Positioning method based on time difference of arrival of source signal under non-line-of-sight condition

Abstract

The invention belongs to the technical field of source positioning, and particularly relates to a positioning method based on a source signal arrival time difference under a non-line-of-sight condition. A measured value of a distance difference between a sensor and a target source is constructed according to a TDOA measurement method; converting the distance difference measurement model into a weighted robustness least square problem; the weighted robustness least square problem is converted into a non-convex optimization problem which can be corrected to be positive semi-definite by using S-Lemma; converting a non-convex optimization problem into a convex positive semidefinite programming problem by using a positive semidefinite relaxation technology; constructing a positive semidefinite programming problem after inequality constraint tightening on the basis of the convex positive semidefinite programming problem; and an iterative method is utilized to jointly estimate the position of the signal source and the upper bound of the path NLOS error for solving, and the optimal estimation value of the position of the target source is obtained.

Description

Technical Field

[0001] The present invention belongs to the technical field of source positioning, and more specifically, relates to a positioning method based on source signal arrival time difference under non-line-of-sight conditions. Background Art

[0002] Accurate positioning of signal sources is key to many applications, such as emergency service response, mobile computing, and target tracking. Common positioning metrics include time of arrival (TOA) and time difference of arrival (TDOA). In recent years, non-line-of-sight (NLOS) errors have become common in indoor and urban environments, which can severely degrade the quality of source position estimation if not handled properly. Therefore, the identification and mitigation of NLOS has attracted much attention.

[0003] Previous work tends to accurately model NLOS errors or solve NLOS identification and mitigation problems based on TOA systems. However, since NLOS characteristics are usually related to the environment and time, it is expensive to build a model. In addition, TOA measurement requires precise synchronization between the source and the sensor and does not have wide applicability. The TDOA method can be used for passive positioning, does not require synchronization between the sensor and the signal source, and can obtain accurate TDOA positioning in a broadband positioning system, which is widely applicable. And a large number of experiments have shown that in dense non-close visual environments, TDOA has higher positioning accuracy than TOA. Therefore, it is very necessary to study source positioning based on the time difference of arrival of source signals under non-line-of-sight conditions. Summary of the invention

[0004] In view of the above problems existing in the prior art, the present invention proposes a positioning method based on the time difference of arrival of source signals under non-line-of-sight conditions, which has high positioning accuracy.

[0005] To achieve the above object, the present invention adopts the following technical solution:

[0006] The positioning method based on the time difference of arrival of source signals under non-line-of-sight conditions comprises the following steps:

[0007] Step 1: Establish a coordinate system and initialize the sensor position and signal source position;

[0008] Step 2: Use the TDOA measurement method to build a distance measurement model, that is, to build a measurement value of the distance difference between the reference path sensor and other path sensors and the signal source position;

[0009] Step 3: Convert the distance measurement model into a constrained weighted robust least squares problem (RWLS for short);

[0010] Step 4: Use S-Lemma to transform the weighted robust least squares problem into a non-convex optimization problem that can be corrected to a semidefinite relaxation (SDR).

[0011] Step 5: Use semi-definite relaxation technology to transform the non-convex optimization problem into a convex semi-definite programming problem;

[0012] Step 6: Based on the convex semidefinite programming problem (SDP), a semidefinite programming problem with tightened inequality constraints is constructed;

[0013] Step 7: Use an iterative method to jointly estimate the signal source position and the upper bound of the path NLOS error to obtain the optimal estimate of the target source position.

[0014] The technical solution is further optimized, and the step 1 specifically includes:

[0015] Establish a k-dimensional positioning scenario. Assume that a wireless sensor network has N+1 sensors and 1 unknown signal source. The position of the i-th sensor is s i ∈R k The signal source position is represented by x∈R k Indicates that, R k represents a k-dimensional real vector, and s0 represents the reference sensor position.

