Underwater moving target positioning method based on wake diffusion gradient

Abstract

The application discloses a kind of underwater moving target positioning method based on wake diffusion gradient, obtains active sensor set, constructs in-point determination strategy to obtain sensor in-point set, extracts wake diffusion gradient characteristic vector using principal component analysis, selects optimal reference sensor node by time-space double weight index function to obtain reference point, orthogonally projects sensor node in sensor in-point set to axial straight line, obtains projection point position to construct wake diffusion gradient profile function, realizes direction disambiguation of wake diffusion gradient vector after based on wake diffusion gradient profile function, defines disturbance intensity critical point, by interpolation fitting and least square ellipse fitting algorithm, according to disturbance intensity critical point, obtains the isosceles triangle wake diffusion area of the direction and scale of the wake position of underwater moving target. For the problem that the adaptability of traditional sound, light and magnetic detection methods is limited in complex underwater environment, a new way of underwater moving target positioning based on wake characteristics is proposed.

Description

Technical Field

[0001] This invention relates to the field of underwater moving target localization technology, and in particular to an underwater moving target localization method based on wake diffusion gradient. Background Technology

[0002] Underwater target localization has broad application value and significant strategic importance in marine resource development and national defense. Target localization technology based on underwater sensor networks has become a new research hotspot due to its advantages such as wide coverage, long observation time, and real-time fusion. However, the low visibility, strong time-varying characteristics, and multipath propagation prevalent in real-world ocean environments pose challenges to the stable estimation of target motion states.

[0003] Existing systems primarily rely on acoustic methods: active sonar offers long detection range and high accuracy, but is susceptible to echo cancellation stealth techniques and its performance degrades in shallow reverberant environments; passive sonar provides good concealment but depends on target noise radiation, limiting its detection capability under quiet conditions. Optical methods offer high resolution at close range, but have limited effective range and are affected by water turbidity and lighting conditions; magnetic anomaly detection methods are passive and concealed, but depend on the target's magnetic signature and are easily affected by background noise. Therefore, the robustness and applicability of traditional methods in complex environments remain limited. Consequently, a method for locating underwater moving targets based on wake diffusion gradients is urgently needed. Summary of the Invention

[0004] This invention provides a method for locating underwater moving targets based on wake diffusion gradients to overcome the aforementioned technical problems.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows:

[0006] A method for locating underwater moving targets based on wake diffusion gradients, specifically including the following steps:

[0007] S1: Set up several sensor nodes within a given monitoring area;

[0008] Acquire the sensor time-series voltage data of each sensor node, and divide the sensor time-series voltage data into data based on a preset sliding window to obtain sample data of each sensor node, and obtain the disturbance intensity of each sensor node under the action of the wake of the underwater moving target based on the sample data.

[0009] The set of activated sensors is determined based on the intensity of the disturbance.

[0010] S2: Construct an interior point determination strategy for estimating the sensor nodes corresponding to the wake diffusion gradient direction, and obtain the sensor interior point set based on the set of activated sensors;

[0011] S3: Perform principal component analysis (PCA) on the sensor point set to extract the wake diffusion gradient vector corresponding to the current frame of the underwater moving target, and select the optimal reference sensor node from the sensor point set through the constructed time-space dual-weight index function;

[0012] At the same time, the location of the optimal sensor node is orthogonally projected onto the straight line where the wake diffusion gradient vector of the current frame is located to obtain a reference point;

[0013] S4: Define the axial straight line of the wake diffusion gradient with the reference point as the center, and orthogonally project the positions of all sensor nodes in the sensor point set onto the axial straight line to obtain the position of the projection point;

[0014] S5: Construct a wake diffusion gradient profile function based on the projection point location, and define the critical point of disturbance intensity after realizing the direction disambiguation of the wake diffusion gradient vector based on the wake diffusion gradient profile function.

[0015] S6: Within the local neighborhood of the sensor point set, select high-confidence sensor points that satisfy the preset connected region as sample points; use the least squares ellipse fitting algorithm to fit the sample points to obtain sample ellipses, and make the major axis of the sample ellipse collinear with the direction of the current wake diffusion gradient vector.

[0016] S7: Draw the normal to the major axis of the ellipse at the critical point of disturbance intensity, and take the intersection of the normal and the sample ellipse as the endpoint of the base. Connect the endpoint of the base and the reference point to form an isosceles triangular wake diffusion region. The isosceles triangular wake diffusion region is used to characterize the wake position, direction and scale of the underwater moving target, thereby realizing the positioning of the underwater moving target.

[0017] Furthermore, step S1 specifically includes the following steps:

[0018] S11: In a given monitoring area Internal settings A discrete sensor node, defining the index of the sensor node. ; Represents the two-dimensional planar position of the sensor node and ;

[0019] Acquire the sensor time-series voltage data of each sensor node, and divide the sensor time-series voltage data into data based on a preset sliding window to obtain sample data of each sensor node, and obtain the disturbance intensity of each sensor node under the action of the wake of the underwater moving target based on the sample data.

[0020] The expression for the disturbance intensity is:

[0021]

[0022]

[0023] In the formula: This represents the sensor's timing voltage data; Indicates a sliding window and ; Indicates the first The length of each sensor is The average voltage within the sliding window; This represents the sample variance, i.e., the intensity of the disturbance.

