Spectrum clustering-based underwater target positioning and system error compensation method and device

Abstract

The embodiment of the application provides a spectrum clustering-based underwater target positioning and system error compensation method and device, which comprises the following steps: obtaining an initial measurement model; selecting a polynomial optimal order to constrain an underwater target track according to the initial measurement model, and constructing an underwater target positioning model; performing spectrum clustering on the measurement error of a measurement station according to the relative distance between the measurement station and the underwater target, the rotation angle of the underwater target and the measurement accuracy of the equipment; combining the spectrum clustering result of the measurement error of the measurement station with the underwater target positioning model to form a fusion positioning model; and obtaining the accuracy of the target position according to the fusion positioning model. The measurement element accuracy of the application is about 0.1 m, the positioning accuracy is high, reaches within 0.5 m, and the calculated track almost coincides with the reference track. The accuracy of target positioning is improved.

Description

Technical Field

[0001] This invention relates to the field of underwater target localization technology, and in particular to a method and apparatus for underwater target localization and system error compensation based on spectral clustering. Background Technology

[0002] To address the location inconsistency error caused by treating underwater targets as point masses during the positioning process, as well as observation system errors such as underwater array site errors, sound velocity errors, and time delay errors, the traditional ballistic error model optimal estimation (EMBET) suffers from ill-conditioned parameter estimation models when there is a small amount of observation data and too many parameters to be estimated. This makes it difficult to effectively identify observation system errors and result in low positioning accuracy.

[0003] The applicant has found at least the following problems in the existing technology: the accuracy of underwater target tracking and positioning is not high and cannot meet the requirements. Summary of the Invention

[0004] The technical problem solved by the embodiments of the present invention is how to solve the problem of low accuracy in underwater target tracking and positioning.

[0005] To achieve the above objectives, in one aspect, embodiments of the present invention provide an underwater target localization and system error compensation method based on spectral clustering, comprising the following steps:

[0006] Obtain the initial measurement model;

[0007] Based on the initial measurement model, the optimal order of the polynomial is selected to constrain the underwater target trajectory, thereby constructing an underwater target positioning model;

[0008] The measurement error of the station is subjected to spectral clustering based on the relative distance between the station and the underwater target, the rotation angle of the underwater target, and the measurement accuracy of the equipment.

[0009] Based on the spectral clustering results of the measurement errors of the stations, a fusion positioning model is formed by combining the underwater target positioning model;

[0010] The accuracy of the target position is obtained based on the fusion positioning model. If the maximum number of iterations is reached or the station spectral clustering result converges, the accuracy of the target position is output. Otherwise, the spectral clustering of the underwater station's measurement error based on the relative distance between the station and the underwater target and the measurement accuracy of the equipment is returned.

[0011] On the other hand, embodiments of the present invention provide an underwater target localization and system error compensation device based on spectral clustering, including:

[0012] The acquisition unit is used to acquire the initial measurement model;

[0013] The selection unit is used to select the optimal order of the polynomial to constrain the underwater target trajectory based on the initial measurement model, and to construct an underwater target positioning model.

[0014] Clustering units are used to perform spectral clustering of the measurement error of the station based on the relative distance between the station and the underwater target, the rotation angle of the underwater target, and the measurement accuracy of the equipment.

[0015] The modeling unit is used to form a fusion positioning model based on the spectral clustering results of the measurement error of the station and the underwater target positioning model.

[0016] The output unit is used to obtain the accuracy of the target position based on the fusion positioning model. If the maximum number of iterations is reached or the station spectral clustering result converges, the accuracy of the target position is output. Otherwise, the spectral clustering of the underwater station's measurement error based on the relative distance between the station and the underwater target and the measurement accuracy of the equipment is returned.

[0017] The above technical solution has the following beneficial effects: Without considering the target rotation angle or the system error of the measuring station, the calculation results are inaccurate and have low precision, and the calculated trajectory deviates significantly from the reference trajectory. This invention employs an underwater target positioning and system error compensation method based on spectral clustering. The target rotation angle and the measuring station's system error are calculated more accurately, with a measurement element accuracy of approximately 0.1m and a high positioning accuracy within 0.5m. The calculated trajectory almost coincides with the reference trajectory, thus improving the accuracy of target positioning. Attached Figure Description

[0018] 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 only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a flowchart of the underwater target localization and system error compensation method based on spectral clustering provided in an embodiment of the present invention;

[0020] Figure 2 This is a schematic diagram of the underwater target localization and system error compensation device based on spectral clustering provided in an embodiment of the present invention;

[0021] Figure 3 This is a schematic diagram of the underwater acoustic positioning system provided in an embodiment of the present invention;

[0022] Figure 4 This is a flowchart of the second implementation of the underwater target localization and system error compensation method based on spectral clustering provided in this invention.

[0023] Figure 5 This is an overall layout diagram of the reference trajectory of the cylinder and the acoustic array in a lake test scenario provided by an embodiment of the present invention;

[0024] Figure 6 This is an embodiment of the present invention showing the reference trajectory of the cylinder and the overall layout of the acoustic array in a sea trial scenario. Detailed Implementation

[0025] 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, and 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.

[0026] The technical solution of this invention is as follows: Utilizing the principle of underwater long baseline positioning, and then, based on the traditional EMBET model, adaptively selecting the order of the polynomial function using the optimal model selection criterion to represent the motion model of the underwater target, thereby achieving matching between the target position and velocity. In addition, considering the positional error between the target center and the beacon, the three types of measurement element errors (time delay measurement error, sound velocity correlation error, and site error) are equivalent to the constant system errors of each acoustic array device, thus achieving unified and parameter-saving modeling of the target trajectory and system errors.

