A one-dimensional angle of arrival based vertical array underwater cooperative target location method

Abstract

The application discloses a vertical array underwater cooperative target positioning method based on one-dimensional angle of arrival, and the method is used for the positioning scene of multiple vertical line arrays cooperative targets under water, and the specific steps comprise the following steps: firstly, a positioning system is constructed, and measurement parameters are obtained; secondly, a positioning equation set of the measurement parameters and the target is established; thirdly, an initial estimation of a target coordinate vector is solved by using a weighted least square algorithm; fourthly, a weighted matrix is updated, and a coarse estimation of a target coordinate information vector is solved by using the weighted least square algorithm again; fifthly, a new positioning equation set is constructed by using a square relationship of target longitudinal and transverse coordinates, a target longitudinal and transverse coordinate horizontal direction vector is solved by using the weighted least square algorithm; and finally, a final estimation of the target position is obtained. The method has the advantages of simple line array arrangement and low complexity, can be used for real-time underwater positioning, and can improve the positioning precision of underwater targets.

Description

Technical Field

[0001] This invention relates to the field of target positioning technology, and specifically to a vertical array underwater cooperative target positioning method based on one-dimensional angle of arrival. Background Technology

[0002] Underwater acoustic source localization technology has important application value in fields such as marine resource exploration and underwater sensor networks.

[0003] In related technologies, the two-step method first estimates the observation parameters related to the target position from the signals received by the sensor, and then solves the problem based on the mathematical relationship between these intermediate parameters and the target position. The two-step method does not require prior acoustic field information and can achieve rapid positioning. Its methods mainly include TDOA (Time Difference of Arrival) positioning based on hyperbola intersection, 1-D AOA (One-Dimensional Angle of Arrival) positioning based on conical intersection, and TOA (Time of Arrival) positioning based on circular intersection. Among these, the TOA positioning method requires time synchronization between the target and the sensor, while TDOA requires time synchronization between the sensors. 1-D AOA estimation is simpler than two-dimensional spectral estimation. Furthermore, since target depth estimation based on non-cooperative algorithms often has large errors, while cooperative targets can accurately obtain depth measurements through pressure sensors, underwater target positioning methods based on one-dimensional angle of arrival using cooperative target depth measurements have attracted attention. Summary of the Invention

[0004] The purpose of this invention is to overcome the aforementioned deficiencies in the prior art and provide a method for underwater cooperative target localization based on a one-dimensional angle of arrival (AOA) vertical array. First, a 1-D AOA (One-Dimensional Angle of Arrival) localization system for multiple underwater vertical linear array cooperative targets is constructed. Then, considering the measurement errors of the AOA and depth, a pseudo-linear equation relating the 1-D AOA to the target position is constructed, and a weighted least squares algorithm is used to obtain a coarse estimate of the target position. Finally, an equation is constructed using the relationship between the target position and auxiliary variables, and a weighted least squares algorithm is used again to obtain a more accurate target position estimate.

[0005] The objective of this invention can be achieved by adopting the following technical solutions:

[0006] A method for locating underwater cooperative targets using a vertical array based on one-dimensional angle of arrival, the method comprising the following steps:

[0007] S1. Construct a positioning system and obtain measurement parameters: Let the true position coordinates of a cooperative target u in three-dimensional space be [x, y, z].T ,in[·] T This represents the transpose of the matrix, where x, y, and z represent the coordinates of the cooperative objective along the X, Y, and Z axes in three-dimensional space, respectively. The measured value of depth z, the depth measurement value The pressure is obtained through pressure sensors on the cooperative target; M ≥ 3 vertical linear arrays are randomly deployed in the target's activity area, and the coordinates of the midpoint of the i-th vertical linear array in three-dimensional space are denoted as s. i =[x i ,y i ,z i ] T Where i = 1, 2, ..., M, x i ,y i ,z i Let X, Y, and Z represent the coordinates of the midpoint of the i-th vertical linear array along the X, Y, and Z axes in three-dimensional space, respectively. The one-dimensional angle of arrival from the target to the linear array is estimated using a direction-finding algorithm from the received signal of the i-th vertical linear array. The one-dimensional angle of arrival is abbreviated as 1-D AOA; let the direction-finding error vectors of M 1-D AOAs and the target depth measurement error be Δθ=[Δθ1,…,Δθ M ] T and Δz, Δθ1,..., Δθ M Let Q represent the direction-finding errors of the 1st to Mth vertical linear arrays and the cooperative target, respectively. Assuming that the direction-finding error vectors of the 1-D AOA are independent and all follow a zero-mean Gaussian distribution, the covariance matrix of the direction-finding errors is set to Q based on the array characteristics and the performance of the direction-finding algorithm. θ Based on the performance of the depth measuring device, the variance of the target depth z measurement error is set as follows:

[0008] S2. Establish the target's positioning equations: Based on the geometric relationship between the target and the vertical linear array, construct a positioning equation set, expressed in matrix form as h1-G1η1=ε1; where h1 and G1 are the one-dimensional angle of arrival measurements from the vertical linear array. Cooperative target depth measurement value And the coordinates s of the midpoint of the vertical linear array i The vectors and matrices formed, h1 and G1, have dimensions of M×1 and M×3 respectively, and η1 = [x 2 +y 2 [x,y] T ε1 is a vector containing the target's unknown longitudinal and transverse coordinates, and ε1 is the first error vector, used to construct the measurement error adjustment parameters of the positioning system.

[0009] S3. Use the weighted least squares algorithm to obtain the initial estimate of the target coordinate vector: Calculate the weighting matrix ψ1 in the first step, and then use the weighted least squares algorithm to calculate the initial estimate of the target's longitudinal and transverse coordinate information vectors. in The true coordinates of the target location x 2 +y 2 Estimates of x and y;

[0010] S4. Update the weighted matrix and perform the weighted least squares algorithm again to obtain a coarse estimate of the target's ordinate and abscissa information vector: use the initial estimate of the target's ordinate and abscissa information vector. and Update the weighted matrix to obtain in Representing vectors The j-th element, j = 1, 2, 3, will be the new Substituting the values ​​into the weighted least squares algorithm formula again, a coarse estimate of the target's longitudinal and transverse coordinate information vectors is obtained.

[0011] S5. Construct a new system of positioning equations: Let η2 = [x 2 ,y 2 ] T Given a vector formed by the squares of the target's x and y coordinates, construct a new system of equations and write it in matrix form as h² - G²η² = ε², where the calculation formula is... in Representing vectors The k-th element, k = 1, 2, 3, G2 = [1, 1, 0; 1, 0, 1] T ε2 is the second error vector;

[0012] S6. Solve for the target's squared coordinate vectors using the weighted least squares algorithm: Calculate the weighting matrix ψ2 in the second step, and then use the weighted least squares algorithm to estimate the target's squared coordinate vectors.

[0013] S7. Obtain the final estimate of the target location: Square root extraction yields the estimated x and y coordinates of the target location. in Representing vectors The l-th element, l = 1, 2, the choice of sign and the rough estimation of the target position in step S4 The estimates of the vertical and horizontal coordinates remain consistent; The target location is estimated, and the final target location is estimated by combining the depth information.

[0014] Furthermore, in step S1, the MUSIC or Capon direction-finding algorithm is used to estimate the one-dimensional angle of arrival (AOA) using the linear array received signal. Higher angle estimation accuracy improves positioning performance. For measurement parameters, errors cannot be ignored. Assuming that the direction-finding error vectors of 1-D AOA are independent and all follow a zero-mean Gaussian distribution, the 1-D AOA measurement value with errors is estimated from the i-th vertical linear array received signal. And target position and depth measurements obtained through pressure sensors on the cooperative target. Let the direction-finding error vectors of M 1-D AOAs and the target depth measurement error be Δθ=[Δθ1,...,Δθ M ] T and Δz, Δθ1,...,Δθ M The direction finding errors of M vertical linear arrays and the cooperative target are respectively expressed as follows: The relationship between the measured values, errors and true values ​​of direction finding and depth are expressed as follows:

[0015]

[0016] Furthermore, in step S2, the coordinates s of the midpoint of the i-th vertical linear array i Linear array one-dimensional angle of arrival measurement value Depth of cooperation goals The relationship between the target's true position x and y yields the following set of nonlinear equations:

[0017]

[0018] The system of equations is pseudo-linearized, with three unknown variables. When the number of vertical linear arrays is greater than or equal to three, the number of nonlinear equations obtained is greater than or equal to the number of unknown variables. The analytical expression solution can be obtained through the equation system solving method.

[0019] Furthermore, in step S3, h1 and G1 are calculated by the following formulas respectively.

[0020]

[0021]

[0022] Since the number of nonlinear equations must be greater than or equal to the number of unknown variables, the weighted least squares method is used to make full use of redundant data. When the measurement error follows an ideal Gaussian distribution, it has high positioning accuracy and low computational cost. Furthermore, the algorithm accuracy can be improved by increasing the number of vertical arrays.

[0023] Considering that observations with smaller errors have higher weights, and assigning smaller weights to larger squared residuals, the weighting matrix ψ1, combined with the new positioning equations constructed in step S2, is calculated by the following formula.

[0024]

[0025] Where B1 is an M-order identity matrix, Q θ Let Q be the covariance matrix of the direction-finding error. z The variance σ of the measurement error for the target depth z, where all diagonal elements are diagonal elements. z For an M×M dimensional matrix with all other elements equal to 0, the diagonal matrix C1 is calculated using the following formula.

[0026]

[0027] Where diag[·] represents a square matrix in which all elements except the main diagonal are 0.

[0028] The initial estimate of the target coordinate vector η1 is calculated using the following formula.

[0029]

[0030] Furthermore, in step S4, the target longitudinal and transverse coordinate information vectors obtained in step S3 are initially estimated. Estimated values ​​of the horizontal and vertical coordinate positions and The initial estimate can be used to update B1, and a weighted least squares algorithm can be performed again to obtain a more accurate coordinate position estimate. This is combined with the target depth measurement obtained in step S1. Construct an initial estimate of the target position Calculate the coordinates s of the target position relative to the midpoint of the i-th vertical linear array. i =[x i ,y i ,z i ] T Distance estimation

[0031]

[0032] The diagonal matrix is ​​calculated using the following formula.

[0033]

[0034] in This represents the distance from the target to the midpoint of the i-th vertical linear array.

[0035] The new Substituting B1 into equation (4) yields the covariance matrix of the new error vector. Then the Substituting into the weighted least squares algorithm (8) yields a coarse estimate.

[0036] Furthermore, in step S5, the preceding weighted least squares algorithm assumed that the unknowns were uncorrelated, but in reality they have a sum of squares relationship, which can be used to estimate... The relationship between the obtained target's longitudinal and transverse coordinates and their sum of squares is used to construct a new set of positioning equations, which are then solved to obtain a more accurate target position estimate.

[0037] Furthermore, in step S6, considering that observations with smaller errors have higher weights, smaller weights are assigned to larger squared residuals. Combined with the new positioning equations constructed in step S5, the weighting matrix ψ2 is calculated using the following formula.

[0038]

[0039] in

[0040]

[0041] An estimate of η² can be obtained based on the weighted least squares algorithm:

[0042]

[0043] Further, in step S7, the vector from step S6 is... The final target coordinates are estimated by taking the square root of the elements. The final target has two values ​​for both the x and y coordinates; based on prior information, these two values ​​can be discarded. Each has an invalid value, meaning the choice of positive or negative sign is related to the coarse estimation of the target position in step S4. Maintain consistency.

[0044] The present invention has the following advantages and effects compared with the prior art:

[0045] (1) The underwater cooperative target localization method disclosed in this invention is a closed-loop solution algorithm, which does not require iterative calculation, has low computational complexity, high computational efficiency, and is suitable for real-time localization.