[0024] S12: Obtain the set of activated sensors based on the disturbance intensity;

[0025] And the formula for obtaining the set of activated sensors is:

[0026]

[0027]

[0028]

[0029] In the formula: Indicates the activation of the sensor set; Describes a given set of long-term online sensors and ; This represents a set of dormant sensors; Indicates the activation threshold and ; Represents the radius of the redundant neighborhood and ; This refers to a set of long-term online sensors that exceed a set activation threshold. express An active set of redundant sensors; Indicates the first A dormant redundant sensor; Indicates the first .

[0030] Furthermore, the interior point determination strategy described in S2 specifically includes the following steps:

[0031] S21: Using the RANSAC method to activate the sensor set Two different points are randomly selected from the middle. and And construct the reference line as follows:

[0032]

[0033] In the formula: B and C represent intermediate parameters and B= C= ; Represents sensor nodes The x and y coordinates; Represents sensor nodes The x and y coordinates;

[0034] S22: Acquire sensor nodes Distance to the reference line Its expression is:

[0035]

[0036] S23: Given a distance threshold and ,minimum number of interior points Define the initial set of interior points of the sensor:

[0037]

[0038] S24: Constructing the Interior Point Consistency Index Function Its expression is

[0039]

[0040] The sensor node with the largest internal point consistency index function value in the initial set of sensor internal points is taken as the sensor internal point, and steps S21 to S23 are repeated iteratively until the preset number of iterations is reached to obtain the set of sensor internal points.

[0041] Furthermore, step S3 specifically includes the following steps:

[0042] S31: Perform Principal Component Analysis (PCA) on the sensor's point set to extract the wake diffusion gradient vector corresponding to the underwater moving target in the current frame. Specifically:

[0043] Within the sensor's point set, the perturbation centroid, weighted by the normalized perturbation intensity, is calculated as follows:

[0044]

[0045]

[0046] In the formula: Indicates the normalized perturbation strength; Indicates the perturbation of the center of mass;

[0047] Construct a weighted decentering matrix based on the perturbation centroid. for:

[0048]

[0049] In the formula: Represent the space of real numbers; Indicates the first i The weighted, decentralized value of each sensor node location; Y represents ;

[0050] For weighted decentering matrix Perform singular value decomposition, and take the first column vector of the right singular value matrix as the candidate vector of the wake diffusion gradient at the current time. Its expression is:

[0051]

[0052]

[0053]

[0054] In the formula: Represents an orthogonal matrix; Indicates transpose; The vector corresponding to the largest eigenvalue is the principal gradient direction vector; Indicates second only to The vector corresponding to the eigenvalues; Candidate vectors for disambiguation of wake diffusion gradients;

[0055] S32: Select the optimal reference sensor node from the set of sensor in-situ points by constructing a time-space dual-weight index function. ;

[0056] And the expression for the time-space dual-weight index function is:

[0057]

[0058]

[0059]

[0060]

[0061]

[0062] In the formula: Indicates the spatial proximity of diffusion source points. This indicates the location of the diffusion source at the previous moment, and the location of the diffusion source is equivalent to the location of the underwater target. Represents the scale constant and ; Indicates the temporal proximity of the diffusion source points. Represents sensor nodes The most recent high-disturbance trigger time; Representing the time scale and ; Indicates the weighting coefficient; Represents sensor nodes Comprehensive indicators; This represents the final evaluation index after correction for the disturbance intensity amplitude. This represents the function for selecting the optimal reference sensor node;

[0063] S33: Orthogonally project the location of the optimal sensor node onto the straight line containing the wake diffusion gradient vector of the current frame to obtain a reference point;

[0064] And obtain reference points The expression is:

[0065] .

[0066] Furthermore, step S4 specifically includes the following steps:

[0067] S41: An axial straight line defining the wake diffusion gradient centered on the reference point. for:

[0068]

[0069] In the formula: express The axial straight line of the wake diffusion gradient at time step; Indicates the linear scale factor; This indicates the range of values ​​for the linear scale factor;

[0070] S42: Orthogonally project the positions of all sensor nodes in the sensor point set onto the axial line to obtain the projected point positions. ;

[0071] And the formula for obtaining the position of the projection point is:

[0072] .

[0073] Furthermore, S5 specifically includes the following steps:

[0074] S51: Utilization Triangulation of the sensor interior point set Each sensor node in Construct its corresponding Thiessen polygon region Add the projected point location to the sensor's internal point set and re-execute. Triangulation to obtain new Thiessen polygon regions ;

[0075] S52: Calculate the original Thiessen polygon region The Thiessen polygon region corresponding to the addition of interpolated projection points By analyzing the changes in area between regions, we can obtain the weight of each region. for:

[0076]

[0077] In the formula: Indicates only the projection point The corresponding Thiessen polygon region;

[0078] S53: Based on the weighted proportion of each region and the disturbance intensity of the sensor nodes within that region, obtain the disturbance intensity of each projection point, i.e., the interpolation point. for:

[0079]

[0080] S54: Polynomial fitting is performed on the disturbance intensity and projection point position at each projection point to obtain the wake diffusion gradient profile function:

[0081]

[0082] In the formula: A two-dimensional scatter interpolation function representing the polynomial fitting of the projected point positions;

[0083] S55: Based on the wake diffusion gradient profile function, with Center along Positive and negative directions for a given effective equal distance Integration, by comparing the magnitudes of the integrals, determines the principal direction of wake diffusion, thus achieving direction disambiguation of the wake diffusion gradient vector. Its expression is:

[0084]

[0085] like Then let This allows for gradient vector direction disambiguation. ;

[0086] S56: After completing the direction disambiguation of the wake diffusion gradient vector, the position and peak value of the wake gradient main peak in the local neighborhood of the sensor's point set are obtained based on the wake gradient profile function. Its expression is as follows:

[0087]

[0088]

[0089] In the formula: Indicates the location The peak value is the wake diffusion gradient profile function value at that point. Indicates the location of the main peak; This indicates the amplitude or peak value of the main peak.

