A toa-doa joint positioning method in a complex non-line-of-sight environment

Abstract

The application discloses a TOA-DOA joint positioning method in a complex non-line-of-sight environment. The method obtains the positions of reference nodes, TOA observations, array received signals and link state probabilities; non-line-of-sight deviation variables and link state probabilities are introduced, TOA cost items and DOA cost items are constructed based on a maximum likelihood estimation criterion, and a joint positioning target function is established; the target position and the non-line-of-sight deviation variable are iteratively updated through an alternating optimization mode, and the target position estimation result is output after the convergence condition is met. The application can directly utilize the array received signals to construct the position-related DOA cost, avoid error transmission caused by estimating the DOA angle first and then performing joint positioning, and adjust the non-line-of-sight deviation compensation strength by using the link state probability, thereby improving the positioning precision and robustness in the complex non-line-of-sight environment.

Description

Technical Field

[0001] This invention relates to the field of wireless positioning technology, and more specifically to a TOA-DOA joint positioning method in complex non-line-of-sight environments. Background Technology

[0002] High-precision location awareness is a core prerequisite for intelligent collaboration in the Internet of Things (IoT), unmanned systems, and wireless ad hoc networks. In GNSS-denied or signal-limited environments such as urban canyons and indoor spaces, the reliability of traditional satellite navigation systems drops sharply, often requiring the reliance on ground anchor nodes or multi-antenna arrays to construct local auxiliary positioning networks. Especially for highly dynamic wireless ad hoc networks, accurate node topology location is not only the foundation of location services but also a crucial cornerstone for efficient routing and collaborative detection. However, severe obstruction and multipath effects in complex electromagnetic propagation environments can easily degrade observation information. Therefore, exploring high-precision, robust wireless node positioning methods for complex environments has become a significant research hotspot in the interdisciplinary field of communication and navigation.

[0003] Among existing wireless positioning methods, joint positioning based on Time of Arrival (TOA) and Direction of Arrival (DOA) can simultaneously utilize ranging and angle information to create strong geometric constraints on the target object, thus exhibiting good positioning potential in complex environments. Especially in multi-base station collaborative sensing or array receiving scenarios, the TOA-DOA joint positioning method can comprehensively utilize the time delay observations of each base station and the array direction observations to improve the position estimation accuracy of the target or network node. However, in some existing schemes, TOA observations are usually directly used in positioning as ranging values, while for DOA observations, the angle of arrival parameter is usually estimated independently based on the array received signal first, and then the estimated angle parameter is input into the subsequent positioning model. Although this approach is more direct, it compresses the original array observations into an angle scalar, causing the angle estimation error to propagate into the position estimation process, making it difficult to fully utilize the structural information in the array received signal.

[0004] In practical applications, the propagation link between the target and the base station is often obstructed by buildings, walls, vehicles, or other obstacles, accompanied by complex propagation effects such as reflection, scattering, and diffraction, thus forming a non-line-of-sight (NLOS) propagation link. Under NLOS conditions, the signal propagation path is usually longer than the geometrically direct path, leading to a non-negative bias in TOA (Time of Arrival) observations. Simultaneously, the main incident direction of the array-received signal may deviate from the target's true geometric direction relative to the base station, contaminating DOA (Distance at Point of Arrival) observations with errors. These effects cause a mismatch between the joint localization model based on the ideal line-of-sight assumption and actual observations, thereby reducing the accuracy of target node position estimation, and in severe cases, even leading to significant deviations or failure of the localization results.

[0005] To address positioning errors caused by non-line-of-sight (NLOS) propagation, existing technologies have proposed various suppression schemes. One type of scheme introduces non-negative bias variables into the TOA observation model and utilizes L1 regularization terms to constrain the sparsity of the bias vector, thereby identifying and suppressing the impact of a small number of NLOS links on the positioning results. Another type of scheme corrects, weakens, or eliminates NLOS errors through statistical learning, error compensation, or line-of-sight / non-line-of-sight identification. While these schemes can improve positioning performance under certain conditions, they still have shortcomings: For methods using L1 regularized sparse bias modeling, they typically implicitly assume that only a small number of links are in NLOS. When multiple node signal links are simultaneously in NLOS states in complex environments such as severe obstruction, abundant reflections, or satellite denial, the bias vector often no longer satisfies the sparsity assumption, easily leading to prior mismatch. For methods based on error learning or signal recognition, they often use hard-decision results for line-of-sight / non-line-of-sight. When link state identification is misjudged, effective line-of-sight links are easily deleted, or links contaminated by non-line-of-sight are incorrectly retained, thus affecting the stability of the positioning results. Summary of the Invention

