A multi-mobile base station cooperative passive positioning method based on three-dimensional projection

Abstract

This invention discloses a multi-mobile base station collaborative passive positioning method based on three-dimensional projection, comprising the following steps: emergency communication network coverage is achieved by using three UAVs equipped with aerial base stations; the LS algorithm is used to perform initial elevation positioning of the target using known locations, setting the initial location as a virtual mobile base station, and then the target is repositioned, using VDOP to search for the optimal elevation position information of the target; a joint passive positioning model of path difference and azimuth is established using a projection transformation method; the weighted least squares method is used to estimate the initial horizontal position of the ground target, and then the correlation between the initial solution components is used to re-establish the equation through a second WLS algorithm to correct the initial horizontal position estimate, obtaining the optimal horizontal position information of the target. This invention can provide emergency response in cases of large-scale destruction of fixed base stations, reduce the number of mobile base stations used, reduce the complexity of position estimation, and improve positioning accuracy.

Description

Technical Field

[0001] This invention relates to passive positioning methods, and more particularly to a multi-mobile base station cooperative passive positioning method based on three-dimensional projection. Background Technology

[0002] Based on the method of target detection, target location technology can be divided into active detection location and passive detection location. Active detection location technology mainly uses electromagnetic waves actively emitted by radar to locate targets. Its advantages are fast location speed, high location accuracy, and no influence from weather and season. However, because the electromagnetic waves emitted by such devices are generally in a fixed electromagnetic frequency band, they are easily exposed and vulnerable to attack. In addition, the high transmission power leads to high energy consumption. Passive detection location technology, on the other hand, does not actively emit electromagnetic wave signals. It uses known observation points to receive electromagnetic wave signals from the target's radiation source, and then extracts relevant data for target location to estimate the target's position.

[0003] Direction of Arrival (DOA) based positioning technology was the earliest passive positioning method. It uses high-precision direction-finding equipment to check the DOA of the target radiation source signal, and then uses the intersection of the direction-finding lines of multiple azimuth angles as the estimated value of the target position. DOA positioning technology is simple and easy to implement, but as the distance between the target and the base station increases, even a small angle measurement error can lead to a large positioning error. In order to improve positioning accuracy, WANG Y et al. (MA S, CHEN CL P. TOA-Based Passive Localization in Quasi-Synchronous Networks[J]. IEEE Communications Letters, 2014, 18(4): 592-595) proposed a positioning technology based on Time of Arrival (TOA). This technology mainly uses the time delay of the electromagnetic wave signal emitted by the target radiation source to reach the observation point, and converts it into distance information for target positioning. However, TOA-based passive positioning technology requires high-precision time synchronization between the observation point and the radiation source target, which is difficult to achieve in actual positioning scenarios.

[0004] Existing passive positioning methods based on multi-base station collaboration for TDOA / DOA are all based on fixed base stations. When complex urban buildings or major natural disasters occur, fixed base stations are usually damaged over a large area, so positioning methods based on fixed base stations cannot meet the target positioning requirements in emergency scenarios.

[0005] Fusing TDOA and DOA can avoid the shortcomings of either method alone, achieving higher positioning accuracy with fewer base stations. To improve positioning accuracy, ZHU Hongwei et al. (SONG Qiang, et al. Systemerrors estimation of DOA and TDOA jointed locating system using sequential least squares[C] / / Proceedings of 2011 IEEE CIE International Conference on Radar. Chengdu: IEEE, 2011: 1025-1028.) proposed a joint TDOA / DOA passive positioning algorithm based on Sequential Least Squares (SLS). This algorithm transforms the positioning problem into an SLS optimization model before using Taylor expansion for positioning. However, to achieve more accurate positioning performance, this algorithm requires accumulating a certain number of observations for positioning. To enable real-time localization of target radiation sources, HO KC et al. (XUWenwei. An accurate algebraic solution for moving source location using TDOA and FDOA measurements[J]. IEEE Transactions on Signal Processing, 2004, 52(9): 2453-2463.) proposed a joint TDOA / DOA passive localization algorithm based on weighted least squares (WLS). This algorithm adds azimuth information to the classic Chan algorithm for localization. However, the localization accuracy is low when the target radiation source and the base station are far apart. Summary of the Invention

[0006] Purpose of the invention: The purpose of this invention is to provide a multi-mobile base station collaborative passive positioning method based on three-dimensional projection, which can be used in emergency situations where fixed base stations are destroyed over a large area, reduce the number of mobile base stations used, reduce the complexity of location estimation, and improve positioning accuracy.

