Unmanned aerial vehicle navigation adaptive beam forming method and system based on MISC common matrix interpolation

Abstract

The invention discloses an unmanned aerial vehicle navigation adaptive beam forming method and system based on MISC common matrix interpolation, and relates to the field of unmanned aerial vehicle navigation. The problems that various errors such as calibration errors and direction errors exist in an existing unmanned aerial vehicle self-adaptive beam former, and the interference suppression freedom degree of the self-adaptive beam forming algorithm is limited by the number of array elements due to the fact that the self-adaptive beam forming algorithm is based on a uniform linear array are solved. The method comprises the following steps: deducing an unmanned aerial vehicle navigation receiver MISC array receiving signal vector; obtaining an MISC differential common array and a virtual signal vector; converting the MISC differential common array into a virtual uniform linear array through an interpolation technology; performing signal solving on the virtual uniform linear array after interpolation; estimating all signal directions and signal power; reconstructing an interference and noise covariance matrix of the MISC array based on the received signal; and according to the reconstructed covariance matrix and the direction of the target signal, calculating a weighted vector of adaptive beamforming. The method is applied to satellite navigation.

Description

Technical Field

[0001] The present invention relates to the field of unmanned aerial vehicle navigation, and in particular to an unmanned aerial vehicle navigation adaptive beam forming method based on MISC common array interpolation. Background Art

[0002] Unmanned aerial vehicles (UAVs) are widely used in military and civilian fields such as plant spraying, crop monitoring, soil sampling, power inspection, military reconnaissance, and border monitoring. The advancement of navigation technology is one of the reasons for the rapid development of UAVs. The Global Navigation Satellite System (GNSS) can provide users with high-precision position, speed, and timing services, and is one of the main inputs of UAV navigation and control systems. UAVs mainly use satellite-based navigation systems to determine their own position, attitude, and speed in order to carry out flight missions smoothly. However, for the flight missions of UAVs, the normal operation of satellite navigation signals is a prerequisite and cannot be interfered with. However, the satellite orbit is located at a very high position on the ground, and the satellite signal will experience attenuation when it reaches the ground, which is easily affected by interference. Therefore, in order to solve the vulnerability problem of satellite navigation systems, it is very necessary to study the interference suppression method of satellite navigation receivers.

[0003] Satellite navigation receiver interference suppression methods are divided into single antenna interference suppression methods and array interference suppression methods. Single antenna interference suppression methods filter out interference components in the received signal based on the characteristic differences between the desired signal and the interference signal in the time domain, frequency domain and other transform domains. However, the performance of this type of method is often affected by the form of the interference signal. The array interference suppression method can not only suppress interference in the time domain and frequency domain, but also will not be affected by the form of the interference signal. The adaptive beamforming method is a typical spatial domain processing method. It adjusts the weights of the antenna array so that the beam pattern forms a main lobe in the direction of the desired signal and a deep null in the interference direction. If there is no error, the adaptive beamformer can exert the best spatial domain filtering performance. However, there are many errors such as calibration error and directional error in the actual system. Therefore, many scholars have proposed a large number of robust adaptive beamforming algorithms, such as diagonal loading algorithm, subspace projection algorithm, uncertainty set algorithm, and covariance matrix reconstruction algorithm. However, these algorithms are all based on uniform linear arrays, and their interference suppression freedom is restricted by the number of array elements. Summary of the invention

[0004] Aiming at the problem that the existing UAV adaptive beamformer has multiple errors such as calibration error and direction error, and the interference suppression freedom is restricted by the number of array elements because the adaptive beamforming algorithm is based on a uniform linear array, the present invention proposes a UAV navigation adaptive beamforming method based on MISC common array interpolation, the method comprising:

[0005] Step 1: Derive the received signal vector of the MISC array of the UAV navigation receiver;

[0006] Step 2: Calculate the differential signals between different receiving points to obtain the MISC differential common array and virtual signal vector;

[0007] Step 3: Convert the MISC differential common array into a virtual uniform linear array through interpolation technology;

[0008] Step 4: Perform signal analysis on the interpolated virtual uniform linear array;

[0009] Step 5: Estimate all signal directions and signal powers;

[0010] Step 6: Reconstruct the MISC array interference plus noise covariance matrix based on the received signal;

[0011] Step 7: Calculate the weight vector for adaptive beamforming based on the reconstructed covariance matrix and the direction of the target signal.

