Target three-dimensional positioning method based on multivariate data fusion

Abstract

The invention discloses a target three-dimensional positioning method based on multivariate data fusion, and belongs to the field of signal and information processing. The positioning method is applicable to the scenes that a single radar transmitter serves as a radiation source, a multi-part scattered receiver receives signals, and data fusion processing is carried out. According to the target three-dimensional positioning method based on multivariate data fusion provided by the invention, a target observation overdetermined equation set is established by using positioning parameters such as time difference of arrival and direction of arrival, and auxiliary variables are introduced to realize linear solution of a target three-dimensional coordinate, so that improvement of target three-dimensional positioning precision is completed; the method has the main advantages that various positioning parameters and geometric characteristics of the three-dimensional position of the target are fused, an overdetermined linear equation set is established, rapid solving of the three-dimensional coordinates of the target is achieved through an analytical expression, the three-dimensional positioning precision of the target can be further improved, and the positioning accuracy of the target is improved. And the method has more robust positioning precision performance on time difference of arrival measurement errors, direction of arrival measurement errors and receiver site errors.

Description

Technical Field

[0001] This invention relates to the field of signal and information processing technology, and in particular to a target three-dimensional localization method based on multi-source data fusion. Background Technology

[0002] Based on the type of receiving platform, positioning technologies are mainly divided into spaceborne positioning systems and ground-based positioning systems. Spaceborne positioning systems, due to their unique advantages such as all-weather, all-day detection and independence from the Earth's curvature, are widely used for aerial target detection and positioning, especially suitable for scenarios requiring dynamic monitoring and real-time navigation. Ground-based positioning systems primarily utilize ground base stations or other ground sensors to locate targets, offering better anti-interference capabilities and achieving high-precision target positioning in complex electromagnetic environments. Meanwhile, due to the limitations of both spaceborne and ground-based positioning systems, extensive research has been conducted in recent years on multi-platform joint positioning systems. In positioning technology, based on positioning parameters, positioning methods can be summarized as time-of-flight positioning, direction-finding positioning, Doppler positioning, and joint positioning methods using multiple parameters. Correspondingly, the solution algorithms include least squares algorithms, iterative optimization algorithms, and semidefinite programming algorithms. Selecting appropriate positioning parameters, constructing the target positioning solution equations, and designing the solution algorithm have a crucial impact on the accuracy of the target's three-dimensional positioning. Summary of the Invention

[0003] This invention provides a target 3D positioning method based on multi-source data fusion. This method can leverage the advantages of redundant information acquisition from multiple receivers, utilize time difference of arrival and angle of arrival positioning parameters, cleverly design a target 3D positioning model, reduce the condition number of the positioning model coefficient matrix to ensure the stability of the target 3D position output, derive the target 3D positioning analytical expression to avoid introducing positioning errors by neglecting higher-order parameters, and ensure the accuracy and robustness of the target 3D positioning method.

[0004] Firstly, a target 3D localization method based on multi-source data fusion is provided, including:

[0005] Get D TPi And the angle of arrival parameters of N receivers, D TPi The distance d from the transmitter to the target TP Distance d from the target to receiver i Pi The sum, where i takes values ​​from 1 to N;

[0006] The target's three-dimensional position is solved using an overdetermined system of linear equations relating the target's three-dimensional coordinates and the distance from the transmitter to the target. The overdetermined system of linear equations satisfies AX = B, where X = [xyzd]. TP ] T The target coordinate distance matrix, The coefficient matrix, For measurement matrix;

[0007]

[0008] (x0, y0, z0) are the coordinates of the transmitter, (x i ,y i ,z i () represents the coordinates of receiver i, D TPi The distance d from the transmitter to the target TP Distance d from the target to receiver i Pi The sum of θ i Let be the azimuth angle of the target's scattered echo relative to receiver i. Let be the elevation angle of the target's scattered echo relative to receiver i. Let be the distance from receiver i to the origin of the coordinate system.

[0009] In conjunction with the first aspect, in some implementations of the first aspect, the solution of the overdetermined linear equation system includes:

[0010] For the optimization function The solution obtained using the least squares algorithm is as follows:

[0011] X = (A T A) -1 A T B.

[0012] In conjunction with the first aspect, in some implementations of the first aspect, D TPi D is determined based on the distances from the transmitter to each of the N receivers and the time differences in arrival among the N receivers. TPi satisfy:

[0013] D TPi =d Ti +τ i c

[0014] d Ti Let τ be the distance from transmitter to receiver i. i Let be the time difference of arrival of receiver i, and c be the speed of light.

