Unmanned aerial vehicle DOA joint estimation method based on dual-polarization RIS assistance

Abstract

The invention discloses an unmanned aerial vehicle DOA joint estimation method based on dual-polarization RIS assistance, and the method comprises the steps: designing a joint reflection matrix of a dual-polarization RIS, and fully utilizing the polarization diversity characteristic to extend the degree of freedom of an array, thereby achieving the effective discrimination of more signal sources under the same physical aperture; the RIS phase is optimized by means of a random optimization subspace mapping algorithm, a high-dimensional problem is subjected to dimension reduction processing through a random projection technology, and the calculation complexity is remarkably reduced while convergence is guaranteed; and a spatial spectrum function is constructed based on a multi-signal classification algorithm, and high-precision and high-resolution DOA estimation is realized by combining global spectrum peak search and a characteristic subspace orthogonality principle. According to the method, the signal source resolution capability and the estimation precision of unmanned aerial vehicle positioning are effectively improved, and meanwhile, the calculation efficiency and the system reliability are better.

Description

Technical Field

[0001] This invention belongs to the field of unmanned aerial vehicle (UAV) technology, specifically relating to a joint estimation method for UAV DOA based on dual-polarization RIS-assisted estimation. Background Technology

[0002] With the rapid development of 6G communication technology, drones, with their advantages of high mobility, flexible deployment, and low cost, have become key nodes in the integrated air-space-ground network, demonstrating enormous potential in fields such as military reconnaissance, emergency rescue and disaster relief, and smart logistics. Meanwhile, Reconfigurable Smart Surfaces (RIS), as an emerging electromagnetic control technology, provide a revolutionary solution for overcoming the line-of-sight (LoS) limitations of traditional communication and optimizing channel conditions by intelligently reconfiguring the wireless propagation environment. Deeply integrating RIS technology with drone systems not only fully leverages the synergistic advantages of drone three-dimensional maneuverability and RIS dynamic beamforming, but also significantly improves positioning accuracy and communication reliability in complex environments. Especially in scenarios where traditional positioning technologies are limited, such as urban canyons and areas with strong interference, RIS-assisted drone positioning systems can effectively overcome multipath effects and signal obstruction problems by optimizing signal reflection paths in real time. This provides an innovative technical approach for the high-precision, high-dynamic positioning requirements of 6G networks, representing an important direction for the future development of integrated intelligent communication and sensing.

[0003] Classical direction-of-arrival (DOA) estimation methods, such as the Multi-Signal Classification (MUSIC) algorithm based on subspace decomposition, the Signal Parameter Estimation (ESPRIT) algorithm based on rotation invariant techniques, and minimum variance distortionless response beamforming, perform well in high signal-to-noise ratio (SNR) environments. However, they still have significant limitations in practical applications, including significant performance degradation under low SNR conditions, difficulty in handling coherent sources, and high computational complexity. While single-polarization RIS-assisted DOA estimation can improve the signal propagation environment through intelligent reflection, the limited polarization degrees of freedom make it difficult to fully utilize the spatial characteristics of the signal under finite physical aperture conditions, resulting in insufficient resolution of multiple signal sources. Especially in complex electromagnetic environments and dynamic scenarios, the single-polarization design further restricts the system's degrees of freedom. This causes the inherent angle estimation performance bottleneck of traditional arrays to overlap with the polarization constraints of RIS, jointly limiting the application effect of existing DOA estimation technologies in complex scenarios such as 6G integrated air-space-ground networks. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, this invention provides a joint DOA estimation method for UAVs based on dual-polarized RIS (Reflection-Reflection Matrix) assistance. By designing a joint reflection matrix for dual-polarized RIS, the polarization diversity characteristic is fully utilized to expand the array's degrees of freedom, thereby achieving effective resolution of more signal sources under the same physical aperture. The RIS phase is optimized using a stochastic subspace mapping algorithm, and the high-dimensional problem is reduced through stochastic projection techniques, significantly reducing computational complexity while ensuring convergence. Furthermore, a spatial spectral function is constructed based on a multiple signal classification algorithm, and combined with global spectral peak search and the orthogonality principle of feature subspaces, high-precision, high-resolution DOA estimation is achieved. This invention effectively improves the signal source resolution capability and estimation accuracy of UAV positioning, while also possessing superior computational efficiency and system reliability.