[0012] Furthermore, a preferred method is proposed, wherein step 1 comprises:

[0013] Determine the position of the array element according to the wavelength of the incident signal and the array element spacing;

[0014] Construct a mathematical model of the received signal;

[0015] Define the output signal-to-interference-and-noise ratio and set up the optimization problem;

[0016] Solve the optimal beamforming weight vector through optimization algorithm;

[0017] calculating an output signal of an adaptive beamformer;

[0018] The true covariance matrix is ​​estimated from the sample covariance matrix.

[0019] Furthermore, a preferred method is proposed, wherein step 2 comprises:

[0020] Vectorized sample covariance matrix

[0021]

[0022] Where B is the virtual co-array steering matrix, γ is the power vector, is the noise power, i=vec(I M );

[0023] The repeated elements are removed, and the results are reordered according to the position set of the differential co-array virtual array elements to obtain the differential co-array virtual signal vector.

[0024] Furthermore, a preferred method is proposed, wherein step 3 comprises:

[0025] Constructing an interpolated virtual uniform linear array IVULA, wherein the virtual uniform linear array IVULA includes a minimum uniform linear array of differential common arrays;

[0026] The location set of virtual array elements in IVULA is:

[0027]

[0028] in, is an integer, and

[0029] IVULA Virtual Signal It is expressed as:

[0030]

[0031] Among them, <·> μ represents the signal corresponding to the virtual array element located at μd; is the differential common array virtual signal vector.

[0032] Furthermore, a preferred embodiment is proposed, wherein step 5 comprises:

[0033] Construct the optimization problem:

[0034]

[0035] in, Reason The IVULA virtual signal is composed of is the optimization variable of the optimization problem, is the position set of virtual array elements in IVULA, Reason The positive semidefinite Toeplitz matrix formed as the first column vector;

[0036] Use CVX to solve the optimization problem, and the solution vector obtained can restore the interpolated uniform linear array signal.

[0037] Furthermore, a preferred embodiment is proposed, wherein step 6 comprises:

[0038]

[0039] in, is the reconstructed MISC array interference plus noise covariance matrix; λ{·} is the eigenvalue operation, I M is the M×M identity matrix, is the estimated signal steering vector, (·) H represents the conjugate transpose.

[0040] Furthermore, a preferred embodiment is proposed, wherein step 7 comprises:

[0041] Using the MISC array interference noise covariance matrix and the expected signal-directed vector The adaptive beamforming weight vector of the UAV navigation receiver is calculated as:

[0042]

[0043] Based on the same inventive concept, the present invention also proposes a UAV navigation adaptive beamforming system based on MISC common array interpolation, the system comprising:

[0044] A signal vector acquisition unit, used to derive a signal vector received by the MISC array of the UAV navigation receiver;

[0045] The differential common array unit is used to calculate the differential signals between different receiving points and obtain the MISC differential common array and virtual signal vector;

[0046] An interpolation unit, used for converting the MISC differential common array into a virtual uniform linear array by using an interpolation technique;

[0047] A solution unit, used for performing signal solution on the interpolated virtual uniform linear array;

[0048] An estimation unit, used for estimating all signal directions and signal powers;

[0049] A reconstruction unit, configured to reconstruct a MISC array interference plus noise covariance matrix based on the received signal;

[0050] The weighting unit is used to calculate a weighting vector for adaptive beamforming according to the reconstructed covariance matrix and the direction of the target signal.

[0051] Based on the same inventive concept, the present invention also proposes a computer device, including a memory and a processor, wherein a computer program is stored in the memory. When the processor runs the computer program stored in the memory, the processor executes a UAV navigation adaptive beamforming method based on MISC common array interpolation as described in any one of the above items.

[0052] Based on the same inventive concept, the present invention also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of a UAV navigation adaptive beamforming method based on MISC common array interpolation as described in any one of the above items are executed.

