Reliable receiver subset selection method and system under non-line-of-sight condition

Abstract

The invention discloses a reliable receiver subset selection method and system under a non-line-of-sight condition, belongs to the technical field of time difference of arrival positioning, and solves the problem of false low residual but positioning errors caused by selection of subsets only depending on minimum fitting residual under a non-line-of-sight (NLOS) condition in the prior art. The method comprises the following steps: constructing a candidate receiver subset, and determining a traversal sequence; a balance parameter is introduced to form an extended set, screening is carried out, and a reliable newly-added receiver set is determined; and combining the candidate receiver subset with the reliable newly-added receiver set to obtain a reconstructed receiver set, and performing reference consistency check on the reconstructed receiver set to obtain a final reliable receiver set. The method is suitable for a time difference of arrival positioning scene.

Description

Technical Field

[0001] This invention belongs to the field of time difference of arrival positioning technology, specifically relating to a reliable receiver subset selection method under non-line-of-sight conditions. Background Technology

[0002] Time difference of arrival (TDOA) positioning is widely used in various positioning systems because it does not require absolute time synchronization between the transmitter and receiver networks. However, in non-line-of-sight (NLOS) environments, the direct path is often blocked, and multipath components introduce additional propagation delays, resulting in a positive bias in TDOA measurements and a significant decrease in positioning accuracy.

[0003] To mitigate the impact of NLOS, a common approach is to replace the traditional quadratic loss function with a robust loss function to reduce the dominance of large residuals on the estimation results. Typical robust loss functions include Smooth L1, Cauchy, and Geman–McClure. It should be noted that the effectiveness of such methods often relies on the assumption of "outlier sparsity." When the proportion of NLOS measurements is high, the robust penalty function's ability to suppress outliers will significantly decrease.

[0004] Another type of approach employs explicit bias modeling, treating the NLOS effect as a parameterized unknown bias, typically achieved by introducing balancing parameters or jointly estimating the location and bias. These methods mitigate the NLOS effect by estimating and compensating for the bias. However, when modeling biases for multiple measurement links simultaneously, the problem easily becomes underdetermined or unidentifiable, increasing optimization difficulty. To address this issue, existing methods impose stricter spatial constraints to limit the solvable region and guarantee solvability; other studies estimate the bias only for the reference receiver or reference path, thus avoiding the underdetermined problem.

[0005] In recent years, robust convex optimization methods based on the min–max framework have also been developed. These methods typically require an upper bound on the NLOS bias and minimizing the worst-case localization error within the corresponding uncertainty set to obtain a more stable solution under bias perturbations. The paper "Robust convex approximation methods for TDOA-based localization under NLOS conditions" proposes two approximate solution strategies based on convex relaxation within this framework, demonstrating good stability and robustness under different NLOS conditions. To mitigate the conservatism and performance loss caused by excessively large error bounds or insufficiently tight trigonometric inequality constraints, the paper "Consistent and accurate TDOA localization in dynamic NLOS environments via prior information independentestimation" further proposes an improved RLS form, introducing a balance parameter and utilizing the S-lemma to enhance the method's practicality.

[0006] In addition, another class of methods focuses on NLOS identification and measurement selection. These methods distinguish between LOS and NLOS measurements using information such as geometric consistency or signal characteristics, or detect outliers, and then perform localization based on a filtered subset of measurements or selected anchor points. Related work includes detection methods based on residual thresholds and consistency-based TDOA subset selection methods. The main risk of these methods is that NLOS measurements may be incorrectly retained; once biased NLOS measurements are included in the localization solution, the localization results will deteriorate significantly.

[0007] However, theoretically, if LOS / NLOS identification is accurate enough, localization based on a clean measurement set is closest to the ideal LOS scenario, and therefore has the potential to achieve near-optimal accuracy.

[0008] Although existing identification technologies have mitigated the impact of NLOS on TDOA localization to some extent, the following shortcomings still exist: (1) The receiver subset selection method based on minimum fitting residuals is unreliable: Existing technologies often employ the minimum fitting cost or minimum residual criterion to select the subset that minimizes the TDOA fitting error from multiple receiver subsets for positioning. However, under NLOS conditions, measurements affected by bias may geometrically create "spurious consistency," meaning that even if the positioning result deviates significantly from the true location, a small fitting residual may still occur, leading to the selection of an incorrect subset and reducing positioning reliability.

