A method and system for accurate target positioning in a non-line-of-sight environment

Abstract

The application discloses a kind of accurate target positioning method and system under non-line-of-sight environment.Method includes: the coordinate of N anchor nodes in positioning scene and a target node coordinate are substituted into distance formula, obtain the distance expression for representing target node and each anchor node between, carry out square expansion, obtain overdetermined equation and the intermediate variable matrix b that represents target node and the position information and positioning error information of each anchor node, overdetermined equation solving problem is converted into fractional programming constraint optimization problem, by introducing expected value to the optimization problem, obtain fractional programming constraint optimization problem variant;The optimization problem variant is converted into parameter programming constraint optimization problem, and matrix b is used to solve parameter programming constraint optimization problem using Lagrange multiplier method, and the optimal position coordinate is obtained.The application has low computational complexity and can effectively eliminate the influence of non-line-of-sight error in TOA measurement value.

Description

Technical Field

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

[0002] Target localization is an important method in wireless positioning technology, widely used in indoor positioning and tracking systems. To locate target nodes, ranging techniques based on TOA (Time of Arrival) are typically employed. TOA localization determines the target location by measuring the time of arrival of the signal between the transmitter and receiver. In specific environments, the signal propagation speed is known, and the distance between the two can be calculated by measuring the TOA. Multiple distance measurements can then be used to determine the target location. However, in actual signal propagation, the signal path may be blocked by obstacles, leading to severe degradation or even complete failure of the positioning system. In such cases, the measured TOA often contains various errors, primarily measurement noise and significant non-line-of-sight (NOS) errors, which drastically degrade positioning performance. Therefore, a high-precision and low-complexity positioning algorithm is essential for determining target locations in complex real-world environments.

[0003] Existing non-line-of-sight (NOS) error estimation methods are typically based on certain assumptions and statistical models, but noise in real-world environments can be far more complex, leading to performance degradation. To mitigate the impact of NOS errors on positioning performance, existing technologies disclose NOS error suppression methods for source localization. In the absence of prior knowledge about NOS errors, several algorithms have been proposed to address the target localization problem. For example, by applying the squared range (SR) and weighted least squares (WLS) criteria, the original localization problem is transformed into a generalized trust region subproblem (GTRS) framework, the solution of which is readily obtained through bisection. It is then 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 influence of non-line-of-sight (LOS) errors in TOA measurements. Therefore, a convex optimization localization algorithm for hybrid LOS / LOS environments is proposed. Considering LOS bias and measurement noise, the existing paper "A Convex Optimization Approach For NLOS Error Mitigation in TOA-Based Localization" proposes using the SDP method within a least squares (RTLS) framework with adjustment terms to solve the localization problem. This algorithm achieves high localization accuracy without requiring any prior knowledge of biases and non-LOS links. However, its computational complexity is not optimal, requiring a significant amount of time. Summary of the Invention

[0005] To overcome the problems of high computational complexity and difficulty in eliminating the influence of non-line-of-sight errors in TOA measurements in the prior art, this invention provides a method and system for accurate target localization in non-line-of-sight environments.

[0006] The primary objective of this invention is to solve the aforementioned technical problems. The technical solution of this invention is as follows:

[0007] The first aspect of this invention provides a method for accurate target localization 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 localization scene into the distance formula to obtain an expression representing the distance between the target node and each anchor node;

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

[0010] S3: The optimization problem variant is transformed into a parametric programming constraint optimization problem using a preset algorithm. The parametric programming constraint optimization problem is then solved using the Lagrange multiplier method in combination with matrix b to obtain the optimal position coordinates.

[0011] Furthermore, the pre-defined algorithm for converting the variant of the fractional programming constrained optimization problem into a parametric programming constrained optimization problem is the Dinkelbach algorithm.

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

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

[0014] Furthermore, the signal propagation link type between the target node and each anchor node includes: line-of-sight and non-line-of-sight; used to characterize the distance between the target node and each anchor node. The formula is shown below:

[0015]

[0016] in, These are the coordinates of the target node. This represents the coordinates of the i-th anchor node. Let be the measurement noise in the propagation path between the i-th anchor node and the target node, and let have a variance of . The zero-mean Gaussian distribution; This is a 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... The value is zero; if the signal propagation link type is non-line-of-sight, then .