[0053] The present invention is beneficial in that:

[0054] The present invention proposes an adaptive beamforming method for UAV navigation based on MISC common array interpolation. By introducing the MISC common array interpolation method, the freedom of interference suppression can be effectively expanded and the interference suppression capability of the system can be improved. This enables the UAV to better complete tasks in complex environments. The method effectively reduces calibration and direction errors and improves the accuracy of signal processing by differential signal calculation and virtual signal vector generation. The MISC differential common array is converted into a virtual uniform linear array, and the interpolation technology is used to make up for the shortcomings of the actual array, thereby enhancing the flexibility and adaptability of the system. Through real-time signal solution and covariance matrix reconstruction, it can respond quickly in a dynamic environment, adapt to signal changes, and improve the navigation accuracy of the UAV. The method has good scalability, and the number and configuration of array elements can be adjusted as needed, and it is suitable for UAV systems of different scales and needs.

[0055] The present invention proposes a UAV navigation adaptive beamforming method based on MISC common array interpolation, which can suppress MISC array interference and improve the robustness of the UAV navigation receiver adaptive beamforming by utilizing all virtual array element information in the MISC differential common array.

[0056] The present invention proposes an adaptive beamforming method for unmanned aerial vehicle navigation based on MISC common array interpolation and is applied to the field of satellite navigation. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 This is a flow chart of a method for adaptive beamforming for UAV navigation based on MISC common array interpolation as described in implementation mode 1;

[0058] Figure 2 Schematic diagram of the MISC array structure described in Implementation Example 11. DETAILED DESCRIPTION

[0059] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments.

[0060] Implementation method 1, see Figure 1 The present embodiment describes a method for adaptive beamforming for UAV navigation based on MISC common array interpolation, the method comprising:

[0061] Step 1: Derive the received signal vector of the MISC array of the UAV navigation receiver;

[0062] Step 2: Calculate the differential signals between different receiving points to obtain the MISC differential common array and virtual signal vector;

[0063] Step 3: Convert the MISC differential common array into a virtual uniform linear array through interpolation technology;

[0064] Step 4: Perform signal analysis on the interpolated virtual uniform linear array;

[0065] Step 5: Estimate all signal directions and signal powers;

[0066] Step 6: Reconstruct the MISC array interference plus noise covariance matrix based on the received signal;

[0067] Step 7: Calculate the weight vector for adaptive beamforming based on the reconstructed covariance matrix and the direction of the target signal.

[0068] The adaptive beamforming method for UAV navigation based on MISC common array interpolation proposed in this embodiment can effectively expand the interference suppression freedom and improve the system's interference suppression capability by introducing the MISC common array interpolation method. This enables the UAV to better complete tasks in complex environments. The method effectively reduces calibration and direction errors and improves the accuracy of signal processing by differential signal calculation and virtual signal vector generation. The MISC differential common array is converted into a virtual uniform linear array, and the interpolation technology is used to make up for the shortcomings of the actual array, thereby enhancing the flexibility and adaptability of the system. Through real-time signal solution and covariance matrix reconstruction, it can respond quickly in a dynamic environment, adapt to signal changes, and improve the navigation accuracy of the UAV. The method has good scalability, and the number and configuration of array elements can be adjusted as needed. It is suitable for UAV systems of different scales and needs.

[0069] The principle of the UAV navigation adaptive beamforming method based on MISC common array interpolation described in this embodiment is:

[0070] In the first step, the MISC array receiving signal vector is derived, which lays the foundation for subsequent processing based on the multi-channel signal data received by the drone. The differential signal between different receiving points is calculated to obtain the MISC differential common array and virtual signal vector, which can effectively capture the phase difference between signals and provide key information for beamforming. The differential common array is converted into a virtual uniform linear array using interpolation technology. This process can expand the spatial sampling capability of the array and improve the resolution of the signal. The virtual uniform linear array is signal solved to determine the direction and power of the signal, and this information is used for subsequent interference suppression and signal enhancement. The interference plus noise covariance matrix of the MISC array is reconstructed through the received signal to provide the necessary statistical information for calculating the weighted vector. Based on the reconstructed covariance matrix and the direction of the target signal, the weighted vector of adaptive beamforming is calculated, and finally the signal enhancement and interference suppression are achieved.