[0046] (2) The underwater cooperative target positioning method disclosed in this invention considers obtaining depth data through cooperative target pressure sensors, which has a smaller depth error and can reduce the number of unknown parameters of the target coordinates, making the target's horizontal and vertical coordinates more accurate.

[0047] (3) The underwater cooperative target positioning method disclosed in this invention uses only a vertical linear array to locate the target. The deployment and calibration of the linear array and the comparison of the two-dimensional surface array are relatively simple and applicable to more underwater scenarios. Attached Figure Description

[0048] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, illustrate exemplary embodiments of the invention and, together with their description, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings:

[0049] Figure 1 This is a schematic diagram illustrating the principle of a vertical array underwater cooperative target localization method based on one-dimensional angle of arrival proposed in this invention.

[0050] Figure 2 This is a schematic diagram of the vertical array and target position arrangement in Embodiment 1 of the present invention;

[0051] Figure 3 This is a schematic diagram of the RMSE simulation results of the localization algorithm under different 1-D AOA errors in Embodiment 1 of the present invention;

[0052] Figure 4 This is a flowchart of a vertical array underwater cooperative target localization method based on one-dimensional angle of arrival, as disclosed in this invention. Detailed Implementation

[0053] 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.

[0054] Example 1

[0055] This embodiment uses MATLAB for simulation demonstration. This embodiment discloses a vertical array underwater cooperative target localization method based on one-dimensional angle of arrival. The principle of the localization method is as follows: Figure 1 As shown, the specific steps are as follows:

[0056] S1. Assume the three-dimensional spatial coordinates of the unknown target in the water are u = [416, 529, 397]. T Within a space centered at the origin with X and Y axes measuring 300 meters × 300 meters and a Z-axis depth of 150 meters, M = 7 vertical linear arrays are set up. A schematic diagram of the placement of each vertical array relative to the target position is shown below. Figure 2 As shown, the coordinates of the midpoint of the i-th vertical linear array in three-dimensional space are denoted as s. i =[x i ,y i ,z i ] T x i ,y i ,z iLet represent the coordinates of the i-th vertical linear array midpoint in the three-dimensional space along the X, Y, and Z axes, respectively. The coordinates of the midpoint of each vertical linear array midpoint are denoted as s1 = [236.9, -254.3, 90.8]. T s2 = [2.4, -250, 107.5] T s2 = [37.3, -114.1, 23.8] T s2 = [173.6, 213.2, 124] T s5 = [-89.4, -15.4, 79.4] T s6 = [-167.8, 105, 137.9] T s7 = [193.6, -23.9, 46.7] T In the simulation, the depth measurement value is obtained by directly adding the error to the depth of the target u. The one-dimensional angle of arrival (1-D AOA) measurement of the target to the linear array is... Where i = 1, 2, ..., 7; let the direction-finding errors of the 7 1-D AOAs be denoted as Δθ = [Δθ1, ..., Δθ7]. T The target depth measurement error is Δz, which differs from the true value θ = [θ1,...,θ7]. T The relationship between z and z is expressed as follows:

[0057]

[0058] Assuming that the 1-D AOA direction-finding error vectors are mutually independent and all follow a Gaussian distribution with zero mean, the covariance matrix of the direction-finding error is set to Q based on the array characteristics and the performance of the direction-finding algorithm. θ The variance of the depth measurement error is set according to the performance of the depth measuring device.

[0059] S2. Establish the target's positioning equations. The coordinates of the midpoint of the i-th vertical linear array are s. i Linear array one-dimensional angle of arrival measurement value Depth of cooperation goals The relationship between the target's true position x and y is as follows:

[0060]

[0061] Based on the geometric relationship between the target and the vertical linear array, a set of positioning equations is constructed, which is expressed in matrix form as h1-G1η1=ε1;

[0062] Where h1 and G1 are the one-dimensional arrival angle measurements of the i-th vertical linear array. Cooperative target depth measurement value And the coordinates s of the midpoint of the i-th vertical linear array iThe vectors and matrices formed, h1 and G1, have dimensions of 7×1 and 7×3 respectively. h1 and G1 are calculated by the following formulas.