[0015] In conjunction with the first aspect, in some implementations of the first aspect, the method further includes:

[0016] Solve for the target localization error matrix:

[0017] dX=(dA H dA) -1 dA H (dB-dH)

[0018] in, Let dA be the measurement error matrix, and dA be the error coefficient matrix. Let dX be the site location error matrix, where dX = [dx dy dz]. T The target positioning error matrix; τ i Let i be the time difference of arrival of receiver i.

[0019]

[0020]

[0021] d Ti Let be the distance from transmitter to receiver i; the i-th row, i+N-th row, and i+N+1-th row of dH all correspond to receiver i. The i-th row of dH satisfies dH(i,1), the i+N-th row of dH satisfies dH(i+N,1), and the i+N+1-th row of dH satisfies dH(i+1+N,1).

[0022] In conjunction with the first aspect, in some implementations of the first aspect, the method further includes:

[0023] The geometric dilution of positioning accuracy (GDOP) is used to measure the 3D positioning accuracy of the target. The GDOP is measured by the positioning error covariance matrix P. x Please solve.

[0024] P X =(dA) H dA) -1 dA H [E{dBdB H}-E{dHdH H}]dA(dA H dA) -1

[0025]

[0026]

[0027] The variance of the time difference error of receiver i is The variance of the azimuth error is The variance of pitch angle error is The variance of the transmitter site error is The receiver site error variance is The subscripts i or j of intermediate quantity h correspond to the receiver number, the subscripts i or j of intermediate quantity f correspond to the receiver number, and the subscripts i or j of intermediate quantity g correspond to the receiver number; (x j ,y j ,z j ) represents the coordinates of receiver j, and d Tj P is the distance from the transmitter to the receiver j; x(1,1) represents the positioning error covariance matrix P. x The result of the element in the first row and first column, P x (2,2) represents the positioning error covariance matrix P. x The result of the element in the second row and second column, P x (3,3) represents the positioning error covariance matrix P. x The value of the element in the 3rd row and 3rd column.

[0028] Secondly, a target 3D localization method based on multi-source data fusion is provided, including:

[0029] Get D TPi And the azimuth parameter information of N receivers, D TPi The distance d from the transmitter to the target TP Distance d from the target to receiver i Pi The sum, where i takes values ​​from 1 to N;

[0030] The target's three-dimensional position is solved using an overdetermined system of linear equations relating the target's three-dimensional coordinates and the distance from the transmitter to the target. The overdetermined system of linear equations satisfies AX = B, where X = [xyzd]. TP ] T The target coordinate distance matrix, The coefficient matrix, For measurement matrix;

[0031]

[0032] (x0, y0, z0) are the coordinates of the transmitter, (x i ,y i ,z i () represents the coordinates of receiver i, D TPi The distance d from the transmitter to the target TP Distance d from the target to receiver i Pi The sum of θ i Let be the azimuth angle of the target's scattered echo relative to receiver i. Let be the distance from receiver i to the origin of the coordinate system.

[0033] In conjunction with the second aspect, in some implementations of the second aspect, the solution of the overdetermined linear equation system includes:

[0034] For the optimization function The solution obtained using the least squares algorithm is as follows:

[0035] X = (A T A) -1 A T B.

[0036] In conjunction with the second aspect, in some implementations of the second aspect, D TPi D is determined based on the distances from the transmitter to each of the N receivers and the time differences in arrival among the N receivers. TPi satisfy:

[0037] D TPi =d Ti +τ i c

[0038] d Ti Let τ be the distance from transmitter to receiver i. i Let be the time difference of arrival of receiver i, and c be the speed of light.

[0039] In conjunction with the second aspect, in some implementations of the second aspect, the method further includes:

[0040] Solve for the target localization error matrix:

[0041] dX=(dA H dA) -1 dA H (dB-dH)

[0042] Where dB=[cdτ1 … cdτ N dθ1 … dθ N ] T Let dA be the measurement error matrix, and dA be the error coefficient matrix. Let dX be the site location error matrix, where dX = [dx dy dz]. T The target positioning error matrix; τ i Let i be the time difference of arrival of receiver i.

[0043]

[0044] d Ti Let be the distance from transmitter to receiver i; the i-th row and the (i+N)-th row of dH correspond to receiver i, the i-th row of dH satisfies dH(i,1), and the (i+N)-th row of dH satisfies dH(i+N,1).