[0090] Based on a given relative threshold Define the critical point of disturbance intensity. for:

[0091] .

[0092] Furthermore, in S6, high-confidence sensor points within a pre-defined connected region are selected as sample points, with the following constraints:

[0093]

[0094] In the formula: Indicates a position distinct from discrete sensors. 0 consecutive arbitrary positions; This represents the wake diffusion gradient profile function value corresponding to the perturbation centroid within the local neighborhood of the set of points inside the sensor.

[0095] Beneficial Effects: This invention provides an underwater moving target localization method based on wake diffusion gradient. It obtains a set of activated sensors affected by the wake, constructs an interior point determination strategy to remove outlier sensor nodes from the activated sensor set, and filters a set of high-confidence nodes to obtain a sensor interior point set. Principal Component Analysis (PCA) is used to extract the wake diffusion gradient feature vector, thereby determining the position, direction, and disturbance intensity of the wake. Through a constructed time-space dual-weight index function, the optimal reference sensor node is selected from the sensor interior point set, and the location of the optimal sensor node is simultaneously determined. A reference point is obtained by orthogonally projecting the wake diffusion gradient vector onto the straight line containing the vector. An axial line for the wake diffusion gradient is defined with the reference point as its center. The positions of all sensor nodes in the sensor's point set are orthogonally projected onto this axial line to obtain the projection point positions, thus constructing a wake diffusion gradient profile function. After disambiguating the direction of the wake diffusion gradient vector based on this profile function, a critical point for disturbance intensity is defined. Using interpolation fitting and a least-squares ellipse fitting algorithm, an isosceles triangular wake diffusion region characterizing the wake position, direction, and scale of an underwater moving target is obtained based on this critical point. This invention demonstrates high robustness and accuracy even under background current interference, providing a new approach for underwater moving target localization. Attached Figure Description

[0096] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0097] Figure 1 This is a flowchart of the underwater moving target localization method based on wake diffusion gradient of the present invention;

[0098] Figure 2 This is a schematic diagram illustrating the positioning of an underwater moving target in this embodiment;

[0099] Figure 3 This is a diagram showing the effect of the greedy algorithm optimizing the redundant sensor layout in this embodiment;

[0100] Figure 4 This is a flowchart of the wake diffusion gradient calculation in this embodiment;

[0101] Figure 5 This is a diagram showing the target location trajectory estimation result in this embodiment;

[0102] Figure 6 This is a diagram showing the target trajectory fitting results in this embodiment;

[0103] Figure 7 This example compares the target positioning trajectory estimation errors.

[0104] Figure 8 This is a schematic diagram of the Thiessen polygon division in this embodiment;

[0105] Figure 9 This is a schematic diagram of the wake diffusion gradient profile function in this embodiment;

[0106] Figure 10 This is a technical roadmap diagram of the method described in this embodiment. Detailed Implementation

[0107] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0108] This embodiment provides a method for locating underwater moving targets based on wake diffusion gradients, such as... Figure 1 and Figure 10As shown, the specific steps include:

[0109] S1: Set up several sensor nodes in a given monitoring area; acquire the sensor time-series voltage data of each sensor node, and divide the sensor time-series voltage data into data based on a preset sliding window to obtain sample data of each sensor node, and obtain the disturbance intensity of each sensor node under the action of the wake of the underwater moving target based on the sample data; obtain the set of active sensors based on the disturbance intensity.

[0110] The specific steps include:

[0111] S11: As Figure 3 As shown, in a given monitoring area Internal settings A discrete sensor node, defining the index of the sensor node. ; Represents the two-dimensional planar position of the sensor node and Discrete time The voltage is denoted as For each node, use a length of sliding window ;

[0112] Acquire the sensor time-series voltage data of each sensor node, and divide the sensor time-series voltage data into data based on a preset sliding window to obtain sample data of each sensor node, and obtain the disturbance intensity of each sensor node under the action of the wake of the underwater moving target based on the sample data.

[0113] The expression for the disturbance intensity is:

[0114] (1)

[0115] (2)

[0116] In the formula: This represents the sensor's timing voltage data; Indicates a sliding window and ; Indicates the first The length of each sensor is The average voltage within the sliding window; This represents the sample variance, i.e., the intensity of the disturbance.

[0117] S12: Obtain the set of activated sensors based on the disturbance intensity;

[0118] And the formula for obtaining the set of activated sensors is:

[0119]

[0120] (3)

[0121]

[0122] In the formula: Indicates the activation of the sensor set; Given a set of long-term online sensors selected under the constraints of maximum coverage and minimum number of nodes, and ; Represents a set of sleep sensors ; Indicates the activation threshold and ; Represents the radius of the redundant neighborhood and And activate threshold With redundant neighborhood radius It acts between sensor node pairs; This refers to the set of key sensors that are online for extended periods and whose activation threshold is greater than a set value. express An active set of redundant sensors; Indicates the first A dormant redundant sensor; Indicates the first ;

[0123] In this embodiment, data acquisition is performed as follows: First, the location information of all sensors is obtained from the sensor locations, and a greedy algorithm is used to determine which sensors should be activated. The role of the greedy algorithm here is to select the best sensor node for data acquisition based on the distance relationship between the wake diffusion area and the sensor. Sensor voltage data is recorded through voltage data acquisition. The variance of these voltage signals reflects the disturbance intensity under the wake effect and is the basis for subsequent calculations.