[0009] (2) Existing methods cannot fully utilize the one-sided characteristics of NLOS bias: The additional delay introduced by NLOS propagation has a non-negative one-sided property, but many existing methods have failed to effectively utilize this prior information during modeling or screening, resulting in limited ability to identify NLOS measurements and a tendency to misclassify or miss them.

[0010] (3) Single-shot decision-making mechanisms are susceptible to false positives: Some existing subset selection or measurement screening methods judge receiver subsets based on a single reference receiver or a single decision result. If the decision is affected by noise or geometric conditions and fails, the final positioning result will be greatly affected, and the overall robustness is insufficient. Summary of the Invention

[0011] This invention provides a reliable receiver subset selection method and system under non-line-of-sight (NLOS) conditions. Its purpose is to solve the problem that existing technologies rely solely on minimum fitting residuals to select subsets under NLOS conditions, resulting in false low residuals but incorrect positioning. Furthermore, it improves the accuracy of reliable receiver subset identification through multiple verifications and consistency checks, thereby enhancing positioning accuracy and stability.

[0012] In a first aspect, the present invention aims to provide a reliable receiver subset selection method under non-line-of-sight conditions, comprising the following steps: S1: Construct a subset of candidate receivers. For each candidate subset, select any receiver as the reference receiver. Use weighted least squares cost to characterize the fitting performance of the candidate subset. Calculate the cost value of each candidate subset. Sort all candidate subsets in ascending order of cost value to determine the traversal order. S2: Introduce a balance parameter, which is used to characterize the bias associated with the reference receiver; based on the sorted candidate subset, select any receiver that is not included in the current candidate subset and combine it with the current candidate subset to form an extended set; fix the reference receiver in the extended set, and use the TDOA measurement data in the extended set to jointly estimate the transmitter position and balance parameter; based on the preset threshold coefficient and the standard deviation estimate of the balance parameter, screen the newly added receivers in the extended set to determine a reliable set of newly added receivers; S3: Merge the subset of candidate receivers in S1 with the set of reliable new receivers obtained in S2 to form the reconstructed receiver set; S4: Perform a reference consistency check on the reconstructed receiver set to obtain the final reliable receiver set.

[0013] Furthermore, a preferred solution is provided: In S1, the subset of candidate receivers is constructed according to a preset number, which is 4.

[0014] Furthermore, a preferred solution is provided: in the calculation of the weighted least squares cost, the residual is the difference between the measured TDOA value and the ideal TDOA value, and the weight is a preset weight coefficient.

[0015] Furthermore, a preferred solution is provided: in S2, the joint estimation problem is solved by at least one optimization algorithm among the alternating direction multiplier method and the gradient method.

[0016] Furthermore, a preferred solution is provided: In S2, the specific judgment logic for screening is as follows: if the balance parameter corresponding to a newly added receiver meets the preset threshold condition, then the extended set is considered to contain NLOS-contaminated receivers, and the current candidate subset is rejected; if the balance parameter corresponding to all newly added receivers meets the reliability condition, then the newly added receiver is included in the reliable newly added receiver set; if the balance parameter corresponding to a newly added receiver does not meet the reliability condition, then the newly added receiver is considered to be affected by NLOS and is excluded.

[0017] Furthermore, a preferred embodiment is provided: S4 includes: traversing each receiver in the reconstructed receiver set as a reference receiver, performing weighted least squares positioning using the TDOA measurement data of the remaining receivers in the set to obtain multiple position estimates; calculating the average position of the multiple position estimates, and determining the maximum deviation of each position estimate from the average position; comparing the maximum deviation with a preset consistency threshold; if the consistency condition is met, the reconstructed receiver set is identified as a reliable receiver subset, and the average position is output as the final positioning result; if the consistency condition is not met, the next candidate subset is selected according to the traversal order of S1, and S2 to S4 are repeated until a reliable receiver subset that meets the consistency condition is obtained, which is taken as the final reliable receiver set, and the positioning result is output.

[0018] Furthermore, a preferred solution is provided: In step S2, using TDOA measurement data within the extended set, the transmitter position and balancing parameters are jointly estimated as follows: , in, Indicates the transmitter location. Represents the balance parameters. Indicates weight, , This represents the TDOA measurement model. Indicates the receiver coordinates. Indicates the speed of signal propagation.