[0017] Furthermore, the problem of solving overdetermined equations is transformed into a fractional programming constrained optimization problem, including the following steps:

[0018] Expanding equation (1) by squares, as shown below:

[0019]

[0020] in, Too small to be considered. , ,definition:

[0021]

[0022]

[0023]

[0024] Will , , Substituting into formula (2), we obtain the overdetermined equation:

[0025]

[0026] in, Formulas for representing intermediate variables such as the position information of the target node and each anchor node, and the positioning error information;

[0027] The overdetermined equations are solved using the total least squares method. The problem is as follows:

[0028]

[0029] By using regularization strategies and quadratic constraints, the problem (3) is transformed into a fractional programming constrained optimization problem, as shown below:

[0030]

[0031]

[0032] in, ρ is a given positive constant;

[0033] Introducing an expectation value into the fractional programming constrained optimization problem yields a variant of the fractional programming constrained optimization problem. The constrained optimization problem (4) is reformulated as follows:

[0034]

[0035] in, Expressing the expectation, based on the properties of expectation, formula (5) can be transformed into:

[0036]

[0037]

[0038] Where ρ is a given positive constant.

[0039] Furthermore, the solution for the optimal position coordinates includes the following steps:

[0040] Using the Dinkelbach algorithm, the fractional programming constrained optimization problem is transformed into a non-convex parametric programming constrained optimization problem with only one constraint. Problem (6) is equivalent to:

[0041]

[0042]

[0043] in, For matrix The i-th element, ;

[0044] In the optimization problem (7), an unknown parameter is introduced using the Dinkelbach algorithm. Assuming For function The zero point, from which the derivation is made

[0045]

[0046] get ;

[0047] Solving using the Lagrange multiplier method, the Lagrange function corresponding to problem (7) is:

[0048]

[0049] in, For a multiplier, a necessary condition for the optimal solution is the gradient of the Lagrange function. ,Right now:

[0050]

[0051] The optimal solution can be derived from this:

[0052] (10)

[0053] in, Given a 3x3 identity matrix, substituting equation (10) into the inequality constraints, we get:

[0054]

[0055] definition ,get:

[0056]

[0057] in, , They are matrices The elements on the diagonal are numerically solved for by the multiplier α using the bisection method or Newton's method. Due to duality, ,Right now .

[0058] when hour, ;when hour, The derivative of the function is:

[0059]

[0060] For all α, make This means It is strictly monotonically decreasing within this region, therefore The solution is unique, depending on the actual situation. ,equation In the interval The memory is located at a root, and the parameters can be solved using the binary search method or Newton's method. The parameter μ is solved using the Dinkelbach algorithm, and the parameter is... Substituting the values ​​of μ into equation (10), we obtain the optimal solution. .

[0061] A second aspect of the present invention provides a precise target localization system in a non-line-of-sight environment, comprising a memory and a processor. The memory includes a program for a precise target localization method in a non-line-of-sight environment, which, when executed by the processor, implements the steps of a precise target localization method in a non-line-of-sight environment.

[0062] A third aspect of the present invention provides a computer-readable storage medium including a program for a precise target localization method in a non-line-of-sight environment, wherein when the program is executed by a processor, it implements the steps of a precise target localization method in a non-line-of-sight environment.

[0063] Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

[0064] This invention introduces the expectation value approach to address the impact of non-line-of-sight (NOS) errors and measurement noise. In complex NOS / NOS mixed environments where the actual magnitudes of NOS errors and measurement noise are lacking, the expectation value of NOS errors and measurement noise is calculated to obtain a computational representation of the intermediate variable matrix characterizing the position information of the target node and each anchor node, as well as the positioning error information. This further yields the solution to the optimization problem, effectively eliminating the influence of NOS errors and measurement noise. By applying the Dinkelbach algorithm combined with the Lagrange multiplier method, the complex nonlinear problem is transformed into a series of easier-to-solve subproblems, similar to linear computation, simplifying the calculation process, significantly reducing computational complexity, and effectively alleviating the overall computational burden. Attached Figure Description

[0065] To make the objectives and technical solutions of this invention clearer, the following drawings are provided and described:

[0066] Figure 1 A flowchart of the method provided in an embodiment of the present invention;

[0067] Figure 2 This is a schematic diagram of an experimental scenario provided in an embodiment of the present invention;

[0068] Figure 3 A comparison chart of the root mean square error of various algorithms under different noise levels provided in the embodiments of the present invention;

[0069] Figure 4 A comparison chart of the root mean square error of various algorithms under different non-line-of-sight deviations provided in the embodiments of the present invention;

[0070] Figure 5 This is a comparison chart of the root mean square error of different anchor node numbers under different non-line-of-sight deviations provided in the embodiments of the present invention. Detailed Implementation

[0071] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0072] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0073] Example 1:

[0074] This invention provides a method for accurate target localization in non-line-of-sight environments, such as... Figure 1 The diagram shows a flowchart of a precise target localization method in a non-line-of-sight environment. The specific steps are as follows:

[0075] S1: Substitute the coordinates of N anchor nodes and one target node in the two-dimensional TOA positioning scene into the distance formula to obtain the distance expression used to characterize the distance between the target node and each anchor node.