[0027] This invention provides a method for underwater target localization and system error compensation based on spectral clustering, such as... Figure 1 As shown, it includes the following steps:

[0028] S101: Obtain the initial measurement model;

[0029] Underwater long baseline positioning systems mainly consist of seabed acoustic arrays, acoustic beacons mounted on the target, and a targeting vessel. For example... Figure 3 As shown, taking underwater maneuvering target measurement as an example, three or more acoustic arrays are deployed on the seabed, forming a seabed positioning baseline array with a specific geometric shape. The positions of the acoustic arrays are pre-calibrated by a calibration vessel. The function of the acoustic arrays is to receive signals emitted by acoustic beacons and measure the signal propagation time. Assume the target is a cylinder located within the baseline array, with its center position at X = (x, y, z). T Assume the positions of the m acoustic arrays are X and X', respectively. i =(x i ,y i ,z i ) T If (i = 1, ..., m), then the measurement equation for the i-th acoustic array is:

[0030]

[0031] Where R i For the observation of the i-th acoustic array, Δ i Let ε be the observation system error of the i-th acoustic array caused by clock bias. i To measure random error.

[0032] However, with the increasing complexity of underwater maneuvering target motion and the improvement of underwater observation accuracy, methods that describe underwater targets as point masses are no longer sufficient to meet the requirements of high-precision tracking and positioning of underwater targets. Assuming n acoustic beacons are uniformly installed on the surface of a cylinder, in... Figure 3 In the middle, the location of the command beacon is Assuming the cylinder rotates during its motion, with an initial phase of θ, the relationship between the beacon position and the cylinder center position is as follows:

[0033]

[0034] Where r is the radius of the cylinder, θ0 is the angle between the lines connecting two adjacent beacons to the center of the cylinder, and is the rotation angle in degrees. The advantage of considering the rotation angle is that it describes the fact that underwater targets are not point masses, takes into account the inconsistency error of underwater target parts, and uses the rotation angle to model the inconsistency error, thereby effectively compensating for this error.

[0035] If at a certain moment the i-th acoustic array randomly receives the signal from the j-th beacon, then the measurement equation (initial measurement model) becomes:

[0036]

[0037] Substituting equation (2) into equation (3) and writing it in functional form, we get:

[0038] R ij =h i (x,y,z,θ,Δ i ,ε i (4)

[0039] S102: Based on the initial measurement model, select the optimal order of the polynomial to constrain the underwater target trajectory and construct an underwater target positioning model;

[0040] The target trajectory model with optimal polynomial constraints should be selected to minimize the sum of squared residuals while also minimizing the number of parameters to be estimated. By comparing the test statistic S of models with different polynomial orders, the model with the smallest S is selected as the multi-station fusion system error model with optimal polynomial constraints based on the optimal selection criterion.

[0041] S103: Perform spectral clustering of the measurement error of the station based on the relative distance between the station and the underwater target, the rotation angle of the underwater target, and the measurement accuracy of the equipment;

[0042] S104: Based on the spectral clustering results of the measurement errors of the stations, a fusion positioning model is formed by combining the underwater target positioning model;

[0043] S105: Obtain the accuracy of the target position based on the fusion positioning model. If the maximum number of iterations is reached or the station spectral clustering result converges, output the accuracy of the target position. Otherwise, return to the step of performing spectral clustering on the measurement error of the underwater station based on the relative distance between the station and the underwater target and the measurement accuracy of the equipment.

[0044] The selection of a polynomial to constrain the underwater target trajectory includes: comparing the test statistics of models with different polynomial orders, selecting the polynomial order with the smallest test statistic as the optimal polynomial, and using it to constrain the underwater target trajectory.

[0045] Based on the relative distance between the station and the underwater target, the rotation angle of the underwater target, and the measurement accuracy of the equipment, spectral clustering was performed on the measurement error of the station. The result of the spectral clustering is as follows:

[0046] A i ={X j |u j ∈C i},

[0047] Among them, X j C represents the position of station j; i For the tag set, u j For the original sample x j The data after dimensionality reduction.

[0048] The fusion positioning model is as follows:

[0049]

[0050] in, The cluster to which the i-th station belongs The corresponding systematic error, R i Let θ0 be the observation of the i-th acoustic array, where θ0 is the angle between the lines connecting two adjacent beacons and the center of the cylinder, in degrees; a and b are polynomial parameters, Ri ij Let g be the distance observation from the i-th acoustic array to the j-th acoustic beacon. m It is an explicit function of the distance observation with respect to polynomial parameters, systematic error, and the angle between the lines connecting the two beacons and the center of the cylinder.

[0051] If the maximum number of iterations is not reached and the station spectral clustering results do not converge, then return to the step of performing spectral clustering on the measurement error of the underwater station based on the relative distance between the station and the underwater target and the measurement accuracy of the equipment, including:

[0052] The similarity matrix is ​​updated based on the station spectrum clustering results as follows:

[0053]

[0054] in, This indicates that station i and station j belong to the same category in this classification result; These respectively indicate that station i and station j belong to different classes in this classification result. To calculate the average accuracy of the measured element, This is the parameter estimation result for station i and station j as belonging to the same new class.