[0005] The technical solution adopted by this invention to solve its technical problem is as follows: Step 1: Construct the dual-polarization RIS array steering vector matrix and EMVS receiver array configuration parameters; Step 2: Receive the UAV dual-polarization signal based on the steering vector matrix and perform polarization separation preprocessing; Step 3: Construct a joint received data matrix containing horizontal / vertical polarization using the polarization-separated signals; Step 4: Optimize and generate the optimal dual-polarization RIS joint reflection matrix using the ROSM algorithm; Step 5: Calculate the polarization-space joint covariance matrix and perform eigenvalue decomposition to extract the signal subspace and noise subspace; Step 6: Based on the noise subspace and the dual-polarization steering vector, construct the dual-polarization MUSIC spatial spectrum function, and search for the spatial spectrum peaks to obtain the final two-dimensional DOA estimate; Step 7: Calculate RMSE and CRLB theoretical lower bound to evaluate the estimation performance; Preferably, step 1 specifically comprises: Step 1-1: Define A drone target, define the target. The incident azimuth angle of the signal is The pitch angle is The array at the receiving end consists of It consists of individual array elements; RIS is composed of It consists of 1 unit, with a unit spacing of half a wavelength. The reflected signal is divided into horizontal polarization components. and vertical polarization components Its expression is as follows: (1) (2) in, These are the horizontal and vertical initial phases of the simulated RIS cell, respectively, and are of length [missing information]. A random vector, each element of which independently follows a uniform distribution; the Toeplitz matrix simulates the mutual coupling between RIS units; Step 1-2: Define the array response vector The expression is as follows, which characterizes the signal from the direction The collection of phase delays induced at the incident points on each sensor in the array: (3) in, Let be the position vector of the array element. Indicates wavelength.

[0006] Preferably, step 2 specifically comprises: Define the horizontal / vertical polarization response matrices as follows: , The expression is as follows: Define the horizontal / vertical polarization response matrices as follows: , The expression is as follows: (4) (5) (6) (7) in, , These are the horizontal / vertical polarization steering vectors, respectively.

[0007] Preferably, step 3 specifically comprises: The observation information from the horizontal and vertical directions is concatenated into a joint observation matrix G, expressed as: (8) in, and The horizontal phase of RIS and vertical phase Polarization components after phase optimization 1× A column vector, with all elements being 1; the superscript T indicates transpose; The expression for the reflected signal received by the EMVS array is: (9) in, Given a complex Gaussian random signal matrix simulating the signal emitted by a target, each element independently follows a complex Gaussian random distribution. It is additive white Gaussian noise. K Indicates the number of snapshots.

[0008] Preferably, step 4 specifically comprises: Initialize the phase of RIS and ,conduct The next iteration involves first performing RIS phase mapping, and then constructing the joint observation matrix. Calculate signal power In each iteration, a perturbation phase is generated, and the new signal power is calculated. If the new signal power is higher than the current optimal signal power, the phase of the RIS is updated until the iteration is completed and the optimal RIS phase is obtained. and This process is represented by the following optimization algorithm: (10) (11) (12) in, Indicates the received signal power. This represents the optimal joint observation matrix obtained after RIS phase optimization. This is the joint observation matrix of RIS. The set of all possible joint observation matrices, determined by RIS phase. , generate, This represents the Kronecker product operation.

[0009] Preferably, step 5 specifically comprises: By jointly modeling the covariance matrices of the horizontal and vertical polarization channels, the covariance matrix of the received signal is obtained as follows: (13) in, Then perform eigenvalue decomposition: (14) in It is a diagonal matrix composed of eigenvectors; A diagonal matrix composed of eigenvalues, arranged in ascending order; the first... The eigenvectors corresponding to the large eigenvalues ​​constitute the signal subspace, defined as follows: The remaining eigenvectors constitute the noise subspace, defined as follows: .

