TDOA multi-base station distance constraint secondary positioning method based on 5G external radiation source signal

Abstract

The TDOA multi-base station distance constraint secondary positioning method based on 5G external radiation source signal obtains the new measurement sample value of each base station detection result through sliding window processing, and uses the measurement sample value for initial target positioning; then based on the initial positioning coordinates and combined with the base station location information, the target position is secondary positioned through distance constraint, and finally the accuracy of target positioning is improved; the specific steps include: S1, space-time technology to obtain location information; S2, obtain dual-base distance and information; S3, sliding window processing to obtain new measurement sample value; S4, least squares method initial positioning; S5, 5G base station location information re-acquisition; S6, build correlation matrix; S7, secondary positioning target position; S8, estimate the final position of the target. The present invention can reduce noise interference to a certain extent, use the initial positioning coordinates combined with the base station location information to secondary locate the target, and improve the positioning accuracy of multi-radiation source targets.

Description

Technical Field

[0001] The present invention belongs to the technical field of 5G external radiation source radar, and in particular to a TDOA multi-base station distance constraint secondary positioning method based on 5G external radiation source signals. Background Art

[0002] The exotropic radar system uses existing third-party electromagnetic signals in the environment to detect targets. Since the exotropic radar itself does not radiate electromagnetic waves, it is difficult for the enemy to detect it, and its survival and anti-interference capabilities are greatly improved, and it will not cause electromagnetic pollution. In addition, since it does not require high-power transmitting equipment to transmit electromagnetic waves, its detection system only needs to include a smaller receiver, which reduces hardware costs and can be used as a low-cost, efficient solution. At the same time, the exotropic radar is also suitable for real-time monitoring needs in complex environments.

[0003] TDOA (Time Difference of Arrival) is a passive positioning technology mainly used to determine the location of the signal source. This technology does not directly measure the absolute time when the signal arrives at a specific point, but rather measures the time difference between the signal arriving at multiple base stations to locate. Each receiving station records the time of signal arrival, and then calculates the time difference between the signal arrivals of any two stations. These time differences provide information about the location of the signal source relative to the receiving station pair.

[0004] At present, in urban environments, 5G communication signals, as emerging external radiation sources, have important research value in the field of target detection. With its rich spectrum resources and highly flexible transmission characteristics, 5G signals have become an ideal choice for external radiation source radar systems. By using 5G signals as an illumination source, external radiation source radar systems can achieve more accurate target detection in complex urban environments. However, the weak target echo signal of 5G external radiation source radar leads to inaccurate arrival time measurement and large measurement errors in different base stations, which will reduce the accuracy of multi-station collaborative positioning.

[0005] Compared with the prior art, the differences are as follows:

[0006] Targeting direction;

[0007] (1) CN115718276A (A TDOA short baseline positioning method and system with zero base station position error) This patent is mainly aimed at eliminating the influence of TDOA positioning base station position error on positioning accuracy, so that TDOA short baseline positioning can be realized in engineering.

[0008] (2) CN112218236A (A TDOA positioning base station selection method and system based on multi-dimensional scoring) This patent mainly focuses on how to select the base station location with the best positioning effect among many existing base stations by using three stages of design and three dimensional criteria. There is no innovation in TDOA target positioning and positioning algorithm processing.

[0009] (3) This patent (a TDOA multi-radiator base station distance-constrained secondary positioning method based on 5G external radiation source signals) mainly addresses two points: first, the weak echo signal of the 5G external radiation source radar target leads to inaccurate arrival time measurement; second, the large measurement errors in different base stations affect the accuracy of multi-station collaborative positioning.

[0010] Implementation method;

[0011] (1) CN115718276A (A TDOA short baseline positioning method and system with zero error in base station position) This patent first uses a high-precision measuring instrument to measure the straight-line distance between base stations, which is a prerequisite for achieving zero error; then any base station is selected as the coordinate origin, and the TDOA positioning method and Taylor expansion calculation are used to iterate the target estimated position multiple times through the set threshold; then the GPS is used to obtain the latitude and longitude coordinates of the base station, and then the estimated position is converted into absolute geographic coordinates through calculation.