[0007] Technical solution: The multi-mobile base station cooperative passive positioning method of the present invention includes the following steps:

[0008] S1. When fixed base stations are damaged over a large area, emergency communication network coverage is achieved by using drones to carry airborne base stations. The LS algorithm is used to locate the target at an initial elevation using known location information. The initial location is set as a virtual mobile base station. Then, the target is located at an elevation again. The location result is set as a new virtual mobile base station to replace the old one. The solution set is obtained by iteratively obtaining the solution set. The VDOP is used to search for the best elevation location information of the target.

[0009] S2, using the projection transformation method to project the mobile base station in three-dimensional space onto the ground plane for two-dimensional planar positioning; using the electromagnetic wave signals of the ground target received by the three mobile base stations and the data transmitted between the mobile base stations, a joint passive positioning model of path difference and azimuth angle is established.

[0010] S3 uses the weighted least squares method to estimate the initial horizontal position of the ground target. Then, by utilizing the correlation between the components of the initial solution, the equation is re-established through the second WLS algorithm to correct the initial horizontal position information estimate, thereby obtaining the optimal elevation position information and the optimal horizontal position information of the target. Combining the estimated optimal elevation position information and the optimal horizontal position information, the final estimated position of the target is obtained.

[0011] Furthermore, in step S1, let's assume that... At time 1, the location coordinates of the mobile base station in three-dimensional space are known. The location coordinates of each mobile base station are represented as follows: The obtained azimuth and depression angles of the ground targets are expressed as follows: , , The location coordinates of the ground target are unknown, represented as... ;

[0012] The distance measurement equation at time t is expressed as follows:

[0013] ,

[0014] Will The initial positioning target is set at each moment. The location coordinates of the virtual mobile base station at any given time are expressed as follows:

[0015] ,

[0016] Virtual mobile base station Substitute the matrix into the distance measurement equation In the middle, we get:

[0017] ,

[0018] ,

[0019] ,

[0020] ,

[0021] Then we have:

[0022] ,

[0023] use The distance measurement equation at time and Real-time location coordinates of virtual mobile base stations After the second iteration, the following is obtained:

[0024] Solution set ,

[0025] Elevation accuracy factor set ;

[0026] The final estimated coordinates of the ground target are then obtained. as follows:

[0027] ,

[0028] in, This is the index of the minimum value in the set of elevation accuracy factors. .

[0029] Furthermore, in step S2, the implementation steps for projecting the mobile base station in three-dimensional space onto the ground plane using the projection transformation method are as follows:

[0030] S21, move the origin of the coordinate system to the location of the ground target, then the coordinate transformation will result in the following... The location coordinates of each mobile base station are represented as follows: The position coordinates of the ground target are represented as ;

[0031] S22, projecting the mobile base station onto... If the projection of the mobile base station is obtained, then Time of the first The two-dimensional position coordinates of each projection mobile base station are represented as follows: , ;

[0032] The two-dimensional position coordinates of the ground target at time t are then represented as .

[0033] Furthermore, in step S2, the expression for the joint passive positioning model of path difference and azimuth angle is as follows:

[0034] ,

[0035] in, , indicating the first The actual distance between a projected mobile base station and a ground target. , representing the actual distance between the first projected mobile base station and the ground target; For the first The path difference measurement error of ground targets obtained by each projection mobile base station, and ,in This represents the variance of the measurement error. The path difference measurement error of the ground target obtained by the first projection mobile base station, and ; For the first projection mobile base station The azimuth angle measurement error of the obtained ground target, and ,in This represents the variance of the angle measurement error.

[0036] Furthermore, in step S2, after performing localization using the WLS algorithm twice, the final estimation result of the ground target is obtained. :

[0037] ,

[0038] in, ,

[0039] , This is a function for determining the sign of a sign; express The first element, express The second element; Indicate the estimation result The third element.

[0040] Compared with the prior art, the significant advantages of this invention are as follows:

[0041] 1. This invention utilizes a mobile base station formed by an aerial base station mounted on a drone to provide emergency communication for fixed base stations destroyed on a large scale due to disasters, and uses passive positioning to ensure that the target does not consume additional energy.