[0076] More specifically, the signal propagation link types between the target node and each anchor node include: line-of-sight (LOS) and non-line-of-sight (NLOS).

[0077] The specific process is as follows:

[0078] Used to characterize the distance between the target node and each anchor node. The formula is shown below:

[0079]

[0080] in, These are the coordinates of the target node. This represents the coordinates of the i-th anchor node. Let be the measurement noise in the propagation path between the i-th anchor node and the target node, and let have a variance of . The zero-mean Gaussian distribution; This is a 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... The value is zero; if the signal propagation link type is non-line-of-sight, then .

[0081] In this example, the coordinates (in meters) of the 8 base stations are: (±20, ±20), (0, ±20), and (±20, 0). Assume there exists an actual target node to be located (-1.4538, -13.4756).

[0082] There are 3 line-of-sight links and 5 non-line-of-sight links.

[0083] noise variance The upper limit of the non-line-of-sight error is 3m. It is 10m.

[0084] The actual distances from the 8 base stations to the target node are as follows (in meters): 23.3644, 37.5809, 17.9055, 46.8695, 34.9870, 9.7718, 23.8485, and 28.9418.

[0085] Non-line-of-sight error (in meters): 0, 0, 0, 8.4431, 1.9476, 2.2592, 1.7071, 2.2766.

[0086] The measured noise levels (in meters) are: 3.7040, -0.6889, -4.5185, -1.3339, -0.4678, 0.8282, -0.7835, 1.3303.

[0087] S2: Expand the distance expression by square to obtain the overdetermined equation and the intermediate variable matrix b representing the position information of the target node and each anchor node and the positioning error information. Using the total least squares method (TLS), the overdetermined equation solving problem is transformed into a fractional programming constrained optimization problem by regularization strategy and quadratic constraints. By introducing the expectation value into the optimization problem, a variant of the fractional programming constrained optimization problem is obtained.

[0088] The specific process is as follows:

[0089] Expanding equation (1) by squares, as shown below:

[0090]

[0091] in, Too small to be considered. , ,definition:

[0092]

[0093]

[0094]

[0095] Will , , Substituting into formula (2), we obtain the overdetermined equation:

[0096]

[0097] in, Formulas for representing intermediate variables such as the position information of the target node and each anchor node, and the positioning error information;

[0098] The overdetermined equations are solved using the total least squares (TLS) method, as shown in the following problem:

[0099]

[0100] Since the coefficient matrix A is ill-posed, the least squares method (TLS) will produce poor-quality solutions. By using regularization strategies and quadratic constraints, the problem (3) is transformed into a fractional programming constrained optimization problem, as shown below:

[0101]

[0102]

[0103] in, ρ is a given positive constant with a value of 3;

[0104] In practice, noise measurement Non-line-of-sight error It cannot be fully known, therefore the matrix It cannot be calculated directly. The aim is to find the matrix by calculating the expectation of errors and measurement noise in the non-line-of-sight environment of the constrained optimization problem. The expectation, thus obtaining The calculation representation.

[0105] Introducing an expectation value into the fractional programming constrained optimization problem yields a variant of the fractional programming constrained optimization problem. The constrained optimization problem (4) is reformulated as follows:

[0106]

[0107] in, Expressing the expectation, based on the properties of expectation, formula (5) can be transformed into:

[0108]

[0109]

[0110] Where ρ is a given positive constant with a value of 3.

[0111] The expected value is introduced to handle the influence of non-line-of-sight errors and measurement noise. In complex line-of-sight / non-line-of-sight mixed environments and when the actual values ​​of non-line-of-sight errors and measurement noise are not available, the expected value of non-line-of-sight errors and measurement noise is calculated to obtain the intermediate variable matrix representing the position information of the target node and each anchor node and the positioning error information. The solution to the optimization problem is then obtained, effectively eliminating the influence of non-line-of-sight errors and measurement noise.

