Accurate target positioning method and system in non-line-of-sight environment

Abstract

The invention discloses an accurate target positioning method and system in a non-line-of-sight environment. The method comprises the following steps: substituting N anchor node coordinates and a target node coordinate in a positioning scene into a distance formula to obtain an expression for representing the distance between a target node and each anchor node, performing square expansion on the expression to obtain an overdetermined equation and an intermediate variable matrix b for representing position information and positioning error information of the target node and each anchor node, converting an overdetermined equation solving problem into a fractional programming constraint optimization problem, and introducing an expected value into the optimization problem to obtain a variant of the fractional programming constraint optimization problem; and converting the optimization problem variant into a parameter planning constraint optimization problem, and solving the parameter planning constraint optimization problem by using a Lagrangian multiplier method in combination with the matrix b to obtain an optimal position coordinate. According to the method, the calculation complexity is low, and the influence of the non-line-of-sight error in the TOA measurement value can be effectively eliminated.

Description

Technical Field

[0001] The present invention belongs to the field of target positioning methods, and more specifically, relates to a precise target positioning method and system in a non-line-of-sight environment. Background Art

[0002] Target positioning is an important method in wireless positioning technology and is widely used in indoor positioning and tracking systems. In order to achieve the positioning of the target node, a distance measurement technology based on TOA (Time of Arrival) is usually used. The TOA positioning method is a way to determine the target position based on the arrival time of the measured signal between the transmitter and the receiver. In a specific environment, the signal propagation speed is known. By measuring TOA, the distance between the two can be calculated, and the target position can be determined using multiple distance measurement values. However, in the actual signal propagation process, the signal propagation path may be blocked by obstacles, which will cause the positioning system to seriously degrade or even completely fail. In this case, the measured TOA often has multiple errors, mainly including measurement noise and large non-line-of-sight errors, and non-line-of-sight errors will cause the positioning performance to drop sharply. Therefore, a high-precision and low-complexity positioning algorithm is essential for determining the target position in an actual complex positioning environment.

[0003] Existing non-line-of-sight error estimation methods are usually based on certain assumptions and statistical models, but the noise in the actual environment may be more complex, resulting in a decrease in algorithm performance. In order to mitigate the impact of non-line-of-sight error on positioning performance, the prior art discloses a non-line-of-sight error suppression method for source positioning. In the absence of prior knowledge of non-line-of-sight error, some algorithms are proposed to solve the target positioning problem. For example, the square range (SR) and weighted least squares (WLS) criteria are applied to transform the original positioning problem into a generalized trust region subproblem (GTRS) framework, and its solution is easily obtained by bisection. It is reshaped into an optimization form using second-order cone relaxation (SOCR) and constraint terms, and solved using semidefinite programming (SDP), robust SDP (RSDP) and robust second-order cone programming (RSOCP).

[0004] Unfortunately, these algorithms cannot eliminate the impact of non-line-of-sight errors in TOA measurements. In view of this, a convex optimization positioning algorithm in a mixed line-of-sight / non-line-of-sight environment is proposed. Taking into account non-line-of-sight bias and measurement noise, the prior art "A Convex Optimization Approach For NLOS Error Mitigation in TOA-Based Localization" proposes to solve the positioning problem using the SDP method under the framework of least squares with adjustment terms (RTLS). The algorithm does not require any prior knowledge about bias and non-line-of-sight links to achieve higher positioning accuracy. However, the computational complexity of the algorithm is not optimal and requires a lot of time. Summary of the invention

[0005] The present invention provides a method and system for accurately locating a target in a non-line-of-sight environment in order to overcome the problems in the prior art of high computational complexity and difficulty in eliminating the influence of non-line-of-sight errors in TOA measurements.

[0006] The primary purpose of the present invention is to solve the above technical problems. The technical solution of the present invention is as follows:

[0007] A first aspect of the present invention provides a method for accurately locating a target in a non-line-of-sight environment, comprising the following steps:

[0008] S1: Substitute the coordinates of N anchor nodes and one target node in the positioning scene into the distance formula to obtain an expression for representing the distance between the target node and each anchor node;

[0009] S2: Expand the distance expression by square to obtain an overdetermined equation and an intermediate variable matrix b that represents the position information and positioning error information of the target node and each anchor node. Use the regularization strategy and quadratic constraints to convert the overdetermined equation solution problem into a fractional programming constrained optimization problem. By introducing the expected value into the optimization problem, a variant of the fractional programming constrained optimization problem is obtained.