[0042] 2. This invention utilizes virtual mobile base stations to obtain the elevation position information of the target, transforming the three-dimensional positioning problem into two-dimensional planar positioning through projection. This enables three mobile base stations in three-dimensional space to coordinate passively locate the ground target and obtain the horizontal position information of the target, thereby reducing the number of mobile base stations used and reducing emergency communication costs.

[0043] 3. The multi-mobile base station cooperative passive positioning method of the present invention can be applied to emergency communication scenarios, with a positioning accuracy of up to 5 meters. Compared with the passive radio frequency-based joint TDOA / AOA positioning method proposed by C. Xu et al. (Z. Wang, Y. Wang, Z. Wang and L. Yu. Three PassiveTDOA-AOA Receivers-Based Flying-UAV Positioning in Extreme Environments[J].IEEE Sensors Journal, vol. 20, no. 16, pp. 9589-9595, 15 Aug.15, 2020), which has a positioning accuracy of up to 6 meters, the positioning accuracy of the present invention is improved by 16.7%. Attached Figure Description

[0044] Figure 1 A schematic diagram of a three-dimensional mobile base station positioning model;

[0045] Figure 2 This is a flowchart of the present invention;

[0046] Figure 3 A schematic diagram of a positioning model incorporating a virtual mobile base station;

[0047] Figure 4 This is a schematic diagram of a three-dimensional coordinate projection model;

[0048] Figure 5 A comparative diagram showing the impact of ranging error on positioning performance;

[0049] Figure 6 This is a schematic diagram of CDF comparison under conditions of large error;

[0050] Figure 7 A diagram illustrating the impact of the elevation difference between the target and the mobile base station on positioning performance;

[0051] Figure 8 This is a schematic diagram of CDF comparison when the elevation difference between the target and the mobile base station is small. Detailed Implementation

[0052] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0053] With the development of drone and mobile communication technologies, emergency communication network coverage can be achieved by using drones equipped with aerial base stations. Passive positioning technology eliminates the need for the target to actively send signals to the base station, thus requiring no energy. Existing mobile base station cooperative positioning methods require at least four mobile base stations for passive target positioning. This invention, however, utilizes virtual mobile base stations to obtain the target's elevation position information and uses a projection transformation method to transform the three-dimensional positioning problem into a two-dimensional positioning problem to obtain the target's horizontal position information. This reduces the number of mobile base stations required, achieving passive positioning using only three mobile base stations, thus improving the feasibility of using drones equipped with aerial base stations for passive positioning in emergency scenarios.

[0054] (I) Implementation of Multi-Mobile Base Station Cooperative Passive Positioning Method

[0055] In a three-dimensional space, when fixed base stations are damaged or insufficient due to sudden disasters or sudden communication demands, mobile base stations carried by drones can provide emergency communication network coverage. (See below.) Figure 1 As shown, a three-dimensional coordinate system is established with the ground plane as the XOY axis and the height as the Z axis.

[0056] Suppose At time 1, the location coordinates of the mobile base station in three-dimensional space are known. The location coordinates of each mobile base station are represented as follows: The obtained azimuth and depression angles of the ground targets are expressed as follows: , , The location coordinates of the ground target are unknown, represented as... Therefore, the distance measurement equation can be obtained:

[0057]

[0058] in, Indicates in Time of the first The distance between a mobile base station and a ground target is measured.

[0059] Use an additional variable Eliminating the quadratic term in equation (1), equation (1) can be expressed as:

[0060]

[0061] in,

[0062] ,

[0063] ,

[0064] .

[0065] To achieve high-precision positioning in three-dimensional space, at least four non-coplanar mobile base stations are required to locate the ground target. However, in this embodiment, to reduce the number of mobile base stations while maintaining high-precision positioning performance, a virtual mobile base station is first used to locate the ground target and obtain its estimated z-coordinates. Then, a three-dimensional projection method is used to locate the target and obtain its estimated x / y coordinates, as shown below. Figure 2 As shown, the implementation steps are as follows:

[0066] Step 1: Use virtual mobile base stations for positioning

[0067] like Figure 3 As shown, in At any given time, the location coordinates of the virtual mobile base station are represented as follows: .

[0068] From equation (2), we can obtain The distance measurement equation at time t is expressed as follows:

[0069] (3)

[0070] Will The initial positioning target is set at each moment. The location coordinates of the virtual mobile base station at any given time, i.e.

[0071]

[0072] To estimate more accurate target location information, the resulting virtual mobile base station To locate the object, we need to incorporate the distance measurement equation, which is to substitute equation (4) into equation (2) to obtain...