[0016] This technical solution is further optimized, and the step 2 specifically includes:

[0017] Assuming that the sensor position is accurately measured and there is NLOS signal propagation between the signal source and the sensor, the TDOA method is used to measure, which is described as:

[0018]

[0019] Where N is the number of sensors on other paths, t i represents the time difference between the source signal reaching the reference path sensor and the i-th path sensor, c represents the speed of light, and n i represents the measurement noise, e i is the NLOS error in TDOA measurement, ω0 and ω i They represent the non-line-of-sight errors on the reference path and the other i sensor paths, and the error values ​​are all greater than 0. |||| is the two-norm identifier. Multiplying both sides of the above equation in equation (1.1) by the speed of light c, we get the measured value of the distance difference between the reference path sensor and other path sensors and the signal source position, which is described as:

[0020]

[0021] Among them, d i is the distance difference between the reference path sensor and the i-th path sensor to the signal source position. In addition, a vector n=[n1,...,n N ] T represents the measurement noise on different paths, and defines n to obey the mean value of 0 and the covariance of Gaussian distribution, where I N represents the N-order identity matrix, 1 N represents an N-order all-one matrix, T represents the transpose of a vector or matrix, σ is the variance of the measurement noise error, and it is assumed that there is an upper bound of the non-line-of-sight error ρ i Make ω i Satisfy 0≤ω i ≤ρ i ;

[0022] Easy to get Its length is 2ρ i , where ρ0 is the upper bound of the non-line-of-sight error on the reference path. However, according to formula (1.2), -ω0≤e i ≤ρ i -ω0, whose length is ρ i ; Too large an upper bound may reduce the positioning performance, so let Substituting it into formula (1.2), we get:

[0023]

[0024] in, and denote the non-line-of-sight errors on the corrected reference path and the other i sensor paths, is the distance difference between the corrected reference path sensor and the i-th path sensor to the signal source position;

[0025] By transposing terms in equation (1.3), we get:

[0026]

[0027] Square both sides and move the terms, and we get

[0028]

[0029] Among them, r i is the distance difference between the ith sensor and the signal source, and r0 is the distance difference between the reference path sensor and the signal source. It is much smaller than the first-order noise term and can be ignored;

[0030] To express problem (1.5) conveniently, let

[0031]

[0032] Substituting into (1.5), we have:

[0033]

[0034] If the weight of the robust least squares problem (RLS) is only related to the unknown NLOS error on the path related, will cause When the range and amplitude of the change are too large, the model performance is reduced and the positioning effect is poor. Therefore, the variable c is added. i As the weight of the signal source location problem, the main function is introduced, and equation (1.5) can be described as:

[0035]

[0036] This technical solution is further optimized, and the step three is specifically as follows:

[0037] The signal source localization problem is transformed into a weighted robust least squares problem, which is described as:

[0038]

[0039] To further simplify the weighted robust least squares problem, let Then it satisfies (1.7) can be described as:

[0040]

[0041] This technical solution is further optimized, and the step 4 is specifically as follows:

[0042] In order to use S-Lemma to directly transform the above RWLS problem into a non-convex optimization problem that can be modified into SDR, equation (1.9) can be equivalently transformed into:

[0043]

[0044] in, η=[η1,...,η N ] T , η i represents the relaxation degree of the i-th constraint, min() is the minimization function, max() is the maximization function, and st means "subject to...". This constraint condition shows that for i=1,...,N, we have:

[0045]

[0046] Right now

[0047]

[0048] According to S-Lemma, Make

[0049]

[0050] Substituting formula (1.12) for the constraint condition (1.10) in the RWLS problem, we get

[0051]

[0052] This technical solution is further optimized, and the step 5 is specifically as follows:

[0053] Introduce auxiliary variable Y=yy T , using the semi-positive definite relaxation technique, it is relaxed into a convex semi-positive definite programming problem for easy solution, then (1.13) can be transformed into:

[0054]