[0010] Preferably, step 6 specifically comprises: Construct a joint guidance vector for each angle grid. The expression is as follows: (15) in, and These represent the discrete values ​​of the azimuth and elevation angles, respectively. This represents the horizontal polarization steering vector. Indicates the vertical polarization steering vector; Then the spatial spectrum is calculated, as shown in the following expression: (16) in, Represents the noise subspace matrix The conjugate transpose of; Searching on the spatial spectrum The highest peak value corresponds to the angle of the estimated DOA value.

[0011] Preferably, step 7 specifically comprises: The RMSE expression is as follows: (17) in, and It is the first The second quick shot The estimated azimuth and pitch angles of the drone; The formula for calculating CRLB is: (18) (19) (20) in, It is the Fisher information matrix; Noise power; The parameter vector consists of the azimuth and elevation angles to be estimated; This is the derivative of the joint observation matrix with respect to the parameters; Let be the projection matrix, representing the noise subspace; Let be the covariance matrix of the signal source.

[0012] The beneficial effects of this invention are as follows: (1) The present invention adopts a dual-polarization RIS structure, which utilizes the orthogonality of polarization dimensions to effectively improve angular resolution and enhance the ability to distinguish dense signal sources.

[0013] (2) Adapt the existing ROSM method to the dual-polarized RIS architecture and use iterative perturbation search to achieve phase optimization. This reduces computational complexity while ensuring convergence, and requires no additional hardware overhead.

[0014] (3) Combining electromagnetic wave polarization characteristics with the MUSIC algorithm, multipath interference is effectively suppressed through polarization-space joint eigenvalue decomposition.

[0015] (4) Under the same physical aperture conditions, compared with the traditional method, the present invention has better multi-signal resolution and higher positioning accuracy, and its performance advantages are verified by quantitative evaluation. Attached Figure Description

[0016] Figure 1 This is a flowchart of the method of the present invention.

[0017] Figure 2 This is a schematic diagram of a UAV DOA joint estimation system model based on dual-polarization RIS assistance.

[0018] Figure 3 This is a comparison chart of RMSE and CRLB under different array element numbers and SNR in embodiments of the present invention.

[0019] Figure 4 This is a comparison chart of RMSE and CRLB under different RIS cell spacing and SNR in embodiments of the present invention.

[0020] Figure 5 This is a comparison chart of RMSE and CRLB under different numbers of RIS units and SNR in embodiments of the present invention.

[0021] Figure 6 This is a comparison chart of the DOA estimation RMSE of the method of the present invention with that of OMP, ESPRIT, FFT and other methods in the embodiments of the present invention. Detailed Implementation

[0022] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0023] This invention aims to overcome the limitations of traditional single-polarization RIS in terms of degrees of freedom and estimation performance, and provides a joint DOA estimation method and system for UAVs based on dual-polarization RIS assistance. By designing the joint reflection matrix of the dual-polarization RIS, the polarization diversity characteristic is fully utilized to expand the array's degrees of freedom, thereby achieving effective resolution of more signal sources under the same physical aperture. The RIS phase is optimized using a stochastic subspace mapping algorithm, and the high-dimensional problem is reduced through stochastic projection technology, significantly reducing computational complexity while ensuring convergence. Furthermore, a spatial spectral function is constructed based on a multiple signal classification algorithm, and combined with global spectral peak search and the orthogonality principle of feature subspaces, high-precision, high-resolution DOA estimation is achieved. This invention effectively improves the signal source resolution capability and estimation accuracy of UAV localization, while also possessing superior computational efficiency and system reliability.