[0073]

[0074] in,

[0075] ,

[0076] ,

[0077] ;

[0078] but:

[0079]

[0080] therefore Jacobian matrix at time It can be represented as:

[0081]

[0082] Then the weight matrix It can be represented as:

[0083]

[0084] in, Represents the weight coefficient matrix The diagonal elements, This represents the variance of the user's ranging error. Therefore, the elevation accuracy factor... It can be represented as:

[0085]

[0086] Iterate through equations (3) to (9). The solution set can be obtained this time. and elevation accuracy factor set , Therefore, the index of the minimum value in the set of elevation accuracy factors can be obtained. The final estimated coordinates of the ground target are then obtained. as follows:

[0087] .

[0088] Step 2: Construct a 3D projection positioning model

[0089] like Figure 4 As shown, the coordinates are first transformed by moving the origin to the location of the ground target. Then, after the coordinate transformation, the [number of points] is... The location coordinates of each mobile base station are represented as follows: The position coordinates of the ground target are represented as Then the mobile base station is projected onto... If the projection of the mobile base station is obtained, then Time of the first The two-dimensional position coordinates of each projection mobile base station are represented as follows: , . The two-dimensional position coordinates of the ground target at time t are then represented as .

[0090] Therefore, the joint positioning equation of the path difference and azimuth angle can be expressed as:

[0091]

[0092] in, , indicating the first The actual distance between a projected mobile base station and a ground target. , representing the actual distance between the first projected mobile base station and the ground target; For the first The path difference measurement error of ground targets obtained by each projection mobile base station, and ,in This represents the variance of the measurement error. The path difference measurement error of the ground target obtained by the first projection mobile base station, and . For the first projection mobile base station The azimuth angle measurement error of the obtained ground target, and ,in This represents the variance of the angle measurement error.

[0093] The path difference equation can be rearranged into vector form according to equation (11):

[0094]

[0095] in, Let be a vector of path difference measurements with noise error, which is known, where This refers to the ranging error between the second projection mobile base station and the ground target. This represents the ranging error between the third projection mobile base station and the ground target. This is the true path difference vector formed by the three projected mobile base stations. For the first The distance between each projection mobile base station and the ground target is the same as that of the first projection mobile base station. The true distance difference from the ground target, vector It is unknown; Let be the path difference measurement error vector formed by three projected mobile base stations, where For the first The path difference measurement error of the ground target obtained by each projection mobile base station is compared with that of the first projection mobile base station. The difference in path difference measurement error from the obtained ground target. The corresponding covariance matrix. It can be represented as:

[0096]

[0097] Then the error covariance matrix It can be represented as:

[0098]

[0099] in, for The covariance matrix formed by the azimuth angle error of the ground target obtained by the projection mobile base station.

[0100] When the azimuth angle measurement error of the ground target obtained by the mobile base station is small, the corresponding error of the azimuth angle is:

[0101]

[0102] According to equations (11) and (15), the final joint positioning equation for the path difference and azimuth angle can be expressed as:

[0103]

[0104] Where, vector This indicates the horizontal coordinate information of the ground target without coordinate transformation.

[0105] Step 3: Perform localization using the WLS algorithm twice.

[0106] Suppose At time t, the unknown variable to be determined is Then, the error vector corresponding to the ground target position obtained from equation (16) It can be represented as:

[0107]

[0108] in, and They are represented as follows:

[0109]

[0110]

[0111] Solving equation (17) using the weighted least squares method yields:

[0112]

[0113] in, Error vector for joint positioning of range difference and azimuth. The inverse of the covariance matrix, and

[0114]

[0115] in, , Let the error covariance matrix be represented as shown in equation (14).

[0116] According to the result calculated by equation (20), The covariance matrix can be expressed as:

[0117]

[0118] Considering The correlation between elements, i.e. Therefore, a new error vector can be constructed. :

[0119]

[0120] in and They are represented as follows:

[0121]

[0122]

[0123] Solving equation (23) using WLS yields the following:

[0124]

[0125] in, Error vector The inverse of the covariance matrix can be expressed as:

[0126]

[0127] in, .

[0128] right After solving, the initial values ​​of the ground target can be updated using the following formula to obtain more accurate location information:

[0129]

[0130] in, , This is a function for determining the sign of a sign. express The first element, express The second element.