[0012] (2) CN112218236A (A TDOA positioning base station selection method and system based on multi-dimensional scoring) This patent inputs multiple base station location information and signals and performs three stages of screening. In the first stage, the positioning base stations corresponding to the signals with the largest signal energy are selected; in the second stage, each base station combination is weightedly scored based on the three dimensions of the distance between the target and the base station, the credibility of the arrival time difference, and the geometric shape of the base station; in the third stage, the highest scoring combination is selected as the positioning base station combination, and TDOA positioning is performed using the selected base station combination. There is no special improvement in the subsequent positioning processing.

[0013] (3) This patent (a TDOA multi-radiation source base station distance constraint secondary positioning method based on 5G external radiation source signal) adopts sliding window processing to obtain new measurement sample values ​​​​due to the weak echo signal of the 5G external radiation source radar target, which leads to inaccurate arrival time. The new sample values ​​can be used for more accurate initial positioning; in order to address the problem that large measurement errors in different base stations affect the accuracy of multi-station collaborative positioning, the centroid of the base station is used as the coordinate origin, and the feasibility of using the distance from the centroid point C to the target as a distance constraint is deduced; the final positioning position is calculated by combining the initial positioning result and the distance constraint formula.

[0014] Scope of application;

[0015] (1) CN115718276A (A TDOA short baseline positioning method and system with zero base station position error) This patent is only applicable to the case where the base stations are relatively close due to the limitation of requiring high-precision instrument measurement. This patent has no requirements on the base station distance and is more universal.

[0016] (2) CN112218236A (A TDOA positioning base station selection method and system based on multi-dimensional scoring) This patent mainly focuses on the optimal selection of base stations. In terms of positioning algorithm, it is not comparable to the method proposed in this patent. Summary of the invention

[0017] The purpose of the present invention is to overcome the problem of multi-station collaborative positioning accuracy caused by the weak echo signal of the 5G external radiation source radar target, which leads to inaccurate arrival time measurement and large measurement errors between different base stations. A TDOA multi-base station distance constraint secondary positioning method based on the 5G external radiation source signal is provided. A new measurement sample value of the detection result of each base station is obtained through sliding window processing, and the measurement sample value is used for initial target positioning; then, based on the initial positioning result, the target position is secondary positioned through distance constraint in combination with the base station position information.

[0018] To achieve the above object, the present invention provides a TDOA multi-base station distance constraint secondary positioning method based on 5G external radiation source signals, comprising the following method steps:

[0019] S1. Space-time technology to obtain location information:

[0020] Obtain the location coordinates of three or more 5G base stations and detection systems through time-space synchronization technology;

[0021] S2. Get the distance and information of the two bases:

[0022] The detection system receives the direct wave signal of the reference channel and the echo signal reflected by the target of the monitoring channel. After signal processing, it can obtain the time difference between the 5G base station signal to the detection system and the 5G base station signal reflected by the target and then to the ground passive detection system. Then, the sum of the distance from the external radiation source to the target and the distance from the target to the detection system is obtained by combining the positions of the base station and the receiving station.

[0023] S3, sliding window processing to obtain new measurement sample values:

[0024] Set sliding window related parameters, window length L win , step length L step , sliding window number Num win , and perform sliding window averaging on the dual-channel distance difference samples to obtain new sample values;

[0025] S4, least squares method initial positioning:

[0026] Construct the equivalent observation equation for linearization, and obtain the initial value of target position estimation by least squares;

[0027] S5. Get the 5G base station location information again:

[0028] Determine the centroid coordinates based on the currently calculated 5G base station coordinates, and recalculate the base station position coordinates using the centroid position as the coordinate origin;

[0029] S6. Construct the correlation matrix:

[0030] Construct distance-constrained positioning correlation matrix;

[0031] S7, secondary positioning target position:

[0032] The secondary positioning position is calculated by combining the base station position coordinates with the distance constraint and the positioning equation;

[0033] S8. Estimation of the final position of the target:

[0034] Combine the initial target location X1 and the secondary location X2 to determine the final target location X Fin .