[0071] Implementation method 2: This implementation method further limits the method for adaptive beamforming for UAV navigation based on MISC common array interpolation described in implementation method 1, and step 1 includes:

[0072] Determine the position of the array element according to the wavelength of the incident signal and the array element spacing;

[0073] Construct a mathematical model of the received signal;

[0074] Define the output signal-to-interference-and-noise ratio and set up the optimization problem;

[0075] Solve the optimal beamforming weight vector through optimization algorithm;

[0076] calculating an output signal of an adaptive beamformer;

[0077] The true covariance matrix is ​​estimated from the sample covariance matrix.

[0078] In step 1 of this embodiment, the optimal beamforming weighting vector is solved by an optimization algorithm, which can significantly improve the signal-to-noise ratio (SNR). In a complex electromagnetic environment, this method can effectively suppress noise and interference, thereby ensuring the quality of the received signal. The adaptive beamformer can dynamically adjust its weighting vector according to the changes in the real-time received signal. This adaptability enables the drone to maintain good navigation performance in various environments, especially in the presence of multipath effects or interference. By estimating the sample covariance matrix, the true covariance matrix can be captured more accurately, thereby improving the accuracy of positioning and navigation. This is particularly important for the execution of drone missions in complex scenarios (such as search and rescue, monitoring, etc.).

[0079] The advantages of this embodiment are explained in conjunction with the first embodiment. The MISC common array interpolation method proposed in this embodiment reduces the hardware requirements and system complexity by simplifying the array structure. This reduces the design and manufacturing costs of the drone and is suitable for large-scale applications.

[0080] Furthermore, this embodiment also constructs a mathematical model of the received signal and adopts an efficient optimization algorithm. The method can calculate the optimal beamforming weighting vector in a short time to meet the UAV's requirements for real-time performance and response speed. In complex multipath environments such as urban environments or mountainous areas, traditional beamforming methods may face difficulties, and the adaptive beamforming method based on MISC common array interpolation can better cope with these challenges and improve the working ability of UAVs.

[0081] Implementation method 3: This implementation method is a further limitation of the UAV navigation adaptive beamforming method based on MISC common array interpolation described in implementation method 1, and step 2 includes:

[0082] Vectorized sample covariance matrix

[0083]

[0084] Where B is the virtual co-array steering matrix, γ is the power vector, is the noise power, i=vec(I M );I M is the M×M identity matrix;

[0085] The repeated elements are removed, and the results are reordered according to the position set of the differential co-array virtual array elements to obtain the differential co-array virtual signal vector.

[0086] In this embodiment, by calculating the differential signal between different receiving points, the impact of noise on the signal can be effectively reduced and the signal-to-noise ratio of the signal can be improved. This differential processing can help extract clearer and more accurate navigation information. By using a virtual common array steering matrix, richer spatial information can be generated between different receiving points, thereby improving the positioning accuracy of the drone. This is particularly important for navigation in complex environments. Furthermore, the adaptive beamforming method proposed in this embodiment allows the system to adjust the beam shape and direction according to real-time environmental changes, and can better cope with navigation requirements in dynamic environments. This flexibility makes the drone perform better in complex scenes. By vectorizing the sample covariance matrix and removing duplicate elements, the complexity of the calculation can be reduced, making real-time processing possible. This is crucial for real-time navigation of drones in flight.

[0087] Embodiment 4: This embodiment further limits the method for adaptive beamforming for UAV navigation based on MISC common array interpolation described in embodiment 1, and step 3 includes:

[0088] Constructing an interpolated virtual uniform linear array IVULA, wherein the virtual uniform linear array IVULA includes a minimum uniform linear array of differential common arrays;

[0089] The location set of virtual array elements in IVULA is:

[0090]

[0091] in, is an integer, and

[0092] IVULA Virtual Signal It is expressed as:

[0093]

[0094] Among them, <·> μ represents the signal corresponding to the virtual array element located at μd; is the differential common array virtual signal vector.