[0055] This invention also provides an underwater target localization and system error compensation device based on spectral clustering, such as... Figure 2 As shown, it includes:

[0056] Acquisition unit 21 is used to acquire the initial measurement model;

[0057] Underwater long baseline positioning systems mainly consist of seabed acoustic arrays, acoustic beacons mounted on the target, and a targeting vessel. For example... Figure 3 As shown, taking underwater maneuvering target measurement as an example, three or more acoustic arrays are deployed on the seabed, forming a seabed positioning baseline array with a specific geometric shape. The positions of the acoustic arrays are pre-calibrated by a calibration vessel. The function of the acoustic arrays is to receive signals emitted by acoustic beacons and measure the signal propagation time. Assume the target is a cylinder located within the baseline array, with its center position at X = (x, y, z). T Assume the positions of the m acoustic arrays are X and X', respectively. i =(x i ,y i ,z i ) T If (i = 1, ..., m), then the measurement equation for the i-th acoustic array is:

[0058]

[0059] Where R i For the observation of the i-th acoustic array, Δ i Let ε be the observation system error of the i-th acoustic array caused by clock bias. i To measure random error.

[0060] However, with the increasing complexity of underwater maneuvering target motion and the improvement of underwater observation accuracy, methods that describe underwater targets as point masses are no longer sufficient to meet the requirements of high-precision tracking and positioning of underwater targets. Assuming n acoustic beacons are uniformly installed on the surface of a cylinder, in... Figure 3 In the middle, the location of the command beacon is Assuming the cylinder rotates during its motion, with an initial phase of θ, the relationship between the beacon position and the cylinder center position is as follows:

[0061]

[0062] Where r is the radius of the cylinder, and θ0 is the angle between the lines connecting two adjacent beacons and the center of the cylinder.

[0063] If at a certain moment the i-th acoustic array randomly receives the signal from the j-th beacon, then the measurement equation (initial measurement model) becomes:

[0064]

[0065] Substituting equation (2) into equation (3) and writing it in functional form, we get:

[0066] R ij =h i (x,y,z,θ,Δ i ,ε i (8)

[0067] Selection unit 22 is used to select the optimal order of the polynomial to constrain the underwater target trajectory according to the initial measurement model, and to construct an underwater target positioning model.

[0068] Clustering unit 23 is used to perform spectral clustering of the measurement error of the station based on the relative distance between the station and the underwater target, the rotation angle of the underwater target, and the measurement accuracy of the equipment;

[0069] Modeling unit 24 is used to form a fusion positioning model based on the spectral clustering results of the measurement error of the station and the underwater target positioning model.

[0070] Output unit 25 is used to obtain the accuracy of the target position according to the fusion positioning model. If the maximum number of iterations is reached or the station spectrum clustering result converges, the accuracy of the target position is output. Otherwise, the spectral clustering of the underwater station measurement error based on the relative distance between the station and the underwater target and the measurement accuracy of the equipment is returned.

[0071] The selection unit includes: selecting the polynomial with the smallest test statistic as the optimal polynomial by comparing the test statistics of models with different polynomial orders, and constraining the underwater target trajectory.

[0072] The result of spectral clustering in the clustering unit is as follows:

[0073] A i ={X j |u j ∈C i},

[0074] Among them, X j C represents the position of station j; i For the tag set, u j For the original sample x j The data after dimensionality reduction.

[0075] The fusion positioning model is specifically as follows:

[0076]

[0077] in, The cluster to which the i-th station belongs The corresponding systematic error, R i Let θ0 be the observation of the i-th acoustic array, where θ0 is the angle between the lines connecting two adjacent beacons and the center of the cylinder, in degrees; a and b are polynomial parameters, Ri ij Let g be the distance observation from the i-th acoustic array to the j-th acoustic beacon. m It is an explicit function of the distance observation with respect to polynomial parameters, systematic error, and the angle between the lines connecting the two beacons and the center of the cylinder.

[0078] θ0 is the angle between the lines connecting two adjacent beacons and the center of the cylinder, and is the rotation angle. The advantage of considering the rotation angle is that it describes the fact that the underwater target is not a point mass, takes into account the inconsistency error of the underwater target parts, and uses the rotation angle to model the inconsistency error of the parts, thereby effectively compensating for this error.

[0079] If the maximum number of iterations is not reached and the station spectral clustering results do not converge, then return to the step of performing spectral clustering on the measurement error of the underwater station based on the relative distance between the station and the underwater target and the measurement accuracy of the equipment, including:

[0080] The similarity matrix is ​​updated based on the station spectrum clustering results as follows:

[0081]

[0082] in, This indicates that station i and station j belong to the same category in this classification result; These respectively indicate that station i and station j belong to different classes in this classification result. To calculate the average accuracy of the measured element, This is the parameter estimation result for station i and station j as belonging to the same new class.

[0083] This invention employs an underwater target localization and system error compensation method based on spectral clustering. The calculation of target rotation angle and station system error is relatively accurate, with a measurement element accuracy of approximately 0.1m and a high localization accuracy within 0.5m. The calculated trajectory almost perfectly matches the reference trajectory, thus improving the accuracy of target localization.

[0084] Example 1:

[0085] This invention provides a method for underwater target localization and system error compensation based on spectral clustering, such as... Figure 4 As shown, it includes:

[0086] Underwater long baseline positioning systems mainly consist of seabed acoustic arrays, acoustic beacons mounted on the target, and a targeting vessel. For example... Figure 3 As shown, taking underwater maneuvering target measurement as an example, three or more acoustic arrays are deployed on the seabed, forming a seabed positioning baseline array with a specific geometric shape. The positions of the acoustic arrays are pre-calibrated by a calibration vessel. The function of the acoustic arrays is to receive signals emitted by acoustic beacons and measure the signal propagation time. Assume the target is a cylinder located within the baseline array, with its center position at X = (x, y, z). T Assume the positions of the m acoustic arrays are X and X', respectively. i =(x i ,y i ,z i ) T If (i = 1, ..., m), then the measurement equation for the i-th acoustic array is:

[0087]

[0088] Where R i For the observation of the i-th acoustic array, Δ i Let ε be the observation system error of the i-th acoustic array caused by clock bias. i To measure random error.