[0035] Further, the process of obtaining a new measurement sample value by the S3 sliding window processing specifically includes:

[0036] Set the window length L win , step length L step =1 and sliding window number Num win If the sliding window exceeds the number of samples, it can be filled with the starting sample. According to the geometric relationship between the base station, the receiving detection system and the target in S2, the observation equation is constructed:

[0037] ρ i +l r -l i =c×Δτ i

[0038] Where L is the total length of the sequence, and the distance from the target X to the i-th external radiation source is ρ i , the distance from the target to the receiving station is l r , the distance from the i-th 5G external radiation source to the receiving station is l i , where i = 1, 2…M; c represents the speed of light, Δτ i It represents the difference between the time it takes for the signal to be reflected from the source to the target and then to reach the receiving station, and the time it takes for the signal to reach the receiving station directly. The calculation equation for obtaining the new measurement sample value is:

[0039]

[0040] The L samples of the measurement error of the ith radiation source are expressed as (m i1 ,m i2 ,…,m iL ), satisfying the covariance of Gaussian distribution; window length L win , step length L step =1, the number of sliding windows is Num win ;

[0041] Take the first new sample variance after sliding window and the first sample variance before sliding window as an example, that is:

[0042]

[0043] The measurement noise variance after sliding window is reduced, resulting in a smaller error impact on target positioning. The measurement equation of the i-th radiation source after sliding window can be expressed as:

[0044]

[0045] in is the measurement error after sliding window.

[0046] Further, the S5, 5G base station location information is obtained again, specifically including:

[0047] The spatial centroid coordinates C(x c ,y c ,z c ) as an example, the centroid point C is as follows:

[0048]

[0049] Where (x i ,y i ,z i )i=1,2,3,4, is base station B i The coordinates of .

[0050] Using matrix transformation T r =[-x c -y c -z c ] T After translating the origin to the center of mass, the new coordinates of the four base stations are: B1(x1-x c ,y1-y c ,z1-z c ), B2(x2-x c ,y2-y c ,z2-z c ), B3(x3-x c ,y3-y c ,z3-z c), the initial positioning target position X1 in S4 is now: X1(X r 1-x c ,X r 2-y c ,X r 3-z c ).

[0051] Further, the S6, constructing a correlation matrix, specifically includes: the distance d from the particle point C to the target X1 c for:

[0052]

[0053] where d jk represents the distance from base station j to base station k, d i is the distance from base station i to the target;

[0054] Each distance measurement d i , i=1,2,3,4 satisfies Gaussian distribution, and the standard deviation δ is the same; then the distance d from the centroid C to the target c The error propagation formula is:

[0055]

[0056] Among them, δ c Yes c The standard deviation of Yes c For variable d i The partial derivative of

[0057] From the above formula, we can see that d c The standard deviation of c Less than the original measured value d i The standard deviation δ, d c It has higher accuracy. Therefore, the distance from the centroid point C to the target is taken as the distance constraint, and the distance constraint formula is:

[0058] (xx c ) 2 +(yy c ) 2 +(zz c ) 2 =d c 2 .

[0059] The beneficial effects of the present invention are as follows: a new signal is obtained by sliding window mean processing, and then the least squares initial positioning is performed; based on the initial positioning position, the target position is secondarily positioned by distance constraint in combination with the base station position information. The final target position is determined, which can improve the accuracy of target positioning. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Attached Figure 1 This is a schematic diagram of the structure of the 5G external radiation source radar system;

[0061] Attached Figure 2 This is a schematic diagram of the multi-source positioning structure of 5G external radiation source radar signal;

[0062] Attached Figure 3 This is a schematic diagram of the processing flow structure of the 5G external radiation source radar signal positioning algorithm. DETAILED DESCRIPTION

[0063] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. It should be noted that the words "front", "rear", "left", "right", "upper" and "lower" used in the following description refer to directions in the accompanying drawings, and the words "inner" and "outer" refer to directions toward or away from the geometric center of a specific component, respectively.