[0055] Where y(5) represents the fifth element of y, Y(4,4) represents the fourth element of the fourth row of Y, Y(3,4) represents the fourth element of the third row of Y, and rank() represents the rank of the matrix;

[0056] In problem (1.14), only rank(Y)=1 is a non-convex constraint, which can be discarded and the following constraints can be added to tighten the problem:

[0057]

[0058] Among them, Y(3,3) represents the third element of the third row of Y, Y(2,2) represents the second element of the second row of Y, and y(1:2) represents the first to second elements of y;

[0059] Then problem (1.14) can be described as:

[0060]

[0061] This technical solution is further optimized, and the step six is ​​specifically as follows:

[0062] Usually, the SDP problem obtained after relaxation cannot generate the global optimal solution of the original RWLS; in order to avoid local convergence or divergence, new constraints are introduced to tighten the problem (1.16), and the second-order cone constraint is used to relax the non-convex equality constraint r i =||xs i || to convex inequality constraint: ||xs i||≤r i ,Right now:

[0063] y(3)≥||y(1:2)-s0|| (1.17)

[0064] where y(3) represents the third element of y. Similarly, the equality constraint ω i r i =ω i ||xs i ||, which can be relaxed to ω i r i ≥ω i ||xs i ||, that is:

[0065] y(5)-Y(4,4)≥2||Y(1:2,4)-s0·y(4)|| (1.18)

[0066] Furthermore, based on the known prior information, the following constraints can be obtained: In addition, in order to better handle the impact of non-line-of-sight errors, prevent overestimation of non-line-of-sight errors, and provide a more accurate error range, So described as:

[0067]

[0068] Where Y(5,5) is the fifth element in the fifth row of Y. Substituting constraints (1.17), (1.18), and (1.19) into problem (1.16), we get:

[0069]

[0070] The technical solution is further optimized, and the step seven includes using an iterative method to jointly estimate the signal source position and the NLOS error upper bound; updating the signal source position with the error upper bound obtained in each iteration process under a specified maximum number of iterations; and terminating the iteration until the distance between the calculated signal source position and the actual signal source position is less than a specified value or the number of iterations exceeds the maximum number of iterations.

[0071] Different from the prior art, the above technical solution has the following beneficial effects:

[0072] 1. Existing methods either need to know the specific distribution of NLOS errors, or use TOA method to measure, which requires complete synchronization between the signal source and the sensor. The present invention only needs to specify the upper bound of the NLOS error, and does not require synchronization between the sensors of the signal source. It innovatively uses the method of calculating the time difference of arrival to model and estimate the position of the signal source.

[0073] 2. In order to avoid excessive upper error bounds that reduce positioning performance, the present invention cleverly subtracts the upper NOLS error bounds from

[0074] A new NLOS error upper bound is formed and substituted into the problem for further solution. The NLOS error upper bound is iteratively updated, and the method of jointly estimating the signal source position and the NLOS error upper bound is used to reduce the impact of an excessively large error upper bound on the positioning performance. In addition, the present invention cleverly uses S-Lemma to eliminate the maximum term in the weighted robust least squares problem, and transforms the RWLS problem into a non-convex optimization problem that can be corrected to a semi-positive definite relaxation.

[0075] 3. The present invention adds variable c i As the weight of the RWLS problem. Avoid the RWLS problem in the NLOS error upper bound When the range and amplitude of changes are too large, the positioning performance of the model will be degraded.

