Three base station assisted vehicle positioning method based on adaptive near-end split sparse direction of arrival estimation
Patent Information
- Application Number
- CN202610584172.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-04-29
- Publication Date
- 2026-10-13
AI Technical Summary
[0004]本发明是为了克服现有技术中，基于稀疏表示的波达方向（DOA）估计方法计算复杂度过高，在要求高实时性的高机动性车联网场景中难以实际部署，且难以满足少快拍数据下快速定位需求的问题，提供了一种能够避免矩阵求逆与特征值分解、显著降低计算复杂度，并利用自适应步长加速收敛以实时定位的基于自适应近端分裂稀疏波达方向估计的三基站辅助车辆定位方法及系统
[0050]本发明是基于自适应近端分裂稀疏波达方向估计的三基站辅助车辆定位方法与系统，能够通过能够避免矩阵求逆以降低复杂度，并利用自适应步长加速收敛。相比于传统的稀疏恢复DOA算法，本发明的算法可以实现大大减小算法复杂度，且实现在低快拍场景的精确车辆定位。
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Figure CN122909507A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of intelligent transportation cooperative positioning technology, specifically to a three-base station assisted vehicle positioning method and system based on adaptive near-end splitting sparse wave direction-of-arrival estimation. Background Technology
[0002] Currently, with the rapid evolution of autonomous driving technology, the number of terminals such as autonomous vehicles in the Internet of Things (IoT) is increasing dramatically. High-precision vehicle positioning in the vehicle-to-everything (V2X) environment has become one of the key technologies for ensuring safe navigation. Accurate location information is the foundation for data transmission and vehicle-road cooperation, especially in highly mobile vehicle scenarios where the positioning system must possess excellent real-time response capabilities. In open environments where GNSS signals are available, fusing GPS and motion sensors can usually achieve effective positioning. However, in environments where GNSS is limited, such as urban canyons and tunnels, GPS signals are often unreliable or even completely lost. Therefore, assisted positioning technologies relying on radar and multi-sensor fusion have become a research hotspot.
[0003] Currently, target localization methods based on direction-of-arrival (DOA) estimation have attracted widespread attention due to their low dependence on channel environment. Compared to the limitations of received signal strength indication (RSI) techniques, which rely on prior knowledge of spatial fading, and time difference of arrival (TDA) techniques, which are highly sensitive to time measurement errors, the performance of DOA positioning mainly depends on the accuracy of angle estimation, which can be achieved through various array signal processing algorithms. Among them, subspace-based algorithms, such as multiple signal classification and estimation of signal parameters using rotation-invariant techniques, are typical examples. These methods divide the signal and noise subspaces by performing eigenvalue decomposition or singular value decomposition on the sample covariance matrix, achieving good estimation results in scenarios with sufficient signal-to-noise ratio and a large number of snapshots. However, due to the limitation of local perception in convolution operations, these subspace-based algorithms face severe challenges in practical vehicle-to-everything (V2X) applications. Because the high-speed movement of vehicles significantly compresses the coherence time of the wireless channel, the observation window is extremely limited, resulting in a severe shortage of available snapshots. Under conditions of low signal-to-noise ratio or small snapshots, the performance of subspace algorithms drops sharply. Moreover, their implementation usually requires a known number of information sources and involves high-dimensional matrix factorization, resulting in a heavy computational burden and making it difficult to meet the stringent real-time requirements of vehicle networking. Summary of the Invention
[0004] This invention aims to overcome the problems of high computational complexity in existing sparse representation-based direction-of-arrival (DOA) estimation methods, which are difficult to deploy in highly mobile vehicular networking scenarios requiring high real-time performance and cannot meet the rapid positioning needs with limited snapshot data. It provides a three-base station-assisted vehicle positioning method and system based on adaptive near-end splitting sparse DOA estimation, which avoids matrix inversion and eigenvalue decomposition, significantly reduces computational complexity, and utilizes adaptive step size to accelerate convergence for real-time positioning. To achieve the above-mentioned objectives, this invention adopts the following technical solution:
[0005] The three-base station vehicle localization method based on the APS-DOA optimization algorithm includes the following steps:
[0006] S1. Construct a three-base station model with known positioning and collect array signals containing vehicle location information;
[0007] S2, Building Integration The joint optimization objective function of norm and total variation constraint;
[0008] S3. Based on the optimization objective function, estimate the angle of arrival of the vehicle relative to the base station using the APS-DOA algorithm;
[0009] S4. Perform cross-positioning based on the vehicle's angle of arrival relative to the base station to obtain the vehicle's final high-precision coordinates.