[0024] This invention discloses a method and system for joint DOA estimation of unmanned aerial vehicles (UAVs) based on dual-polarized RIS (Radio Reflection Matrix) assistance, relating to the fields of wireless communication and array signal processing technology. The method mainly consists of three parts: First, a joint reflection matrix of dual-polarized RIS is designed, extending the array's degrees of freedom through polarization diversity characteristics, enabling the resolution of more signal sources under the same physical aperture; second, a stochastic optimization subspace mapping algorithm is used for RIS phase optimization, introducing stochastic projection technology to reduce the dimensionality of the high-dimensional optimization problem, significantly reducing computational complexity while ensuring algorithm convergence; finally, a spatial spectral function is constructed based on a multi-signal classification algorithm, and candidate solutions for DOA are obtained through global spectral peak search, combined with the orthogonality principle of characteristic subspaces to achieve high-precision DOA estimation. This invention breaks through the degree-of-freedom limitations of traditional single-polarized RIS, significantly improving signal source resolution and DOA estimation accuracy, while reducing computational complexity, providing a more efficient and reliable solution for UAV positioning.

[0025] The present invention specifically includes the following steps: Step 1: Construct the dual-polarization RIS array steering vector matrix and EMVS receiver array configuration parameters.

[0026] Definitions have A drone target, define the target. The incident azimuth angle of the signal is The pitch angle is The array at the receiving end consists of It consists of individual array elements; RIS is composed of It consists of 1 unit, with a unit spacing of half a wavelength. The reflected signal is divided into horizontal polarization components. and vertical polarization components Its expression is as follows: (1) (2) in, These are the horizontal and vertical initial phases of the simulated RIS cell, respectively, and are of length [missing information]. A random vector, each element of which independently follows a uniform distribution; the Toeplitz matrix simulates the mutual coupling between RIS units; Define array response vector The expression is as follows, which characterizes the signal from the direction The collection of phase delays induced at the incident points on each sensor in the array: (3) in, is the position vector of the array element.

[0027] Step 2: Receive the dual-polarization signal from the UAV based on the steering vector matrix and perform polarization separation preprocessing.

[0028] Define the horizontal / vertical polarization response matrices as follows: , The expression is as follows: (4) (5) (6) (7) in, , These are the horizontal / vertical polarization steering vectors, respectively.

[0029] Step 3: Construct a joint received data matrix containing horizontal / vertical polarization using the polarization-separated signals.

[0030] The observation information from the horizontal and vertical directions is concatenated into a joint observation matrix G, expressed as: (8) in, and The horizontal phase of RIS and vertical phase Polarization components after phase optimization 1× A column vector, where all elements are 1; The expression for the reflected signal received by the EMVS array is: (9) in, For the joint observation matrix, Given a complex Gaussian random signal matrix simulating the signal emitted by a target, each element independently follows a complex Gaussian random distribution. It is additive white Gaussian noise.

[0031] Step 4: Optimize and generate the optimal dual-polarization RIS joint reflection matrix using the ROSM algorithm.

[0032] Initialize the phase of RIS and ,conduct The next iteration involves first performing RIS phase mapping, and then constructing the joint observation matrix. Calculate signal power In each iteration, a perturbation phase is generated, and the new signal power is calculated. If the new signal power is higher than the current optimal signal power, the phase of the RIS is updated until the iteration is complete, at which point the optimal RIS phase is obtained. and This process is represented by the following optimization algorithm: (10) (11) (12) in, This is the joint observation matrix of RIS. The set of all possible joint observation matrices, determined by RIS phase. , generate.

[0033] Step 5: Calculate the polarization-space joint covariance matrix and perform eigenvalue decomposition to extract the signal subspace and noise subspace.

[0034] By jointly modeling the covariance matrices of the horizontal and vertical polarization channels, the covariance matrix of the received signal is obtained as follows: (13) in, , The number of snapshots is used; then eigenvalue decomposition is performed: (14) in It is a diagonal matrix composed of eigenvectors; A diagonal matrix composed of eigenvalues, arranged in ascending order; the first... The eigenvectors corresponding to the large eigenvalues ​​constitute the signal subspace, defined as follows: The remaining eigenvectors constitute the noise subspace, defined as follows: .