[0076] 4. The present invention uses prior information and the intrinsic relationship between variables to tighten the convex semi-definite programming problem. Compared with the method of only relaxing but not tightening, this method can effectively obtain the global optimal solution of the original robust least squares problem. It avoids local divergence and convergence and improves the algorithm accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 It is a flow chart of a positioning method based on the time difference of arrival of source signals under non-line-of-sight conditions;

[0078] Figure 2 Schematic diagram of a scenario with N+1 sensors and source locations in 2D conditions;

[0079] Figure 3 The trend graph of the mean square error (RMSE) of the signal source position estimation versus the upper bound of the error of other paths;

[0080] Figure 4 The trend graph of the mean square error (RMSE) of the signal source position estimation versus the upper bound of the error of other paths;

[0081] Figure 5 The trend graph of the mean square error (RMSE) of the signal source position estimation versus the number of sensors;

[0082] Figure 6 The trend diagram of the mean square error (RMSE) and noise error covariance parameter changes of the signal source position estimation. DETAILED DESCRIPTION

[0083] In order to explain the technical content, structural features, achieved objectives and effects of the technical solution in detail, the following is a detailed description in conjunction with specific embodiments and accompanying drawings.

[0084] See also Figure 1 The present invention gives priority to an embodiment, a positioning method based on the time difference of arrival of source signals under non-line-of-sight conditions, comprising the following steps:

[0085] Step 1: Establish a coordinate system and initialize the sensor position and signal source position.

[0086] Establish a k-dimensional positioning scenario. Assume that a wireless sensor network has N+1 sensors and 1 unknown signal source. The position of the i-th sensor is s i ∈R k The signal source position is represented by x∈R k Indicates. Among them, R k represents a k-dimensional real vector, and s0 represents the reference sensor position. Figure 2 A schematic diagram of a scenario with N+1 sensor and signal source locations under 2D conditions is given (one of the scenario examples is taken with the reference path error upper bound of 0.5 and the other path error upper bounds of 6α (α=0.1,...,1.2), where the hollow triangles represent sensors on other paths, the solid triangles represent sensors on the reference path, and the hollow circles represent signal sources).

[0087] Step 2: Use the TDOA measurement method to build a distance measurement model, that is, build the measurement value of the distance difference between the reference path sensor and other path sensors to the signal source position.

[0088] Assuming that the sensor position is accurately measured and there is NLOS signal propagation between the signal source and the sensor, the TDOA method is used to measure, which is described as:

[0089]

[0090] Where N is the number of sensors on other paths, t i represents the time difference between the source signal reaching the reference path sensor and the i-th path sensor, c represents the speed of light, and n i represents the measurement noise, e i is the NLOS error in TDOA measurement, ω0 and ω i Respectively represent the non-line-of-sight errors on the reference path and the other i sensor paths, and the error values ​​are all greater than 0, and || || is the two-norm identifier. Multiplying both sides of the above equation in equation (1.1) by the speed of light c, we get the distance difference between the reference path sensor and other path sensors to the signal source position, which is described as:

[0091]

[0092] Among them, d iis the measured value of the distance difference between the reference path sensor and the i-th path sensor to the signal source position. In addition, a vector n = [n1,...,n N ] T represents the measurement noise on different paths, and defines n to obey the mean value of 0 and the covariance of Gaussian distribution, where I N represents the N-order identity matrix, 1 N represents an N-order all-one matrix, T represents the transpose of a vector or matrix, and σ is the variance of the measurement noise error. It is assumed that there is an upper bound of the non-line-of-sight error ρ i Make ω i Satisfy 0≤ω i ≤ρ i .

[0093] Easy to get Its length is 2ρ i , where ρ0 is the upper bound of the non-line-of-sight error on the reference path. However, according to equation (1.2), -ω0≤e i ≤ρ i -ω0, whose length is ρ i Too large an upper bound may reduce the positioning performance. Therefore, let Substituting it into (1.2), we get:

[0094]

[0095] in, and denote the non-line-of-sight errors on the corrected reference path and the other i sensor paths, is the distance difference between the corrected reference path sensor and the i-th path sensor to the signal source position.