[0112] S3: The Dinkelbach algorithm is used to transform the variant of the optimization problem into a non-convex parametric programming constraint optimization problem with only one constraint. The Lagrange multiplier method is then used to solve the parametric programming constraint optimization problem in combination with matrix b to obtain the optimal position coordinates.

[0113] The specific process is as follows:

[0114] Using the Dinkelbach algorithm, the fractional programming constrained optimization problem is transformed into a non-convex parametric programming constrained optimization problem with only one constraint. Problem (6) is equivalent to:

[0115]

[0116]

[0117] in, For matrix The i-th element, ;

[0118] In the optimization problem (7), an unknown parameter is introduced using the Dinkelbach algorithm. Assuming For function The zero point, from which the derivation is made

[0119]

[0120] get ;

[0121] Solving the problem using the Lagrange multiplier method transforms the complex nonlinear problem into a series of easier-to-solve subproblems, similar to linear computation. This simplifies the calculation process, significantly reduces computational complexity, and effectively alleviates the overall computational burden. The Lagrange function corresponding to problem (7) is:

[0122]

[0123] in, For a multiplier, a necessary condition for the optimal solution is the gradient of the Lagrange function. ,Right now:

[0124]

[0125] The optimal solution can be derived from this:

[0126] (10)

[0127] in, Given a 3x3 identity matrix, substituting equation (10) into the inequality constraints, we get:

[0128]

[0129] definition ,get:

[0130]

[0131] in, , They are matrices The elements on the diagonal are numerically solved for by the multiplier α using the bisection method or Newton's method. Due to duality, ,Right now .

[0132] when hour, ;when hour, The derivative of the function is:

[0133]

[0134] For all α, make This means It is strictly monotonically decreasing within this region, therefore The solution is unique, depending on the actual situation. ,equation In the interval The memory is located at a root, and the parameters can be solved using the binary search method or Newton's method. The parameters are solved using the Dinkelbach algorithm. , parameters and Substituting the value into equation (10), we obtain the optimal solution. In this example, the optimal solution coordinates are (-1.4044, -13.0838), and the root mean square error of the location is 0.394943m.

[0135] To evaluate the performance of the RTLS-Dinkelbach method, comparative experiments were conducted with existing schemes RTLS-SDP, RSOCP, and SR-WLS. In the simulation, all anchor nodes were randomly placed within a 50m × 50m area, and in each Monte Carlo (MC) test, the target node was randomly selected from the same area. (Measurement noise...) It follows a pattern with a mean of zero and a variance of . The Gaussian distribution, i.e., when i=1,...,N, Assuming the maximum value of the non-line-of-sight deviation is λ = 10m, that is, the non-line-of-sight deviation... .like Figure 3 The figure shown is a comparison of the root mean square error of each algorithm under different noise levels. Figure 4 The figure shows a comparison of the root mean square error of each algorithm under different non-line-of-sight deviations.

[0136] The experimental results demonstrate the performance of the RTLS-Dinkelbach algorithm under different noise levels and non-line-of-sight (NLOS) bias conditions. With increasing interference, the root mean square error (RMSE) of the RTLS-Dinkelbach algorithm gradually increases. Nevertheless, its RMSE value remains relatively low, second only to the best-performing RTLS-SDP method. This indicates that the RTLS-Dinkelbach algorithm exhibits high robustness in handling noise and NLOS bias.

[0137] Table 1 below provides a comparative analysis of the average running time of various algorithms. The analysis results show that the RTLS-Dinkelbach method of this invention is significantly better than other existing methods in terms of running efficiency. This significant improvement means higher processing speed and lower latency in practical applications.

[0138] Table 1

[0139]

[0140] like Figure 5 The figure shows a comparison of the root mean square error (RMSE) of the present invention for different numbers of anchor nodes under different non-line-of-sight deviations. As can be seen from the figure, when λ is the same, that is, under the same non-line-of-sight deviation condition, the RMSE decreases as the number of anchor nodes increases. The proposed algorithm does not suffer from a performance degradation due to the increase in the number of anchor nodes, indicating that the algorithm has good robustness.

[0141] Example 2:

[0142] This embodiment provides a precise target positioning system in a non-line-of-sight environment, including a memory and a processor. The memory includes a program for a precise target positioning method in a non-line-of-sight environment. When the processor executes the program for a precise target positioning method in a non-line-of-sight environment, it implements the steps of a precise target positioning method in a non-line-of-sight environment as described in Embodiment 1.