[0019] Secondly, the object of the present invention is to provide a reliable receiver subset selection system under non-line-of-sight conditions, the system being implemented based on a reliable receiver subset selection method under non-line-of-sight conditions as described in any one or more of the above-described schemes, the system comprising: Subset construction and cost ranking module: used to construct candidate receiver subsets. For each candidate subset, any receiver in it is selected as the reference receiver. The weighted least squares cost is used to characterize the fitting performance of the candidate subset. The cost value of each candidate subset is calculated. All candidate subsets are sorted in ascending order of cost value to determine the traversal order. Subset expansion and balance parameter detection module: This module introduces balance parameters, which characterize the bias associated with the reference receiver; based on the sorted candidate subsets, it selects any receiver not included in the current candidate subset and combines it with the current candidate subset to form an expansion set; it fixes the reference receiver in the expansion set and uses TDOA measurement data within the expansion set to jointly estimate the transmitter position and balance parameters; based on preset threshold coefficients and the standard deviation estimation of the balance parameters, it filters newly added receivers in the expansion set to determine a reliable set of new receivers. Reliable Receiver Set Reconstruction Module: This module merges the candidate receiver subset from the subset construction and cost ranking module with the reliable new receiver set obtained from the subset expansion and balance parameter detection module to form a reconstructed receiver set. Reference consistency check module: Used to perform reference consistency checks on the reconstructed receiver set to obtain the final reliable receiver set.

[0020] Thirdly, the present invention aims to provide a computer device comprising a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes a reliable receiver subset selection method under non-line-of-sight conditions according to any one or more of the above-described schemes.

[0021] Fourthly, the present invention aims to provide a computer-readable storage medium for storing a computer program that executes a reliable receiver subset selection method under non-line-of-sight conditions as described in any one or more of the above-described schemes.

[0022] Compared with the prior art, the advantages of the present invention are: 1. Reduce the risk of false low residuals and significantly improve reliability in NLOS environments: Existing methods, when selecting subsets based solely on fitting residuals or costs, may suffer from NLOS bias, leading to geometrically "spurious consistency" in measurements and resulting in situations where "residuals are small but localization is incorrect." This invention does not directly rely on a single fitting result but expands the subset and repeatedly verifies it under multiple expanded configurations, significantly reducing the probability of misjudgment and thus improving the reliability of subset selection and localization results.

[0023] 2. Fully utilize the one-sided non-negativity of the additional latency of NLOS to improve NLOS identification and rejection capabilities: The additional delay introduced by NLOS has a non-negative property, but existing technologies often fail to effectively utilize this prior information. This invention, by introducing a balance parameter associated with the reference receiver and employing a threshold discrimination mechanism, can more effectively distinguish between random noise and systematic bias, thereby improving the ability to identify NLOS receivers / measurements and reducing missed detections and false detections.

[0024] 3. Shifting from a single decision-making process to multiple independent judgments improves resistance to noise and randomness: Some existing methods make a single judgment on a single subset or a single reference receiver, which is susceptible to noise disturbances or improper reference selection. This invention uses "subset expansion" to allow the same candidate subset to be judged repeatedly under multiple expansion configurations, forming multiple independent pieces of evidence. This significantly reduces the impact of a single misjudgment on the final result and improves overall robustness.

[0025] 4. Introduce a reference consistency check to suppress unstable positioning caused by geometric disadvantages and residual biases: Existing technologies lack systematic verification of positioning stability under different reference receiver selections, which can lead to unstable positioning results when receiver geometry is poor or residual NLOS effects exist. This invention evaluates whether position estimates are consistent under different reference selections through a consistency check, effectively filtering out receiver sets with unfavorable geometry or still affected by bias, thereby improving positioning stability and accuracy.

[0026] In summary, this invention can more reliably identify the set of available receivers in non-line-of-sight environments, significantly improving positioning accuracy and stability while maintaining good engineering feasibility and promotional value. This invention is applicable to time difference of arrival (TDOA) positioning scenarios. Attached Figure Description

[0027] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0028] Figure 1 A comparison chart showing the changes in RMSE for the three method variants described in a specific embodiment of the present invention; Figure 2 This is a comparison chart of the empirical cumulative distribution function of RMSE described in a specific embodiment of the present invention; Figure 3 This is a graph showing the relationship between the average running time and the number of receivers according to a specific embodiment of the present invention; Figure 4 This is a flowchart illustrating a reliable receiver subset selection method under non-line-of-sight conditions, as described in a specific embodiment of the present invention. Detailed Implementation

[0029] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application can also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of this application with unnecessary detail.