[0045] In conjunction with the second aspect, in some implementations of the second aspect, the method further includes:

[0046] The geometric dilution of positioning accuracy (GDOP) is used to measure the 3D positioning accuracy of the target. The GDOP is measured by the positioning error covariance matrix P. x Please solve.

[0047] P X =(dA) H dA) -1 dA H[E{dBdB H}-E{dHdH H}]dA(dA H dA) -1

[0048]

[0049]

[0050] The variance of the time difference error of receiver i is The variance of the azimuth error is The variance of the transmitter site error is The receiver site error variance is The subscripts i or j of intermediate quantity h correspond to the receiver number, and the subscripts i or j of intermediate quantity f correspond to the receiver number; (x j ,y j ,z j ) represents the coordinates of receiver j, and d Tj P is the distance from the transmitter to the receiver j; x (1,1) represents the positioning error covariance matrix P. x The result of the element in the first row and first column, P x (2,2) represents the positioning error covariance matrix P. x The result of the element in the second row and second column, P x (3,3) represents the positioning error covariance matrix P. x The value of the element in the 3rd row and 3rd column.

[0051] Compared with the prior art, the solution provided by the present invention has at least the following beneficial technical effects:

[0052] This invention fully leverages the potential advantages of multi-domain and multi-element data acquisition from multiple receivers. By utilizing time difference of arrival (TDOA) and angle of arrival (ADR) parameters, it establishes an overdetermined linear equation system, realizing the transformation from single-receiver single-data positioning to multi-receiver multi-element information fusion. Furthermore, it utilizes analytical expressions to achieve rapid solution of the target's three-dimensional coordinates, which can further improve the target's three-dimensional positioning accuracy and exhibit more robust positioning accuracy performance against TDOA measurement errors, ADR measurement errors, and receiver site errors. Attached Figure Description

[0053] Figure 1 A geometrical diagram illustrating the construction of a linear model for the time difference of arrival.

[0054] Figure 2 A geometrical diagram illustrating the construction of a linear model for the angle of arrival. Detailed Implementation

[0055] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0056] This invention provides a target 3D localization method based on multi-source data fusion. This method utilizes positioning parameters such as time difference of arrival (TDOA) and angle of arrival (AHA) to establish an overdetermined set of equations for target observation, and introduces auxiliary variables to achieve a linear solution for the target's 3D coordinates, thereby improving the accuracy of the target's 3D localization. Multiple receivers acquire direct wave signals from the transmitter and echo signals scattered from the target, estimating the TDOA and AHA positioning parameters. Combining the signal propagation path and the localization observation equations, the target is determined to be located on an ellipsoid with the transmitter and receiver as foci. Based on the AHA (including azimuth and elevation) of the target echo relative to the receiving station, the target is determined to be located on a ray with a known slope passing through the receiver. When the receiver array configuration limits effective azimuth estimation, the target is determined to be located on an azimuth plane passing through the receiver and parallel to the Z-axis. By fusing the TDOA and AHA parameters from multiple receivers, an overdetermined linear equation system corresponding to the ellipsoid, azimuth plane, and ray is established, allowing for cross-localization and solution of the target's 3D coordinates.

[0057] The specific steps of the target three-dimensional localization method based on multi-source data fusion provided by this invention are as follows.

[0058] S1: Determine that the target is located on an ellipsoid with the radiation source and receiver as its foci.

[0059] like Figure 1 As shown, assume the coordinates of receiver n are (x... n ,y n ,z n The target's coordinates are (x, y, z), and the transmitter's coordinates are (x0, y0, z0). The time difference τ is the time difference between the arrival time of the target's scattered echo signal and the transmitter's direct wave signal at the receiver n. n According to the definition of the time difference of arrival parameter, we know that...

[0060] D TPn =d TP +d Pn =d Tn +τ n c (1)

[0061] Among them, D TPn The distance d from the transmitter to the target TP The distance d from the target to the receiver n Pn The sum of d Tn Let n be the distance from the transmitter to the receiver, and c be the speed of light. Substituting the three-dimensional coordinates of each node into the above equation, we can obtain...

[0062]

[0063] After simplification and reorganization, it becomes

[0064]

[0065] in, and Let n be the distances from the transmitter and receiver n to the origin, respectively.

[0066] Introduce a common variable related to the time difference of arrival parameter: the distance d from the transmitter to the target. TP By linearizing the quadratic ellipsoidal expression, a linear expression for the time difference of arrival observation equation is obtained.