[0089] However, with the increasing complexity of underwater maneuvering target motion and the improvement of underwater observation accuracy, methods that describe underwater targets as point masses are no longer sufficient to meet the requirements of high-precision tracking and positioning of underwater targets. Assuming n acoustic beacons are uniformly installed on the surface of a cylinder, in... Figure 3 In the middle, the location of the command beacon is Assuming the cylinder rotates during its motion, with an initial phase of θ, the relationship between the beacon position and the cylinder center position is as follows:

[0090]

[0091] Where r is the radius of the cylinder, and θ0 is the angle between the lines connecting two adjacent beacons and the center of the cylinder.

[0092] If at a certain moment the i-th acoustic array randomly receives the signal from the j-th beacon, then the measurement equation (initial measurement model) becomes:

[0093]

[0094] Substituting equation (2) into equation (3) and writing it in functional form, we get:

[0095] R ij =h i (x,y,z,θ,Δ i ,ε i (12)

[0096] By combining the measurement equations for the m acoustic arrays at time t, we can obtain the set of measurement equations for the target center position, initial phase, and system error at time t:

[0097]

[0098] Where j1, j2, ..., j m Let:

[0099]

[0100] By fusing the measurement equations of the N time-sampling points of the target trajectory, the EMBET model is obtained as follows:

[0101]

[0102] As shown in Equation (15), the traditional EMBET model does not utilize ballistic kinematics characteristics and matching information. When the amount of observation data is small, the model will become ill-conditioned due to the large number of parameters to be estimated. The target trajectory constrained by a polynomial function based on the optimal selection criterion is given below, and the optimal polynomial coefficients, target spin angle and measurement system error are modeled in a unified manner to save parameters.

[0103] In shallow waters, targets move quickly underwater for short periods, so their trajectories approximately satisfy polynomial constraints, i.e., the target position X = (x, y, z). T satisfy:

[0104]

[0105] Where f1, f2, and f3 are polynomial functions of indefinite order, a and b are polynomial parameters, and t is time. The order of the polynomial is determined by the optimal model selection criterion, and the target center coordinates X = (x, y, z) satisfying equation (16) are used.T Substituting into measurement equation (3) and equating the time delay measurement error, station location error, and sound velocity correlation error to constant measurement errors, the measurement equation becomes:

[0106]

[0107] Where R ij Let ΔR be the observation from the i-th acoustic array to the j-th acoustic beacon. i This is a constant ranging error equivalent to the time delay measurement error, site error, and sound velocity correlation error of the i-th acoustic array.

[0108] Similarly, in the m measurement equations at time t, writing equation (17) in functional form yields the measurement equation set at time t concerning the polynomial parameters, initial phase, and system error:

[0109]

[0110] Where j1, j2, ..., j m Let represent the beacon indices of the acoustic signals received by the m acoustic arrays at time t, respectively. The measurement equations of the N time-sampling points of the target trajectory are fused together, and let...

[0111]

[0112] The fused model is as follows:

[0113]

[0114] The above formula is the EMBET model of multi-station fusion system error based on polynomials, where the order of the indefinite polynomial is determined by the optimal model selection criterion.

[0115] In the linear model, it is assumed that the true range value during long baseline fusion positioning is R = [R1, R2, ..., R]. mN ] T The measured value is D = [D1, D2, ..., D mN ] T The measurement data model is as follows:

[0116]

[0117] Where e is a matrix with a mean of 0 and a covariance matrix of δ 2 The random error vector of I.

[0118] Suppose the parameters to be estimated under a certain system error identification model are Let H be the design matrix, and let b be the system error of R after combining the parameter β to be estimated and the design matrix H.

[0119] R=Hβ+b (22)

[0120] Then equation (21) can be written as:

[0121] D=Hβ+b+e (23)

[0122] Based on the above formula, the least squares estimate of β can be obtained as follows:

[0123]

[0124] therefore The estimation error is:

[0125]

[0126] Where n β Let H be the number of parameters to be estimated, i.e., the dimension of β. X =H(H) T H) -1 H T The above formula can be written as:

[0127]

[0128] According to equation (22), we have:

[0129]

[0130] According to the formula for calculating the residual sum of squares, the residual sum of squares (RSS) of the model is:

[0131]

[0132] Combining equations (26), (27), and (28), we can obtain:

[0133]

[0134] The above formula is the optimal test statistic for the systematic error model, denoted as:

[0135] S = RSS + (2n) β -mN)δ 2 (30)

[0136] As can be seen from the above expression, the test statistic does not depend on whether the model is linear. Therefore, for nonlinear multi-beacon measurement systems, the above statistic is still used. When selecting the target trajectory model with optimal polynomial constraints, the goal is to minimize the sum of squared residuals while also minimizing the number of parameters to be estimated. By comparing the magnitudes of the test statistic S for models with different polynomial orders, the model with the smallest S is selected as the optimal polynomial constraint multi-station fusion system error model based on the optimal selection criterion.