[0124] Sensor Activation: Sensor Sleep and Activation: Underwater sensors (including ADC digital-to-analog converter modules) generally require independent battery power to maintain long-term monitoring and high sampling frequency operation. To avoid frequent battery replacements for underwater sensor arrays, redundant sensors can enter sleep mode and be activated by events triggered by nearby critical sensors. Critical Sensors Online: Critical sensors maintain real-time wake perception and operate at a long-term low sampling frequency. When a target appears and the wake intensity exceeds a set threshold, the sensor switches to a high sampling frequency mode and activates surrounding redundant sensors to obtain more detailed wake information.

[0125] S2: Construct an interior point determination strategy for estimating the sensor nodes corresponding to the wake diffusion gradient direction, and obtain the sensor interior point set based on the set of activated sensors;

[0126] The interior point determination strategy specifically includes the following steps:

[0127] S21: To robustly estimate the wake diffusion gradient direction, the RANSAC method is used to activate the sensor set. Two different points are randomly selected from the middle. and And construct the reference line as follows:

[0128] (4)

[0129] In the formula: B and C represent intermediate parameters and B= C= ; Represents sensor nodes The x and y coordinates; Represents sensor nodes The x and y coordinates;

[0130] S22: For any Acquire sensor nodes Distance to the reference line Its expression is:

[0131] (5)

[0132] S23: Given a distance threshold and ,minimum number of interior points Define the initial set of interior points of the sensor:

[0133] (6)

[0134] S24: Construct the interior point consistency index function, the expression of which is: ;

[0135] The sensor node with the largest internal point consistency index function value in the initial set of sensor internal points is selected as the sensor internal point, and steps S21 to S23 are repeated iteratively until the preset number of iterations is reached. KTo obtain the set of sensor inliers, this embodiment uses repeated scoring K times, a key step in the RANSAC algorithm, to increase the probability of finding the optimal solution. According to formulas (4) and (5), two points are randomly selected from the set of active sensors to construct a straight line model, and the distances of all active sensors to the straight line are calculated. If the distance of a sensor to the straight line is less than or equal to the threshold δ, the sensor is determined to be an inlier. For all sensor nodes determined to be inliers, the sum of their disturbance intensities is calculated, which is one score. The reason for choosing a straight line model is that wake diffusion usually presents an approximately elongated shape. The larger the sum of disturbance intensities, the closer the active sensors covered by the inlier set are to the wake disturbance area, or the wider their coverage area, both of which are helpful for the accurate positioning of underwater targets. At the same time, setting the threshold δ also significantly reduces the possibility of discrete sensors being incorrectly rated as inliers due to noise.

[0136] In this embodiment, the RANSAC algorithm is used to determine which sensor data points belong to inliers. RANSAC (Random Sample Consensus) is used to filter out outlier data. It determines which data points are reliable inliers by repeatedly selecting samples and evaluating the consistency of the model. The number of active sensors is determined as follows: if more than three sensors are active, the currently active sensor data is considered valid, and the calculation of the wake propagation direction can continue. If fewer than three sensors are active, the data processing of the current frame is skipped. The physical significance of this step is that wake propagation is a complex spatial process, requiring a certain number of sensors to accurately capture its characteristics.

[0137] S3: Perform Principal Component Analysis (PCA) on the sensor point set to extract the wake diffusion gradient vector corresponding to the underwater moving target in the current frame. Then, select the optimal reference sensor node from the sensor point set using a constructed time-space dual-weight index function. Simultaneously, orthogonally project the location of the optimal sensor node onto the line containing the wake diffusion gradient vector corresponding to the current frame to obtain the reference point. Specific steps include:

[0138] S31: Perform Principal Component Analysis (PCA) on the sensor's point set to extract the wake diffusion gradient vector corresponding to the underwater moving target in the current frame. Specifically:

[0139] Within the sensor's point set, the perturbation centroid, weighted by the normalized perturbation intensity, is calculated as follows:

[0140] (7)

[0141] (8)

[0142] In the formula: Indicates the normalized perturbation strength; Indicates the perturbation of the center of mass;

[0143] Construct a weighted decentering matrix based on the perturbation centroid. for:

[0144] (9)

[0145] In the formula: Represent the space of real numbers; Indicates the first i The weighted, decentralized value of each sensor node location; Y represents ;

[0146] For weighted decentering matrix Perform Singular Value Decomposition (SVD), and take the first column vector of the right singular value matrix as the candidate vector of the wake diffusion gradient at the current time step. The expression is as follows:

[0147] (10)

[0148] (11)

[0149] (12)

[0150] In the formula: Represents an orthogonal matrix; Indicates transpose; The vector corresponding to the largest eigenvalue is the principal gradient direction vector; Indicates second only to The vector corresponding to the eigenvalues; Candidate vectors for disambiguation of wake diffusion gradients;

[0151] S32: Select the optimal reference sensor node from the set of sensor in-situ points by constructing a time-space dual-weight index function. The wake gradient vector obtained by SVD in this embodiment has sign uncertainty. To determine a unique direction, in the set of interior points The internal structure employs a time-space dual-weighting index, defining the sensor whose activation time is closest to the current moment and whose spatial location is near the wake diffusion source as the optimal reference sensor. Specifically, within the inlier set... In the above, the gradient vector at the previous time step Measuring the proximity of diffusion sources;