[0095] In this embodiment, by constructing a virtual uniform linear array, signals from different directions can be captured and processed more accurately. This uniformly structured array can effectively reduce phase errors, thereby improving the overall quality and accuracy of the signal. The virtual uniform linear array can achieve higher spatial resolution, allowing the system to more clearly distinguish similar signal sources. This is of great significance for positioning and navigation in complex environments. By constructing IVULA through interpolation technology, the complex structure of the differential common array can be simplified into a uniform array. This simplification not only reduces the complexity of the hardware, but also reduces the system cost and design difficulty. Further, the construction of the virtual uniform linear array in this embodiment enables the system to flexibly select and configure the array element position to adapt to different application scenarios and signal conditions. This flexibility enhances the adaptability of the drone in various environments. Through the definition of virtual signals in IVULA, the combination of signals is more efficient. Through the differential common array virtual signal vector, effective signal weighting and synthesis can be quickly achieved, thereby further improving the response speed and performance of the system. After being converted into a virtual uniform linear array, the system's resistance to signal interference and multipath effects is enhanced, and it can maintain stable navigation performance in various harsh environments, ensuring the safe flight of the drone.

[0096] Embodiment 5: This embodiment further limits the method for adaptive beamforming for UAV navigation based on MISC common array interpolation described in embodiment 1, and step 5 includes:

[0097] Construct the optimization problem:

[0098]

[0099] in, Reason The IVULA virtual signal is composed of is the optimization variable of the optimization problem, is the position set of virtual array elements in IVULA, Reason The positive semidefinite Toeplitz matrix formed as the first column vector;

[0100] Use CVX to solve the optimization problem and obtain the solution vector to restore the interpolated uniform linear array signal, including:

[0101] Use CVX syntax to build optimization models and define variables and constraints;

[0102] Call CVX's solver to calculate and obtain the optimal solution;

[0103] The obtained solution vector is analyzed to restore the interpolated uniform linear array signal.

[0104] Embodiment 6: This embodiment further limits the method for adaptive beamforming for UAV navigation based on MISC common array interpolation described in embodiment 1, and step 6 includes:

[0105]

[0106] in, is the reconstructed MISC array interference plus noise covariance matrix; λ{·} is the eigenvalue operation, I M is the M×M identity matrix, is the estimated signal steering vector, (·) H represents the conjugate transpose.

[0107] In this embodiment, by reconstructing the covariance matrix, the interference and noise in the system can be estimated more accurately. This accurate noise assessment helps to improve subsequent signal processing and enhance the availability of the signal. Further, the reconstructed covariance matrix provides a more reliable basis for adaptive beamforming, enabling the system to dynamically adjust beam parameters according to environmental changes. This adaptive capability enables the UAV to maintain excellent navigation performance in complex environments. An effective interference plus noise covariance matrix helps to optimize the beamforming algorithm, thereby effectively suppressing interference from irrelevant signal sources and ensuring the clarity and stability of the navigation signal. By reconstructing the received signal, redundant information in the calculation process can be reduced and the efficiency of signal processing can be improved. This optimization is particularly important in real-time applications and can reduce processing delays. The reconstructed covariance matrix can enhance the robustness of the system to various interferences, enabling the UAV to maintain stable navigation and positioning capabilities under different flight conditions.

[0108] Implementation 7: This implementation is a further limitation of the UAV navigation adaptive beamforming method based on MISC common array interpolation described in Implementation 1, and step 7 includes:

[0109] Using the MISC array interference noise covariance matrix and the expected signal-directed vector The adaptive beamforming weight vector of the UAV navigation receiver is calculated as:

[0110]

[0111] Embodiment 8: A UAV navigation adaptive beamforming system based on MISC common array interpolation described in this embodiment includes:

[0112] A signal vector acquisition unit, used to derive a signal vector received by the MISC array of the UAV navigation receiver;

[0113] The differential common array unit is used to calculate the differential signals between different receiving points and obtain the MISC differential common array and virtual signal vector;

[0114] An interpolation unit, used for converting the MISC differential common array into a virtual uniform linear array by using an interpolation technique;

[0115] A solution unit, used for performing signal solution on the interpolated virtual uniform linear array;

[0116] An estimation unit, used for estimating all signal directions and signal powers;

[0117] A reconstruction unit, configured to reconstruct a MISC array interference plus noise covariance matrix based on the received signal;

[0118] The weighting unit is used to calculate a weighting vector for adaptive beamforming according to the reconstructed covariance matrix and the direction of the target signal.