[0131] Therefore, combining equations (10) and (28) yields the final estimation result of the ground target. :

[0132]

[0133] in, The estimation results in expression (10) The third element is the optimal elevation location information obtained.

[0134] The specific execution steps of the multi-mobile base station cooperative passive localization algorithm based on 3D projection are shown in Table 1, as in Algorithm 1.

[0135] Table 1 Algorithm for multi-mobile base station cooperative passive localization based on 3D projection 1

[0136]

[0137] (II) Experimental Verification

[0138] In this embodiment, three mobile base stations are selected to perform cooperative passive localization of the ground target. Monte Carlo simulation is used for simulation, and the simulation results are analyzed. Under the same simulation scenario, the method proposed in this invention is compared with the virtual anchor point algorithm and the ALGEB algorithm. The impact of ranging error and the elevation difference between the ground target and the mobile base station on the positioning accuracy is analyzed.

[0139] (A) The impact of ranging error on positioning accuracy

[0140] When analyzing the impact of ranging error on positioning accuracy, the angular error of the fixed azimuth angle is 0.3 degrees. At any given time, the coordinates of the three mobile base stations and the ground target are shown in Table 2, with the coordinate unit being meters.

[0141] Table 2. Coordinates of the three mobile base stations and ground targets

[0142]

[0143] like Figure 5 The figure shows a comparison of the positioning error affected by changes in ranging error in the proposed method, the virtual anchor point algorithm, and the ALGEB algorithm. Figure 5 It can be seen that the three methods show a consistent overall trend, with the root mean square error (RMSE) increasing with the range error. When the range error is 2 meters, the RMSEs of the three methods are 2.55 meters, 3.84 meters, and 7.16 meters, respectively. Compared with the ALGEB algorithm, the positioning accuracy is improved by 64.39%, and compared with the virtual anchor point algorithm, the positioning accuracy is improved by 33.59%. This is because, compared with the ALGEB algorithm, the method proposed in this invention not only incorporates the azimuth angle but also uses the WLS algorithm twice, which effectively suppresses the positioning error and achieves higher positioning accuracy. The virtual anchor point method, due to only one iteration, has weaker noise resistance than the ALGEB algorithm, and therefore has the largest positioning error.

[0144] like Figure 6 As shown, when the distance difference measurement error is 2.5 meters, the cumulative distribution function (CDF) of the positioning error of the method proposed in this invention is compared with that of the virtual anchor point algorithm and the ALGEB algorithm. Figure 6It can be seen that the probabilities of positioning errors below 5 meters for the method proposed in this invention, the virtual anchor point algorithm, and the ALGEB algorithm are 63.5%, 27.7%, and 11.6%, respectively. Because the ALGEB algorithm has stronger positioning capabilities than the virtual anchor point algorithm which only iterates once, and because the method proposed in this invention performs two WLS operations and uses multiple iterations to calculate elevation position information, the positioning performance of the proposed method is the best.

[0145] (B) The impact of the elevation difference between the target and the mobile base station on positioning accuracy

[0146] In this embodiment, the measurement error of the distance difference is fixed at 2 meters, and the horizontal position information of the three mobile base stations and the coordinate position of the ground target are set according to the parameters in Table 2.

[0147] like Figure 7 The figure shown is a comparison of the positioning errors of the proposed method, the virtual anchor point algorithm, and the ALGEB algorithm affected by the elevation difference between the target and the mobile base station. Figure 7 It can be seen that the root mean square error (RMSE) of all three methods increases with the increase of the elevation difference between the target and the mobile base station. When the elevation difference between the target and the mobile base station is 35 meters, the RMSEs of the three methods are 3.05 meters, 4.23 meters, and 9.15 meters, respectively. Compared with the virtual anchor point algorithm, the positioning accuracy is improved by 66.67%, and compared with the ALGEB algorithm, the positioning accuracy is improved by 27.90%. Because the virtual anchor point algorithm does not utilize two WLS algorithms to update the horizontal plane position information, its ability to suppress positioning errors is significantly lower than that of the method proposed in this invention. Furthermore, the ALGEB algorithm has stronger noise resistance than the virtual anchor point algorithm; therefore, the virtual anchor point algorithm has the worst positioning performance.