[0010] S3: Using a preset algorithm, the optimization problem variant is converted into a parameter planning constraint optimization problem, and the parameter planning constraint optimization problem is solved using the Lagrange multiplier method in combination with the matrix b to obtain the optimal position coordinates.

[0011] Furthermore, the preset algorithm for converting the fractional programming constrained optimization problem variant into the parameter programming constrained optimization problem is the Dinkelbach algorithm.

[0012] Furthermore, the multipliers in the Lagrange multiplier method are solved using a bisection method.

[0013] Furthermore, the multipliers in the Lagrange multiplier method are solved using Newton's method.

[0014] Furthermore, the signal propagation link types between the target node and each anchor node include: line-of-sight and non-line-of-sight; used to characterize the distance d between the target node and each anchor node i The formula is as follows:

[0015] d i =||Xa i ||+n i +e i (1)

[0016] Where X = [x, y] T is the target node coordinate, a i =[a i1 ,a i2 ] T represents the coordinates of the i-th anchor node, n i is the measurement noise in the propagation path between the i-th anchor node and the target node, with variance σ 2 Zero-mean Gaussian distribution; e i is the non-line-of-sight error, with an upper bound λ, which is adjusted according to the signal propagation link type. If the signal propagation link type is line-of-sight, then e i is zero; if the signal propagation link type is non-line-of-sight, then 0≤e i ≤λ.

[0017] Furthermore, the overdetermined equation solving problem is converted into a fractional programming constrained optimization problem, which includes the following steps:

[0018] The square expansion of formula (1) is as follows:

[0019] 2a i1 x+2a i2 y-η≈ξ i -(r i -e i ) 2 +2(r i -e i ) i (2

[0020] in, Too small to be ignored, η=X T X, definition:

[0021]

[0022] Substituting θ, A, and b into formula (2), we get the overdetermined equation:

[0023] Aθ≈b

[0024] Wherein, b is a formula representing the intermediate variables of the position information and positioning error information of the target node and each anchor node;

[0025] The total least squares method is used to solve the overdetermined equation. The solution is as follows:

[0026]

[0027] The regularization strategy and quadratic constraints are used to transform the problem (3) into a fractional programming constrained optimization problem, as shown below:

[0028]

[0029] st||Lθ|| 2 +2q T θ≤ρ (4)

[0030] Where L = diag(1,1,0), q = [0,0,-1 / 2] T , ρ is a given positive constant;

[0031] By introducing the expected value into the fractional programming constrained optimization problem, we get a variant of the fractional programming constrained optimization problem. The constrained optimization problem (4) can be reformulated as follows:

[0032]

[0033] Where E(·) represents expectation. According to the properties of expectation, formula (5) is converted into:

[0034]

[0035] st||Lθ|| 2 +2q T θ≤ρ

[0036] Here, ρ is a given positive constant.

[0037] Furthermore, the solution of the optimal position coordinates includes the following steps:

[0038] The Dinkelbach algorithm is used to transform the fractional programming constrained optimization problem into a non-convex parameter programming constrained optimization problem with only one constraint. Problem (6) is equivalently transformed into:

[0039]

[0040] st||Lθ|| 2 +2q T θ≤ρ (7)

[0041] Among them, τ i =E(bi ) is the i-th element of the matrix τ, ν=E(b T b);

[0042] In the optimization problem (7), an unknown parameter μ is introduced using the Dinkelbach algorithm. Assume that μ * The function F(μ)=θ T A T Aθ-2τ T Aθ+ν+μ(||θ|| 2 +1), we can deduce

[0043]

[0044] Get μ * <0;

[0045] Using the Lagrange multiplier method to solve the problem (7), the Lagrange function corresponding to the problem (7) is:

[0046] L=||(Aθ-b|| 2 +μ(||θ|| 2 +1)+α(||Lθ|| 2 +2q T θ-ρ)

[0047] Among them, α is a multiplier, and a necessary condition for the optimal solution is the gradient of the Lagrangian function Right now:

[0048]

[0049] From this we can deduce the optimal solution:

[0050] θ * =(A T A+μI+αL) -1 (A T τ-αq) (10)

[0051] Where I is the third-order identity matrix. Substituting equation (10) into the inequality constraint, we obtain:

[0052] ||L(A T A+μI+αL) -1 (A T τ-αq)|| 2 +2q(A T A+μI+αL) -1 (A T τ-αq)≤ρ

[0053] Define M = A T A,N=A T τ, we get:

[0054]

[0055] Among them, m k ,n k ,l k ,q k are the elements on the diagonal of matrices M, N, L, and q respectively. The multiplier α is numerically solved by bisection or Newton's method. Due to the duality, That is m k +μ+αl k ≥0,

[0056] When l k <0, When l k >0, The derivative of the function is:

[0057]

[0058] For all α, let φ′(α)<0, which means that φ′(α) is strictly monotonically decreasing in this region, so the solution of φ(α)=0 is unique. According to the actual situation, The equation φ(α)=0 in the interval There is a root in the memory. Use the bisection method or Newton's method to solve the parameter α, and use the Dinkelbach algorithm to solve the parameter μ. Substitute the values ​​of parameters α and μ into equation (10) to obtain the optimal solution θ * .

[0059] A second aspect of the present invention provides a precise target positioning system in a non-line-of-sight environment, comprising a memory and a processor, wherein the memory comprises a precise target positioning method program in a non-line-of-sight environment, and when the precise target positioning method program in a non-line-of-sight environment is executed by the processor, the steps of a precise target positioning method in a non-line-of-sight environment are implemented.

[0060] A third aspect of the present invention provides a computer-readable storage medium, which includes a program for a method for accurately locating a target in a non-line-of-sight environment. When the program for the method for accurately locating a target in a non-line-of-sight environment is executed by a processor, the steps of a method for accurately locating a target in a non-line-of-sight environment are implemented.

[0061] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0062] The present invention introduces an expectation value to process the influence of non-line-of-sight error and measurement noise. In a complex line-of-sight / non-line-of-sight mixed environment and when the actual value of the non-line-of-sight error and measurement noise is missing, the expectation of the non-line-of-sight error and measurement noise is calculated to obtain a computational representation of an intermediate variable matrix characterizing position information and positioning error information of a target node and each anchor node, and further obtain a solution to the optimization problem, thereby effectively eliminating the influence of the non-line-of-sight error and measurement noise. By applying the Dinkelbach algorithm in combination with the Lagrange multiplier method, the complex nonlinear problem is converted into a series of sub-problems that are easier to solve, which is similar to linear calculation, simplifies the calculation process, significantly reduces the calculation complexity, and effectively reduces the overall calculation burden. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] In order to make the purpose and technical solution of the present invention clearer, the present invention provides the following drawings and descriptions:

[0064] Figure 1 A flow chart of a method provided by an embodiment of the present invention;

[0065] Figure 2 A schematic diagram of an experimental scenario provided for an embodiment of the present invention;

[0066] Figure 3 A comparison diagram of the root mean square error of each algorithm under different noise levels provided by an embodiment of the present invention;

[0067] Figure 4 A comparison diagram of the root mean square error of each algorithm under different non-line-of-sight deviations provided by an embodiment of the present invention;

[0068] Figure 5 A comparison diagram of the root mean square error of different numbers of anchor nodes under different non-line-of-sight deviations provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0069] In order to more clearly understand the above-mentioned purpose, features and advantages of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that the embodiments of the present application and the features in the embodiments can be combined with each other without conflict.

[0070] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Therefore, the protection scope of the present invention is not limited to the specific embodiments disclosed below.

[0071] Embodiment 1:

[0072] The present invention provides a method for accurately locating a target in a non-line-of-sight environment. Figure 1The figure shows a flow chart of a method for accurate target positioning in a non-line-of-sight environment. The specific steps are as follows:

[0073] S1: Substitute the coordinates of N anchor nodes and one target node in the two-dimensional TOA positioning scenario into the distance formula to obtain an expression for representing the distance between the target node and each anchor node.

[0074] More specifically, the types of signal propagation links between the target node and each anchor node include: line-of-sight (LOS) and non-line-of-sight (NLOS).