[0006] The purpose of this invention is to provide a TOA-DOA joint positioning method in complex non-line-of-sight environments, so as to improve the joint positioning accuracy and robustness in complex non-line-of-sight environments.

[0007] The technical solution to achieve the purpose of this invention is: a TOA-DOA joint localization method in complex non-line-of-sight environments, comprising the following steps:

[0008] Step 1: Build a scene model and obtain the data required for positioning;

[0009] Step 2: Construct the TOA cost term and DOA cost term based on the maximum likelihood estimation criterion;

[0010] Step 3: Construct a joint TOA-DOA localization objective function based on link state probabilities;

[0011] Step 4: Initialize the target position, and use the alternating optimization method to iteratively update the target position and the non-line-of-sight deviation of each link. After the iterative convergence condition is met, output the target position estimation result.

[0012] Compared with the prior art, the advantages of this invention are as follows: (1) Based on the maximum likelihood estimation criterion, this invention constructs the TOA cost term and DOA cost term, and directly introduces the array covariance matrix and array steering vector into the joint positioning objective function. It does not require the array to receive data to obtain the estimated angle value before participating in positioning, thereby reducing error propagation; (2) This invention introduces non-line-of-sight deviation variables and uses NLOS link state probability to adjust the deviation compensation intensity, so that the ranging residual can be adaptively corrected according to the link state, thereby reducing the impact of NLOS distance positive deviation on the positioning result; (3) This invention adopts probabilistic link state modeling, does not rely on strict LOS / NLOS hard decision, and does not completely rely on the NLOS deviation sparsity assumption. It has better adaptability and stability under different NLOS path numbers, different measurement noise levels and different link prior state probabilities. Attached Figure Description

[0013] Figure 1 This is a flowchart of a TOA-DOA joint positioning method in a complex non-line-of-sight environment according to the present invention.

[0014] Figure 2 This is a comparison chart of RMSE for different methods under different numbers of NLOS paths.

[0015] Figure 3 This is a comparison chart of RMSE for different methods under different distance measurement noise levels.

[0016] Figure 4 These are CDF curves showing the positioning errors of different methods.

[0017] Figure 5 This is a comparison chart of RMSE for different methods under different NLOS link prior state probability levels.

[0018] Figure 6 Different regularization parameters Below is a comparison chart of RMSE of the method of this invention. Detailed Implementation

[0019] Combination Figure 1 As shown, this invention provides a TOA-DOA joint localization method for complex non-line-of-sight (NOS) environments. It directly constructs location-related DOA costs based on array received signals and combines link state probabilities to more rationally adjust the NOS bias modeling and observation fusion process, thereby improving localization accuracy and robustness in complex propagation environments. The method includes the following steps:

[0020] Step 1: Establish a scene model and obtain the data required for localization, providing input for the subsequent construction of the TOA and DOA cost terms. The specific steps are as follows:

[0021] Step 1-1: Establish the position representation of the reference node and the target node. The nodes in this invention include reference nodes with known positions and target nodes with positions to be determined, assuming the presence of nodes within the set position region. The reference node with a known location, the first The position of each reference node Represented as

[0022]

[0023] in They represent the first The x and y coordinates of each reference node.

[0024] Target node location to be estimated Represented as

[0025]

[0026] in These represent the x-coordinate and y-coordinate of the target node to be located, respectively.

[0027] Steps 1-2, target node and the first The first reference node forms the... The measurement link, for the first The link is used to obtain the target node and the first link. TOA observations between reference nodes and the The array received signal matrix at each reference node .in This represents the corresponding distance value derived from the time obtained from TOA observations.