[0063]

[0064]

[0065] η1=[x 2 +y 2 [x,y] T ε1 is a vector containing the target's longitudinal and transverse coordinates, and ε1 is the first error vector, which is related to the measurement error and is used to construct the measurement error adjustment parameters of the positioning system.

[0066] S3. Use the weighted least squares algorithm to obtain the initial estimate of the target coordinate vector. The weighting matrix ψ1 is calculated using the following formula:

[0067]

[0068] In step S3 of this embodiment, B1 is a 7th-order identity matrix, Q θ Let Q be the covariance matrix of the direction-finding error. z Let σ be the variance of depth measurement error, where all diagonal elements are diagonal elements. z For a 7×7 matrix where all other elements are 0, the diagonal matrix C1 is calculated using the following formula.

[0069]

[0070] Where diag[·] represents a square matrix in which all elements except the main diagonal are 0.

[0071] The initial estimate of the target coordinate vector η1 is calculated using the following formula.

[0072]

[0073] The initial estimate of the target's longitudinal and transverse coordinate information vectors is calculated using the weighted least squares algorithm. in The true coordinates of the target location x 2 +y 2 Estimates of x and y.

[0074] S4. Update the weighted matrix and perform the weighted least squares algorithm again to obtain a coarse estimate of the target's longitudinal and transverse coordinate information vectors. Initial estimate of the target's longitudinal and transverse coordinate information vectors obtained in step S3. Estimated values ​​of the horizontal and vertical coordinate positions and Right now and in Representing vectors The j-th element, j = 1, 2, 3, and the target depth measurement value obtained in step S1. Construct an initial estimate of the target position Calculate the coordinates s of the target position relative to the midpoint of the i-th vertical linear array. i =[x i ,y i ,z i ] T Distance estimation

[0075]

[0076] The diagonal matrix is ​​calculated using the following formula.

[0077]

[0078] The new Substituting B1 into equation (4) yields the covariance matrix of the new error vector. Then the Substituting into the weighted least squares algorithm (6) yields a coarse estimate.

[0079] S5. Construct a new system of positioning equations. Let η2 = [x 2 ,y 2 ] T Given a vector formed by the squares of the target's x and y coordinates, construct a new system of equations and write it in matrix form: h² - G²η² = ε², where h² is the coarse estimate obtained in step S4. The last two elements are squared to obtain the result, i.e.,

[0080]

[0081]

[0082] in Representing vectors The k-th element, k = 1, 2, 3, and ε2 is the second error vector.

[0083] S6. Solve for the squared vectors of the target's ordinate and abscissa using the weighted least squares algorithm. Calculate the weighting matrix ψ2 using the following formula:

[0084]

[0085] in:

[0086]

[0087] Based on the weighted least squares algorithm (11), the estimate of η2 can be obtained:

[0088]

[0089] S7. Obtain the final estimate of the target location. Square root extraction yields the estimated x and y coordinates of the target location. in Representing vectors The l-th element, l = 1, 2, the choice of sign is related to the coarse estimation of the target position in step S4. Maintain consistency. The target location is estimated, and the final target location is estimated by combining the depth information.

[0090] Figure 3 This is a schematic diagram illustrating the RMSE simulation results of the localization algorithm under different 1-D AOA errors. Figure 3 As can be seen from this, the 1-D AOA error is relatively small (10log(σ)). 2 When σ ≤ -34, the target position estimation results are all close to the Cramer-Raolower bound (CRLB), and the 1-D AOA error is 10log(σ). 2 Even when the value is greater than -34, the target location estimation results are still relatively good.