[0096] By transposing terms in equation (1.3), we get:

[0097]

[0098] Square both sides and move the terms, and we get

[0099]

[0100] Among them, r i is the distance difference between the ith sensor and the signal source, r0 is the distance difference between the reference path sensor and the signal source, and due to the second-order noise term It is much smaller than the first-order noise term and can be ignored;

[0101] To express problem (1.5) conveniently, let

[0102]

[0103] Substituting into (1.5), we have:

[0104]

[0105] If the weights of the robust least squares problem are only related to the unknown NLOS errors on the path related, will cause When the range and amplitude of the change are too large, the model performance is reduced and the positioning effect is poor. Therefore, the variable c is added. i As the weight of the signal source location problem, the main function is introduced, and equation (1.5) can be described as:

[0106]

[0107] Step 3: Convert the distance measurement model into a constrained weighted robust least squares problem.

[0108] The signal source localization problem is transformed into a weighted robust least squares problem, which is described as:

[0109]

[0110] To further simplify the weighted robust least squares problem, let Then it satisfies (1.7) can be described as:

[0111]

[0112] Step 4: Use S-Lemma to transform the weighted robust least squares problem into a non-convex optimization problem that can be corrected to a semi-definite relaxation.

[0113] In order to use S-Lemma to directly transform the above RWLS problem into a non-convex optimization problem that can be modified into SDR, equation (1.9) can be equivalently transformed into:

[0114]

[0115] in, η=[η1,...,η N ] T , η i represents the relaxation degree of the ith constraint, min() is the minimization function, max() is the maximization function, and st means "subject to...". This constraint condition shows that for i=1,…,N, we have:

[0116]

[0117] Right now

[0118]

[0119] According to S-Lemma, Make

[0120]

[0121] Substituting formula (1.12) for the constraint condition (1.10) in the RWLS problem, we get

[0122]

[0123] Step 5: Use semi-definite relaxation technology to transform the non-convex optimization problem into a convex semi-definite programming problem.

[0124] Step 4 eliminates the maximization part in the original RLS problem (1.8), but problem (1.12) is still a non-convex optimization problem and is difficult to solve. Therefore, an auxiliary variable Y = yy is introduced. T , using the semi-positive definite relaxation technique, it is relaxed into a convex semi-positive definite programming problem for easy solution, then (1.13) can be transformed into:

[0125]

[0126] Where y(5) represents the fifth element of y, Y(4,4) represents the fourth element of the fourth row of Y, Y(3,4) represents the fourth element of the third row of Y, and rank() represents the rank of the matrix.

[0127] In problem (1.14), only rank(Y)=1 is a non-convex constraint, which can be discarded and the following constraints can be added to tighten the problem:

[0128]

[0129] Among them, Y(3,3) represents the third element of the third row of Y, Y(2,2) represents the second element of the second row of Y, and y(1:2) represents the first to second elements of y.

[0130] Then problem (1.14) can be described as:

[0131]

[0132] Step 6: Based on the convex semi-positive definite programming problem, construct a semi-positive definite programming problem with tightened inequality constraints.

[0133] Usually, the SDP problem obtained after relaxation cannot generate the global optimal solution of the original RWLS; to avoid local convergence or divergence, new constraints are introduced to tighten the problem (1.16). Using the second-order cone constraint to relax the non-convex equality constraint r i =||xs i|| to convex inequality constraint: ||xs i ||≤r i ,Right now:

[0134] y(3)≥||y(1:2)-s0|| (1.17)

[0135] where y(3) represents the third element of y. Similarly, the equality constraint ω i r i =ω i ||xs i ||, which can be relaxed to ω i r i ≥ω i ||xs i ||, that is:

[0136] y(5)-Y(4,4)≥2||Y(1:2,4)-s0·y(4)|| (1.18)

[0137] Furthermore, based on the known prior information, the following constraints can be obtained: In addition, in order to better handle the impact of non-line-of-sight errors, prevent overestimation of non-line-of-sight errors, and provide a more accurate error range, So described as:

[0138]

[0139] Where Y(5,5) is the fifth element in the fifth row of Y. Substituting constraints (1.17), (1.18), and (1.19) into problem (1.16), we get:

[0140]

[0141] Step 7: Use an iterative method to jointly estimate the signal source position and the upper bound of the path NLOS error to obtain the optimal estimate of the target source position.