[0075] The specific process is:

[0076] It is used to represent the distance d between the target node and each anchor node. i The formula is as follows:

[0077] d i =||Xa i ||+n i +e i (1)

[0078] Where X = [x, y] T is the target node coordinate, a i =[a i1 ,a i2 ] T represents the coordinates of the i-th anchor node, n i is the measurement noise in the propagation path between the i-th anchor node and the target node, with variance σ 2 Zero-mean Gaussian distribution; e i is the non-line-of-sight error, with an upper bound λ, which is 10m in this example. It is adjusted according to the signal propagation link type. If the signal propagation link type is line-of-sight, then e i is zero; if the signal propagation link type is non-line-of-sight, then 0≤e i ≤λ.

[0079] In this example, the coordinates of the eight base stations (in meters) are: (±20, ±20), (0, ±20) and (±20, 0). Assume that there is an actual target node to be located (-1.4538, -13.4756)

[0080] There are 3 line-of-sight links and 5 non-line-of-sight links.

[0081] The noise variance σ is 3m and the upper bound of the non-line-of-sight error λ is 10m.

[0082] The actual distances from the 8 base stations to the target node are (in meters): 23.3644, 37.5809, 17.9055, 46.8695, 34.9870, 9.7718, 23.8485, and 28.9418.

[0083] Non-line-of-sight error size (in meters): 0, 0, 0, 8.4431, 1.9476, 2.2592, 1.7071, 2.2766.

[0084] The measurement noise sizes are (in meters): 3.7040, -0.6889, -4.5185, -1.3339, -0.4678, 0.8282, -0.7835, 1.3303.

[0085] S2: Square the distance expression to obtain an overdetermined equation and an intermediate variable matrix b that represents the position information and positioning error information of the target node and each anchor node. Use the total least squares method (TLS) to convert the overdetermined equation solving problem into a fractional programming constrained optimization problem by using a regularization strategy and quadratic constraints. By introducing the expected value into the optimization problem, a variant of the fractional programming constrained optimization problem is obtained.

[0086] The specific process is:

[0087] The square expansion of formula (1) is as follows:

[0088] 2a i1 x+2a i2 y-η≈ξ i -(r i -e i ) 2 +2(r i -e i ) i (2)

[0089] in, Too small to be ignored, η=X T X, definition:

[0090]

[0091]

[0092] Substituting θ, A, and b into formula (2), we get the overdetermined equation:

[0093] Aθ≈b

[0094] Wherein, b is a formula representing the intermediate variables of the position information and positioning error information of the target node and each anchor node;

[0095] The total least squares (TLS) method is used to solve the overdetermined equation. The solution is as follows:

[0096]

[0097] Since the coefficient matrix A is ill-posed, the least squares method (TLS) will produce a solution of poor quality. The regularization strategy and quadratic constraints are used to transform the solution problem (3) into a fractional programming constrained optimization problem, as shown below:

[0098]

[0099] st||Lθ|| 2 +2q T θ≤ρ (4)

[0100] Where L = diag(1,1,0), q = [0,0,-1 / 2] T , ρ is a given positive constant, with a value of 3;

[0101] In practice, the measurement noise n i and non-line-of-sight error e i It is impossible to know it completely, so the matrix b cannot be calculated directly. By taking the expectation of the error and measurement noise in the non-line-of-sight environment in the constrained optimization problem, the goal is to find the expectation of the matrix b, so as to obtain the computational representation of b.

[0102] By introducing the expected value into the fractional programming constrained optimization problem, we get a variant of the fractional programming constrained optimization problem. The constrained optimization problem (4) can be reformulated as follows:

[0103]

[0104] Where E(·) represents the expectation. According to the properties of the expectation, formula (5) is converted into:

[0105]

[0106] st||Lθ|| 2 +2q T θ≤ρ

[0107] Here, ρ is a given positive constant with a value of 3.

[0108] The expected value is introduced to deal with the influence of non-line-of-sight error and measurement noise. In a complex line-of-sight / non-line-of-sight mixed environment and when the actual value of the non-line-of-sight error and measurement noise is missing, the expectation of the non-line-of-sight error and measurement noise is calculated to obtain the computational representation of the intermediate variable matrix that characterizes the position information and positioning error information of the target node and each anchor node, and further obtain the solution to the optimization problem, effectively eliminating the influence of the non-line-of-sight error and measurement noise.