[0091] Example 2

[0092] This embodiment uses a water tank approximately 7m long, 4m wide, and 1.2m deep for experimental demonstration. The specific steps of the underwater cooperative target localization method based on a one-dimensional angle of arrival using a vertical array, disclosed in this embodiment, are as follows:

[0093] T1. Construct a positioning system and obtain measurement parameters. Using the width of the pool as the x-axis, the length as the y-axis, and the depth as the z-axis, a transducer is used as the target to transmit signals. The transducer is fixed to the pool at coordinates u = [1.8, 0.4, 0.5] using a ladder. T At, among which [·] T This represents the transpose of a matrix, with its depth measurement value. The pressure is obtained through devices such as pressure sensors on the cooperative target; three vertical linear arrays are randomly placed in the pool area, and the coordinates of the midpoint of the i-th vertical linear array in three-dimensional space are denoted as s. i =[x i ,y i ,z i ] T x i ,y i ,z iLet represent the coordinates of the i-th vertical linear array midpoint on the X, Y, and Z axes in three-dimensional space, respectively. Similarly, fix it in the pool using a ladder, and use an infrared rangefinder or other measuring tools to measure the coordinates of the midpoint of the vertical linear array, denoted as s1 = [3.68, 6.07, 0.68]. T s2 = [1.38, 6.07, 0.61] T s3 = [0.31, 6.07, 0.8] T The one-dimensional angle of arrival (1-D AOA) from the target to the linear array is estimated from the received signal of the i-th vertical linear array using a conventional direction-finding algorithm. Where i = 1, 2, 3; let the direction-finding error and target depth measurement error of the three 1-D AOAs be Δθ = [Δθ1, Δθ2, Δθ3] respectively. T And Δz, and assuming that the 1-D AOA direction-finding error vectors are mutually independent and all follow a Gaussian distribution with zero mean, the covariance matrix of the direction-finding error is set to Q based on the array characteristics and the performance of the direction-finding algorithm. θ The variance of the measurement error is set according to the performance of the depth measuring device.

[0094] T2. Establish the target's positioning equations. Based on the geometric relationship between the target and the vertical linear array, construct a positioning equation set, expressed in matrix form as h1 - G1η1 = ε1; where h1 and G1 are the one-dimensional angle of arrival measurements from the vertical linear array. Cooperative target depth measurement value and the coordinates s of the midpoint of the i-th vertical linear array i The vectors and matrices formed, h1 and G1, have dimensions of 3×1 and 3×3 respectively, and η1 = [x 2 +y 2 [x,y] T ε1 is a vector containing the target's unknown coordinates, and ε1 is an error vector used to construct the measurement error adjustment parameters of the positioning system.

[0095] T3. The initial estimate of the target coordinate vector is obtained using the weighted least squares algorithm. The weighting matrix ψ1 is calculated, and the initial estimate of the target's longitudinal and transverse coordinate information vectors is obtained using the weighted least squares algorithm. in The true coordinates of the target location x 2 +y 2 Estimates of x and y;

[0096] T4. Update the weighted matrix and perform a weighted least squares algorithm again to obtain a coarse estimate of the target's x and y coordinate information vectors. Use the initial target coordinate estimate obtained in T3. Update weighted matrix New Substituting the values ​​into the weighted least squares algorithm formula again, a coarse estimate of the target's longitudinal and transverse coordinate information vectors is obtained.

[0097] T5. Construct a new system of positioning equations. Let η2 = [x 2 ,y 2 ] T Given a vector formed by the squares of the target's x and y coordinates, construct a new system of equations and write it in matrix form: h² - G²η² = ε², where h² is the coarse estimate obtained in step S4. The last two elements are squared to obtain the result, i.e. in Representing vectors The k-th element, k = 1, 2, 3, G2 = [1, 1, 0; 1, 0, 1] T ε2 is the error vector.

[0098] T6. Solve for the squared vectors of the target's ordinate and abscissa using the weighted least squares algorithm. Calculate the new weighted matrix ψ2, and then use the weighted least squares algorithm to estimate the squared vectors of the target's ordinate and abscissa.