[0064] In this embodiment, the target is a multi-external radiation source radar positioning system, and its structure is as shown in the attached figure. Figure 1 The implementation process and information processing flow are shown in the attached Figure 2 As shown, the algorithm processing flow structure diagram is as follows Figure 3 , specifically described as the following process:

[0065] S1. Obtaining location information using space-time technology: The location coordinates of the 5G base station and detection system are obtained through space-time technology. Each set of independent time differences can obtain an elliptical positioning surface;

[0066] As attached Figure 2 As shown in the figure, it is a 5G external radiation source multi-source single-receiver external radiation source radar positioning system model. Figure 2 5G communication base station B i The coordinates are [x i ,y i ,z i ] T , where i is the base station number, i = 1, 2, ..., M, M is the number of base station radiation sources, and the coordinates of the target X are [x, y, z] T , receiving station S r The position coordinates [x r ,y r ,z r ] T is the coordinate origin, and the distance from the target X to the i-th external radiation source is ρ i , the distance from the target to the receiving station is l r , the distance from the i-th external radiation source to the receiving station is l i , where i=1,2…M.

[0067] S2. Obtaining dual-base distance and information: The detection system receives the direct wave signal of the reference channel and the echo signal reflected by the target of the monitoring channel. After signal processing, it can obtain the time difference between the 5G base station signal to the detection system and the 5G base station signal after being reflected by the target and then reaching the ground passive detection system. Then, the sum of the distance from the external radiation source to the target and the distance from the target to the detection system is obtained by combining the positions of the base station and the receiving station. The intersection of the three elliptical positioning surfaces is the location of the target. According to the geometric relationship between the base station, the receiving detection system and the target, the observation equation is constructed using mathematical expressions:

[0068] ρ i +l r -l i =c×Δτ i

[0069] in:

[0070] Where c represents the speed of light, ||*||2 represents the 2-norm, and t i It represents the time from the signal source of the i-th base station to the receiving station, T i It represents the time it takes for the signal to travel from the i-th signal source to the target and then to the receiving station, Δτ i It represents the difference between the time it takes for a signal to be reflected from the source to the target and then to reach the receiving station, and the time it takes for the signal to reach the receiving station directly. The measured value of the distance difference between the two paths is c×Δτ i .

[0071] S3, sliding window processing to obtain new measurement sample values: set sliding window related parameters, window length L win , step length L step , sliding window number Num win , and perform sliding window averaging on the dual-channel distance difference samples to obtain new sample values; specifically, set the window length L win , the step length is L step =1, if the sliding window exceeds the number of samples, it can be filled with the starting sample, the sliding window number Then the observation equation in S2 is:

[0072]

[0073] Take the first new sample variance after sliding window and the first sample variance before sliding window as an example, that is:

[0074]

[0075] The L samples of the measurement error of the ith radiation source are expressed as (m i1 ,m i2 ,…,m iL ), satisfying the covariance of Gaussian distribution; window length L win , step length L step =1, the number of sliding windows is Num win ;

[0076] The measurement noise variance after sliding window is reduced, and the error impact on target positioning is reduced. The measurement of the i-th radiation source after sliding window can be expressed as:

[0077]

[0078] in is the measurement error after sliding window.

[0079] S4, initial positioning using the least squares method: construct an equivalent observation equation for linearization, and use the least squares method to obtain the initial value of the target position estimate; specifically, the following steps are included:

[0080] S41. Using the observation equation constructed in S2:

[0081] ρ i +l r -l i =c×Δτ i

[0082] In the above formula:

[0083]

[0084] Where c represents the speed of light, and the measured value of the distance difference between the two paths is c×Δτ i .