[0010] The specific steps of step S2 are as follows:
[0011] S21. The array signal model formula is as follows:
[0012] ;
[0013] in, It is the received signal matrix. It is the source signal matrix. It is an array manifold matrix. K is the source-target index, and K is the number of sources. It is a noise signal matrix. A complete dictionary matrix is introduced. The sparse recovery formula is constructed as follows:
[0014] ;
[0015] in, It is the source signal Augmented matrix:
[0016] ;
[0017] according to Row sparsity and column smoothness (column vectors) (They are similar), so the DOA optimization problem is constructed as follows:
[0018] ;
[0019] in, and They represent Total variation of Norm, Is with the first The upper bound of the noise energy corresponding to each snapshot. This represents the regularization coefficient.
[0020] S22. To use the proximal splitting technique based on the primal-dual iterative scheme, an indicator function is introduced and utilized... The duality of norms will Rewritten as a maximum value of the matrix trace, the joint optimization objective function is constructed as a saddle point optimization problem:
[0021] ;
[0022] in, It is an indicator function, in the constraint set The value in the range is 0, and the value in the range is positive infinity. and Similarly.
[0023] The specific implementation process of step S3, estimating the angle of arrival of the vehicle relative to the base station, is as follows:
[0024] S31. The saddle point optimization problem is expanded into an iterative framework using the proximal splitting technique.
[0025] ;
[0026] ;
[0027] ;
[0028] in, and These are all iteration step sizes.
[0029] S32. Initialize iteration step size parameters , With regularization parameters Initialize variables , and ;
[0030] S33, Execute the original variables Projection calculation: intermediate variables Projected to the empirical error limit A defined set of constraints Above. Specifically, by calculating the observation residuals. And judge its Does the norm exceed the error limit? If it exceeds the limit, then use orthogonal basis matrices. The transpose is linearly corrected; if it does not exceed the limit, the original value is retained, thus directly obtaining the first value. The original variables of the next iteration ;
[0031] S34, Execute dual variables Projection calculation for matrix: = For each row vector in the array, calculate its corresponding... Norm; using a predefined nonlinear projection operator, each row vector is mapped to the unit sphere constrained space. Specifically, if the norm of a row vector is greater than 1, it is normalized and scaled; otherwise, its original value is preserved, thus obtaining the first... The first dual variable of the next iteration ;
[0032] S35, Execute dual variables Projection calculation: Same as S33, for the matrix = Performing the same operation yields the first The dual variable of the next iteration Introduction ;
[0033] S36. Check the backtracking condition; if it is not met, then let... and Calculate the original residuals With dual residual The search step size is dynamically adjusted based on the residual determination results;
[0034] S37. Repeat S33 to S36 until the stopping condition is met and the final original variable is obtained. This variable is used as the recovered sparse matrix and mapped to the angle dictionary to obtain the DOA estimation result.
[0035] The backtracking conditions for the test in step S36 are as follows:
[0036] For the current iteration sequence The energy evolution determination function based on quadratic terms is constructed as follows:
[0037] ;
[0038] in, This is a preset relaxation factor. This function evaluates the algorithm's convergence status in real time by comparing the sum of the squared deviations of the original and dual variables with the inner product of the differences between the original and dual variables. If this inequality is satisfied, the current calculation process is determined to be in a stable convergence region, and the next iteration is directly initiated. Otherwise, the current search step size is determined to be too large, triggering a backtracking mechanism and reducing the step size by a preset value. ;
[0039] The adaptive step size iterative adjustment in step S36 is as follows:
[0040] According to the The original variables obtained in the next iteration With dual variables Each is determined by the joint loss function. Calculate the original residuals that reflect the convergence state of the algorithm. With dual residual The calculation formula is as follows:
[0041] ;
[0042] A preset balance ratio threshold is used to determine the degree of balance between the original and dual domains in the current iteration process by comparing the Frobenius norms of the original and dual residuals. If the original residuals are too small, the balance is determined in real time. Significantly greater than the dual residual Then let , and Conversely, then let , and If the two are of similar size, the step size parameter remains unchanged. Among them, the fitness level parameter... With decay factor During the step size adjustment process, the fitness level is simultaneously reduced to ensure that the algorithm can smoothly converge in the later stages of iteration.
[0043] Step S4 performs cross-positioning based on the vehicle's angle of arrival relative to the base station, as detailed below:
[0044] S41, establish a two-dimensional rectangular coordinate system with the second base station among the three cooperating base stations as the origin. Combine this with the azimuth angles of the target vehicle corresponding to each base station obtained in step S3. , and Coordinates of the three cooperating base stations The system of equations is constructed as follows:
[0045] ;
[0046] in, This is the target location. By solving the problem in pairs, three sets of target location coordinates are obtained.