[0028] Steps 1-3, for the first The corresponding channel feature vectors are extracted from each link, and after sliding window denoising and normalization processing, the channel feature vectors are input into the pre-trained link state evaluation model to output the first link. The probability of a link belonging to non-line-of-sight propagation prior link state : .

[0029] The link state evaluation model is pre-trained using samples labeled with link propagation states, and the link state probability is used to characterize the first link state. The probability that a link is in a non-line-of-sight propagation state only reflects the non-line-of-sight confidence level characterized by the current physical characteristics of the channel.

[0030] Step 2: Construct the TOA cost term and DOA cost term based on the maximum likelihood estimation criterion. Specifically, the TOA cost term is constructed using the ranging error between the TOA observation value and the actual geometric distance from the target node to the reference node; the DOA cost term related to the target position is constructed based on the array received signal matrix and the array steering vector. The specific steps are as follows:

[0031] Step 2-1: Construct the geometric distances between the target node and each reference node. (Target node to reference node...) Geometric distance of each reference node Represented as

[0032]

[0033] in The L2 norm of a vector is used to calculate the geometric straight-line distance between two points in space.

[0034] Step 2-2, the The TOA observation model for each link is expressed as follows:

[0035]

[0036] in, Indicates the first The observation distance between each reference node and the target node Indicates the first Non-line-of-sight deviation of the link This indicates ranging noise. When the... When a link is more likely to be a LOS link, i.e. ,at this time , representing the TOA observation model for the LOS link; when the When a link is more likely to be an NLOS link, that is... ,at this time , representing the TOA observation model for the NLOS link.

[0037] Steps 2-3: Under the assumptions of line-of-sight propagation and non-line-of-sight propagation, the first... TOA weight of each link Defined as

[0038]

[0039] in, and They respectively represent when the first The TOA weights used when each reference node is in line-of-sight propagation and non-line-of-sight propagation environments. and They represent the first The ranging noise variance of a link under line-of-sight and non-line-of-sight propagation conditions. The TOA weights are determined by the maximum likelihood estimation criterion under the Gaussian noise assumption.

[0040] Steps 2-4: Construct the TOA cost term. Based on the maximum likelihood estimation criterion, the... The TOA cost term corresponding to each link can be expressed as:

[0041]

[0042] in Indicates the first The TOA cost item corresponding to each link.

[0043] Steps 2-5: Construct the geometric arrival angle. The target node is relative to the first... The geometric angle of arrival of each reference node is expressed as:

[0044]

[0045] in, Indicates from the first The angle between the direction of each reference node pointing to the target node and the array axis direction. In this embodiment, the element arrangement direction of the uniform linear array of each reference node is aligned with the global... Since the axes are aligned, the positive direction of the array axis is taken as the global axis. Positive direction of the axis. This is a bivariate arctangent function, used to calculate the difference between the ordinates. Difference between x and x coordinates The sign of the positive or negative value determines the correct quadrant in which the azimuth angle lies; its output range is typically [missing information]. .

[0046] Steps 2-6: Construct the array guidance vector according to the array structure. In the uniform linear array implementation, the first... Array steering vector of each reference node

[0047]

[0048] in, For the number of array elements, The distance between adjacent array elements. For the signal wavelength, It is the imaginary unit.

[0049] Steps 2-7, according to the... The array received signal matrix of the reference nodes Calculate the covariance matrix of the received signal.

[0050]

[0051] in, Indicates the number of snapshots. This indicates the conjugate transpose.

[0052] Steps 2-8: Construct the orthogonal projection matrix based on the array guide vector.

[0053]

[0054] in, Represents the orthogonal projection matrix. Represents the identity matrix.

[0055] Steps 2-9: Under the assumptions of line-of-sight propagation and non-line-of-sight propagation, the first... DOA weight of each link Defined as

[0056]

[0057] in, and They respectively represent when the first The DOA weights used when each reference node is in line-of-sight propagation and non-line-of-sight propagation environments. and They represent the first The array received noise power of each reference node under line-of-sight propagation and non-line-of-sight propagation conditions. and These represent the DOA adjustment coefficients under line-of-sight propagation and non-line-of-sight propagation conditions, respectively.