[0119] Embodiment 9. A computer device described in this embodiment includes a memory and a processor, wherein a computer program is stored in the memory. When the processor runs the computer program stored in the memory, the processor executes a UAV navigation adaptive beamforming method based on MISC common array interpolation described in any one of embodiments 1 to 7.

[0120] Embodiment 10. A computer-readable storage medium described in this embodiment, on which a computer program is stored, and when the computer program is executed by a processor, the steps of a method for adaptive beamforming of UAV navigation based on MISC common array interpolation as described in any one of embodiments 1 to 7 are executed.

[0121] Implementation Method 11: See Figure 2 This embodiment provides a specific example of the method for adaptive beamforming for UAV navigation based on MISC common array interpolation described in the first embodiment, and is also used to explain the second to seventh embodiments, specifically:

[0122] Step 1: Derive the received signal vector of the MISC array of the UAV navigation receiver. Let Pd be the maximum array element spacing, is the array element spacing set, where d = λ / 2, λ is the wavelength of the incident signal. Then, the array element position in the MISC array is determined by P and jointly determined, where P and The expression is as follows:

[0123]

[0124] in, Refers to the integer part of the rational number in square brackets, consisting of P and Able to determine the element position h of the MISC array i d, and Represents the MISC array element position set. When the number of array elements M (M ≥ 5) is any value, the corresponding P can be determined, and the position set of the MISC array is further obtained. Differential common array virtual element position set of MISC array for:

[0125]

[0126] When L narrowband uncorrelated signals are incident on the MISC array from the far field, the number of array elements in the array is M. The desired signal is emitted from the direction θ 1 Incident, L-1 interference from the direction The received signal of the MISC array at time k is expressed as:

[0127]

[0128] Among them, x s (k) = a(θ 1 )s 1 (k) is the expected signal, is the interference, a(θ l ) is the steering vector of the lth signal, s l (k) represents the beam of the lth signal, and n(k) is the array noise vector. The output signal-to-interference-noise ratio of the MISC array is defined as:

[0129]

[0130] in, is the desired signal power, w represents the adaptive beamforming weight vector, (·) H represents the conjugate transpose, R i+n is the real interference plus noise covariance matrix of the MISC array:

[0131]

[0132] in, is the power of the lth signal, is the noise power, I M is the M×M identity matrix.

[0133] By maximizing the array output signal-to-interference-noise ratio (5), it is equivalent to the following optimization problem:

[0134]

[0135] Solve problem (7) and get the optimal solution:

[0136]

[0137] The output of the adaptive beamformer is defined as:

[0138] y(k)=w H x(k) (9)

[0139] In actual engineering systems, due to the real R i+n It is usually difficult to obtain, and the sample covariance matrix with K sampling snapshots is generally used When K is small, use This will significantly degrade the beamforming performance.

[0140] Step 2: Obtain the MISC differential matrix and virtual signal vector. By vectorizing the sample covariance matrix You can get:

[0141]

[0142] in,

[0143]

[0144] is the virtual co-array steering matrix, is the Kronecker product operation, the power vector Contains the power of the signal, i = vec(I M ). By removing the repeated elements in z, the virtual array element position set is obtained based on the difference common array Rearrange the order to get the differential common array virtual signal vector Then the virtual signal corresponding to the virtual array element at position vd in the differential common array is:

[0145]

[0146] in, and

[0147] Step 3: Interpolate the MISC differential common array into a virtual uniform linear array. Since the differential common array is non-uniform, construct an interpolated virtual uniform linear array IVULA to make it the minimum uniform linear array containing the differential common array. At this time, the position set of the virtual array elements in IVULA is:

[0148]

[0149] in, is an integer, and The interpolated virtual array elements only exist in a mathematical sense and do not exist in reality, so the virtual signals corresponding to them are unknown. Therefore, the IVULA virtual signal can be expressed as:

[0150]

[0151] Among them, <·> μ Represents the signal corresponding to the virtual array element located at μd.