[0085] S42, least squares initial positioning: taking receiving station S r The position coordinates [x r ,y r ,z r ] T As the origin of coordinates, combined with the above formula, we can get:

[0086] xx i +yy i +zz i -(c×Δτ i +l i )×l r = -0.5(c×Δτ i ) 2 -(c×Δτ i )×l i

[0087] Select the distance l from the target to the receiving station r As auxiliary variables, let the auxiliary vector X composed of the target and auxiliary variables r =[xyzlr ] T As an estimate, the above formula can be written in matrix form, namely:

[0088] AX r =B

[0089] Where:

[0090]

[0091] Then we can solve X r for:

[0092] X r =A -1 B

[0093] When the matrix A is not invertible, X r The solution can be obtained by the least squares method of the pseudo-inverse method. That is:

[0094] X r =(A T A) -1 A T B

[0095] So the initial positioning position is X1 * =(X r1 , X r2 , X r3 ).

[0096] S5. Re-acquire the 5G base station location information: Determine the centroid coordinates based on the currently calculated 5G base station coordinates, take the centroid position as the coordinate origin, and recalculate the base station location coordinates; use the base station location positioning equation:

[0097]

[0098] Among them, 5G base station B i The coordinates are [x i ,y i ,z i ] T (i=1,2...M), d i Indicates 5G base station B i The distance to the target location; four non-coplanar base stations can determine a spatial volume, taking 4 base stations as an example:

[0099]

[0100] The above formula can be expressed in matrix form as:

[0101] AX=b

[0102]

[0103] Therefore, the target position X * It can be expressed as:

[0104] X * =(A T A) -1 A T b

[0105] The centroid coordinates of the space formed by the four base stations are C(x c ,y c ,z c )as follows:

[0106]

[0107] Using the transformation T r =[-x c -y c -z c ] T After translating the origin to the centroid, the new coordinates of the four base stations are: B1(x1-x c ,y1-y c ,z1-z c ), B2(x2-x c ,y2-y c ,z2-z c ), B3(x3-x c ,y3-y c ,z3-z c ), the initial positioning target position X1 in S4 is now: X1(X r1 -x c ,X r2 -y c ,X r3 -z c );

[0108] The distance X1 from particle C to the target is:

[0109]

[0110] where d jk represents the distance from base station j to base station k, d i is the distance from base station i to the target;

[0111] Each distance measurement d i , i = 1, 2, 3, 4; is a Gaussian distribution with the same standard deviation δ; then the distance d from particle C to the target c The error propagation formula is:

[0112]

[0113] Among them, δc Yes c The standard deviation of Yes c For variable d i The partial derivative of

[0114] From the above formula, we can see that d c The standard deviation of c Less than the original measured value d i The standard deviation δ, d c With higher precision.

[0115] Therefore, the distance constraint from the centroid point C to the target is taken as the distance constraint, and the distance constraint formula is:

[0116] (xx c ) 2 +(yy c ) 2 +(zz c ) 2 =d c 2

[0117] S6. Constructing correlation matrix: constructing distance constraint positioning correlation matrix;

[0118] The distance constraint in S5 above is expressed in matrix form as follows:

[0119]

[0120] Where X2 is the secondary positioning position X2 = [x2 * ,y2 * ,z2 * ], T r is the transformation vector that translates the origin to point C in S5, T r =[-x c -y c -z c ] T , vector α=[x α y α z α ] T ;

[0121] S7, secondary positioning target position: The secondary positioning position is calculated by combining the base station position coordinates with the distance constraint and the positioning equation, which specifically includes the following steps:

[0122] S71, combined with the distance constraint, the target positioning equation is expressed as: T α=d c 2 Under the constraint, min||A'x-b'|| 2 ;

[0123] Where A', b' is the corresponding matrix under the new coordinates of the base station, min||A'x-b'|| 2 Represents the minimum value of the solution of the equation.