[0058] Step 2-10: Construct the DOA cost term. Based on the deterministic maximum likelihood estimation criterion, after eliminating the unknown signal parameters in the array received signal model, the... The DOA cost term corresponding to each link is represented as follows:

[0059]

[0060] in, Indicates the first The DOA cost of each link, This represents the matrix trace operation.

[0061] Step 3: Construct a joint TOA-DOA localization objective function based on link state probabilities. The non-line-of-sight (LOS) bias, TOA equivalent weight, DOA equivalent weight, and regularization constraint are adjusted using link state probabilities, and the TOA cost and DOA cost are merged into the joint localization objective function. The specific steps are as follows:

[0062] Step 3-1: Construct the TOA equivalent weights. Define the first... The equivalent weight of TOA for each link is

[0063]

[0064] in, Indicates the first The equivalent weight of TOA for each link is obtained based on the link state probability.

[0065] Step 3-2: Construct the equivalent weights of DOA. Define the first... The equivalent weight of DOA for each link is

[0066]

[0067] in, Indicates the first The DOA equivalent weight of each link is obtained based on the link state probability.

[0068] The equivalent weights for TOA and DOA are obtained by weighted averaging of the corresponding weights under both line-of-sight and non-line-of-sight propagation states based on the link state probability. These weights are used to continuously adjust the confidence of TOA and DOA observations when the link state is uncertain. When the value is large, the equivalent weight is closer to the weight under non-line-of-sight propagation conditions; when When the weight is smaller, the equivalent weight is closer to the weight under line-of-sight propagation conditions.

[0069] Step 3-3: Based on the link state probability, jointly model the TOA cost term, DOA cost term, and bias regularization term to obtain the joint localization objective function.

[0070]

[0071] in, Let be the objective function. This represents the deviation vector composed of non-line-of-sight deviation variables of each link. Represents the regularization parameter, link state probability. On the one hand, it is used to adjust the absorption intensity of non-line-of-sight bias on the distance measurement residual; on the other hand, it is used to adjust the equivalent weights corresponding to the TOA and DOA observation terms, and adjust the penalty intensity of the non-line-of-sight bias variable through the bias regularization term.

[0072] The joint localization problem can then be expressed as solving

[0073]

[0074] in To minimize the mathematical optimization operator.

[0075] Step 4: Initialize the target node position. Iteratively update the target node position and the non-line-of-sight deviation of each link using an alternating optimization method. Output the target position estimation result after the iterative convergence condition is met. The specific steps are as follows:

[0076] Step 4-1: Initialize the target node position to obtain the initial target node position estimate. .

[0077] In some implementations, the initial target node position estimate may be the center position of a preset positioning area, or it may be determined based on the TOA observation value, DOA observation value, or a coarse positioning result formed by a combination of the two. This invention does not limit this.

[0078] Step 4-2: Fix the target node position and update the non-line-of-sight deviation variable. In the... In this iteration, the estimated position of the current target node is fixed. Update the non-line-of-sight bias variable link by link. For the first link... For each link, the non-line-of-sight bias variable is updated to...

[0079]

[0080] in, Indicates the first During the nth iteration The non-line-of-sight deviation estimate for each link. This update formula is derived from the subproblem of optimizing the deviation variable after fixing the target node position.

[0081] Step 4-3: Fix the updated non-line-of-sight bias vector ,in, Indicates the first The estimated deviation vector value at the next iteration. The subproblem of updating the target position variable is represented as follows:

[0082]

[0083] The position update subproblem is solved using numerical optimization methods to obtain new estimates of the target node's position. ,in Indicates the first The target position estimate at the next iteration.

[0084] In this embodiment, the Levenberg-Marquardt (LM) method is used to solve the above position update subproblem. First, the first... TOA residuals of each link

[0085]

[0086] in, Indicates the first The TOA residual terms corresponding to each link, This represents the square root operation.

[0087] Further construct the first DOA equivalent residual term of each link

[0088]

[0089] in, Indicates the first The equivalent residual term of DOA for each link.