[0152] Step 4: Solve the interpolated virtual uniform linear array signal. In order to solve The unknown elements in Recover from Construct the following atomic norm minimization problem:

[0153]

[0154] The threshold δ is used to limit The non-zero elements in The difference between corresponding elements in , represents a positive semidefinite Toeplitz matrix, which is expressed as:

[0155]

[0156] in, The atomic norm of can be expressed as:

[0157]

[0158] in, represents the steering vector of the interpolated uniform linear array. The optimization problem (15) can be further expressed as:

[0159]

[0160] Where μ represents the regularization parameter. If You can Vandermonde decomposition is:

[0161]

[0162] matrix The trace of can be calculated as:

[0163]

[0164] Where Tr(·) represents the trace operation. By combining (17) and (20), the following relationship can be derived:

[0165]

[0166] Therefore, the atomic norm minimization problem (18) can be equivalently transformed into:

[0167]

[0168] in, The optimization problem (22) is a convex optimization problem, and the solution vector can be easily obtained using CVX software: Step 5: Estimate all signal directions and their powers. Based on the solution vector Constructing the Toeplitz Matrix for:

[0169]

[0170] right Performing eigenvalue decomposition yields:

[0171]

[0172] in, For the matrix The eigenvalue of i is the eigenvalue λ i The corresponding eigenvector, U s =[u 1 ,u 2 ,L,u L ],∑ s =[λ 1 ,λ 2 ,L,λ L ], matrix The corresponding virtual uniform linear array steering vector for:

[0173]

[0174] in, for The corresponding virtual uniform linear array steering matrix is for:

[0175]

[0176] The matrix This breaks down into:

[0177]

[0178] in, Containment Matrix Before row elements, and Containment Matrix After row element, then and The relationship between can be expressed as:

[0179]

[0180] Among them, the expression of the rotation matrix Γ is:

[0181]

[0182] Similarly, U s can be broken down into:

[0183]

[0184] Among them, U s1 Denotes the matrix U s Before row elements, and U s2 Denotes the matrix U s After row element. The space spanned by the columns and U s1 The space spanned by the columns of represents the same signal subspace, so there exists a non-singular matrix F that satisfies the following relationship:

[0185]

[0186] From (31), we can further deduce:

[0187]

[0188] in,(·) + represents the generalized inverse operation. From equation (32), we can see that: Γ and is a similar matrix and should have the same eigenvalues, while the eigenvalues ​​of the rotation matrix Γ are Therefore, the direction of the signal source can be calculated as:

[0189]

[0190] in, angle(g) is the phase angle of the complex number. Based on the estimated signal direction in (33), the power of the signal can be calculated using the covariance fitting method:

[0191]

[0192] in, L is the estimated signal steering vector.

[0193] Step 6: Reconstruct the MISC array interference plus noise covariance matrix. The noise power can be estimated as The minimum eigenvalue of The reconstructed MISC array interference plus noise covariance matrix is

[0194]

[0195] Step 7: Calculate the adaptive beamforming weight vector. Using the MISC array interference plus noise covariance matrix and the expected signal-directed vector The adaptive beamforming weight vector of the UAV navigation receiver is calculated as:

[0196]

[0197] Those skilled in the art will appreciate that the embodiments of the present disclosure may be provided as methods, systems or computer program products. Therefore, the present disclosure may take the form of a complete hardware embodiment, a complete software embodiment or an embodiment combining software and hardware. Moreover, the present disclosure may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0198] The present disclosure is described with reference to flowcharts and / or block diagrams of methods, devices (systems) and computer program products according to embodiments of the present disclosure. It should be understood that each process and / or block in the flowchart and / or block diagram and the combination of processes and / or blocks in the flowchart and / or block diagram can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 These computer program instructions can also be stored in a computer-readable memory that can guide a computer or other programmable data processing device to work in a specific way, so that the instructions stored in the computer-readable memory produce a product including an instruction device, which implements the functions specified in the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0199] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable device. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0200] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present disclosure rather than to limit its protection scope. Although the present disclosure has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that after reading the present disclosure, those skilled in the art can still make various changes, modifications or equivalent substitutions to the specific implementation methods of the invention, but these changes, modifications or equivalent substitutions are all within the protection scope of the disclosed claims to be approved.