[0030] The technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0031] Many specific details are set forth in the following description in order to provide a full understanding of this application. However, this application may also be implemented in other ways different from those described herein. Those skilled in the art can make similar extensions without departing from the spirit of this application. Therefore, this application is not limited to the specific embodiments disclosed below.

[0032] Implementation Method 1 Reference Figure 4 This implementation method is described below.

[0033] This embodiment proposes a reliable receiver subset selection method under non-line-of-sight conditions. exist In space, let the receiver's coordinates be... The location of the unknown transmitter is The speed of signal propagation is , with receiver The ideal TDOA for reference is defined as follows: , (1) When the actual measured values ​​include Gaussian noise and NLOS additional delay, the TDOA measurement model is defined as follows: , (2) in Measurement error, Indicates receiver Additional latency (NLOS one-sided non-negative characteristic). Indicates receiver Additional latency.

[0034] The method includes the following steps: S1, Construct a subset of candidate receivers and sort them by cost: Construct a subset of candidate receivers consisting of a preset number of receivers to form a set of candidate subsets; For each candidate subset, select any receiver as a reference receiver, use weighted least squares cost to characterize the fitting performance of the candidate subset, calculate the cost value of each candidate subset, sort all candidate subsets by cost value from smallest to largest, and determine the traversal order. S2, Subset Expansion and Balance Parameter Detection: A balance parameter is introduced to characterize the bias associated with the reference receiver; based on the sorted candidate subsets, any receiver not included in the current candidate subset is selected and combined with the current candidate subset to form an expanded set; the reference receiver in the expanded set is fixed, and the transmitter position and balance parameters are jointly estimated using TDOA measurement data within the expanded set; based on a preset threshold coefficient and the standard deviation estimate of the balance parameters, newly added receivers in the expanded set are screened to determine a reliable set of newly added receivers; S3, Reconstruction of the Reliable Receiver Set: The current candidate subset in S1 is merged with the newly added reliable receiver set obtained in S2 to form a reconstructed receiver set; S4, Reference Consistency Check and Final Position Output: Perform a reference consistency check on the reconstructed receiver set. Iterate through each receiver in the reconstructed receiver set as a reference receiver, and use the TDOA measurement data of the other receivers in the set to perform weighted least squares positioning to obtain multiple position estimates. Calculate the average position of the multiple position estimates and determine the maximum deviation of each position estimate from the average position. Compare the maximum deviation with a preset consistency threshold. If the consistency condition is met, the reconstructed receiver set is identified as a reliable receiver subset, and the average position is output as the final positioning result. If the consistency condition is not met, select the next candidate subset according to the traversal order of S1, and repeat S2 to S4 until a reliable receiver subset that meets the consistency condition is obtained and the positioning result is output.

[0035] Implementation Method 2 This embodiment is a further illustrative example of S1 in the reliable receiver subset selection method under non-line-of-sight conditions described in Embodiment 1.

[0036] In S1 described in this embodiment, the preset quantity is 4, specifically including: In a two-dimensional positioning scenario, construct a set of all four receiver subsets. In the candidate subset Selecting a reference receiver within a subset Furthermore, the fitting ability of this subset under the optimal reference selection is measured using weighted least squares cost, which is: , (3) in, Represents the residual. Indicates the weight.

[0037] The above problem can be solved directly using the gradient method, which solves all of them. according to Sort the data from smallest to largest to determine the traversal order for subsequent checks.

[0038] Implementation Method 3 This embodiment is a further illustrative example of S2 in the reliable receiver subset selection method under non-line-of-sight conditions described in Embodiment 2.

[0039] To take advantage of the one-sided nature of the NLOS additional delay, this step introduces a balancing parameter. It is used to characterize the bias associated with the reference receiver and to perform joint estimation for each extended configuration.

[0040] For any sorted candidate subset and any receiver Construct an extended set And fixed. Reference receiver, using only the measurement pair middle Solve for the joint estimate: , (4) in, .

[0041] The aforementioned joint estimation problem is solved using at least one optimization algorithm, either the alternating direction multiplier method or the gradient method.