[0090] By combining the TOA residuals and DOA equivalent residuals of each link, we obtain the joint residual vector:

[0091]

[0092] in, This represents the joint residual vector consisting of the TOA residual term and the DOA equivalent residual term. This indicates the transpose operation.

[0093] Therefore, the target position update subproblem can be expressed as the following nonlinear least squares problem.

[0094]

[0095] Let the first The target position estimate for the next iteration is: Joint residual vector Regarding the target location The Jacobian matrix is

[0096]

[0097] in, Indicates the first The Jacobian matrix corresponding to the next iteration Represents the residual vector The first partial derivative with respect to the target position variable, Indicates the first The target position estimate at the next iteration.

[0098] Then the first The target position increment for the next iteration is

[0099]

[0100] in, Indicates the first The position increment of the next iteration. Indicates the damping factor. This represents the inverse operation. For the Jacobian matrix The transpose of .

[0101] Update the target position according to the position increment.

[0102]

[0103] in, Indicates the first The target position estimate obtained in the next iteration.

[0104] The inner layer iteration is stopped when the following inner layer convergence condition is met.

[0105]

[0106] in, This indicates the threshold for updating the inner layer position.

[0107] After the inner iteration stops, let

[0108]

[0109] Use it as the outermost layer The target position estimate for the next iteration.

[0110] Step 4-4: Stop iteration when the preset convergence condition is met; otherwise, repeat steps 4-2 and 4-3 for non-line-of-sight deviation variables. and target node position variables Alternating updates and optimizations are performed. The convergence condition includes at least one of the following:

[0111] The objective function value changes by less than a preset threshold; the target position changes by less than a preset threshold; the maximum number of iterations is reached. This can be expressed by the formula:

[0112]

[0113] in, Indicates the first The objective function value in the next iteration Indicates the first The objective function value in -1 iterations, This represents the threshold for the relative change of the objective function. To prevent small positive numbers with a denominator of zero, Indicates the threshold for the change in target position. Indicates the number of iterations. Indicates the maximum number of iterations. This indicates taking the absolute value.

[0114] Steps 4-5: Output the target location estimation result after iterative convergence to complete the localization.

[0115] The present invention will be further described in detail below with reference to embodiments.

[0116] This embodiment considers a single-target localization scenario within a two-dimensional plane. Unless otherwise specified, the default parameter settings in this embodiment are as follows: the localization area size is... Number of reference nodes The linear array elements are evenly distributed along the boundary of the positioning area. Array element spacing Take half the signal wavelength, number of snapshots The array-side signal-to-noise ratio is set to The TOA measurement noise follows a zero-mean Gaussian distribution with a uniform standard deviation set to 0. NLOS distance deviation Follow the interval Uniform distribution on, DOA adjustment coefficient NLOS additional angle deviation follows the interval Uniform distribution on the LOS link, the link state probability corresponding to the LOS link Follow the interval The uniform distribution on the NLOS link corresponds to the link status. Probability follows an interval The data is uniformly distributed on the network, with 5 NLOS paths, and the regularization parameter is set to... The number of Monte Carlo experiments was set to 1000. In the Monte Carlo experiment, the target location... It is randomly generated within the specified location area.

[0117] In this embodiment, the proposed TOA-DOA joint positioning method is compared with five representative positioning methods in the prior art. The five comparison methods include: standard distance positioning method using only TOA observations (TOA only), distance squared weighted least squares positioning method (SR-WLS), positioning method based on second-order cone programming convex relaxation (SOCP), positioning method based on grouped residual weighting (RWGH), and joint positioning method based on L1 norm regularization constraints (L1-JLE).

[0118] Figure 2 The figure shows a comparison of the RMSE of various localization methods under different numbers of NLOS paths. As can be seen from the figure, as the number of NLOS paths increases, the method of this invention achieves a lower RMSE and demonstrates better resistance to NLOS bias.

[0119] Figure 3The figure shows a comparison of the RMSE of various positioning methods under different standard deviations of measurement noise. As can be seen from the figure, the method of the present invention maintains a low RMSE under different measurement noise levels, indicating that it has better positioning robustness under varying TOA measurement noise conditions.