[0035] Step 6: Based on the noise subspace and the dual-polarization steering vector, construct the dual-polarization MUSIC spatial spectrum function, and search for the spatial spectrum peaks to obtain the final two-dimensional DOA estimate.

[0036] Construct a joint guidance vector for each angle grid. The expression is as follows: (15) Then the spatial spectrum is calculated, as shown in the following expression: (16) Searching on the spatial spectrum The highest peak value corresponds to the angle of the estimated DOA value.

[0037] Step 7: Calculate RMSE and CRLB theoretical lower bound to evaluate the estimated performance.

[0038] The RMSE expression is as follows: (17) in and It is the first The actual azimuth and pitch angles of the drone. and It is the first The second quick shot The estimated azimuth and pitch angles of the drone; The formula for calculating CRLB is: (18) (19) (20) It is the Fisher information matrix; Noise power; The parameter vector consists of the azimuth and elevation angles to be estimated; This is the derivative of the joint observation matrix with respect to the parameters; Let be the projection matrix, representing the noise subspace; Let be the covariance matrix of the signal source.

[0039] Example: In this implementation example, a complete polarization-space signal reception model is first established by constructing the steering vector matrix of the dual-polarization RIS array and the configuration parameters of the EMVS receiving array. The system captures the dual-polarization signal transmitted by the UAV based on the steering vector matrix and employs polarization separation preprocessing technology to effectively separate the horizontal / vertical polarization components. A joint received data matrix is ​​constructed to provide a complete signal characterization for subsequent processing. Then, the ROSM algorithm is used to dynamically optimize the joint reflection matrix of the dual-polarization RIS. Subsequently, the system calculates the polarization-space joint covariance matrix and performs eigenvalue decomposition. Based on the orthogonality between the signal subspace and the noise subspace, an improved MUSIC spatial spectrum function fusing the dual-polarization steering vector is constructed. Finally, by globally traversing and searching for the peak points of the spatial spectrum function, high-precision estimation of the two-dimensional DOA parameters of the UAV signal is achieved. The system performance is quantitatively evaluated by calculating RMSE and CRLB.

[0040] This embodiment specifically includes the following steps: Step 1: A joint estimation method for DOA of unmanned aerial vehicles (UAVs) based on dual-polarization RIS-assisted model is proposed. The system model diagram of this method is shown below. Figure 2As shown. Assuming the direct channel between the UAV and the receiver is blocked by an obstacle, considering only the non-line-of-sight (NLOS) channel, the UAV signal reaches the base station receiver through reflection by the RIS unit. Each UAV target transmits a far-field narrowband signal. Each RIS unit performs dual-polarization reflection of the incident signal, i.e., horizontal and vertical polarization, while also considering the coupling between RIS elements. The receiver consists of an EMVS array, each capable of simultaneously receiving both horizontally and vertically polarized signals. The process of constructing the dual-polarization RIS array steering vector matrix and configuring the EMVS receiver array parameters is as follows: Definitions have A drone target, define the target. The incident azimuth angle of the signal is The pitch angle is The array at the receiving end consists of It consists of individual array elements; RIS is composed of It consists of 1 unit, with a unit spacing of half a wavelength. The reflected signal is divided into horizontal polarization components. and vertical polarization components Its expression is as follows: (1) (2) in, These are the horizontal and vertical initial phases of the simulated RIS cell, respectively, and are of length [missing information]. A random vector, each element of which independently follows a uniform distribution; the Toeplitz matrix simulates the mutual coupling between RIS units; EMVS arrays can simultaneously capture the spatial angle and polarization information of signals. Define the array response vector. The expression is as follows, which characterizes the signal from the direction The collection of phase delays induced at the incident points on each sensor in the array: (3) in, is the position vector of the array element.

[0041] Step 2: Receive the dual-polarization signal from the UAV based on the steering vector matrix and perform polarization separation preprocessing.

[0042] Define the horizontal / vertical polarization response matrices as follows: , The expression is as follows: (4) (5) (6) (7) in, , These are the horizontal / vertical polarization steering vectors, respectively.