[0152] And the expression for the time-space dual-weight index function is:

[0153] (13)

[0154] (14)

[0155] (15)

[0156] (16)

[0157] (17)

[0158] In the formula: Indicates the spatial proximity of diffusion source points. This indicates the location of the diffusion source at the previous moment, and the location of the diffusion source is equivalent to the location of the underwater target. Represents the scale constant and The larger the value, the more points... along The further the back projection is, the closer it is to the current diffusion source point; Indicates the temporal proximity of the diffusion source points. Represents sensor nodes The most recent high-disturbance trigger time; Representing the time scale and The higher its weight, the closer it is to the current moment; Indicates the weighting coefficient; Represents sensor nodes Comprehensive indicators; This represents the final evaluation index after correction for the disturbance intensity amplitude. This represents the function for selecting the optimal reference sensor node;

[0159] S33: Orthogonally project the location of the optimal sensor node onto the straight line containing the wake diffusion gradient vector of the current frame to obtain a reference point;

[0160] And obtain reference points The expression is:

[0161] (18)

[0162] This embodiment calculates the temporal and spatial (positional) parameters of each sensor, including the sensor activation timestamp, position relative to the target, and distance between sensors. These calculations determine the optimal sensor position and select the best sensor data for further processing. Orthogonal Projection and Reference Point: The position of the optimal sensor (i.e., the sensor activated within the wake's range) is projected onto the wake diffusion gradient axis, defined as a reference point. Wake diffusion is an asymmetric process; theoretically, the wake's influence is concentrated on one side of the reference point. Therefore, the reference point helps to further disambiguate the direction of wake diffusion. PCA Calculation: Principal Component Analysis (PCA) is used to extract the principal axis direction of wake diffusion from the activated sensor data. PCA is a dimensionality reduction technique that extracts the most significant direction of change in the data by calculating the principal components. Here, PCA helps determine the principal direction of wake diffusion, ensuring accurate calculation of the diffusion pattern. Comparison with Previous Frame Direction: The calculated current wake direction is compared with the wake direction of the previous frame. If the directions are consistent, the currently calculated direction will continue to be used; if the directions are inconsistent, a reversal operation will be performed to adjust the wake direction to ensure consistency. The purpose of the reversal operation is to ensure that the wake propagation direction has physical consistency and continuity, and to avoid unreasonable jumps.

[0163] S4: Define the axial straight line of the wake diffusion gradient with the reference point as the center, and orthogonally project the positions of all sensor nodes in the sensor point set onto the axial straight line to obtain the position of the projection point;

[0164] The specific steps include:

[0165] S41: An axial straight line defining the wake diffusion gradient centered on the reference point. for:

[0166] (19)

[0167] In the formula: express The axial straight line of the wake diffusion gradient at time step; Indicates the linear scale factor; This indicates the range of values ​​for the linear scale factor;

[0168] S42: Orthogonally project the positions of all sensor nodes in the sensor point set onto the axial line to obtain the projected point positions. ;

[0169] And the formula for obtaining the position of the projection point is:

[0170] (20)

[0171] S5: Construct a wake diffusion gradient profile function based on the projection point location, and define the critical point of disturbance intensity after realizing the direction disambiguation of the wake diffusion gradient vector based on the wake diffusion gradient profile function.

[0172] The specific steps include:

[0173] S51: Utilization Triangulation of the sensor interior point set Each sensor node in Construct its corresponding Thiessen polygon region Add the projected point location to the sensor's internal point set and re-execute. Triangulation to obtain new Thiessen polygon regions In this embodiment, for the projection point The perturbation intensity of the projection point is estimated using the natural neighborhood interpolation method. First, using Triangulation of interior point set Each sensor in Construct its corresponding Thiessen polygon region ,like Figure 8 As shown: Figure 8 (a) shows the set of interior points. , Triangulation generates a set of triangles, ensuring that no other data points exist within the circumcircle of each triangle. The points to be interpolated are then projected... The Thiessen polygons of all points were recalculated by adding them to the sample to obtain a new region. ,like Figure 8 As shown in (b).

[0174] S52: Calculate the original Thiessen polygon region The Thiessen polygon region corresponding to the addition of interpolated projection points By analyzing the changes in area between regions, we can obtain the weight of each region. for:

[0175] (twenty one)

[0176] In the formula: Indicates only the projection point The corresponding Thiessen polygon region;

[0177] S53: Based on the weighted proportion of each region and the disturbance intensity of the sensor nodes within that region, obtain the disturbance intensity of each projection point, i.e., the interpolation point. for:

[0178] (twenty two)

[0179] S54: Polynomial fitting is performed on the disturbance intensity and projection point position at each projection point to obtain the wake diffusion gradient profile function:

[0180] In the formula: A two-dimensional scattered point interpolation function representing a polynomial fit of the projected point positions, such as... Figure 9 As shown;

[0181] S55: To determine the correct gradient direction, on the wake diffusion gradient profile function, with... Center along Positive and negative directions for a given effective equal distance Integration, by comparing the magnitudes of the integrals, determines the principal direction of wake diffusion, thus achieving direction disambiguation of the wake diffusion gradient vector. Its expression is:

[0182] (twenty three)

[0183] like Then let This allows for gradient vector direction disambiguation. ;

[0184] S56: After completing the direction disambiguation of the wake diffusion gradient vector, the position and peak value of the wake gradient main peak in the local neighborhood of the sensor's point set are obtained based on the wake gradient profile function. Its expression is as follows:

[0185] (twenty four)

[0186] (25)

[0187] In the formula: Indicates the location The peak value is the wake diffusion gradient profile function value at that point. Indicates the location of the main peak; This indicates the amplitude or peak value of the main peak.