Claims

1. A method for adaptive beamforming for UAV navigation based on MISC common array interpolation, characterized in that: The method comprises: Step 1: Derive the received signal vector of the MISC array of the UAV navigation receiver; Step 2: Calculate the differential signals between different receiving points to obtain the MISC differential common array and virtual signal vector; Step 3: Convert the MISC differential common array into a virtual uniform linear array through interpolation technology; Step 4: Perform signal analysis on the interpolated virtual uniform linear array; Step 5: Estimate all signal directions and signal powers; Step 6: Reconstruct the MISC array interference plus noise covariance matrix based on the received signal; Step 7: Calculate the weight vector for adaptive beamforming based on the reconstructed covariance matrix and the direction of the target signal.

2. The method for adaptive beamforming for UAV navigation based on MISC common array interpolation according to claim 1 is characterized in that: The step 1 comprises: Determine the position of the array element according to the wavelength of the incident signal and the array element spacing; Construct a mathematical model of the received signal; Define the output signal-to-interference-and-noise ratio and set up the optimization problem; Solve the optimal beamforming weight vector through optimization algorithm; calculating an output signal of an adaptive beamformer; The true covariance matrix is ​​estimated from the sample covariance matrix.

3. The method for adaptive beamforming for UAV navigation based on MISC common array interpolation according to claim 1, characterized in that: The step 2 comprises: Vectorized sample covariance matrix Where B is the virtual co-array steering matrix, γ is the power vector, is the noise power, i=vec(I M ); The repeated elements are removed, and the results are reordered according to the position set of the differential co-array virtual array elements to obtain the differential co-array virtual signal vector.

4. The method for adaptive beamforming for UAV navigation based on MISC common array interpolation according to claim 1, characterized in that: The step 3 comprises: Constructing an interpolated virtual uniform linear array IVULA, wherein the virtual uniform linear array IVULA includes a minimum uniform linear array of differential common arrays; The location set of virtual array elements in IVULA is: in, is an integer, and IVULA Virtual Signal It is expressed as: Among them, <·> μ represents the signal corresponding to the virtual array element located at μd; is the differential common array virtual signal vector.

5. The method for adaptive beamforming for UAV navigation based on MISC common array interpolation according to claim 1, characterized in that: The step 5 comprises: Construct the optimization problem: in, Reason The IVULA virtual signal is composed of is the optimization variable of the above optimization problem, is the position set of virtual array elements in IVULA, Reason The positive semidefinite Toeplitz matrix formed as the first column vector; Use CVX to solve the optimization problem, and the solution vector obtained can restore the interpolated uniform linear array signal.

6. The method for adaptive beamforming for UAV navigation based on MISC common array interpolation according to claim 1, characterized in that: The step 6 comprises: in, is the reconstructed MISC array interference plus noise covariance matrix; λ{·} is the eigenvalue operation, I M is the M×M identity matrix, is the estimated signal steering vector, (·) H represents the conjugate transpose.

7. The method for adaptive beamforming for UAV navigation based on MISC common array interpolation according to claim 1, characterized in that: The step 7 comprises: Using the MISC array interference noise covariance matrix and the expected signal-directed vector The adaptive beamforming weight vector of the UAV navigation receiver is calculated as:

8. An adaptive beamforming system for UAV navigation based on MISC common array interpolation, characterized in that: The system comprises: A signal vector acquisition unit, used to derive a signal vector received by the MISC array of the UAV navigation receiver; The differential common array unit is used to calculate the differential signals between different receiving points and obtain the MISC differential common array and virtual signal vector; An interpolation unit, used for converting the MISC differential common array into a virtual uniform linear array by using an interpolation technique; A solution unit, used for performing signal solution on the interpolated virtual uniform linear array; An estimation unit, used for estimating all signal directions and signal powers; A reconstruction unit, configured to reconstruct a MISC array interference plus noise covariance matrix based on the received signal; The weighting unit is used to calculate a weighting vector for adaptive beamforming according to the reconstructed covariance matrix and the direction of the target signal.

9. A computer device, characterized in that: The invention comprises a memory and a processor, wherein a computer program is stored in the memory, and when the processor runs the computer program stored in the memory, the processor executes a method for adaptive beamforming for unmanned aerial vehicle navigation based on MISC common array interpolation according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, which, when executed by a processor, executes the steps of a method for adaptive beamforming of unmanned aerial vehicle navigation based on MISC common array interpolation as described in any one of claims 1 to 7.

Images