[0137] If δ2 Unknown, when the statistic Q = mN-n β When the value is large, δ can be given by the sum of squared residuals from the distance measurement. 2 The estimation. Let the sum of squared residuals corresponding to the system error models with polynomial constraints of q different orders be RSS1, RSS2, ..., RSS. q The corresponding statistics Q are Q1, Q2, ..., Q q , then δ 2 Estimate for:

[0138]

[0139] System error identification methods:

[0140] After obtaining the EMBET model of the multi-station fusion system error with optimal polynomial constraints, the traditional identification method uses nonlinear parameter estimation. For ease of description, we assume that the target trajectory satisfies cubic polynomial constraints, then the target's kinematic model becomes:

[0141]

[0142] The Gauss-Newton iterative method is used for parameter estimation, let

[0143]

[0144] Then the ranging information at N time points corresponds to the unknown parameter β=(q1,q2,q3,θ,ΔR1,...,ΔR m The Jacobian matrix of ) is:

[0145]

[0146] because,

[0147]

[0148] Where α=(t 3 ,t 2 ,t,1), and have

[0149]

[0150] because in:

[0151]

[0152] Let be the direction cosine from the i-th station to the j-th beacon. Therefore,

[0153]

[0154] When the observation errors are independent and have a mean of 0 and a variance of σ 2 When the system follows a Gaussian distribution, the stable optimal estimate of the system can be obtained using the following Gauss-Newton iterative formula:

[0155] β k+1 =β k +(J T J) -1 J T (YF(β k ,X i (39)

[0156] Where β k This represents the parameter estimate for the k-th iteration.

[0157] When the observed noise is not independent or does not follow the same distribution, assuming the covariance matrix of the observed noise is Λ, the iterative formula becomes:

[0158] β k+1 =β k +(J T Λ -1 J) -1 J T Λ -1 (YF(β k ,X i (40)

[0159] However, as can be seen from equation (25), the estimation error of the traditional estimation method is:

[0160]

[0161] The above formula shows that, using As an estimate of Hβ, its error is related to n β The size of the approximation is directly proportional to the number of parameters to be estimated; the more parameters to be estimated, the worse the approximation effect.

[0162] By using the optimal model selection criterion to optimize the polynomial and by using a unified modeling method to save parameters for the system error, the traditional identification method will result in low positioning accuracy when the number of system error parameters to be estimated is too small, and inaccurate identification when the number is too large. Therefore, it is necessary to select an appropriate number of system errors to be estimated. Classifying and identifying the system errors of multiple stations is an effective method.

[0163] In the multi-station fusion system error model (20) with preferred polynomial constraints, the system errors ΔR1,...,ΔR mThe accuracy of error identification has a significant impact on the solution results and positioning accuracy. When all stations are assigned the same error parameters, the solution becomes inaccurate and the positioning accuracy is low. However, when there are too many stations, the addition of too many ranging errors to the model can lead to overfitting, resulting in extremely poor solution performance. Therefore, classifying and identifying the system errors of multiple stations and selecting an appropriate number of errors are effective ways to improve positioning accuracy.

[0164] The systematic error of each station is related to the measurement accuracy of the equipment and the distance between the station and the target. Therefore, the selection of the number of ranging systematic errors can be transformed into the classification of stations. Based on the similarity of systematic errors between stations, a clustering algorithm is used to divide m stations into k classes, with each class having the same ranging error. Traditional partition-based clustering methods, such as K-Means and K-Means++ algorithms, and model-based clustering algorithms, such as Gaussian Mixture Model (GMM) clustering algorithms, require prior knowledge of the number of clusters, i.e., the number of systematic errors to be identified. However, in underwater long-baseline fusion positioning, without prior knowledge, it is difficult to determine the appropriate number of systematic errors to identify. Too few or too many systematic errors will lead to inaccurate identification results, thereby reducing the target positioning accuracy. Hierarchical clustering and density-based clustering methods, such as the DBSCAN algorithm, when applied to the systematic error identification problem in underwater fusion positioning, measure the similarity between stations based on Euclidean distance, without considering the similarity of systematic errors between stations, and therefore cannot obtain the correct number of systematic errors.

[0165] Spectral methods transform the clustering problem of data into a graph segmentation problem using a similarity matrix. By calculating the eigenvalues ​​and eigenvectors of the Laplacian matrix, a predefined cut function is optimized to obtain a relaxed solution to the minimum cut problem. This solution is then mapped back to the original problem to obtain the cluster structure of the data. However, a similarity matrix based on distance typically reflects the distance similarity between data points and fails to reflect the similarity of systematic errors between stations. Therefore, this application considers improving the similarity matrix of traditional spectral clustering by utilizing the similarity of systematic errors between stations. Feedback and adjustments are made based on the measurement accuracy, target rotation angle, and the results of systematic error identification, forming an iterative systematic error identification algorithm based on the improved spectral clustering.

[0166] Spectral methods:

[0167] The purpose of spectral clustering is to group data points into different sets based on a similarity matrix, so that data points in the same class are as similar as possible, and data points in different classes are as dissimilar as possible. For a given dataset and similarity graph, this problem can be described in graph theory terms as finding a cut that divides the graph into several subgraphs, such that the connection weights between subgraphs are very low, while the connection weights within each subgraph are very high.

[0168] Given a dataset X = (x1, x2, ..., x...) n The similarity matrix between the data is W = (w ij ) i,j＝1,...,n , where w ij x represents i With x j The similarity between them can be calculated using the Gaussian similarity function:

[0169]

[0170] The hyperparameter σ controls the magnitude of the adjacency relationship. Based on the similarity matrix, each data point is treated as a vertex to generate an undirected graph G(V,E), where V and E represent the vertex set and edge set, respectively. The weighted adjacency matrix of the graph is then the similarity matrix W. For the vertex set V, the degree of each vertex is defined as:

[0171]

[0172] Simultaneously define the degree matrix D = diag(d1,...,d n A subset of vertices. Let its complement be Furthermore, the index vector 1 of the vertex subset A is defined. A :

[0173]

[0174] Where v i Let v represent the i-th vertex in the vertex set V. For convenience, let i∈A. i ∈A. Now, define the distance between any two sets A and B as:

[0175]

[0176] For the graph partitioning A1, A2, ..., A k Its cut is defined as:

[0177]

[0178] Its normalized cut is defined as:

[0179]

[0180] Where vol(A) i ) is used to represent subset A i To minimize the normalized cut, which is the sum of the degrees of the midpoints, we first define a series of index vectors h. j =(h 1j ,...,h nj)′:

[0181]

[0182] Therefore h i ′Dh i =1, let H = (h1,h2,...,h k If ), then H′DH=I. Also note:

[0183]

[0184] Where L = DW is the Laplacian matrix of the graph. Therefore, the problem of minimizing the normalized cut can be written as:

[0185]

[0186] Let T = D 1 / 2 H, its relaxed linear programming is:

[0187]

[0188] in Let T be the regularized Laplace matrix. Clearly, its solution T * Depend on The eigenvectors corresponding to the k smallest eigenvalues ​​are t1,...,t k Composition, namely T * =(t1,...,t k The solution to problem (50) is:

[0189] H * =D -1 / 2 T * (52)

[0190] To map the solution of the relaxed linear programming problem back to the original problem, let H be an example. * =(u1,...,u n ) T ,in For H * The i-th row, i.e., u i Equivalent to the original sample x i The data after dimensionality reduction. The K-Means method is used to analyze n data vectors (u1,...,u...). n Clustering is performed to obtain the label set (C1, C2, ..., C...). k The final clustering result of the original problem is A1,...,A. k satisfy:

[0191] A i ={x j |u j ∈Ci} (53)

[0192] Iterative identification method of system error based on improved spectral clustering

[0193] The system error of different stations is not only related to the relative distance between the station and the target, but also to the measurement accuracy of the equipment. Therefore, when the traditional spectral clustering method is applied to the identification of underwater positioning system error, the similarity matrix based on the station distance shown in Equation (36) cannot fully reflect the similarity of system errors between different stations. Therefore, the similarity matrix of the spectral method is improved on this basis.

[0194] In order to accurately measure the similarity of systematic errors between different stations, considering that the target positioning accuracy is related to the station layout geometry and the accuracy of the back-calculated measurement elements of the parameter estimates, improving the accuracy of the back-calculated measurement elements and the accuracy of the target rotation angle estimation is an effective way to improve the target positioning accuracy when the station position is fixed.

[0195] The smaller the difference between the system error identification results of two stations classified as belonging to the same category and the actual system error, the higher the similarity of the system errors of the two stations. Therefore, when all stations participate in the solution, the similarity of the system errors of any two stations is defined as:

[0196]

[0197] in To inversely calculate the accuracy of the measurement element, The target rotation angle is estimated. This represents the station system error identification result when stations i and j are considered to be of the same type, α=(0,θ,ΔR1,...,ΔR m ), θ and ΔR1,...,ΔR m represents the true value of the target rotation angle and the true value of the station system error, respectively. The similarity matrix is ​​continuously updated iteratively according to equation (54) to obtain accurate station system error classification results and improve the positioning accuracy of underwater targets.

[0198] In an underwater long baseline positioning system, assuming m acoustic arrays are deployed on a seabed platform to range and locate a cylinder, and n acoustic beacons are uniformly installed on the cylinder wall, with the initial phase of the cylinder during its motion assumed to be θ, the error iterative identification algorithm flow for the underwater long baseline positioning system based on improved spectral clustering is as follows: Figure 4 As shown, the specific implementation process is as follows:

[0199] S1, based on the optimal selection criterion of the model, the order of the polynomial is selected, and geometric transformation is performed to construct the kinematic equation of the cylinder's center of mass, determining the relative positional relationship between the beacon and the cylinder, as shown in equations (16) and (2), where:

[0200]

[0201] S2, Construct a weighted undirected graph based on the location of the monitoring stations, with the initial similarity matrix set as follows:

[0202]

[0203] Where X i The location of station i;

[0204] S3, establish the degree matrix D, the Laplacian matrix L, and... right Perform eigenvalue decomposition, determine the number of categories k based on the distribution of eigenvalues, and find the eigenvectors t1,...,t corresponding to the k smallest eigenvalues. k The matrix H is obtained. * =(u1,...,u n ) T The K-Means method is used to analyze n data vectors (u1,...,u...). n Clustering is performed to obtain the label set (C1, C2, ..., C...). k Finally, the clustering result of the original problem is obtained as follows:

[0205] A i ={X j |u j ∈C i}. (57)

[0206] S4. Based on the clustering results, each cluster is assigned a different systematic error. Stations within a cluster have the same systematic error, thus establishing the corresponding measurement equation for a certain moment, as shown in equation (18). The measurement equation becomes:

[0207]

[0208] in The cluster to which the i-th station belongs The corresponding systematic error,

[0209] S5, construct the fusion model as shown in equation (20), and iterate according to equations (32)-(39) to obtain the parameter estimates:

[0210]

[0211] S6, Substituting the parameter estimation equation (59) into the measurement equation (18) yields the back-calculated measurement accuracy at time t:

[0212]

[0213] Where m represents the number of equations at time t, Y t and These represent the measured value and the inverse measured value at time t, respectively;

[0214] S7, Substituting the parameter estimate (59) into equations (16) and (2), we can obtain the target and beacon trajectory estimates, and thus obtain the target's observation geometrical dilution of precision (GDOP) at time t as follows:

[0215]

[0216] J t Here is the direction cosine matrix of the target at time t:

[0217]

[0218] S8, combining the accuracy of the back-calculated data points of the entire target trajectory with GDOP, the accuracy of the target position estimation can be obtained:

[0219]

[0220] in and These represent the average GDOP and the average inverse measurement accuracy of the N sampling points of the target trajectory, respectively.