[0188] Based on a given relative threshold Define the critical point of disturbance intensity. for:

[0189] (26).

[0190] In this embodiment, the weighted centroid of anti-dynamic strength is calculated: the weighted centroid of anti-dynamic strength is calculated based on the wake intensity weighted by the data from all activated sensors. The centroid reflects the center of gravity of the wake in space and is crucial for understanding the wake's propagation pattern and direction. Weighted calculation improves the accuracy of the calculation, especially when the wake distribution is uneven. Anti-dynamic strength critical point calculation: By calculating the wake's critical points, the boundaries of wake diffusion are determined. These critical points represent the locations where the wake intensity decreases to a certain threshold, helping to define the actual range and influence area of ​​the wake. The wake's critical points are the limits of its propagation in space; determining these points is crucial for subsequent wake analysis. Wake diffusion direction disambiguation: By analyzing the wake gradient direction, the system performs disambiguation to ensure that the wake diffusion direction is unique and conforms to physical laws. This step helps to clearly distinguish the wake's propagation direction and reduce ambiguity in the calculation. This embodiment also includes direction sign determination: based on the calculated wake gradient vector direction, it is determined whether it meets the preset positive and negative direction requirements. The wake diffusion direction needs to conform to certain physical laws, such as the wake usually spreading along the direction of underwater target movement.

[0191] If the direction meets the requirements, continue to calculate the detailed characteristics of the wake diffusion;

[0192] If the direction does not meet the requirements, a reversal operation is performed to adjust the direction of the wake diffusion. The purpose of this reversal operation is to ensure that the calculated direction of the wake is consistent with the physical reality and to avoid reverse wake diffusion in the calculation.

[0193] S6: Within the local neighborhood of the sensor's internal point set, select high-confidence sensor internal points that satisfy a preset connected region as sample points; use a least-squares ellipse fitting algorithm to fit the sample points to obtain sample ellipses, and ensure that the major axis of the sample ellipse is collinear with the direction of the current wake diffusion gradient vector. In this embodiment, within the local neighborhood of the internal point set, based on the peak relative threshold... Select the one that satisfies Connected regions, This represents a two-dimensional scattered interpolation function, i.e., a wake diffusion gradient profile function. Indicates a position distinct from discrete sensors. 0 consecutive arbitrary positions; This represents the wake diffusion gradient profile function value corresponding to the perturbation centroid within the local neighborhood of the sensor's point set. Using high-confidence points within the connected region as samples, it employs least-squares elliptic fitting and constrains the major axis direction of the ellipse to the current gradient vector. Collinear, such as Figure 2 As shown;

[0194] S7: At the critical point of disturbance intensity, draw the normal to the major axis of an ellipse, and take the intersection of this normal and the sample ellipse as the endpoint of the base. Connect the endpoint of the base with the reference point to form an isosceles triangular wake diffusion region. The isosceles triangular wake diffusion region is used to characterize the wake position, direction, and scale of underwater moving targets, thereby realizing the positioning of underwater moving targets. In this embodiment, the three points of the triangle and the diffusion direction of the isosceles triangular wake diffusion region are simultaneously filtered by the known Kalman filter algorithm to achieve the tracking and positioning of underwater moving targets.

[0195] This embodiment ultimately determines the gradient direction and range of the wake diffusion through the above steps. These results can help further analyze the motion trajectory of underwater targets, assist in wake analysis and target localization, and the system concludes the wake gradient direction calculation and outputs the results. The flowchart describes the entire process from data acquisition to wake diffusion gradient vector calculation: the core idea is to ensure accurate calculation of the wake diffusion direction and eliminate ambiguity through steps such as sensor activation and selection, PCA calculation of the wake principal axis direction, anti-dynamic strength weighted centroid, and wake diffusion disambiguation and reversal operations. This process emphasizes key steps such as sensor selection, wake data analysis, reverse adjustment, and disambiguation; each step has rigorous physical and mathematical basis, ensuring high accuracy and consistency in wake calculation.

