w(t)·V i (k)+c1·r1·(X′ i,de (k)-X i,pso (k))+c2·r2·(G best (k)-X i,pso (k)) (13) X′ i,pso (k)=X i,pso (k)+V i (k+1) (14) Among them, the update formula of w(t) is as follows: Among them, w max is the maximum value of the inertia weight, w min is the minimum value of inertia weight; Substitute each solution in the particle swarm optimization algorithm PSO solution set B′ into formula (4) to calculate the minimum objective function value h of the particle swarm optimization algorithm PSO pso ; Step 3-4: Compare h de and h pso The larger one is selected as the global minimum objective function value h global ; Calculate the selection probability p of the differential evolution algorithm DE de And the selection probability p of the particle swarm optimization algorithm PSO pso : p pso =1-p de (17) Where, the calculation formulas for λ1 and λ2 are: Step 3-5: Generate a random number N between the interval [0,1] rand , if p de >N rand , select the differential evolution algorithm DE and update the solution set according to step 3-2; if p de ≤N rand , then select the particle swarm optimization algorithm PSO and update the solution set according to step 3-3; Step 3-6: Determine whether the maximum number of iterations has been reached. If not, continue to update the solution set according to step 3-5; if it has been reached, compare h de and h pso , if h de >h pso , then the solution set after the nth update of the DE algorithm is selected As the result of the positioning algorithm; otherwise, the solution set after the nth update of the PSO algorithm As a result of the localization algorithm, the solution set contains the optimal position estimation parameters of the constant current electric dipole source.

4. An electronic device, characterized in that: include: processor and memory; The memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory, so that the electronic device performs the method according to any one of claims 1 to 3.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 3 is implemented.

6. A chip, characterized in that: include: A processor, configured to call and run a computer program from a memory, so that a device equipped with the chip executes the method according to any one of claims 1 to 3.

7. A computer program product, characterized in that The computer program product comprises a computer storage medium storing a computer program, wherein the computer program comprises instructions executable by at least one processor, and when the instructions are executed by the at least one processor, the method according to any one of claims 1 to 3 is implemented.

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