[0120] Figure 4 The empirical cumulative distribution function (CDF) curves of positioning errors for different methods are shown in the figure. As can be seen from the figure, the CDF curve of the method of this invention is closest to the upper left, indicating that it has a smaller positioning error at the same probability level and improves the stability of the positioning error distribution.

[0121] Figure 5 The figure shows a comparison of the RMSE of various positioning methods under different NLOS link prior probability levels. As can be seen from the figure, the method of this invention utilizes the NLOS link state probability to adjust the NLOS bias compensation intensity, and its RMSE decreases as the link prior probability level increases. The other four methods, since they do not utilize the NLOS link prior probability, have essentially unchanged RMSEs. This indicates that when the NLOS prior probability is high, the method of this invention can more accurately identify and compensate for non-line-of-sight biases, thereby achieving lower positioning errors.

[0122] Figure 6 For different regularization parameters The following is a comparison chart of the RMSE of the method of this invention. As can be seen from the chart, when the number of NLOS paths is small, each... The small differences in RMSE corresponding to the values ​​indicate that the method of this invention is insensitive to the regularization parameter in a mild NLOS environment; as the number of NLOS paths increases, the differences in RMSE between different values... The impact on positioning performance is gradually becoming apparent; when When the value is too large, the RMSE increases in high NLOS scenarios. The magnified area in the figure further illustrates the different values ​​under medium NLOS conditions. The subtle impact on positioning error demonstrates that a reasonable selection of regularization parameters can improve the positioning stability and accuracy of the method of this invention in complex NLOS environments.

Claims

1. A TOA-DOA joint positioning method in complex non-line-of-sight environments, characterized in that, Includes the following steps: Step 1: Build a scene model and obtain the data required for positioning; Step 2: Construct the TOA cost term and DOA cost term based on the maximum likelihood estimation criterion; Step 3: Construct a joint TOA-DOA localization objective function based on link state probabilities; Step 4: Initialize the target position, and use the alternating optimization method to iteratively update the target position and the non-line-of-sight deviation of each link. After the iterative convergence condition is met, output the target position estimation result.

2. The TOA-DOA joint positioning method in complex non-line-of-sight environments according to claim 1, characterized in that, The specific steps for step 1, which involves building a scene model and obtaining the data required for positioning, are as follows: Get the TOA observations corresponding to each link and array received signal matrix ; Extract the first The channel feature vectors of each link are denoised and normalized using a sliding window method and then input into a pre-trained link state evaluation model to obtain the prior link state probability that each link belongs to non-line-of-sight propagation. , .

3. The TOA-DOA joint positioning method in complex non-line-of-sight environments according to claim 1, characterized in that, Step 2, based on the maximum likelihood estimation criterion, involves the following specific steps for constructing the TOA cost term and DOA cost term: Step 2-1: Construct the target node to the... Geometric distance of each reference node ; Step 2-2, determine the first The TOA observation model for each link is specifically represented as follows: ； in, Indicates the first The observation distance between each reference node and the target node Indicates the first Non-line-of-sight deviation of the link Indicates ranging noise; Let each link be a priori link state probability belonging to non-line-of-sight propagation, when the... When a link is more likely to be a LOS link, i.e. ,at this time , representing the TOA observation model for the LOS link; when the When a link is more likely to be an NLOS link, that is... ,at this time , representing the TOA observation model for the NLOS link; Steps 2-3: Under the assumptions of line-of-sight propagation and non-line-of-sight propagation, determine the first... TOA weight of each link The TOA weight Including when the TOA weights used when each reference node is in line-of-sight propagation and non-line-of-sight propagation environments and ; Steps 2-4: Based on the maximum likelihood estimation criterion, determine the first... The TOA cost term corresponding to each link is specifically represented as follows: ； in, Indicates the first The TOA cost item corresponding to each link; Steps 2-5: Determine the target node relative to the first... Geometric angle of arrival of each reference node ; Steps 2-6: Construct array steering vectors based on array structure. ; Steps 2-7, according to the... The array received signal matrix of the reference nodes Calculate the covariance matrix of the received signal; Steps 2-8: Construct the orthogonal projection matrix based on the array steering vector, specifically as follows: ； in, Represents the orthogonal projection matrix. Represents the identity matrix; Steps 2-9: Under the assumptions of line-of-sight propagation and non-line-of-sight propagation, determine the first... DOA weight of each link , No. The DOA weight of the link includes when the first link... The DOA weights used when each reference node is in line-of-sight propagation and non-line-of-sight propagation environments; Step 2-10: Based on the deterministic maximum likelihood estimation criterion, after eliminating the unknown signal parameters in the array received signal model, determine the first... The DOA cost term corresponding to each link is specifically represented as follows: ； in, Indicates the first The DOA cost of each link, This represents the matrix trace operation.