[0099] T7. Obtain the final estimate of the target location. Square root extraction yields the estimated x and y coordinates of the target location. in Representing vectors The l-th element, l = 1, 2, the choice of sign is related to the coarse estimation of the target position in step S4. Maintain consistency. The target location is estimated, and the final target location is estimated by combining the depth information.

[0100] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A method for underwater cooperative target localization using a vertical array based on one-dimensional angle of arrival, characterized in that, The underwater cooperative target location method includes the following steps: S1. Construct a positioning system and obtain measurement parameters: Let the true position coordinates of a cooperative target u in three-dimensional space be [x, y, z]. T ,in[·] T This represents the transpose of the matrix, where x, y, and z represent the coordinates of the cooperative objective along the X, Y, and Z axes in three-dimensional space, respectively. The measured value of depth z, the depth measurement value The pressure is obtained through pressure sensors on the cooperative target; M ≥ 3 vertical linear arrays are randomly deployed in the target's activity area, and the coordinates of the midpoint of the i-th vertical linear array in three-dimensional space are denoted as s. i =[x i ,y i ,z i ] T Where i = 1, 2, ..., M, x i ,y i ,z i Let X, Y, and Z represent the coordinates of the midpoint of the i-th vertical linear array along the X, Y, and Z axes in three-dimensional space, respectively. The one-dimensional angle of arrival from the target to the linear array is estimated from the received signal of the i-th vertical linear array using a direction-finding algorithm. The one-dimensional angle of arrival is abbreviated as 1-D AOA; let the direction-finding error vectors of M 1-D AOAs and the target depth measurement error be Δθ=[Δθ1,…,Δθ M ] T and Δz, Δθ1,…,Δθ M Let Q represent the direction-finding errors of the 1st to Mth vertical linear arrays and the cooperative target, respectively. Assuming that the direction-finding error vectors of the 1-D AOA are independent and all follow a zero-mean Gaussian distribution, the covariance matrix of the direction-finding errors is set to Q based on the array characteristics and the performance of the direction-finding algorithm. θ Based on the performance of the depth measuring device, the variance of the target depth z measurement error is set as follows: S2. Establish the target's positioning equations: Based on the geometric relationship between the target and the vertical linear array, construct a positioning equation set, expressed in matrix form as h1-G1η1=ε1; where h1 and G1 are the one-dimensional angle of arrival measurements from the vertical linear array. Cooperative target depth measurement value and the coordinates s of the midpoint of the vertical linear array i The vectors and matrices formed, h1 and G1, have dimensions of M×1 and M×3 respectively, and η1 = [x 2 +y 2 [x,y] T ε1 is a vector containing the target's coordinate information to be estimated, and ε1 is the first error vector used to construct the measurement error adjustment parameters of the positioning system. S3. Use the weighted least squares algorithm to obtain the initial estimate of the target coordinate vector: Calculate the weighting matrix ψ1 in the first step, and then use the weighted least squares algorithm to calculate the initial estimate of the target's longitudinal and transverse coordinate information vectors. in The true coordinates of the target location x 2 +y 2 Estimates of x and y; S4. Update the weighted matrix and perform the weighted least squares algorithm again to obtain a coarse estimate of the target's ordinate and abscissa information vector: use the initial estimate of the target's ordinate and abscissa information vector. and Update the weighted matrix to obtain in Representing vectors The j-th element, j = 1, 2, 3, will be the new Substituting the values ​​into the weighted least squares algorithm formula again, a coarse estimate of the target's longitudinal and transverse coordinate information vectors is obtained. S5. Construct a new system of positioning equations: Let η2 = [x 2 ,y 2 ] T Given a vector formed by the squares of the target's x and y coordinates, construct a new system of equations and write it in matrix form as h² - G²η² = ε², where the calculation formula is... in Representing vectors The k-th element, k = 1, 2, 3, G2 = [1, 1, 0; 1, 0, 1] T ε2 is the second error vector; S6. Solve for the target's squared coordinate vectors using the weighted least squares algorithm: Calculate the weighting matrix ψ2 in the second step, and then use the weighted least squares algorithm to estimate the target's squared coordinate vectors. S7. Obtain the final estimate of the target location: Square root extraction yields the estimated x and y coordinates of the target location. in Representing vectors The l-th element, l = 1, 2, the choice of sign and the rough estimation of the target position in step S4 The estimates of the vertical and horizontal coordinates remain consistent; The target location is estimated, and the final target location is estimated by combining the depth information.