[0124] S72. Use the Lagrange multiplier λ to express the above formula:

[0125]

[0126] Taking the partial derivative of α from the above formula can get the minimum value:

[0127]

[0128] in

[0129]

[0130] (A') T A' and (A') T b' brought in get:

[0131]

[0132] The steps to calculate the target position of secondary positioning are as follows:

[0133] 1) Write the linear equations in the form of an augmented matrix:

[0134]

[0135] And matrix the coefficients into an upper triangular matrix:

[0136]

[0137] Among them, K1=a1+λ,K2=a4,K3=a5,ψ1=b1;K4=-a4 2 / (a1+λ)+a2+λ,

[0138] K5=a6-(a4*a5) / (a1+λ), ψ2=b2-(a4*b1) / (a1+λ);

[0139] K6=a3+λ-[a6-(a4*a5) / (a1+λ)] 2 / [-a4 2 / (a1+λ)+a2+λ]-[a5 2 / (a1+λ)];

[0140] ψ3=b3-[a6-(a4*a5) / (a1+λ)]*[b2-(a4*b1) / (a1+λ)] / [(-a4 2 / (a1+λ))+(a2+λ)-(a5*b1) / (a1+λ)];

[0141] The above coefficient upper triangular matrix contains only the unknown number λ.

[0142] 2) Use the back-substitution method to solve the system of equations.

[0143] Right now:

[0144] We can get:

[0145] 3) Substitute the above calculation result x α ,y α , z α Substitute the expression into the constraint equation α T α=d c 2 , that is, x α 2 +y α 2 +z α 2 =d c 2 ; get the polynomial about λ:

[0146] λ 3 -λ 2 *(al+a2+a3)+λ*(a1*a2+a1*a3+a2*a3-a4 2 -a5 2 -a6 2 )-2*a4*a5*a6-a1*a2*a3+a3*a4 2 +a2*a5 2 +a1*a6 2 =0

[0147] Solve and obtain the eigenvalues: λ1, λ2, λ3;

[0148] 4) Substitute λ1, λ2, and λ3 in 2 into x respectively α1 y α1 z α1 ,x α2 y α2 z α2 ,x α3 y α3 z α3 , we can calculate α1=[x α1 y α1 zα1 ] T ,α2=[x α2 y α2 z α2 ] T ,α3=[x α3 y α3 z α3 ] T ;

[0149] 5) The target position X2 of the secondary positioning is α=X2+T r , that is, X2 = α-T r get.

[0150] S8, estimate the final target position: combine the initial target positioning position X1 and the secondary positioning position X2 to determine the final target position X Fin ; Since the secondary positioning target has three estimated positions, the minimum distance between the secondary positioning position and the initial positioning position is taken as the final position of the target to be measured.

[0151] X Fin =min||X2-X1||

[0152] Where min||X2-X1|| represents the minimum distance from X2 to X1.

[0153] The new signal is obtained by sliding window mean processing, and then the initial positioning is performed by basis and least squares; based on the initial positioning position and combined with the base station position information, the target position is re-positioned through distance constraints. The final position of the target is estimated, which can improve the accuracy of target positioning.

[0154] It should be noted that the above content only illustrates the technical idea of ​​the present invention and cannot be used to limit the protection scope of the present invention. For ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications all fall within the protection scope of the claims of the present invention.