[0196] Figure 1A wake perception model of an underwater moving target is presented. It is mainly used to describe the diffusion characteristics of the interaction between the underwater target and its wake. Each part in the figure has its specific physical meaning: (1) Wake region (black V-shaped dashed line): represents the Kelvin wake generated by the actual movement of the underwater target. Its characteristic is that the intensity of diffusion gradually weakens from the source point along the central axis to both sides and far away; (2) Diffusion region (blue solid line connecting triangles): represents the estimated wake diffusion region based on the feedback data of the sensor array and calculated by the algorithm model; (3) Reference point (blue solid hollow circle): the sensor node that is theoretically closest to the source point is defined as the anchor point. This node represents the sensor in the sensor array with the latest activation time and the optimal position (i.e., closest to the source point and most suitable direction) within the wake's range. The anchor point is projected onto the wake diffusion gradient axis and defined as the reference point. Theoretically, the range of the wake is concentrated only on one side of the reference point, which helps to determine the unique solution of the wake gradient direction. (4) Perturbation intensity weighted centroid (red solid circle): The perturbation intensity weighted centroid calculated based on the obtained inlier set after RANSAC screening of the activated sensor nodes is used to determine the location of the wake diffusion gradient. (5) Perturbation intensity critical point (blue cross): Using 10% of the peak value on the wake diffusion axis as the threshold, the position of the last point below the threshold on both sides of the reference point is calculated, thus reflecting the actual range of the wake. (6) Wake gradient vector (red solid arrow): Calculated by applying principal component analysis (PCA) to the inlier set, reflecting the direction of wake diffusion. Figure 4 This paper demonstrates a complete process for calculating underwater wake gradients, aiming to accurately calculate the wake propagation direction of underwater targets through the processing of sensor data. The detailed physical meaning and reasoning process for each step are as follows: Figure 5 The final trajectory estimation results are presented. This invention uses the estimated trajectory filtered by the Kalman filter algorithm as the final output, marked in red. Overall, the filtered trajectory is highly consistent with the true trajectory in its overall direction, and its local perturbations are effectively suppressed, demonstrating good robustness and consistency. Correspondingly, Figure 7 The real-time position error is shown. Since this method approximates the sensor most recently excited by the wake as the source of the target's diffusion, this prior introduces a fixed spatial bias. Simultaneously, after applying wake geometry constraints, the Kalman filter algorithm exhibits a response lag. The combined effect of these two factors causes the filter error curve to show a baseline shift of approximately 15 m relative to the original error, and may temporarily be inferior to the original estimate near the inflection point. Nevertheless, the overall trajectory fit is as follows... Figure 6 As shown, the shortest distance coverage band of the filtered result is significantly closer to the actual trajectory.

[0197] The beneficial effects of the method described in this embodiment are as follows: First, for sensors activated by wake effects, the Random Sample Consensus (RANSAC) algorithm is used to remove outliers and select a set of high-confidence nodes; then, based on the node voltages within this set, Principal Components Analysis (PCA) is used to extract wake diffusion gradient features, thereby determining the location, direction, and disturbance intensity of the wake; further, interpolation fitting and least squares estimation are used to calculate the axial length and lateral broadening of the wake; finally, it can also be applied using Kalman filtering (… The method performs tracking and localization estimation within the KF (Kinetic Filter) framework. It still exhibits high robustness and accuracy under background current interference conditions, providing a new approach for underwater moving target localization.

[0198] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for locating underwater moving targets based on wake diffusion gradient, characterized in that, Specifically, the following steps are included: S1: Set up several sensor nodes within a given monitoring area; Acquire the sensor time-series voltage data of each sensor node, and divide the sensor time-series voltage data into data based on a preset sliding window to obtain sample data of each sensor node, and obtain the disturbance intensity of each sensor node under the action of the wake of the underwater moving target based on the sample data. The set of activated sensors is determined based on the intensity of the disturbance. S2: Construct an interior point determination strategy for estimating the sensor nodes corresponding to the wake diffusion gradient direction, and obtain the sensor interior point set based on the set of activated sensors; S3: Perform principal component analysis (PCA) on the sensor point set to extract the wake diffusion gradient vector corresponding to the current frame of the underwater moving target, and select the optimal reference sensor node from the sensor point set through the constructed time-space dual-weight index function; At the same time, the location of the optimal sensor node is orthogonally projected onto the straight line where the wake diffusion gradient vector of the current frame is located to obtain a reference point; S4: Define the axial straight line of the wake diffusion gradient with the reference point as the center, and orthogonally project the positions of all sensor nodes in the sensor point set onto the axial straight line to obtain the position of the projection point; S5: Construct a wake diffusion gradient profile function based on the projection point location, and define the critical point of disturbance intensity after realizing the direction disambiguation of the wake diffusion gradient vector based on the wake diffusion gradient profile function. S6: Within the local neighborhood of the sensor point set, select high-confidence sensor points that satisfy the preset connected region as sample points; use the least squares ellipse fitting algorithm to fit the sample points to obtain sample ellipses, and make the major axis of the sample ellipse collinear with the direction of the current wake diffusion gradient vector. S7: Draw the normal to the major axis of the ellipse at the critical point of disturbance intensity, and take the intersection of the normal and the sample ellipse as the endpoint of the base. Connect the endpoint of the base and the reference point to form an isosceles triangular wake diffusion region. The isosceles triangular wake diffusion region is used to characterize the wake position, direction and scale of the underwater moving target, thereby realizing the positioning of the underwater moving target.

2. The underwater moving target localization method based on wake diffusion gradient according to claim 1, characterized in that, S1 specifically includes the following steps: S11: In a given monitoring area Internal settings A discrete sensor node, defining the index of the sensor node. ; Represents the two-dimensional planar position of the sensor node and ; Acquire the sensor time-series voltage data of each sensor node, and divide the sensor time-series voltage data into data based on a preset sliding window to obtain sample data of each sensor node, and obtain the disturbance intensity of each sensor node under the action of the wake of the underwater moving target based on the sample data. The expression for the disturbance intensity is: In the formula: This represents the sensor's timing voltage data; Indicates a sliding window and ; Indicates the first The length of each sensor is The average voltage within the sliding window; This represents the sample variance, i.e., the intensity of the disturbance. S12: Obtain the set of activated sensors based on the disturbance intensity; And the formula for obtaining the set of activated sensors is: In the formula: Indicates the activation of the sensor set; Describes a given set of long-term online sensors and ; This represents a set of dormant sensors; Indicates the activation threshold and ; Represents the radius of the redundant neighborhood and ; This refers to a set of long-term online sensors that exceed a set activation threshold. express An active set of redundant sensors; Indicates the first A dormant redundant sensor; Indicates the first .