[0067]

[0068] S2: Determine if the target is located on the ray or azimuth plane passing through the receiver.

[0069] like Figure 2 As shown, the angle of arrival of the target's scattered echo relative to receiver n includes the azimuth angle θ. n With pitch angle According to the geometric relationship of the angle of arrival parameter, it can be known that

[0070]

[0071] By matrixing the above equation, we obtain a linear expression for the angle-of-arrival (AOA) observation equation.

[0072]

[0073] If the receiver array configuration only allows for azimuth angle measurements, the angle-of-arrival (AHA) observation equation degenerates into:

[0074]

[0075] S3: Establish an overdetermined system of equations for cross-location to obtain the target's three-dimensional position.

[0076] By integrating the time difference of arrival (TDOA) and angle of arrival (ADR) parameters measured by multiple receivers (totaling N), an overdetermined system of equations is established to solve for the target's three-dimensional position. This involves simultaneously establishing a linear model based on TDOA and a linear model based on ADR to construct an overdetermined system of linear equations relating the target's three-dimensional coordinates to the distance from the transmitter to the target. Cross-referencing is then used to obtain the target's three-dimensional position information. Combining equations (4) and (6), a three-dimensional target positioning method is established.

[0077] AX = B (8)

[0078] Wherein, according to formula (8), X=[xyzd TP ] T The target coordinate distance matrix, The coefficient matrix, Let N be the measurement matrix, and N be the total number of receivers.

[0079]

[0080] (x i ,y i ,z i () represents the coordinates of receiver i, D TPi The distance d from the transmitter to the target TP Distance d from the target to receiver i Pi The sum of θ i Let be the azimuth angle of the target's scattered echo relative to receiver i. Let be the elevation angle of the target's scattered echo relative to receiver i, where i takes values ​​from 1 to N.

[0081]

[0082] Let i be the distance from receiver i to the origin of the coordinate system, where i takes values ​​from 1 to N.

[0083] Solving for X is equivalent to optimizing the function The solution is obtained using the least squares algorithm.

[0084] X = (A T A) -1 A T B (11)

[0085] The simplified formula based on formula (7) is given in the second aspect of the invention.

[0086] S4: Target 3D Positioning Accuracy Analysis

[0087] The robustness of the overdetermined equation system-based three-dimensional target localization method to time difference of arrival (TDOA), angle of arrival (ADR), and receiver site error is analyzed. Equations (1) and (2) are combined, and the time difference of arrival (τ) is considered. n Taking the total differential, we can obtain

[0088]

[0089] Equation (5) for the angle of arrival θ n , Taking the total differential, we can obtain

[0090]

[0091] When the receiving array configuration can only perform azimuth angle measurements, the azimuth angle differential equation simplifies to:

[0092]

[0093] Combining the above formulas (excluding formulas (7) and (15), the relevant content of formulas (16) to (29) below formed based on formulas (7) and (15) can be specifically referred to in the second aspect of the invention), a positioning error model based on the time difference of arrival and angle of arrival parameters is constructed.

[0094] dA·dX+dH=dB (16)

[0095] in, Let dA be the measurement error matrix, and dA be the error coefficient matrix. Let dX be the site location error matrix, where dX = [dx dy dz]. T The target positioning error matrix; τ i The time difference is the difference between the time it takes for the target scattered echo signal and the time it takes for the transmitter's direct wave signal to reach the receiver i. The value of i is 1 to N.

[0096]

[0097] d Ti Let be the distance from transmitter to receiver i. The i-th, (i+N)-th, and (i+N+1)-th rows of dH all correspond to receiver i. The i-th row of dH satisfies dH(i,1), the (i+N)-th row of dH satisfies dH(i+N,1), and the (i+N+1)-th row of dH satisfies dH(i+1+N,1). i takes values ​​from 1 to N.

[0098] Solving the positioning error model yields the target positioning error matrix.

[0099] dX=(dA H dA) -1 dA H (dB-dH) (19)

[0100] The geometric dilution of precision (GDOP) is used to measure the three-dimensional positioning accuracy of the target.

[0101]

[0102] in, These are the variances of the positioning errors in the x, y, and z directions, respectively.

[0103] To analyze GDOP performance, the positioning error covariance matrix was calculated, where measurement error and site error are independent.