Claims

1. A TDOA multi-base station distance-constrained secondary positioning method based on 5G external radiation source signals, characterized in that: The method comprises the following steps: S1. Space-time technology to obtain location information: Obtain the location coordinates of three or more 5G base stations and detection systems through time-space synchronization technology; S2. Get the distance and information of the two bases: The detection system receives the direct wave signal of the reference channel and the echo signal reflected by the target of the monitoring channel. After signal processing, it can obtain the time difference between the 5G base station signal to the detection system and the 5G base station signal reflected by the target and then to the ground passive detection system. Then, the sum of the distance from the external radiation source to the target and the distance from the target to the detection system is obtained by combining the positions of the base station and the receiving station. S3, sliding window processing to obtain new measurement sample values: Set sliding window related parameters, window length L win , step length L step , sliding window number Num win , and perform sliding window averaging on the dual-channel distance difference samples to obtain new sample values; The process of obtaining new measurement sample values ​​by S3 sliding window processing specifically includes: Set the window length L win , step length L step =1 and sliding window number Num win If the sliding window exceeds the number of samples, it can be filled with the starting sample. According to the geometric relationship between the base station, the receiving detection system and the target in S2, the observation equation is constructed: r i +l r -l i =c×Δτ i Where L is the total length of the sequence, and the distance from the target X to the i-th external radiation source is ρ i , the distance from the target to the receiving station is l r , the distance from the i-th 5G external radiation source to the receiving station is l i , where i = 1, 2…M, M represents: the number of 5G external radiation sources; c represents the speed of light, Δτ i It represents the difference between the time it takes for the signal to be reflected from the source to the target and then to reach the receiving station, and the time it takes for the signal to reach the receiving station directly. The calculation equation for obtaining the new measurement sample value is: The L samples of the measurement error of the i-th radiation source are represented by m i1 ,m i2 ,…,m iL , satisfying the covariance Gaussian distribution; window length L win , step length L step =1, the number of sliding windows is Num win ; Right now: The measurement noise variance after sliding window is reduced, resulting in a smaller error impact on target positioning. The measurement equation of the i-th radiation source after sliding window can be expressed as: in is the measurement error after sliding window; S4, least squares method initial positioning: Construct the equivalent observation equation for linearization, and obtain the initial value of target position estimation by least squares; S5. Get the 5G base station location information again: Determine the centroid coordinates based on the currently calculated 5G base station coordinates, and recalculate the base station position coordinates using the centroid position as the coordinate origin; The S5, 5G base station location information is obtained again, specifically including: The centroid point C is as follows: Where (x i ,y i ,z i )i=1,2,3,4, is base station B i The coordinates of Using matrix transformation T r =[-x c -y c -z c ] T After translating the origin to the center of mass, the new coordinates of the four base stations are: B1(x1-x c ,y1-y c ,z1-z c ), B2(x2-x c ,y2-y c ,z2-z c ), B3(x3-x c ,y3-y c ,z3-z c ), the initial positioning target position X1 in S4 is now: X1(X r1 -x c ,X r2 -y c ,X r3 -z c ), X r It is the coordinate of the point located for the first time; The distance d from mass point C to target X1 c for: where d jk represents the distance from base station j to base station k, d i is the distance from base station i to the target; Each distance measurement d i , i=1,2,3,4 satisfies Gaussian distribution, and the standard deviation δ is the same; then the distance d from the centroid C to the target c The error propagation formula is: Among them, δ c Yes c The standard deviation of Yes c For variable d i The partial derivative of From the above formula, we can see that d c The standard deviation of c Less than the original measured value d i The standard deviation δ, d c It has higher accuracy, so the distance from the centroid point C to the target is taken as the distance constraint, and the distance constraint formula is: (x-x c ) 2 +(y-y c ) 2 +(z-z c ) 2 =d c 2 ; S6. Construct the correlation matrix: Construct distance-constrained positioning correlation matrix; The S6, constructing a correlation matrix, specifically includes: The distance constraint in S5 above is expressed in matrix form as follows: Where X2 is the secondary positioning position X2 = [x2 * ,y2 * ,z2 * ], T r is the transformation vector that translates the origin to point C in S5, T r =[-x c -y c -z c ] T , vector α=[x α y α z α ] T ; S7, secondary positioning target position: The secondary positioning position is calculated by combining the base station position coordinates with the distance constraint and the positioning equation; S8. Estimation of the final position of the target: Combine the initial target location X1 and the secondary location X2 to determine the final target location X Fin .

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