[0047] S42, based on the proportional relationship between the angular resolution of the uniform linear array and the cosine value of the target angle, the azimuth angle estimated by each base station is used. Calculate the corresponding reliability weighting factor The reliability weighting factor is used to perform a weighted fusion calculation on the three sets of vehicle candidate coordinate components, as shown in the following formula:
[0048] ;
[0049] in, This represents the total weighting coefficient. Finally, the vehicle target position is obtained. .
[0050] This invention relates to a three-base station-assisted vehicle localization method and system based on adaptive near-end splitting sparse direction-of-arrival (DOA) estimation. It reduces complexity by avoiding matrix inversion and accelerates convergence using an adaptive step size. Compared to traditional sparse recovery of DOA algorithms, this invention significantly reduces algorithm complexity and achieves accurate vehicle localization in low-speed-capture scenarios. Attached Figure Description
[0051] Figure 1 This is a flowchart illustrating a three-base station-assisted vehicle positioning method and system based on adaptive near-end splitting sparse wave direction-of-arrival estimation in this invention.
[0052] Figure 2 This is a schematic diagram of a specific model of three base stations in this invention.
[0053] Figure 3 This paper compares the accuracy of the DOA estimation method used in this invention with that of other methods at different snapshot numbers.
[0054] Figure 4-5 This invention provides a comparison of the vehicle positioning method used with other methods in low-speed snapshot scenarios. Detailed Implementation
[0055] To more clearly illustrate the embodiments of the present invention, specific implementation methods will be described below with reference to the accompanying drawings. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings and other implementation methods can be obtained based on these drawings without any creative effort.
[0056] Example:
[0057] like Figures 1-5 As shown, the three-base station vehicle localization method based on the APS-DOA optimization algorithm includes the following steps:
[0058] S1, Reference Figure 2 A three-base station model with known positioning was constructed, and array signals containing vehicle location information were collected.
[0059] S2, Building Integration Joint optimization objective function of norm and total variation constraints:
[0060] S21. The array signal model formula is as follows:
[0061] ;
[0062] in, It is the received signal matrix. It is the source signal matrix. It is an array manifold matrix. K is the source-target index, and K is the number of sources. It is a noise signal matrix. A complete dictionary matrix is introduced. The sparse recovery formula is constructed as follows:
[0063] ;
[0064] in, It is the source signal Augmented matrix:
[0065] ;
[0066] according to Row sparsity and column smoothness (column vectors) (They are similar), so the DOA optimization problem is constructed as follows:
[0067] ;
[0068] in, and They represent Total variation of Norm, Is with the first The upper bound of the noise energy corresponding to each snapshot. This represents the regularization coefficient.
[0069] S22. To use the proximal splitting technique based on the primal-dual iterative scheme, an indicator function is introduced and utilized... The duality of norms will Rewritten as a maximum value of the matrix trace, the joint optimization objective function is constructed as a saddle point optimization problem:
[0070] ;
[0071] in, It is an indicator function, in the constraint set The value in the range is 0, and the value in the range is positive infinity. and Similarly.
[0072] S3. Based on the optimization objective function, the APS-DOA algorithm is used to estimate the angle of arrival (AOA) of the vehicle relative to the base station.
[0073] The specific implementation process of step S3, estimating the angle of arrival of the vehicle relative to the base station, is as follows:
[0074] S31 uses the proximal splitting technique to expand the saddle point optimization problem into an iterative framework.
[0075] ;
[0076] ;
[0077] ;
[0078] in, and These are all iteration step sizes.
[0079] S32, Initialize iteration step size parameters , With regularization parameters Initialize variables , and ;
[0080] S33, execute the original variable Projection calculation: intermediate variables Projected to the empirical error limit A defined set of constraints Above. Specifically, by calculating the observation residuals. And judge its Does the norm exceed the error limit? If it exceeds the limit, then use orthogonal basis matrices. The transpose is linearly corrected; if it does not exceed the limit, the original value is retained, thus directly obtaining the first value. The original variables of the next iteration ;
[0081] S34, Perform dual variable Projection calculation for matrix: = For each row vector in the array, calculate its corresponding... Norm; using a predefined nonlinear projection operator, each row vector is mapped to the unit sphere constrained space. Specifically, if the norm of a row vector is greater than 1, it is normalized and scaled; otherwise, its original value is preserved, thus obtaining the first... The first dual variable of the next iteration ;
[0082] S35, Perform dual variable Projection calculation: Same as S33, for the matrix = Performing the same operation yields the first The dual variable of the next iteration Introduction ;
[0083] S36, check the backtracking condition; if it is not met, then let and Calculate the original residuals With dual residual The search step size is dynamically adjusted based on the residual determination results;
[0084] S37. Repeat S33 to S36 until the stopping condition is met and the final original variable is obtained. This variable is used as the recovered sparse matrix and mapped to the angle dictionary to obtain the DOA estimation result.