[0142] To further reduce the upper bound of the error and avoid excessive upper bound of the error from reducing the experimental performance, the signal source position and the NLOS error upper bound are jointly estimated using an iterative method. Under the specified maximum number of iterations, the signal source position is updated using the error upper bound obtained during each iteration. The iteration is terminated when the distance between the calculated signal source position and the actual signal source position is less than the specified value or the number of iterations exceeds the maximum number of iterations.

[0143] In order to verify the feasibility and effectiveness of the method of the present invention, a simulation test was carried out on the method of the present invention.

[0144] Assume that there are at most 13 sensors and 1 signal source in the 2D space, and their coordinates s in the 2D rectangular coordinate system are i=[x i ,y i ] T ,i=1,...,N,t=[m,n] T is randomly generated, where x i ~(0,10) meters,y i ~(0,10) meters, m~(0,10) meters, n~(0,10) meters. The noise error satisfies the mean value equal to 0 and the covariance value is The Gaussian distribution of NLOS error ω on the reference path and other paths i ,i=0,...,N is randomly generated, ω i ~(0,p i ), where p i is the upper bound of the error on the i-th path.

[0145] In order to demonstrate the performance of the method of the present invention in different situations, the simulation test tested the performance of the method of the present invention under different NLOS error upper bounds, different numbers of sensors, and different measurement noise error variances, and measured the performance of the method by the root mean square error (RMSE). The root mean square error (RMSE) describing the positioning performance in the three situations is the RMSE obtained by running 2000 Monte Carlo experiments in 10 random scenarios, and the trend chart is drawn for visualization. Figure 3 A trend graph of the mean square error (RMSE) of the signal source position estimation of the method of the present invention varying with the upper bounds of the errors of other paths when the upper bound of the reference path error is 0.5, the upper bounds of the errors of other paths are 6α (α=0.1,...,1.2), the number of sensors on other paths is N=6, and the variance of the measurement noise error is σ=0.3 is given. Figure 4 A trend graph of the mean square error (RMSE) of the signal source position estimation of the method of the present invention varying with the upper bounds of the errors of other paths when the upper bound of the reference path error is 6, the upper bounds of the errors of other paths are 6α (α=0.1,...,1.2), the number of sensors on other paths is N=6, and the variance of the measurement noise error is σ=0.3 is given. Figure 5 A trend graph of the mean square error (RMSE) of the signal source position estimation and the number of sensors on other paths of the method of the present invention is given when the reference path error upper bound is 0.5, the other path error upper bound is 6, the number of sensors on other paths is N=[4,5,6,7,8], and the variance of the measurement noise error is σ=0.3. Figure 6The trend diagram of the mean square error (RMSE) noise error covariance parameter change of the signal source position estimation method of the present invention is given when the reference path error upper bound is 0.5, the other path error upper bound is 6, the number of sensors on the other paths is N=6, and the variance of the measurement noise error σ=0.1,...,0.6. Figure 3 , Figure 4 It can be seen that as the upper bound of the NLOS error increases, the RMSE of the method of the present invention increases, but the maximum value does not exceed 2.5, and the positioning accuracy is relatively accurate. Figure 5 It can be seen that when the number of sensors N on other paths increases, the RMSE value of the method of the present invention decreases significantly, which means that when the number of sensors increases, the positioning accuracy of the method of the present invention is significantly improved. In addition, when the measurement noise error increases, the RMSE of the method of the present invention reaches the minimum value when σ=0.3, but the maximum deviation of RMSE under different σ values ​​does not exceed 0.015. This shows that the size of the measurement noise has little effect on the positioning accuracy of the method.

[0146] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that the process, method, article or terminal device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or terminal device. In the absence of further restrictions, the elements defined by the sentence "include..." or "comprise..." do not exclude the existence of other elements in the process, method, article or terminal device including the elements. In addition, in this article, "greater than", "less than", "exceed" and the like are understood to exclude the number itself; "above", "below", "within" and the like are understood to include the number itself.