[0148] like Figure 8 As shown, when the elevation difference between the target and the mobile base station is 25 meters, the CDF diagrams of the proposed method, the virtual anchor point algorithm, and the ALGEB algorithm are compared. Figure 8 It can be seen that the probability of the positioning error being less than 2 meters for the method proposed in this invention and the ALGEB algorithm is 91.3% and 66.2%, respectively. The probability of the positioning error being less than 2 meters for the virtual anchor point algorithm is zero. This is because when the elevation difference is small, the volume of the pyramid formed by the mobile base station and the virtual mobile base station is too small, resulting in low positioning accuracy and making the positioning capability of the virtual anchor point algorithm the weakest. However, the algorithm proposed in this invention iterates over the position of the virtual mobile base station and uses the WLS algorithm twice to improve the accuracy of the horizontal plane position information, thus the positioning performance of the method proposed in this invention is better.

Claims

1. A multi-mobile base station cooperative passive positioning method based on three-dimensional projection, characterized in that, The steps include the following: S1. When fixed base stations are damaged over a large area, emergency communication network coverage is achieved by using drones to carry airborne base stations. The LS algorithm is used to locate the target at an initial elevation using known location information. The initial location is set as a virtual mobile base station. Then, the target is located at an elevation again. The location result is set as a new virtual mobile base station to replace the old one. The solution set is obtained by iteratively obtaining the solution set. The VDOP is used to search for the best elevation location information of the target. S2, using the projection transformation method to project the mobile base station in three-dimensional space onto the ground plane for two-dimensional planar positioning; By utilizing the electromagnetic wave signals from ground targets received by three mobile base stations and the data transmitted between the mobile base stations, a joint passive positioning model based on path difference and azimuth angle is established. S3. The weighted least squares method is used to estimate the initial horizontal position of the ground target. Then, by utilizing the correlation between the components of the initial solution, the equation is re-established through the second WLS algorithm to correct the initial horizontal position information estimate and obtain the optimal elevation position information and optimal horizontal position information of the target. Combining the estimated optimal elevation position information and optimal horizontal position information, the final estimated position of the target is obtained. In step S1, let's assume that... At time 1, the location coordinates of the mobile base station in three-dimensional space are known. The location coordinates of each mobile base station are represented as follows: The obtained azimuth and depression angles of the ground targets are expressed as follows: , , The location coordinates of the ground target are unknown, represented as... ; The distance measurement equation at time t is expressed as follows: ， Will The initial positioning target is set at each moment. The location coordinates of the virtual mobile base station at any given time are expressed as follows: ， Virtual mobile base station Substitute the matrix into the distance measurement equation In the middle, we get: ， ， ， ， Then we have: ， use The distance measurement equation at time and Real-time location coordinates of virtual mobile base stations After the second iteration, the following is obtained: Solution set , Elevation accuracy factor set ; The final estimated coordinates of the ground target are then obtained. as follows: ， in, This is the index of the minimum value in the set of elevation accuracy factors. .

2. The multi-mobile base station cooperative passive positioning method based on three-dimensional projection according to claim 1, characterized in that, In step S2, the implementation steps for projecting the mobile base station in three-dimensional space onto the ground plane using the projection transformation method are as follows: S21, move the origin of the coordinate system to the location of the ground target, then the coordinate transformation will result in the following... The location coordinates of each mobile base station are represented as follows: The position coordinates of the ground target are represented as ; S22, projecting the mobile base station onto... If the projection of the mobile base station is obtained, then Time of the first The two-dimensional position coordinates of each projection mobile base station are represented as follows: , ; The two-dimensional position coordinates of the ground target at time t are then represented as .

3. The multi-mobile base station cooperative passive positioning method based on three-dimensional projection according to claim 2, characterized in that, In step S2, the expression for the joint passive positioning model of path difference and azimuth angle is as follows: ， in, , indicating the first The actual distance between a projected mobile base station and a ground target. , representing the actual distance between the first projected mobile base station and the ground target; For the first The path difference measurement error of ground targets obtained by each projection mobile base station, and ,in This represents the variance of the measurement error. The path difference measurement error of the ground target obtained by the first projection mobile base station, and ; For the first projection mobile base station The azimuth angle measurement error of the obtained ground target, and ,in This represents the variance of the angle measurement error.

4. The multi-mobile base station cooperative passive positioning method based on three-dimensional projection according to claim 3, characterized in that, In step S2, after performing localization using the WLS algorithm twice, the final estimation result of the ground target is obtained. : ， in, , , This is a function for determining the sign of a sign; express The first element, express The second element; Indicate the estimation result The third element.

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