[0042] In this step, the specific judgment logic for screening is as follows: if the balance parameters corresponding to a newly added receiver meet the preset threshold condition, then the extended set is considered to contain NLOS-contaminated receivers, and the current candidate subset is rejected; if the balance parameters corresponding to all newly added receivers meet the reliability condition, then the newly added receiver is included in the reliable newly added receiver set; if the balance parameters corresponding to a newly added receiver do not meet the reliability condition, then the newly added receiver is considered to be affected by NLOS and is excluded.

[0043] Based on the above judgment logic, using Filtering based on the sign and threshold: Let the threshold coefficient be... and the standard deviation estimation of the equilibrium parameters If it exists ,satisfy Then it is determined Include NLOS-contaminated receivers and reject the candidate subset.

[0044] If for all satisfy If the added receiver is considered a reliable receiver, then the set of reliable new receivers is defined. If satisfied If so, adding a receiver is considered to be affected by NLOS and is therefore excluded.

[0045] S3. After the filtering is completed, the original candidate subset from S1 is merged with the set of reliable newly added receivers to obtain the reconstructed receiver set. .

[0046] Implementation Method 4 This embodiment is a further illustrative example of S4 in the reliable receiver subset selection method under non-line-of-sight conditions described in Embodiment 3.

[0047] S4 includes: traversing each receiver in the reconstructed receiver set as a reference receiver, performing weighted least squares positioning using the TDOA measurement data of the other receivers in the set to obtain multiple position estimates; calculating the average position of the multiple position estimates, and determining the maximum deviation of each position estimate from the average position; comparing the maximum deviation with a preset consistency threshold; if the consistency condition is met, the reconstructed receiver set is identified as a reliable receiver subset, and the average position is output as the final positioning result; if the consistency condition is not met, the next candidate subset is selected according to the traversal order of S1, and S2 to S4 are repeated until a reliable receiver subset that meets the consistency condition is obtained, which is taken as the final reliable receiver set, and the positioning result is output.

[0048] This step, to further suppress the effects of residual NLOS and avoid unstable localization results caused by geometrically unfavorable conditions, involves reconstructing the set. Linear reference consistency check. For each Certainly The reference receiver is used to perform weighted least squares positioning using measurements from the other receivers in the set.

[0049] , (5) The above problem is solved using the standard gradient method.

[0050] After solving, average the solution against the reference solution: , (6) The maximum deviation is defined as: , (7) If the consistency condition is met , It is the consistency threshold. Therefore, it is determined that... A reliable receiver set is used to output the final position estimate. .

[0051] If it does not meet the requirements, then remove it. Repeat steps S2 through S4 for the next sorted candidate subset until a subset that meets the conditions is obtained. The traversal is complete.

[0052] Implementation Method 5 This embodiment is a further illustrative example of a reliable receiver subset selection method under non-line-of-sight conditions as described in Embodiments 1 to 4.

[0053] In this embodiment, the number of receivers is set to... The positions are fixed and known, namely (-3,9), (-20,-8), (-14,-16), (-13,-6), (-4,2), (-12,15), (-20,-20), (20,-20), (-20,20) and (20,20) m.

[0054] In each test, the transmitter position From the region The values ​​are randomly generated from a uniform distribution. For receivers operating under non-line-of-sight (NLOS) conditions, the additional delay is independently generated from the interval. Extracted from a uniform distribution.

[0055] Let's assume a total of Independent Monte Carlo simulation experiments were conducted, and the corresponding position estimation results were obtained. Bit accuracy is evaluated using the root mean square error, which is defined as follows: The simulations were all performed on a standard PC equipped with an AMD Ryzen 9 5900HX processor.

[0056] The effectiveness of the proposed two-stage validation strategy was evaluated through ablation experiments.

[0057] Figure 1 (a) gives the additional delay with maximum NLOS. The changes in RMSE for the three method variants.

[0058] The minimum-cost subset selection method exhibits a large RMSE across the entire range, increasing from approximately 4 meters to 5 meters. This indicates that, under NLOS conditions, relying solely on small fitting residuals is not a reliable substitute for positioning accuracy. (Based solely on balance parameters...) The screening method shows a significant improvement in performance, with its RMSE stabilizing at around 1.7 meters. However, the method still has some performance limitations because the screening statistic cannot effectively exclude cases 3 and 4, where the estimated bias, although small, is not accurate. After further introducing a reference consistency test, the method proposed in this invention improves performance in all cases. The values ​​consistently maintain low RMSE, always below 1 meter, fully demonstrating the robustness of the joint strategy.