3. The underwater moving target localization method based on wake diffusion gradient according to claim 2, characterized in that, The interior point determination strategy described in S2 specifically includes the following steps: S21: Using the RANSAC method to activate the sensor set Two different points are randomly selected from the middle. and And construct the reference line as follows: In the formula: B and C represent intermediate parameters and B= C= ; Represents sensor nodes The x and y coordinates; Represents sensor nodes The x and y coordinates; S22: Acquire sensor nodes Distance to the reference line Its expression is: S23: Given a distance threshold and ,minimum number of interior points Define the initial set of interior points of the sensor: S24: Constructing the Interior Point Consistency Index Function Its expression is The sensor node with the largest internal point consistency index function value in the initial set of sensor internal points is taken as the sensor internal point, and steps S21 to S23 are repeated iteratively until the preset number of iterations is reached to obtain the set of sensor internal points.

4. The underwater moving target localization method based on wake diffusion gradient according to claim 3, characterized in that, S3 specifically includes the following steps: S31: Perform Principal Component Analysis (PCA) on the sensor's point set to extract the wake diffusion gradient vector corresponding to the underwater moving target in the current frame. Specifically: Within the sensor's point set, the perturbation centroid, weighted by the normalized perturbation intensity, is calculated as follows: In the formula: Indicates the normalized perturbation strength; Indicates the perturbation of the center of mass; Construct a weighted decentering matrix based on the perturbation centroid. for: In the formula: Represent the space of real numbers; Indicates the first i The weighted, decentralized value of each sensor node location; Y represents ; For weighted decentering matrix Perform singular value decomposition, and take the first column vector of the right singular value matrix as the candidate vector of the wake diffusion gradient at the current time. Its expression is: In the formula: Represents an orthogonal matrix; Indicates transpose; The vector corresponding to the largest eigenvalue is the principal gradient direction vector; Indicates second only to The vector corresponding to the eigenvalues; Candidate vectors for disambiguation of wake diffusion gradients; S32: Select the optimal reference sensor node from the set of sensor in-situ points by constructing a time-space dual-weight index function. ; And the expression for the time-space dual-weight index function is: In the formula: Indicates the spatial proximity of diffusion source points. This indicates the location of the diffusion source at the previous moment, and the location of the diffusion source is equivalent to the location of the underwater target. Represents the scale constant and ; Indicates the temporal proximity of the diffusion source points. Represents sensor nodes The most recent high-disturbance trigger time; Representing the time scale and ; Indicates the weighting coefficient; Represents sensor nodes Comprehensive indicators; This represents the final evaluation index after correction for the disturbance intensity amplitude. This represents the function for selecting the optimal reference sensor node; S33: Orthogonally project the location of the optimal sensor node onto the straight line containing the wake diffusion gradient vector of the current frame to obtain a reference point; And obtain reference points The expression is: 。 5. The underwater moving target localization method based on wake diffusion gradient according to claim 4, characterized in that, S4 specifically includes the following steps: S41: An axial straight line defining the wake diffusion gradient centered on the reference point. for: In the formula: express The axial straight line of the wake diffusion gradient at time step; Indicates the linear scale factor; This indicates the range of values ​​for the linear scale factor; S42: Orthogonally project the positions of all sensor nodes in the sensor point set onto the axial line to obtain the projected point positions. ; And the formula for obtaining the position of the projection point is: 。 6. The underwater moving target localization method based on wake diffusion gradient according to claim 5, characterized in that, S5 specifically includes the following steps: S51: Utilization Triangulation of the sensor interior point set Each sensor node in Construct its corresponding Thiessen polygon region Add the projected point location to the sensor's internal point set and re-execute. Triangulation to obtain new Thiessen polygon regions ; S52: Calculate the original Thiessen polygon region The Thiessen polygon region corresponding to the addition of interpolated projection points By analyzing the changes in area between regions, we can obtain the weight of each region. for: In the formula: Indicates only the projection point The corresponding Thiessen polygon region; S53: Based on the weighted proportion of each region and the disturbance intensity of the sensor nodes within that region, obtain the disturbance intensity of each projection point, i.e., the interpolation point. for: S54: Polynomial fitting is performed on the disturbance intensity and projection point position at each projection point to obtain the wake diffusion gradient profile function: In the formula: A two-dimensional scatter interpolation function representing the polynomial fitting of the projected point positions; S55: Based on the wake diffusion gradient profile function, with Center along Positive and negative directions for a given effective equal distance Integration, by comparing the magnitudes of the integrals, determines the principal direction of wake diffusion, thus achieving direction disambiguation of the wake diffusion gradient vector. Its expression is: like Then let This allows for gradient vector direction disambiguation. ; S56: After completing the direction disambiguation of the wake diffusion gradient vector, the position and peak value of the wake gradient main peak in the local neighborhood of the sensor's point set are obtained based on the wake gradient profile function. Its expression is as follows: In the formula: Indicates the location The peak value is the wake diffusion gradient profile function value at that point. Indicates the location of the main peak; This indicates the amplitude or peak value of the main peak. Based on a given relative threshold Define the critical point of disturbance intensity. for: 。 7. The underwater moving target localization method based on wake diffusion gradient according to claim 6, characterized in that, In S6, high-confidence sensor points within a pre-defined connected region are selected as sample points, with the following constraints: In the formula: Indicates a position distinct from discrete sensors. 0 consecutive arbitrary positions; This represents the wake diffusion gradient profile function value corresponding to the perturbation centroid within the local neighborhood of the set of points inside the sensor.

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