2. The underwater cooperative target localization method based on a one-dimensional angle of arrival using a vertical array, as described in claim 1, is characterized in that... In step S1, the MUSIC or Capon direction-finding algorithm is used to estimate the one-dimensional angle of arrival (AOA) using the linear array received signal. For the measurement parameters, considering the measurement error, the 1-D AOA measurement value with error is estimated from the i-th vertical linear array received signal. And target position and depth measurements obtained through pressure sensors on the cooperative target. Let the direction-finding error vectors of M 1-D AOAs and the target depth measurement error be Δθ=[Δθ1,...,Δθ M ] T and Δz, Δθ1,...,Δθ M The direction finding errors of M vertical linear arrays and the cooperative target are respectively expressed as follows: The relationship between the measured values, errors and true values ​​of direction finding and depth are expressed as follows:

3. The method for underwater cooperative target localization based on a one-dimensional angle of arrival using a vertical array, as described in claim 1, is characterized in that... In step S2, the coordinates s of the midpoint of the i-th vertical linear array i Linear array one-dimensional angle of arrival measurement value Depth of cooperation goals The relationship between the target's true position x and y is as follows:

4. The method for underwater cooperative target localization based on a one-dimensional angle of arrival using a vertical array, as described in claim 1, is characterized in that... In step S3, h1 and G1 are calculated by the following formulas respectively. The weighting matrix ψ1 is calculated by the following formula. Where B1 is an M-order identity matrix, Q θ Let Q be the covariance matrix of the direction-finding error. z The variance σ of the measurement error for the target depth z, where all diagonal elements are diagonal elements. z For an M×M dimensional matrix with all other elements equal to 0, the diagonal matrix C1 is calculated using the following formula. Where diag[·] represents a square matrix in which all elements except the main diagonal are 0; The initial estimate of the target coordinate vector η1 is calculated using the following formula.

5. The method for underwater cooperative target localization based on a one-dimensional angle of arrival using a vertical array, as described in claim 4, is characterized in that... In step S4, the target's longitudinal and transverse coordinate information vectors obtained in step S3 are initially estimated. Estimated values ​​of the horizontal and vertical coordinate positions and And the target depth measurement value obtained in step S1 Construct an initial estimate of the target position Calculate the coordinates s of the target position relative to the midpoint of the i-th vertical linear array. i =[x i ,y i ,z i ] T Distance estimation The diagonal matrix is ​​calculated using the following formula. in This represents the distance from the target to the midpoint of the i-th vertical linear array; The new Substituting B1 into equation (4) yields the covariance matrix of the new error vector. Then the Substituting into the weighted least squares algorithm (8) yields a coarse estimate.

6. The method for underwater cooperative target localization based on a one-dimensional angle of arrival using a vertical array, as described in claim 1, is characterized in that... In step S5, the coarse estimate is used. The relationship between the obtained target coordinates and their sum of squares is used to construct a new set of positioning equations.

7. The method for underwater cooperative target localization based on a one-dimensional angle of arrival using a vertical array, as described in claim 1, is characterized in that... In step S6, the weighting matrix ψ2 is calculated by the following formula. in An estimate of η² can be obtained based on the weighted least squares algorithm:

8. The method for underwater cooperative target localization based on a one-dimensional angle of arrival using a vertical array, as described in claim 7, is characterized in that... In step S7, the vector from step S6 is... The final target coordinates are estimated by taking the square root of the elements. The choice of positive or negative sign is related to the coarse estimation of the target position in step S4. Maintain consistency.

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