[0221] S9. If the maximum number of iterations is reached or the clustering results of the stations converge, then output the clustering results A1,...,A k And precision η; otherwise, return to step S3 and update the similarity matrix based on the existing clustering results as follows:

[0222]

[0223] in, and These respectively indicate that station i and station j belong to the same class and different classes in this classification result. To calculate the average accuracy of the measured element, To estimate the corresponding parameters for station i and station j as belonging to the same new class, repeat steps S3 to S9 based on the updated similarity matrix.

[0224] Example 2:

[0225] This invention utilizes the optimal model selection criterion to adaptively select the polynomial order. After performing parameter-saving unified modeling of multi-station system errors, it employs the proposed iterative identification method for system errors based on improved spectral clustering to identify parameters and estimate and evaluate the accuracy of the cylindrical trajectory. Table 1 shows the residual sum of squares (RSS) and various statistics for different polynomial order models in two experimental scenarios.

[0226] Table 1 Comparison of Polynomial Models of Different Orders

[0227]

[0228] When the polynomial order is less than 3, the statistic decreases as the order increases; when the polynomial order exceeds 3, it begins to increase. Therefore, through model optimization, the cylinder trajectory adopts the form of a cubic polynomial. In the experiment, after data preprocessing of the measured data, the reference trajectory of the cylinder and the overall layout of the acoustic array are as follows: Figure 5 , Figure 6 As shown.

[0229] When the target rotation angle or the systematic error of the station is not considered, the solution results are inaccurate and have low precision, and the calculated trajectory deviates significantly from the reference trajectory. This invention employs an underwater target positioning and systematic error compensation method based on spectral clustering. The target rotation angle and station systematic error are calculated more accurately, with a measurement element accuracy of approximately 0.1m and a high positioning accuracy of within 0.5m. The calculated trajectory almost coincides with the reference trajectory, thus improving the accuracy of target positioning.

[0230] It should be understood that the specific order or hierarchy of steps in the disclosed process is an example of an exemplary method. Based on design preferences, it should be understood that the specific order or hierarchy of steps in the process may be rearranged without departing from the scope of this disclosure. The appended method claims provide elements of various steps in an exemplary order and are not intended to limit the scope to the specific order or hierarchy described.

[0231] In the above detailed description, various features are combined together in a single embodiment to simplify this disclosure. This approach to disclosure should not be construed as reflecting an intention that embodiments of the claimed subject matter require more features than are explicitly stated in each claim. Rather, as reflected in the appended claims, the invention is presented with fewer features than all of the features of the single disclosed embodiment. Therefore, the appended claims are hereby explicitly incorporated into the detailed description, wherein each claim stands alone as a preferred embodiment of the invention.

[0232] The disclosed embodiments have been described above to enable any person skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein can be applied to other embodiments without departing from the spirit and scope of this disclosure. Therefore, this disclosure is not limited to the embodiments given herein, but is consistent with the broadest scope of the principles and novel features disclosed herein.

[0233] The foregoing description includes examples of one or more embodiments. It is certainly impossible to describe all possible combinations of components or methods in order to describe the above embodiments, but those skilled in the art will recognize that further combinations and arrangements of the various embodiments are possible. Therefore, the embodiments described in this application are intended to cover all such changes, modifications, and variations that fall within the scope of the appended claims. Furthermore, the term "comprising" as used in the specification or claims is interpreted in a manner similar to the term "including," as interpreted when used as a conjunction in the claims. Additionally, the use of any term "or" in the specification of the claims is intended to mean "non-exclusive or."

[0234] Those skilled in the art will also understand that the various illustrative logical blocks, units, and steps listed in the embodiments of the present invention can be implemented by electronic hardware, computer software, or a combination of both. To clearly demonstrate the interchangeability of hardware and software, the functions of the various illustrative components, units, and steps described above have been generally described. Whether such functionality is implemented through hardware or software depends on the specific application and the overall system design requirements. Those skilled in the art can implement the described functions using various methods for each specific application, but such implementation should not be construed as exceeding the scope of protection of the embodiments of the present invention.

[0235] The various illustrative logic blocks or units described in the embodiments of this invention can be implemented or operate the described functions using a general-purpose processor, digital signal processor, application-specific integrated circuit (ASIC), field-programmable gate array or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof. The general-purpose processor can be a microprocessor; alternatively, it can be any conventional processor, controller, microcontroller, or state machine. The processor can also be implemented using a combination of computing devices, such as a digital signal processor and a microprocessor, multiple microprocessors, one or more microprocessors combined with a digital signal processor core, or any other similar configuration.

[0236] The steps of the methods or algorithms described in the embodiments of this invention can be directly embedded in hardware, a software module executed by a processor, or a combination of both. The software module can be stored in RAM, flash memory, ROM, EPROM, EEPROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium in the art. Exemplarily, the storage medium can be connected to the processor so that the processor can read information from and write information to the storage medium. Optionally, the storage medium can also be integrated into the processor. The processor and storage medium can be housed in an ASIC, which can be housed in a user terminal. Optionally, the processor and storage medium can also be housed in different components of the user terminal.