4. The TOA-DOA joint positioning method in complex non-line-of-sight environments according to claim 3, characterized in that, When the TOA weights used when each reference node is in line-of-sight propagation and non-line-of-sight propagation environments and Specifically, they are: ； in, and They respectively represent when the first The TOA weights used when each reference node is in line-of-sight propagation and non-line-of-sight propagation environments. and They represent the first The variance of ranging noise for a link under line-of-sight propagation and non-line-of-sight propagation conditions.

5. The TOA-DOA joint positioning method in complex non-line-of-sight environments according to claim 3, characterized in that, The target node relative to the first Geometric angle of arrival of each reference node Specifically, it is expressed as: ； in,( ) is the first The coordinates of the reference nodes, ( () represents the coordinates of the target node. Indicates from the first The angle between the direction from each reference node to the target node and the direction of the array axis; For bivariate arctangent functions, their output range is typically... .

6. The TOA-DOA joint positioning method in complex non-line-of-sight environments according to claim 3, characterized in that, When the The DOA weights used for each reference node in both line-of-sight and non-line-of-sight propagation environments are as follows: ； in, and They respectively represent when the first The DOA weights used when each reference node is in line-of-sight propagation and non-line-of-sight propagation environments. and They represent the first The array received noise power of each reference node under line-of-sight propagation and non-line-of-sight propagation conditions. and These represent the DOA adjustment coefficients under line-of-sight propagation and non-line-of-sight propagation conditions, respectively.

7. The TOA-DOA joint positioning method in complex non-line-of-sight environments according to claim 1, characterized in that, The objective function for joint TOA-DOA localization based on link state probability constructed in step 3 is as follows: ； in, Let be the objective function. This represents the deviation vector composed of non-line-of-sight deviation variables of each link. Represents the regularization parameter. For the first The equivalent weight of TOA for each link, For the first The equivalent weights of DOA, TOA, and DOA for each link are obtained by weighted averaging of the corresponding weights under the link state probabilities for both line-of-sight and non-line-of-sight propagation states.

8. The TOA-DOA joint positioning method in complex non-line-of-sight environments according to claim 7, characterized in that, Step 4 initializes the target position. Iteratively updates the target position and the non-line-of-sight deviations of each link using an alternating optimization method. After the iterative convergence condition is met, the target position estimation result is output. The specific steps are as follows: Step 4-1: Initialize the target position to obtain the initial target position estimate. ; Step 4-2, in the In this iteration, the current target position estimate is fixed. Update the non-line-of-sight bias variables link by link; Step 4-3: Fix the updated non-line-of-sight bias vector The subproblem of updating the target position variable is represented as follows: ； The position update subproblem is solved using numerical optimization methods to obtain a new target position estimate. ; Step 4-4: Stop iterating when the preset convergence condition is met and obtain the target position estimate; otherwise, repeat steps 4-2 and 4-3. Steps 4-5: Output the target position estimation result after iterative convergence to complete the localization.

9. The TOA-DOA joint positioning method in complex non-line-of-sight environments according to claim 8, characterized in that, For the The update formula for the non-line-of-sight bias variable of the link is as follows: ； in, Indicates the first During the nth iteration The non-line-of-sight deviation estimate for each link.

10. The TOA-DOA joint positioning method in complex non-line-of-sight environments according to claim 8, characterized in that, The convergence condition includes at least one of the following: The change in the objective function value is less than a preset threshold; The change in the target position is less than a preset threshold; The maximum number of iterations has been reached.

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