[0104] P X =E{dXdX H}

[0105] =(dA) H dA)-1 dA H [E{dBdB H}-E{dHdH H}]dA(dA H dA) -1 (twenty one)

[0106] Define the variance of the time difference error of receiver i as: The variance of the azimuth error is The variance of pitch angle error is The variance of the transmitter site error is The receiver site error variance is The measurement errors between receivers and the site errors in each direction are independent, with i taking values ​​from 1 to N. The covariance matrix is ​​further derived as follows:

[0107]

[0108] in,

[0109]

[0110] The subscripts i or j of the intermediate quantity h correspond to the receiver's number. (x j ,y j ,z j ) represents the coordinates of receiver j, and d Tj Let j be the distance from the transmitter to the receiver, where j takes values ​​from 1 to N.

[0111]

[0112] The subscripts i or j of the intermediate quantity f correspond to the receiver number.

[0113]

[0114] The subscripts i or j of the intermediate quantity g correspond to the receiver number.

[0115]

[0116]

[0117] Based on the meaning of the covariance matrix, the geometric dilution of positioning accuracy is...

[0118]

[0119] Because the localization result is a 3D result, it is obtained through P. x (1,1),P x (1,1),P x(1,1) yields the geometric dilution GDOP of the positioning accuracy; where, the positioning error covariance matrix P is obtained through formula (21). x P x (1,1) represents the positioning error covariance matrix P. x The result of the element in the first row and first column, P x (2,2) represents the positioning error covariance matrix P. x The result of the element in the second row and second column, P x (3,3) represents the positioning error covariance matrix P. x The value of the element in the 3rd row and 3rd column.

[0120] In summary, this invention aims to further improve the 3D positioning accuracy of targets. First, it establishes observation equations based on the geometric relationship between positioning parameters and target position, introducing a common variable—the distance from the radiation source to the target—as an auxiliary variable to linearize the elliptic quadratic equations. Then, leveraging the advantages of multivariate positioning parameters in improving positioning accuracy, it robustly fuses time difference of arrival (TDOA), azimuth angle, and elevation angle to construct an overdetermined linear equation system, and uses a least squares algorithm to obtain the analytical solution for the target position. Finally, it provides robust analyses of the TDOA parameters, angle of arrival (ADR) parameters, and receiver site errors. The aforementioned 3D target positioning method further improves the 3D target positioning accuracy, exhibiting more robust positioning accuracy performance against TDOA measurement errors, ADR measurement errors, and site errors.

[0121] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope defined in the claims of the present invention.

Claims

1. A target 3D localization method based on multi-source data fusion, characterized in that, include: Get D TPi And the angle of arrival parameters of N receivers, D TPi The distance d from the transmitter to the target TP Distance d from the target to receiver i Pi The sum, where i takes values ​​from 1 to N; The target's three-dimensional position is solved using an overdetermined system of linear equations relating the target's three-dimensional coordinates and the distance from the transmitter to the target. The overdetermined system of linear equations satisfies AX = B, where X = [xyzd]. TP ] T The target coordinate distance matrix, The coefficient matrix, For measurement matrix; (x0, y0, z0) are the coordinates of the transmitter, (x i ,y i ,z i () represents the coordinates of receiver i, D TPi The distance d from the transmitter to the target TP Distance d from the target to receiver i Pi The sum of θ i Let be the azimuth angle of the target's scattered echo relative to receiver i. Let be the elevation angle of the target's scattered echo relative to receiver i. Let be the distance from receiver i to the origin of the coordinate system.

2. The method according to claim 1, characterized in that, The solution to the overdetermined linear equation system includes: For the optimization function The solution obtained using the least squares algorithm is as follows: X=(A T A) -1 A T B。 3. The method according to claim 1, characterized in that, D TPi D is determined based on the distances from the transmitter to each of the N receivers and the time differences in arrival among the N receivers. TPi satisfy: D TPi =d Ti +t i c d Ti Let τ be the distance from transmitter to receiver i. i Let be the time difference of arrival of receiver i, and c be the speed of light.

4. The method according to claim 1, characterized in that, The method further includes: Solve for the target localization error matrix: dX=(dA H dA) -1 dA H (dB-dH) in, Let dA be the measurement error matrix, and dA be the error coefficient matrix. Let dX be the site location error matrix, where dX = [dx dy dz]. T The target positioning error matrix; τ i Let i be the time difference of arrival of receiver i. d Ti Let be the distance from transmitter to receiver i; the i-th row, i+N-th row, and i+N+1-th row of dH all correspond to receiver i. The i-th row of dH satisfies dH(i,1), the i+N-th row of dH satisfies dH(i+N,1), and the i+N+1-th row of dH satisfies dH(i+1+N,1).