[0043] Step 3: Construct a joint received data matrix containing horizontal / vertical polarization using the polarization-separated signals.

[0044] The observation information from the horizontal and vertical directions is concatenated into a joint observation matrix G, expressed as: (8) in, and The horizontal phase of RIS and vertical phase Polarization components after phase optimization 1× A column vector, where all elements are 1; The expression for the reflected signal received by the EMVS array is: (9) in, For the joint observation matrix, Given a complex Gaussian random signal matrix simulating the signal emitted by a target, each element independently follows a complex Gaussian random distribution. It is additive white Gaussian noise.

[0045] Step 4: The computationally inefficient ROSM algorithm is combined with the dual-polarization RIS algorithm for RIS phase optimization. The RIS phase optimization problem is modeled as maximizing received signal power and solved using an iterative perturbation search strategy. This significantly reduces computational complexity while ensuring algorithm convergence, achieving an effective balance between system performance and computational efficiency. The process of generating the optimal dual-polarization RIS joint reflection matrix using the ROSM algorithm is as follows: Initialize the phase of RIS and Perform RIS phase mapping and then construct a joint observation matrix. Calculate signal power ;conduct In each iteration, a perturbation phase is generated, and the new signal power is calculated. If the new signal power is higher than the current optimal signal power, the phase of the RIS is updated. This process continues until the iteration is complete, at which point the optimal RIS phase is obtained. and This process is represented by the following optimization algorithm: (10) (11) (12) in, This is the joint observation matrix of RIS. The set of all possible joint observation matrices, determined by RIS phase. , generate.

[0046] Step 5: Calculate the polarization-space joint covariance matrix and perform eigenvalue decomposition to extract the signal subspace and noise subspace.

[0047] The MUSIC algorithm can be extended to multi-polarization signal processing; by jointly modeling the covariance matrices of the horizontal / vertical polarization channels, the polarization difference can be directly used to enhance the angle resolution capability without the need to design an additional sparse model.

[0048] The covariance matrix of the received signal is: (13) in, , The number of snapshots is used; then eigenvalue decomposition is performed: (14) in It is a diagonal matrix composed of eigenvectors; A diagonal matrix composed of eigenvalues, arranged in ascending order; the first... The eigenvectors corresponding to the large eigenvalues ​​constitute the signal subspace, defined as follows: The remaining eigenvectors constitute the noise subspace, defined as follows: .

[0049] Step 6: Based on the noise subspace and the dual-polarization steering vector, construct the dual-polarization MUSIC spatial spectrum function, and search for the spatial spectrum peaks to obtain the final two-dimensional DOA estimate.

[0050] Construct a joint guidance vector for each angle grid. The expression is as follows: (15) Then the spatial spectrum is calculated, as shown in the following expression: (16) Searching on the spatial spectrum The highest peak value corresponds to the angle of the estimated DOA value.

[0051] Step 7: RMSE is used as an indicator to evaluate the performance of DOA estimation. Compared to indicators such as mean absolute error, RMSE is more sensitive to outliers and better reflects the dispersion of the estimation error. In DOA estimation, the smaller the RMSE value, the better the algorithm performance. CRLB provides a theoretical lower bound for evaluating the algorithm's performance and is of great significance for DOA estimation. When the RMSE value is close to the CRLB, it indicates that the algorithm has reached the theoretically optimal estimation accuracy. The process of calculating the theoretical lower bounds of RMSE and CRLB to evaluate the estimation performance is as follows: The RMSE expression is as follows: (17) in and It is the first The actual azimuth and pitch angles of the drone. and It is the first The second quick shot The estimated azimuth and pitch angles of the drone; The formula for calculating CRLB is: (18) (19) (20) It is the Fisher information matrix; Noise power; The parameter vector consists of the azimuth and elevation angles to be estimated; This is the derivative of the joint observation matrix with respect to the parameters; Let be the projection matrix, representing the noise subspace; Let be the covariance matrix of the signal source.