[0059] The proposed method is further compared with four baseline methods: the RLS method for worst-case optimization, the Smooth L1 method based on robust loss minimization, the NMI method based on residual and bias detection, and the GS-RSC method based on random sampling of the entire TDOA set combined with residual testing. In addition, a maximum likelihood estimation using only LOS measurements (LOS-only MLE) is introduced as an upper bound reference for performance. Figure 1 (b) Results show the RMSE as a function of the number of NLOS receivers. The NMI method produces the largest error among all comparison methods, mainly due to its potential selection of a subset of receivers with unfavorable geometry, thus amplifying the positioning error. Furthermore, the method's detection relies on a single decision based on a single subset, making it susceptible to false positives. Smooth L1 is an improvement over NMI but remains sensitive to NLOS bias. GS-RSC exhibits the best performance when the number of receivers affected by NLOS is small, as it utilizes the complete TDOA measurement set, providing more measurement information in lightly contaminated scenarios and improving positioning accuracy. However, as the degree of NLOS contamination increases, the probability of the complete measurement set containing multiple severely biased measurements rises rapidly, causing a sharp decline in GS-RSC performance, which falls short of the RLS method at approximately four NLOS receivers. The RMSE of RLS shows a moderate and approximately linear increase with the number of NLOS receivers. Under all test settings, the proposed method consistently maintains a low RMSE and its performance approaches the upper bound of the LOS-only MLE. The key reason is that this method expands the receiver combination, allowing the same basic combination to be judged multiple times, thereby reducing the probability of misclassification and improving robustness to NLOS.

[0060] Figure 2 (a) and Figure 2 (b) Empirical cumulative distribution functions (CDFs) of positioning errors are presented for 4 and 6 receivers affected by NLOS, respectively. The CDF curve of NMI grows relatively slowly, indicating a higher probability of generating large positioning errors. GS-RSC achieves smaller errors in some experiments, but its CDF curve exhibits a significant long-tail characteristic. This is mainly attributed to its random sampling and residual selection mechanism based on the full TDOA set, which rapidly decreases its success probability as the number of NLOS receivers increases. In contrast, the method proposed in this invention exhibits the steepest CDF curve in both scenarios, and its overall performance is closest to LOS-only MLE, indicating that the strategy of combining subset expansion and multiple decisions can effectively mitigate the impact of NLOS bias in most experiments.

[0061] Running time as a number of receivers The function is evaluated. For each The deployment area remained unchanged, and the receiver position was randomly generated in each Monte Carlo experiment. Subsequently, TDOA measurements were generated using the same noise level and NLOS model as in the previous experiments, and the average value was taken over the running time.

[0062] Figure 3 The average running time as a function of the number of receivers is given. The relationship of change. The Smooth L1 method varies within the test range. The changes are relatively small because the addition of a receiver only introduces limited computational overhead to its search process. The RLS method exhibits a similar trend, but its overall runtime is longer due to the involvement of semidefinite programming. The runtime of GS-RSC varies with... The speed increase is the fastest because the computational cost of its greedy search process rises sharply with the increase in the number of receivers. The runtime of NMI also increases rapidly. It is longer, but the growth rate is smaller than that of GS-RSC. Compared with the baseline methods mentioned above, the method proposed in this invention has different... It maintains low runtime under all conditions and exhibits good scalability.

[0063] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. A reliable receiver subset selection method under non-line-of-sight conditions, characterized in that, Includes the following steps: S1: Construct a subset of candidate receivers. For each candidate subset, select any receiver as the reference receiver. Use weighted least squares cost to characterize the fitting performance of the candidate subset. Calculate the cost value of each candidate subset. Sort all candidate subsets in ascending order of cost value to determine the traversal order. S2: Introduce a balancing parameter, which is used to characterize the bias associated with the reference receiver; Based on the sorted candidate subset, select any receiver that is not involved in the formation of the current candidate subset and combine it with the current candidate subset to form an extended set; The reference receiver in the fixed extended set uses the TDOA measurement data in the extended set to jointly estimate the transmitter position and balance parameters. Based on the standard deviation estimation of the preset threshold coefficient and balance parameter, the newly added receivers in the extended set are screened to determine the reliable set of newly added receivers; S3: Merge the subset of candidate receivers in S1 with the set of reliable new receivers obtained in S2 to form the reconstructed receiver set; S4: Perform a reference consistency check on the reconstructed receiver set to obtain the final reliable receiver set.