5. The method according to claim 4, characterized in that, The method further includes: The geometric dilution of positioning accuracy (GDOP) is used to measure the 3D positioning accuracy of the target. The GDOP is measured by the positioning error covariance matrix P. x Please solve. P X =(dA H and) -1 and H [E{dBdB H }-E{dHdH H }]dA(dA H and) -1 The variance of the time difference error of receiver i is The variance of the azimuth error is The variance of pitch angle error is The variance of the transmitter site error is The receiver site error variance is The subscripts i or j of intermediate quantity h correspond to the receiver number, the subscripts i or j of intermediate quantity f correspond to the receiver number, and the subscripts i or j of intermediate quantity g correspond to the receiver number; (x j ,y j ,z j ) represents the coordinates of receiver j, and d Tj P is the distance from the transmitter to the receiver j; x (1,1) represents the positioning error covariance matrix P. x The result of the element in the first row and first column, P x (2,2) represents the positioning error covariance matrix P. x The result of the element in the second row and second column, P x (3,3) represents the positioning error covariance matrix P. x The result of the value of the element in the 3rd row and 3rd column.

6. A target three-dimensional localization method based on multi-source data fusion, characterized in that, include: Get D TPi And the azimuth parameter information of N receivers, D TPi The distance d from the transmitter to the target TP Distance d from the target to receiver i Pi The sum, where i takes values ​​from 1 to N; The target's three-dimensional position is solved using an overdetermined system of linear equations relating the target's three-dimensional coordinates and the distance from the transmitter to the target. The overdetermined system of linear equations satisfies AX = B, where X = [xyzd]. TP ] T The target coordinate distance matrix, The coefficient matrix, For measurement matrix; (x0, y0, z0) are the coordinates of the transmitter, (x i ,y i ,z i () represents the coordinates of receiver i, D TPi The distance d from the transmitter to the target TP Distance d from the target to receiver i Pi The sum of θ i Let be the azimuth angle of the target's scattered echo relative to receiver i. Let be the distance from receiver i to the origin of the coordinate system.

7. The method according to claim 6, characterized in that, The solution to the overdetermined linear equation system includes: For the optimization function The solution obtained using the least squares algorithm is as follows: X=(A T A) -1 A T B。 8. The method according to claim 6, characterized in that, D TPi D is determined based on the distances from the transmitter to each of the N receivers and the time differences in arrival among the N receivers. TPi satisfy: D TPi =d Ti +t i c d Ti Let τ be the distance from transmitter to receiver i. i Let be the time difference of arrival of receiver i, and c be the speed of light.

9. The method according to claim 6, characterized in that, The method further includes: Solve for the target localization error matrix: dX=(dA H dA) -1 dA H (dB-dH) Where dB=[cdτ1 … cdτ N dθ1 … dθ N ] T Let dA be the measurement error matrix, and dA be the error coefficient matrix. Let dX be the site location error matrix, where dX = [dx dy dz]. T The target positioning error matrix; τ i Let i be the time difference of arrival of receiver i. d Ti Let be the distance from transmitter to receiver i; the i-th row and the (i+N)-th row of dH correspond to receiver i, the i-th row of dH satisfies dH(i,1), and the (i+N)-th row of dH satisfies dH(i+N,1).

10. The method according to claim 9, characterized in that, The method further includes: The geometric dilution of positioning accuracy (GDOP) is used to measure the 3D positioning accuracy of the target. The GDOP is measured by the positioning error covariance matrix P. x Please solve. P X =(dA H and) -1 and H [E{dBdB H }-E{dHdH H }]dA(dA H and) -1 The variance of the time difference error of receiver i is The variance of the azimuth error is The variance of the transmitter site error is The receiver site error variance is The subscripts i or j of intermediate quantity h correspond to the receiver number, and the subscripts i or j of intermediate quantity f correspond to the receiver number; (x j ,y j ,z j ) represents the coordinates of receiver j, and d Tj P is the distance from the transmitter to the receiver j; x (1,1) represents the positioning error covariance matrix P. x The result of the element in the first row and first column, P x (2,2) represents the positioning error covariance matrix P. x The result of the element in the second row and second column, P x (3,3) represents the positioning error covariance matrix P. x The result of the value of the element in the 3rd row and 3rd column.

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