[0109] S3: Use the Dinkelbach algorithm to convert the optimization problem variant into a non-convex parameter planning constrained optimization problem with only one constraint, and use the Lagrange multiplier method to solve the parameter planning constrained optimization problem in combination with the matrix b to obtain the optimal position coordinates.

[0110] The specific process is:

[0111] The Dinkelbach algorithm is used to transform the fractional programming constrained optimization problem into a non-convex parameter programming constrained optimization problem with only one constraint. Problem (6) is equivalently transformed into:

[0112]

[0113] st||Lθ|| 2 +2q T θ≤ρ (7)

[0114] Among them, τ i =E(b i ) is the i-th element of the matrix τ, ν=E(b T b);

[0115] In the optimization problem (7), an unknown parameter μ is introduced using the Dinkelbach algorithm. Assume that μ * The function F(μ)=θ T A T Aθ-2τ T Aθ+ν+μ(||θ|| 2 +1), we can deduce

[0116]

[0117] Get μ * <0;

[0118] The Lagrange multiplier method is used to solve the complex nonlinear problem, which is converted into a series of sub-problems that are easier to solve. This method is similar to linear calculation, simplifies the calculation process, significantly reduces the calculation complexity, and effectively reduces the overall calculation burden. The Lagrange function corresponding to problem (7) is:

[0119] L=||(Aθ-b)|| 2 +μ(||θ|| 2 +1)+α(||θ|| 2 +2q T θ-ρ)

[0120] Among them, α is a multiplier, and a necessary condition for the optimal solution is the gradient of the Lagrangian function Right now:

[0121]

[0122] From this we can deduce the optimal solution:

[0123] θ * =(A T A+μI+αL) -1 (A T τ-αq) (10)

[0124] Where I is the third-order identity matrix. Substituting equation (10) into the inequality constraint, we obtain:

[0125] ||L(A T A+μI+αL) -1 (A T τ-αq)|| 2 +2q(A T A+μI+αL) -1 (A T τ-αq)≤ρ

[0126] Definition: M = A T A,N=A T τ, we get:

[0127]

[0128] Among them, m k ,n k ,l k ,q k are the elements on the diagonal of matrices M, N, L, and q respectively. The multiplier α is numerically solved by bisection or Newton's method. Due to the duality, That is m k +μ+αl k ≥0,

[0129] When l k <0, When l k >0, The derivative of the function is:

[0130]

[0131] For all α, let φ′(α)<0, which means that φ′(α) is strictly monotonically decreasing in this region, so the solution of φ(α)=0 is unique. According to the actual situation, The equation φ(α)=0 in the interval There is a root in the memory. Use the bisection method or Newton's method to solve the parameter α, and use the Dinkelbach algorithm to solve the parameter μ. Substitute the values ​​of the parameters α and μ into equation (10) to obtain the optimal solution θ * In this example, the optimal solution coordinates are (-1.4044, -13.0838), and the root mean square error of positioning is 0.394943m.

[0132] In order to evaluate the performance of the RTLS-Dinkelbach proposed in this paper, a comparative experiment was conducted with the existing schemes RTLS-SDP, RSOCP, and SR-WLS. In the simulation, all anchor nodes were randomly placed in a 50m×50m area, and in each Monte Carlo (MC) test, the target node was randomly selected from the same area. i It has a mean of zero and a variance of σ 2 Gaussian distribution, that is, when i=1,...,N, σ i =σ, assuming that the maximum value of the non-line-of-sight deviation λ = 10m, that is, the non-line-of-sight deviation e i ~u[0,10]. like Figure 3 The following is a comparison of the root mean square error of each algorithm under different noise levels. Figure 4 The figure shows the comparison of the root mean square error of each algorithm under different non-line-of-sight deviations.

[0133] From the experimental results, it can be seen that the performance of the RTLS-Dinkelbach algorithm of the present invention under different noise levels and non-line-of-sight deviation conditions. As the interference factors increase, the root mean square error (RMSE) of the RTLS-Dinkelbach algorithm shows a gradually increasing trend. Despite this, its RMSE value remains at a relatively low level, second only to the best performing RTLS-SDP method. This shows that the RTLS-Dinkelbach algorithm has high robustness in dealing with noise and NLOS deviations.