[0147] Although the above embodiments have been described, once those skilled in the art know the basic creative concepts, they can make additional changes and modifications to these embodiments. Therefore, the above description is only an embodiment of the present invention and does not limit the patent protection scope of the present invention. Any equivalent structure or equivalent process transformation made by using the contents of the specification and drawings of the present invention, or directly or indirectly used in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A positioning method based on the time difference of arrival of source signals under non-line-of-sight conditions, characterized in that: The following steps are included: Step 1: Establish a coordinate system and initialize the sensor position and signal source position; Step 2: Use the TDOA measurement method to build a distance measurement model, that is, to build a measurement value of the distance difference between the reference path sensor and other path sensors and the signal source position; Step 3: Convert the distance measurement model into a constrained weighted robust least squares problem; Step 4: Use S-Lemma to transform the weighted robust least squares problem into a non-convex optimization problem that can be corrected to a semi-definite relaxation; Step 5: Use semi-definite relaxation technology to transform the non-convex optimization problem into a convex semi-definite programming problem; Step 6: Based on the convex semi-positive definite programming problem, a semi-positive definite programming problem with tightened inequality constraints is constructed; Step 7: Use an iterative method to jointly estimate the signal source position and the upper bound of the path NLOS error to obtain the optimal estimate of the target source position.

2. The positioning method based on the time difference of arrival of source signals under non-line-of-sight conditions as claimed in claim 1, characterized in that: The step 1 specifically includes: Establish a k-dimensional positioning scenario. Assume that a wireless sensor network has N+1 sensors and 1 unknown signal source. The position of the i-th sensor is s i ∈R k The signal source position is represented by x∈R k Indicates that, R k represents a k-dimensional real vector, and s0 represents the reference sensor position.

3. The positioning method based on the time difference of arrival of source signals under non-line-of-sight conditions as claimed in claim 2, characterized in that: The step 2 specifically includes: Assuming that the sensor position is accurately measured and there is NLOS signal propagation between the signal source and the sensor, the TDOA method is used to measure, which is described as: Where N is the number of sensors in other paths, t i represents the time difference between the source signal reaching the reference path sensor and the i-th path sensor, c represents the speed of light, and n i represents the measurement noise, e i is the NLOS error in TDOA measurement, ω0 and ω i They represent the non-line-of-sight errors on the reference path and the other i sensor paths, and the error values ​​are all greater than 0. ‖‖ is the two-norm identifier. Multiplying both sides of the above equation in equation (1.1) by the speed of light c, we get the measured value of the distance difference between the reference path sensor and other path sensors and the signal source position, which is described as: Among them, d i is the distance difference between the reference path sensor and the i-th path sensor to the signal source position. In addition, a vector n=[n1,...,n N ] T represents the measurement noise on different paths, and defines n to obey the mean value of 0 and the covariance of Gaussian distribution, where I N represents the N-order identity matrix, 1 N represents an N-order all-one matrix, T represents the transpose of a vector or matrix, σ is the variance of the measurement noise error, and it is assumed that there is an upper bound of the non-line-of-sight error ρ i Make ω i Satisfy 0≤ω i ≤ρ i ; Easy to get Its length is 2ρ i , where ρ0 is the upper bound of the non-line-of-sight error on the reference path. However, according to formula (1.2), -ω0≤e i ≤ρ i -ω0, whose length is ρ i ; Too large an upper bound may reduce the positioning performance, so let Substituting it into formula (1.2), we get: in, and denote the non-line-of-sight errors on the corrected reference path and the i-th sensor path, respectively. is the distance difference between the corrected reference path sensor and the i-th path sensor to the signal source position; By transposing terms in equation (1.3), we get: Square both sides and move the terms, and we get Among them, r i is the distance difference between the ith sensor and the signal source, r0 is the distance difference between the reference path sensor and the signal source, and due to the second-order noise term It is much smaller than the first-order noise term and can be ignored; To express problem (1.5) conveniently, let Substituting into (1.5), we have: If the weights of the robust least squares problem are only related to the unknown NLOS errors on the path related, will cause When the range and amplitude of the change are too large, the model performance is reduced and the positioning effect is poor. Therefore, the variable c is added. i As the weight of the signal source location problem, the main function is introduced, and then formula (1.5) can be described as:

4. The positioning method based on the time difference of arrival of source signals under non-line-of-sight conditions as claimed in claim 3, characterized in that: The step three is as follows: The source signal localization problem is transformed into a weighted robust least squares problem, which is described as: To further simplify the weighted robust least squares problem, let Then it satisfies (1.7) can be described as:

5. The positioning method based on the time difference of arrival of source signals under non-line-of-sight conditions as claimed in claim 4, characterized in that: The step 4 is specifically as follows: In order to use S-Lemma to directly transform the above RWLS problem into a non-convex optimization problem that can be modified into SDR, equation (1.9) can be equivalently transformed into: in, η i Indicates the degree of relaxation of the i-th constraint, min() is the minimization function, max() is the maximization function, and st means "subject to...". This constraint condition shows that for i=1,...,N, we have: Right now According to S-Lemma, Make Substituting formula (1.12) for the constraint condition (1.10) in the RWLS problem, we get 6. The positioning method based on the time difference of arrival of source signals under non-line-of-sight conditions as claimed in claim 5, characterized in that: The step five is as follows: Introduce auxiliary variable Y=yy T , using the semi-positive definite relaxation technique, it is relaxed into a convex semi-positive definite programming problem for easy solution, then (1.13) can be transformed into: Where y(5) represents the fifth element of y, Y(4,4) represents the fourth element of the fourth row of Y, Y(3,4) represents the fourth element of the third row of Y, and rank() represents the rank of the matrix; In problem (1.14), only rank(Y)=1 is a non-convex constraint, which can be discarded and the following constraints can be added to tighten the problem: Among them, Y(3,3) represents the third element of the third row of Y, Y(2,2) represents the second element of the second row of Y, and y(1:2) represents the first to second elements of y; Then problem (1.14) can be described as:

7. The positioning method based on the time difference of arrival of source signals under non-line-of-sight conditions as claimed in claim 6, characterized in that: The step six is ​​as follows: Usually, the SDP problem obtained after relaxation cannot generate the global optimal solution of the original RWLS; in order to avoid local convergence or divergence, new constraints are introduced to tighten the problem (1.16), and the second-order cone constraint is used to relax the non-convex equality constraint r i =||xs i || to convex inequality constraint: ||xs i ||≤r i ,Right now: y(3)≥||y(1:2)-s0|| (1.17) where y(3) represents the third element of y. Similarly, the equality constraint ω i r i =ω i ||xs i ||, which can be relaxed to ω i r i ≥ω i ||xs i ||, that is: y(5)-Y(4,4)≥2||Y(1:2,4)-s0·y(4)|| (1.18) Furthermore, based on the known prior information, the following constraints can be obtained: In addition, in order to better handle the impact of non-line-of-sight errors, prevent overestimation of non-line-of-sight errors, and provide a more accurate error range, So described as: Where Y(5,5) is the fifth element in the fifth row of Y. Substituting constraints (1.17), (1.18), and (1.19) into problem (1.16), we get:

8. The positioning method based on the time difference of arrival of source signals under non-line-of-sight conditions as claimed in claim 1, characterized in that: The step 7 includes jointly estimating the signal source position and the NLOS error upper bound by using an iterative method; Under the specified maximum number of iterations, the signal source position is updated using the upper bound of the error obtained in each iteration process; The iteration is terminated when the distance between the calculated signal source position and the actual signal source position is less than the specified value or the number of iterations exceeds the maximum number of iterations.

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