[0143] Example 3:

[0144] This embodiment provides a computer-readable storage medium that includes a program for a precise target localization method in a non-line-of-sight environment. When the program is executed by a processor, it implements the steps of a precise target localization method in a non-line-of-sight environment as described in Embodiment 1.

[0145] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A method for precise target localization in a non-line-of-sight environment, characterized in that, Includes the following steps: S1: Substitute the coordinates of N anchor nodes and one target node in the localization scene into the distance formula to obtain an expression representing the distance between the target node and each anchor node; S2: Expand the distance expression by square to obtain the overdetermined equation and the intermediate variable matrix b representing the position information and positioning error information of the target node and each anchor node. Use regularization strategy and quadratic constraints to transform the overdetermined equation solving problem into a fractional programming constrained optimization problem. By introducing the expectation value into the optimization problem, a variant of the fractional programming constrained optimization problem is obtained. S3: Use a preset algorithm to convert the variant of the optimization problem into a parametric programming constraint optimization problem, and use the Lagrange multiplier method to solve the parametric programming constraint optimization problem in combination with matrix b to obtain the optimal position coordinates; The signal propagation link types between the target node and each anchor node include: line-of-sight and non-line-of-sight; these are used to characterize the distance between the target node and each anchor node. The formula is shown below: in, These are the coordinates of the target node. This represents the coordinates of the i-th anchor node. Let be the measurement noise in the propagation path between the i-th anchor node and the target node, and let have a variance of . The zero-mean Gaussian distribution; This is a 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... The value is zero; if the signal propagation link type is non-line-of-sight, then ; Transforming the overdetermined equations problem into a fractional programming constrained optimization problem includes the following steps: Expanding equation (1) by squares, as shown below: in, Too small to be considered. , ,definition: Will , , Substituting into formula (2), we obtain the overdetermined equation: in, Formulas for representing intermediate variables such as the position information of the target node and each anchor node, and the positioning error information; The overdetermined equations are solved using the total least squares method. The problem is as follows: By using regularization strategies and quadratic constraints, the problem (3) is transformed into a fractional programming constrained optimization problem, as shown below: in, ρ is a given positive constant; Introducing an expectation value into the fractional programming constrained optimization problem yields a variant of the fractional programming constrained optimization problem. The constrained optimization problem (4) is reformulated as follows: in, Expressing the expectation, based on the properties of expectation, formula (5) can be transformed into: Where ρ is a given positive constant; Solving for the optimal position coordinates includes the following steps: Using the Dinkelbach algorithm, the fractional programming constrained optimization problem is transformed into a non-convex parametric programming constrained optimization problem with only one constraint. Problem (6) is equivalent to: in, For matrix The i-th element, ; In the optimization problem (7), an unknown parameter is introduced using the Dinkelbach algorithm. Assuming For function The zero point, from which the derivation is made get ; Solving using the Lagrange multiplier method, the Lagrange function corresponding to problem (7) is: in, For a multiplier, a necessary condition for the optimal solution is the gradient of the Lagrange function. ,Right now: The optimal solution can be derived from this: （10） in, Given a 3x3 identity matrix, substituting equation (10) into the inequality constraints, we get: definition ,get: in, , They are matrices The elements on the diagonal are numerically solved for by the multiplier α using the bisection method or Newton's method. Due to duality, ,Right now ; when hour, ;when hour, The derivative of the function is: For all α, make This means It is strictly monotonically decreasing within this region, therefore The solution is unique, depending on the actual situation. ,equation In the interval The memory is located at a root, and the parameters can be solved using the binary search method or Newton's method. The parameter μ is solved using the Dinkelbach algorithm, and the parameter is... Substituting the values ​​of μ into equation (10), we obtain the optimal solution. .

2. The method for precise target localization 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 precise target localization in a non-line-of-sight environment according to claim 1, characterized in that, The default algorithm for converting a variant of a fractional programming constrained optimization problem into a parametric programming constrained optimization problem is the Dinkelbach algorithm.

4. The method for precise target localization 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 precise target localization 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. A precise target positioning system in a non-line-of-sight environment, characterized in that, The system includes: a memory and a processor. The memory includes a program for a precise target localization method in a non-line-of-sight environment. When the processor executes the program for the precise target localization method in a non-line-of-sight environment, it implements the steps of a precise target localization method in a non-line-of-sight environment as described in any one of claims 1 to 5.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a program for a precise target localization method in a non-line-of-sight environment. When the program is executed by a processor, it implements the steps of a precise target localization method in a non-line-of-sight environment as described in any one of claims 1 to 5.

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