[0134] Table 1 below provides a comparative analysis of the average running time of various algorithms. The analysis results show that the RTLS-Dinkelbach of the present invention is significantly superior to other existing methods in terms of operating efficiency. This significant improvement means higher processing speed and lower latency in practical applications.

[0135] Table 1

[0136] method SR-WLS RSOCP RTLS-SDP RTLS-Dinkelbach Run time(s) 0.00871 0.39763 0.73774 0.00036

[0137] like Figure 5The figure shows a comparison of the root mean square error of the present invention corresponding to different numbers of anchor nodes under different non-line-of-sight deviations. It can be seen from the figure that when λ is the same, that is, under the same non-line-of-sight deviation condition, as the number of anchor nodes increases, the corresponding RMSE decreases instead, and the performance of the proposed algorithm will not decrease due to the increase in the number of anchor nodes, indicating that the algorithm has good robustness.

[0138] Embodiment 2:

[0139] The present embodiment provides a precise target positioning system in a non-line-of-sight environment, including a memory and a processor, wherein the memory includes a precise target positioning method program in a non-line-of-sight environment, and when the precise target positioning method program in a non-line-of-sight environment is executed by the processor, the steps of a precise target positioning method in a non-line-of-sight environment as described in Example 1 are implemented.

[0140] Embodiment 3:

[0141] This embodiment provides a computer-readable storage medium, which includes a program for a method for accurately locating a target in a non-line-of-sight environment. When the program for the method for accurately locating a target in a non-line-of-sight environment is executed by a processor, the steps of a method for accurately locating a target in a non-line-of-sight environment as described in Example 1 are implemented.

[0142] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the embodiments here. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A method for accurate target positioning in a non-line-of-sight environment, characterized in that: The steps include: S1: Substitute the coordinates of N anchor nodes and one target node in the positioning scene into the distance formula to obtain an expression for representing the distance between the target node and each anchor node; S2: Expand the distance expression by square to obtain an overdetermined equation and an intermediate variable matrix b that represents the position information and positioning error information of the target node and each anchor node. Use the regularization strategy and quadratic constraints to convert the overdetermined equation solution problem into a fractional programming constrained optimization problem. By introducing the expected value into the optimization problem, a variant of the fractional programming constrained optimization problem is obtained. S3: Using a preset algorithm, the optimization problem variant is converted into a parameter planning constraint optimization problem, and the parameter planning constraint optimization problem is solved using the Lagrange multiplier method in combination with the matrix b to obtain the optimal position coordinates.

2. The method for accurate target positioning in a non-line-of-sight environment according to claim 1, characterized in that: The method for solving overdetermined equations is the total least squares method.

3. The method for accurate target positioning in a non-line-of-sight environment according to claim 1, characterized in that: The default algorithm for converting fractional programming constrained optimization problem variants into parameter programming constrained optimization problems is the Dinkelbach algorithm.

4. The method for accurate target positioning in a non-line-of-sight environment according to claim 1, characterized in that: The multipliers in the Lagrange multiplier method are solved using the bisection method.

5. The method for accurate target positioning in a non-line-of-sight environment according to claim 1, characterized in that: The multipliers in the Lagrange multiplier method are solved using Newton's method.

6. The method for accurate target positioning in a non-line-of-sight environment according to claim 1, characterized in that: The signal propagation link types between the target node and each anchor node include: line-of-sight and non-line-of-sight; used to characterize the distance d between the target node and each anchor node i The formula is as follows: d i =||X-a i ||+n i +e i (1) Where X = [x, y] T is the target node coordinate, a i =[a i1 ,a i2 ] T represents the coordinates of the i-th anchor node, n i is the measurement noise in the propagation path between the i-th anchor node and the target node, with variance σ 2 Zero-mean Gaussian distribution; e i is the non-line-of-sight error, with an upper bound λ, which is adjusted according to the signal propagation link type. If the signal propagation link type is line-of-sight, then e i is zero; if the signal propagation link type is non-line-of-sight, then 0≤e i ≤λ.