[0085] The backtracking conditions for the test in step S36 are as follows:
[0086] For the current iteration sequence The energy evolution determination function based on quadratic terms is constructed as follows:
[0087] ;
[0088] in, This is a preset relaxation factor. This function evaluates the algorithm's convergence status in real time by comparing the sum of the squared deviations of the original and dual variables with the inner product of the differences between the original and dual variables. If this inequality is satisfied, the current calculation process is determined to be in a stable convergence region, and the next iteration is directly initiated. Otherwise, the current search step size is determined to be too large, triggering a backtracking mechanism and reducing the step size by a preset value. ;
[0089] The adaptive step size iterative adjustment in step S36 is as follows:
[0090] According to the The original variables obtained in the next iteration With dual variables Each is determined by the joint loss function. Calculate the original residuals that reflect the convergence state of the algorithm. With dual residual The calculation formula is as follows:
[0091] ;
[0092] A preset balance ratio threshold is used to determine the degree of balance between the original and dual domains in the current iteration process by comparing the Frobenius norms of the original and dual residuals. If the original residuals are too small, the balance is determined in real time. Significantly greater than the dual residual Then let , and Conversely, then let , and If the two are of similar size, the step size parameter remains unchanged. Among them, the fitness level parameter... With decay factor During the step size adjustment process, the fitness level is simultaneously reduced to ensure that the algorithm can smoothly converge in the later stages of iteration.
[0093] S4. Cross-positioning is performed based on the vehicle's angle of arrival relative to the base station to obtain the vehicle's final high-precision coordinates.
[0094] refer to Figure 4 , 5 The image shows a comparison between the vehicle positioning method used in this invention and other methods in a low-speed snapshot scenario.
[0095] The compensation results show that the APS-DOA algorithm has a significant advantage in positioning accuracy in low-speed-capture scenarios. Other methods generally have larger average positioning errors and more outliers, indicating larger errors and insufficient stability. In contrast, the APS-DOA algorithm significantly suppresses this instability, resulting in a marked improvement in both positioning accuracy and stability throughout the simulation experiment.
[0096] Experimental results show that the three-base station-assisted vehicle positioning method and system based on adaptive near-end splitting sparse direction-of-arrival estimation can achieve accurate vehicle positioning in low-speed-capture scenarios.
[0097] The above description is merely a detailed explanation of preferred embodiments and principles of the present invention. For those skilled in the art, there may be changes in specific implementation methods based on the ideas provided by the present invention, and these changes should also be considered within the scope of protection of the present invention.
Claims
1. A three-base station-assisted vehicle localization method based on adaptive near-end splitting sparse direction-of-arrival estimation, characterized in that, Includes the following steps: S1. Construct a three-base station model with known positioning and collect array signals containing vehicle location information; S2, Building Integration The joint optimization objective function of norm and total variation constraint; S3. Based on the optimization objective function, estimate the angle of arrival of the vehicle relative to the base station using the APS-DOA algorithm; S4. Perform cross-positioning based on the vehicle's angle of arrival relative to the base station to obtain the vehicle's final high-precision coordinates.
2. The three-base station vehicle positioning method based on the APS-DOA optimization algorithm according to claim 1, characterized in that... In step S1, three cooperative base stations with known coordinates are deployed in the traffic environment, and the antenna arrays of each base station are used to capture array signals containing vehicle location information; a data model containing vehicle direction of arrival (DOA) parameters is established based on the received signals.
3. The three-base station vehicle positioning method based on the APS-DOA optimization algorithm according to claim 2, characterized in that... The specific implementation process of step S2 is as follows: S21. The array signal model formula is as follows: ； in, It is the received signal matrix. It is the source signal matrix. It is an array manifold matrix. K is the source-target index, and K is the number of sources. It is a noise signal matrix. A complete dictionary matrix is introduced. The sparse recovery formula is constructed as follows: ； in, It is the source signal Augmented matrix: ； according to Row sparsity and column smoothness (column vectors) (They are similar), so the DOA optimization problem is constructed as follows: ； in, and They represent Total variation of Norm, Is with the first The upper bound of the noise energy corresponding to each snapshot. This represents the regularization coefficient. S22. To use the proximal splitting technique based on the primal-dual iterative scheme, an indicator function is introduced and utilized... The duality of norms will Rewritten as a maximum value of the matrix trace, the joint optimization objective function is constructed as a saddle point optimization problem: ； in, It is an indicator function, in the constraint set The value in the range is 0, and the value in the range is positive infinity. and Similarly.