[0052] Step 8: A comparison chart of RMSE and CRLB under different parameter variable values ​​is provided: Figure 3 (The horizontal axis represents the number of array elements in the antenna array) The vertical axis represents the RMSE estimated by DOA, which is the result of the method of this invention in different... Comparison chart of RMSE and CRLB under SNR; from Figure 3 It can be seen that with With the increase of SNR, the RMSE of DOA estimation monotonically decreases under all SNR conditions, indicating improved performance; the curve is flat at low SNR; the RMSE decreases faster at high SNR and gradually approaches CRLB with the increase of array element number, indicating that appropriately increasing the number of array elements can effectively improve the accuracy of DOA estimation.

[0053] Figure 4 (The horizontal axis represents the RIS cell spacing) The vertical axis represents the RMSE estimated by DOA, which is the result of the method of this invention in different... Comparison chart of RMSE and CRLB under SNR; from Figure 4 It can be seen that the RMSE value under different SNRs varies with The increase of d gradually decreases; when d increases to a certain extent, the RMSE value tends to increase sharply, because when When the wavelength exceeds half the wavelength, RIS will cause spatial aliasing, resulting in multiple main lobes in the beam pattern, which will blur the incident direction of the signal and reduce the accuracy of DOA estimation.

[0054] Figure 5 (The horizontal axis represents the number of RIS units) The vertical axis represents the RMSE estimated by DOA, which is the result of the method of this invention in different... Comparison chart of RMSE and CRLB under SNR; from Figure 5 It can be seen that RMSE increases with The overall trend of increasing RIS units is downward; therefore, more RIS units can provide higher spatial resolution and stronger noise suppression, but after reaching a certain scale, the increase in hardware cost and computational complexity may no longer bring significant performance improvement.

[0055] Step Nine: A comparison chart of the DOA estimation RMSE of the method of this invention with methods such as OMP, ESPRIT, and FFT is provided: Figure 6 (The horizontal axis represents SNR, and the vertical axis represents the RMSE estimated by DOA) is a comparison chart of the RMSE of the method of this invention with methods such as OMP, ESPRIT, and FFT. from Figure 6 It can be seen that as the SNR increases, the RMSE of all methods except FFT decreases significantly, indicating that SNR has a decisive impact on the estimation accuracy. Due to the limited spectral resolution, the RMSE of the FFT method remains high and the improvement is limited. At low SNR, the performance of all methods is constrained by noise. Compared with traditional methods, unoptimized RIS and single-polarized RIS schemes, the method proposed in this paper shows better estimation accuracy and significantly reduced RMSE.

Claims

1. A joint estimation method for DOA of unmanned aerial vehicles based on dual-polarization RIS-assisted estimation, characterized in that, Includes the following steps: Step 1: Construct the dual-polarization RIS array steering vector matrix and EMVS receiver array configuration parameters; Step 2: Receive the UAV dual-polarization signal based on the steering vector matrix and perform polarization separation preprocessing; Step 3: Construct a joint received data matrix containing horizontal / vertical polarization using the polarization-separated signals; Step 4: Optimize and generate the optimal dual-polarization RIS joint reflection matrix using the ROSM algorithm; Step 5: Calculate the polarization-space joint covariance matrix and perform eigenvalue decomposition to extract the signal subspace and noise subspace; Step 6: Based on the noise subspace and the dual-polarization steering vector, construct the dual-polarization MUSIC spatial spectrum function, and search for the spatial spectrum peaks to obtain the final two-dimensional DOA estimate; Step 7: Calculate RMSE and CRLB theoretical lower bound to evaluate the estimated performance.

2. The method for joint estimation of DOA of unmanned aerial vehicles based on dual-polarization RIS assistance according to claim 1, characterized in that, Step 1 specifically involves: Step 1-1: Define A drone target, define the target. The signal incident azimuth angle is The pitch angle is The array at the receiving end consists of It consists of individual array elements; RIS is composed of It consists of 1 unit, with a unit spacing of half a wavelength. The reflected signal is divided into horizontal polarization components. and vertical polarization components Its expression is as follows: （1） （2） in, These are the horizontal and vertical initial phases of the simulated RIS cell, respectively, and are of length [missing information]. A random vector, each element of which independently follows a uniform distribution; the Toeplitz matrix simulates the mutual coupling between RIS units; Step 1-2: Define the array response vector The expression is as follows, which characterizes the signal from the direction The collection of phase delays induced at the incident points on each sensor in the array: （3） in, Let be the position vector of the array element. Indicates wavelength.