[0237] In one or more exemplary designs, the functions described in the embodiments of the present invention can be implemented in hardware, software, firmware, or any combination of these three. If implemented in software, these functions can be stored on a computer-readable medium or transmitted on a computer-readable medium in the form of one or more instructions or code. Computer-readable media include computer storage media and communication media that facilitate the transfer of computer programs from one place to another. Storage media can be any available media that can be accessed by a general-purpose or special-purpose computer. For example, such computer-readable media can include, but is not limited to, RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store program code in the form of instructions or data structures and other forms that can be read by a general-purpose or special-purpose computer, or a general-purpose or special-purpose processor. Furthermore, any connection can be suitably defined as a computer-readable medium, for example, if the software is transmitted from a website, server or other remote resource via a coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL) or wirelessly, such as infrared, wireless and microwave, it is also included in the defined computer-readable medium. The disks and discs mentioned include compressed disks, laser discs, optical discs, DVDs, floppy disks, and Blu-ray discs. Disks typically copy data magnetically, while disks typically copy data optically using lasers. Combinations of the above can also be contained in computer-readable media.

[0238] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for underwater target localization and system error compensation based on spectral clustering, characterized in that, Includes the following steps: Obtain the initial measurement model; Based on the initial measurement model, the optimal order of the polynomial is selected to constrain the underwater target trajectory, thereby constructing an underwater target localization model; The measurement error of the station is subjected to spectral clustering based on the relative distance between the station and the underwater target, the rotation angle of the underwater target, and the measurement accuracy of the equipment. Based on the spectral clustering results of the measurement errors of the stations, a fusion positioning model is formed by combining the underwater target positioning model; The accuracy of the target location is obtained based on the fusion positioning model. If the maximum number of iterations is reached or the station spectrum clustering result converges, the accuracy of the target location is output. Otherwise, the process of performing spectrum clustering on the measurement error of the underwater station based on the relative distance between the station and the underwater target and the measurement accuracy of the equipment is returned. The fusion positioning model is specifically as follows: in, For the first The cluster to which each station belongs The corresponding systematic error, ; For the first Observations of an acoustic array The angle between the lines connecting two adjacent beacons to the center of the cylinder, expressed in degrees. and For polynomial parameters, For the first The sound array to the first The distance observation of a single acoustic beacon, g m It is an explicit function of the distance observation with respect to polynomial parameters, systematic errors, and the angle between the lines connecting the two beacons and the center of the cylinder; If the maximum number of iterations is not reached and the station spectral clustering results do not converge, then return to the step of performing spectral clustering on the measurement error of the underwater station based on the relative distance between the station and the underwater target and the measurement accuracy of the equipment, including: The similarity matrix is ​​updated based on the station spectrum clustering results as follows: ； in, This indicates the stations in this classification result. and monitoring station They belong to the same category; These respectively represent the stations in this classification result. and monitoring station For different categories, , To calculate the average accuracy of the measured element, To measure the station and monitoring station This serves as the corresponding parameter estimation result for the same new class.

2. The underwater target localization and system error compensation method based on spectral clustering according to claim 1, characterized in that, The method of constraining the underwater target trajectory by selecting a polynomial includes: comparing the test statistics of models with different polynomial orders, selecting the polynomial order with the smallest test statistics as the optimal polynomial, and constraining the underwater target trajectory.

3. The underwater target localization and system error compensation method based on spectral clustering according to claim 1, characterized in that, The measurement error of the station is subjected to spectral clustering based on the relative distance between the station and the underwater target, the rotation angle of the underwater target, and the measurement accuracy of the equipment. The result of the spectral clustering is as follows: ， in, For the station Location; For tag set, Original sample The data after dimensionality reduction.

4. An underwater target localization and system error compensation device based on spectral clustering, characterized in that, include: The acquisition unit is used to acquire the initial measurement model; The selection unit is used to select the optimal order of the polynomial to constrain the underwater target trajectory based on the initial measurement model, and to construct an underwater target positioning model. Clustering units are used to perform spectral clustering of the measurement error of the station based on the relative distance between the station and the underwater target, the rotation angle of the underwater target, and the measurement accuracy of the equipment. The modeling unit is used to form a fusion positioning model by combining the spectral clustering results of the measurement error of the station with the underwater target positioning model; The output unit is used to obtain the accuracy of the target position based on the fusion positioning model. If the maximum number of iterations is reached or the station spectrum clustering result converges, the accuracy of the target position is output. Otherwise, the spectral clustering of the underwater station measurement error based on the relative distance between the station and the underwater target and the measurement accuracy of the equipment is returned. The fusion positioning model is specifically as follows: in, For the first The cluster to which each station belongs The corresponding systematic error, ; For the first Observations of an acoustic array The angle between the lines connecting two adjacent beacons to the center of the cylinder, in degrees. and For polynomial parameters, For the first The sound array to the first The distance observation of a single acoustic beacon, g m It is an explicit function of the distance observation with respect to polynomial parameters, systematic errors, and the angle between the lines connecting the two beacons and the center of the cylinder; If the maximum number of iterations is not reached and the station spectral clustering results do not converge, then return to the step of performing spectral clustering on the measurement error of the underwater station based on the relative distance between the station and the underwater target and the measurement accuracy of the equipment, including: The similarity matrix is ​​updated based on the station spectrum clustering results as follows: ； in, This indicates the stations in this classification result. and monitoring station They belong to the same category; These respectively represent the stations in this classification result. and monitoring station For different categories, , To calculate the average accuracy of the measured element, To measure the station and monitoring station This serves as the corresponding parameter estimation result for the same new class.

5. The underwater target localization and system error compensation device based on spectral clustering according to claim 4, characterized in that, The selection unit includes: selecting the polynomial with the smallest test statistic as the optimal polynomial by comparing the test statistics of models with different polynomial orders, and constraining the underwater target trajectory.

6. The underwater target localization and system error compensation device based on spectral clustering according to claim 4, characterized in that, The result of spectral clustering in the clustering unit is as follows: ， in, For the station Location; For tag set, Original sample The data after dimensionality reduction.

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