4. The three-base station vehicle positioning method based on the APS-DOA optimization algorithm according to claim 3, characterized in that... The specific implementation process of step S3 is as follows: S31. The saddle point optimization problem is expanded into an iterative framework using the proximal splitting technique. ； ； ； in, and These are all iteration step sizes. S32. Initialize iteration step size parameters , With regularization parameters Initialize variables , and ; S33, Execute the original variables Projection calculation: intermediate variables Projected to the empirical error limit A defined set of constraints Above. Specifically, by calculating the observation residuals. And judge its Does the norm exceed the error limit? If it exceeds the limit, then use orthogonal basis matrices. The transpose is linearly corrected; if it does not exceed the limit, the original value is retained, thus directly obtaining the first value. The original variables of the next iteration ; S34, Execute dual variables Projection calculation for matrix: = For each row vector in the array, calculate its corresponding... Norm; using a predefined nonlinear projection operator, each row vector is mapped to the unit sphere constrained space. Specifically, if the norm of a row vector is greater than 1, it is normalized and scaled; otherwise, its original value is preserved, thus obtaining the first... The first dual variable of the next iteration ; S35, Execute dual variables Projection calculation: Same as S33, for the matrix = Performing the same operation yields the first The dual variable of the next iteration Introduction ; S36. Check the backtracking condition; if it is not met, then let and Calculate the original residuals With dual residual The search step size is dynamically adjusted based on the residual determination results; S37. Repeat S33 to S36 until the stopping condition is met and the final original variable is obtained. This variable is used as the recovered sparse matrix and mapped to the angle dictionary to obtain the DOA estimation result.
5. The three-base station vehicle positioning method based on the APS-DOA optimization algorithm according to claim 4, characterized in that... The backtracking conditions for the verification in step S36 are as follows: For the current iteration sequence The energy evolution determination function based on quadratic terms is constructed as follows: ； in, This is a preset relaxation factor. This function evaluates the algorithm's convergence status in real time by comparing the sum of the squared deviations of the original and dual variables with the inner product of the differences between the original and dual variables. If this inequality is satisfied, the current calculation process is determined to be in a stable convergence region, and the next iteration is directly initiated. Otherwise, the current search step size is determined to be too large, triggering a backtracking mechanism and reducing the step size by a preset value. .
6. The three-base station vehicle positioning method based on the APS-DOA optimization algorithm according to claim 4, characterized in that... The adaptive step size iterative adjustment in step S36 is as follows: According to the The original variables obtained in the next iteration With dual variables Each is determined by the joint loss function. Calculate the original residuals that reflect the convergence state of the algorithm. With dual residual The calculation formula is as follows: ； A preset balance ratio threshold is used to determine the degree of balance between the original and dual domains in the current iteration process by comparing the Frobenius norms of the original and dual residuals. If the original residuals are too small, the balance is determined in real time. Significantly greater than the dual residual Then let , and Conversely, then let , and If the two are of similar size, the step size parameter remains unchanged. Among them, the fitness level parameter... With decay factor During the step size adjustment process, the fitness level is simultaneously reduced to ensure that the algorithm can smoothly converge in the later stages of iteration.
7. The three-base station vehicle positioning method based on the APS-DOA optimization algorithm according to claim 3, characterized in that... The specific implementation process of step S4 is as follows: S41, establish a two-dimensional rectangular coordinate system with the second base station among the three cooperating base stations as the origin. Combine this with the azimuth angles of the target vehicle corresponding to each base station obtained in step S3. , and Coordinates of the three cooperating base stations The system of equations is constructed as follows: ； in, This is the target location. By solving the problem in pairs, three sets of target location coordinates are obtained. S42, based on the proportional relationship between the angular resolution of the uniform linear array and the cosine value of the target angle, the azimuth angle estimated by each base station is used. Calculate the corresponding reliability weighting factor The reliability weighting factor is used to perform a weighted fusion calculation on the three sets of vehicle candidate coordinate components, as shown in the following formula: ； in, This is the total weighting coefficient. Finally, the vehicle target position is obtained. .