3. The UAV DOA joint estimation method based on dual-polarization RIS assistance according to claim 2, characterized in that, Step 2 specifically involves: Define the horizontal / vertical polarization response matrices as follows: , The expression is as follows: Define the horizontal / vertical polarization response matrices as follows: , The expression is as follows: （4） （5） （6） （7） in, , These are the horizontal / vertical polarization steering vectors, respectively.

4. The UAV DOA joint estimation method based on dual-polarization RIS assistance according to claim 3, characterized in that, Step 3 specifically involves: The observation information from the horizontal and vertical directions is concatenated into a joint observation matrix G, expressed as: （8） in, and The horizontal phase of RIS and vertical phase Polarization components after phase optimization 1× A column vector, with all elements being 1; the superscript T indicates transpose; The expression for the reflected signal received by the EMVS array is: （9） in, Given a complex Gaussian random signal matrix simulating the signal emitted by a target, each element independently follows a complex Gaussian random distribution. It is additive white Gaussian noise. K Indicates the number of snapshots.

5. The UAV DOA joint estimation method based on dual-polarization RIS assistance according to claim 4, characterized in that, Step 4 specifically involves: Initialize the phase of RIS and ,conduct The next iteration involves first performing RIS phase mapping, and then constructing the joint observation matrix. Calculate signal power In each iteration, a perturbation phase is generated, and the new signal power is calculated. If the new signal power is higher than the current optimal signal power, the phase of the RIS is updated until the iteration is completed and the optimal RIS phase is obtained. and This process is represented by the following optimization algorithm: （10） （11） （12） in, Indicates the received signal power. This represents the optimal joint observation matrix obtained after RIS phase optimization. This is the joint observation matrix of RIS. The set of all possible joint observation matrices, determined by RIS phase. , generate, This represents the Kronecker product operation.

6. The UAV DOA joint estimation method based on dual-polarization RIS-assisted method according to claim 5, characterized in that, Step 5 specifically involves: By jointly modeling the covariance matrices of the horizontal and vertical polarization channels, the covariance matrix of the received signal is obtained as follows: （13） in, Then perform eigenvalue decomposition: （14） in It is a diagonal matrix composed of eigenvectors; A diagonal matrix composed of eigenvalues, arranged in ascending order; the first... The eigenvectors corresponding to the large eigenvalues ​​constitute the signal subspace, defined as follows: The remaining eigenvectors constitute the noise subspace, defined as follows: .

7. The UAV DOA joint estimation method based on dual-polarization RIS assistance according to claim 6, characterized in that, Step 6 specifically involves: Construct a joint guidance vector for each angle grid. The expression is as follows: （15） in, and These represent the discrete values ​​of the azimuth and elevation angles, respectively. This represents the horizontal polarization steering vector. Indicates the vertical polarization steering vector; Then the spatial spectrum is calculated, as shown in the following expression: （16） in, Represents the noise subspace matrix The conjugate transpose of; Searching on the spatial spectrum The highest peak value corresponds to the angle of the estimated DOA value.

8. The UAV DOA joint estimation method based on dual-polarization RIS assistance according to claim 7, characterized in that, Step 7 specifically involves: The RMSE expression is as follows: （17） in, and It is the first The second quick shot The estimated azimuth and pitch angles of the drone; The formula for calculating CRLB is: （18） （19） （20） in, It is the Fisher information matrix; Noise power; The parameter vector consists of the azimuth and elevation angles to be estimated; This is the derivative of the joint observation matrix with respect to the parameters; Let be the projection matrix, representing the noise subspace; Let be the covariance matrix of the signal source.

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