2. The reliable receiver subset selection method under non-line-of-sight conditions according to claim 1, characterized in that, In S1, the candidate receiver subset is constructed according to a preset number, which is 4.

3. The reliable receiver subset selection method under non-line-of-sight conditions according to claim 1, characterized in that, In the calculation of the weighted least squares cost, the residual is the difference between the measured TDOA value and the ideal TDOA value, and the weight is a preset weight coefficient.

4. The reliable receiver subset selection method under non-line-of-sight conditions according to claim 1, characterized in that, In S2, the joint estimation problem is solved by at least one optimization algorithm, namely the alternating direction multiplier method and the gradient method.

5. The reliable receiver subset selection method under non-line-of-sight conditions according to claim 1, characterized in that, In S2, the specific judgment logic for screening is as follows: if the balance parameter corresponding to a newly added receiver meets the preset threshold condition, then the extended set is considered to contain NLOS-contaminated receivers, and the current candidate subset is rejected; if the balance parameter corresponding to all newly added receivers meets the reliability condition, then the newly added receiver is included in the reliable newly added receiver set; if the balance parameter corresponding to a newly added receiver does not meet the reliability condition, then the newly added receiver is considered to be affected by NLOS and is excluded.

6. The reliable receiver subset selection method under non-line-of-sight conditions according to claim 1, characterized in that, S4 includes: traversing each receiver in the reconstructed receiver set as a reference receiver, performing weighted least squares positioning using the TDOA measurement data of the other receivers in the set to obtain multiple position estimates; calculating the average position of the multiple position estimates, and determining the maximum deviation of each position estimate from the average position; comparing the maximum deviation with a preset consistency threshold; if the consistency condition is met, the reconstructed receiver set is identified as a reliable receiver subset, and the average position is output as the final positioning result; if the consistency condition is not met, the next candidate subset is selected according to the traversal order of S1, and S2 to S4 are repeated until a reliable receiver subset that meets the consistency condition is obtained, which is taken as the final reliable receiver set, and the positioning result is output.

7. The reliable receiver subset selection method under non-line-of-sight conditions according to claim 1, characterized in that, In step S2, the transmitter position and balancing parameters are jointly estimated using TDOA measurement data from the extended set, as follows: ， in, Indicates the transmitter location. Represents the balance parameters. Indicates weight, , This represents the TDOA measurement model. Indicates the receiver coordinates. Indicates the speed of signal propagation.

8. A reliable receiver subset selection system under non-line-of-sight conditions, characterized in that, The system is implemented based on a reliable receiver subset selection method under non-line-of-sight conditions as described in any one of claims 1-7, and the system includes: Subset construction and cost ranking module: used to construct candidate receiver subsets. For each candidate subset, any receiver in it is selected as the reference receiver. The weighted least squares cost is used to characterize the fitting performance of the candidate subset. The cost value of each candidate subset is calculated. All candidate subsets are sorted in ascending order of cost value to determine the traversal order. Subset expansion and balance parameter detection module: This module introduces balance parameters, which characterize the bias associated with the reference receiver; based on the sorted candidate subsets, it selects any receiver not included in the current candidate subset and combines it with the current candidate subset to form an expansion set; it fixes the reference receiver in the expansion set and uses TDOA measurement data within the expansion set to jointly estimate the transmitter position and balance parameters; based on preset threshold coefficients and the standard deviation estimation of the balance parameters, it filters newly added receivers in the expansion set to determine a reliable set of new receivers. Reliable Receiver Set Reconstruction Module: This module merges the candidate receiver subset from the subset construction and cost ranking module with the reliable new receiver set obtained from the subset expansion and balance parameter detection module to form a reconstructed receiver set. Reference consistency check module: Used to perform reference consistency checks on the reconstructed receiver set to obtain the final reliable receiver set.

9. A computer device, characterized in that, The computer device includes a memory and a processor. The memory stores a computer program. When the processor runs the computer program stored in the memory, the processor executes a reliable receiver subset selection method under non-line-of-sight conditions according to any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium is used to store a computer program that executes a reliable receiver subset selection method under non-line-of-sight conditions according to any one of claims 1-7.

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