7. The method for accurate target positioning in a non-line-of-sight environment according to claim 6, characterized in that: The overdetermined equation solving problem is converted into a fractional programming constrained optimization problem, which includes the following steps: The square expansion of formula (1) is as follows: 2a i1 x+2a i2 y-η≈ξ i -(r i -e i ) 2 +2(r i -e i )n i (2) in, Too small to be ignored, η×X T X, definition: Substituting θ, A, and b into formula (2), we get the overdetermined equation: Aθ≈b Wherein, b is a formula representing the intermediate variables of the position information and positioning error information of the target node and each anchor node; The total least squares method is used to solve the overdetermined equation. The solution is as follows: The regularization strategy and quadratic constraints are used to transform the problem (3) into a fractional programming constrained optimization problem, as shown below: s.t.||Lθ|| 2 +2q T θ≤ρ (4) Where L = diag(1,1,0), q = [0,0,-1 / 2] T , ρ is a given positive constant; By introducing the expected value into the fractional programming constrained optimization problem, we get a variant of the fractional programming constrained optimization problem. The constrained optimization problem (4) can be reformulated as follows: Where E(·) represents the expectation. According to the properties of the expectation, formula (5) is converted into: s.t.||Lθ|| 2 +2q T θ≤ρ Here, ρ is a given positive constant.

8. The method for accurate target positioning in a non-line-of-sight environment according to claim 7, characterized in that: The solution of the optimal position coordinates includes the following steps: The fractional programming constrained optimization problem is converted into a non-convex parameter programming constrained optimization problem with only one constraint using the Dinkelbach algorithm. Problem (6) is equivalently converted into: s.t.||Lθ|| 2 +2q T θ≤ρ (7) Among them, τ i =E(b i ) is the i-th element of the matrix τ, ν=E(b t b); In the optimization problem (7), an unknown parameter μ is introduced using the Dinkelbach algorithm. Assume that μ * The function F(μ)=θ T A T Aθ-2τ T Aθ+ν+μ(||θ|| 2 +1), we can deduce Get μ * <0; Using the Lagrange multiplier method to solve the problem (7), the Lagrange function corresponding to the problem (7) is: L=||(Aθ-b)|| 2 +μ(||θ|| 2 +1)+α(||Lθ|| 2 +2q T i-r) Among them, α is a multiplier, and a necessary condition for the optimal solution is the gradient of the Lagrangian function Right now: From this we can deduce the optimal solution: i * =(A T A+μI+αL) -1 (A T τ-αq) (10) Where I is the third-order identity matrix. Substituting equation (10) into the inequality constraint, we obtain: ||L(A T A+μI+αL) -1 (A T τ-αq)|| 2 +2q(A T A+μI+αL) -1 (A T τ-αq)≤ρ Define M = A T A,N=A T τ, we get: Among them, m k ,n k ,l k ,q k are the elements on the diagonal of matrices M, N, L, and q respectively. The multiplier α is numerically solved by bisection or Newton's method. Due to the duality, A T A+μI+αL≥0, that is When l k <0: When l k >0 o'clock, The derivative of the function is: For all α, let φ ′ (α)<0, which means φ ′ (α) is strictly monotonically decreasing in this region, so the solution of φ(α)=0 is unique. According to the actual situation, L≥0, the equation φ(α)=0 in the interval There is a root in the memory. Use the bisection method or Newton's method to solve the parameter α, and use the Dinkelbach algorithm to solve the parameter μ. Substitute the values ​​of parameters α and μ into equation (10) to obtain the optimal solution θ * .

9. A precise target positioning system in a non-line-of-sight environment, characterized in that: The system includes: a memory and a processor, wherein the memory includes a program of a method for accurately locating a target in a non-line-of-sight environment, and when the program of the method for accurately locating a target in a non-line-of-sight environment is executed by the processor, the steps of a method for accurately locating a target in a non-line-of-sight environment as described in any one of claims 1 to 8 are implemented.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium includes a program for a method for accurately locating a target in a non-line-of-sight environment. When the program for the method for accurately locating a target in a non-line-of-sight environment is executed by a processor, the steps of a method for accurately locating a target in a non-line-of-sight environment as described in any one of claims 1 to 8 are implemented.

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