A Method and System for Real-Time Estimation of the Direction of an Unmanned Aerial Vehicle

Abstract

The present invention provides a method and system for real-time estimation of the direction of an unmanned aerial vehicle, which relates to the technical field of signal processing. The method includes calculating a covariance matrix located on a uniform linear array based on a two-dimensional array, and mapping the covariance matrix into a real-domain covariance matrix; if the number of unmanned aerial vehicles is known, taking the first K columns of the real-domain covariance matrix to construct a signal subspace matrix, and calculating a noise subspace matrix based on the signal subspace matrix; otherwise, calculating the noise subspace matrix based on the real-domain covariance matrix; constructing a polynomial of the noise subspace matrix, solving the polynomial to obtain an uncoupled solution, and analyzing the uncoupled solution to obtain the angles between the directions of the unmanned aerial vehicles and the X-axis and the Y-axis respectively; performing matrix transformation processing on the angles to obtain a sorting matrix, and using the sorting matrix to process the angles to obtain a real-time estimated value of the direction of the unmanned aerial vehicle. The present invention reduces the computational complexity, reduces the running time of the algorithm, reduces the direction estimation delay, and realizes real-time direction estimation.

Description

Technical Field

[0001] The present invention relates to the technical field of signal processing, and particularly relates to a method and system for real-time estimation of the direction of an unmanned aerial vehicle (UAV). Background Art

[0002] With the gradual improvement of UAV technology and industry, UAVs have begun to assist various aspects of social life. However, there are also criminals using UAVs for illegal activities, such as using UAVs for stalking and secretly taking pictures, operating UAVs to enter restricted areas, and UAV attacks. Therefore, how to quickly identify UAVs and estimate their directions is of great significance for preventing UAV attacks.

[0003] During flight, a UAV will emit or radiate signals. By receiving the UAV signals through an array antenna and estimating the direction of arrival (DOA) of the signals, the direction of the UAV can be obtained. DOA estimation is an important research topic in the field of array signal processing. Among them, the subspace-based DOA estimation method is the most advanced and mature. The most representative one is the multiple signal classification (MUSIC) algorithm proposed by Schmidt R O et al. The main idea of this algorithm is to divide the covariance matrix of the array received data into a signal subspace and a noise subspace orthogonal to it according to the spectral decomposition theory of the matrix. The angle estimation value of the signal is obtained by solving the peak value of the spectral function established by using the orthogonality of these two subspaces. To estimate the direction of the UAV, the pitch angle and azimuth angle of the DOA of the UAV signal need to be obtained. The pitch angle is the angle between the direction where the UAV is located and the XY plane, and the azimuth angle is the angle between the projection of the direction where the UAV is located on the XY plane and the X axis. The MUSIC algorithm is proposed based on a one-dimensional array and cannot perform two-dimensional DOA (pitch angle and azimuth angle) estimation. Therefore, in the prior art, a two-dimensional MUSIC algorithm based on an "L"-shaped array is used for two-dimensional DOA estimation, but it has the following disadvantages: the data of the two-dimensional MUSIC algorithm in the prior art is complex data, and a single multiplication of complex data involves 4 multiplication operations, resulting in a large amount of computation; in the prior art, the noise subspace is extracted through eigenvalue decomposition, and the eigenvalue decomposition has a high computational complexity and a computational cost much greater than that of general matrix operations; in the prior art, a two-dimensional search is used to obtain the estimated values of the UAV direction (azimuth angle and pitch angle), and the estimation accuracy is related to the search step size. The smaller the search step size, the higher the accuracy, but the smaller the search step size, the greater the number of loops in the search process, which will lead to a higher computational complexity. Moreover, since the search dimension is two-dimensional, as the step size decreases, the computational complexity increases exponentially; in addition, the premise of the prior art is that the number of UAVs is known or correctly estimated. In the face of an unknown number of UAVs, it is difficult to accurately estimate in real time. Summary of the Invention

[0004] To solve the problems in the above-mentioned existing technologies, namely high computational complexity, long algorithm running time, time delay in direction estimation, and difficulty in achieving real-time direction estimation, the present invention proposes a method and system for real-time direction estimation of an unmanned aerial vehicle, which reduces the computational complexity, shortens the algorithm running time, reduces the direction estimation time delay, and achieves real-time direction estimation.

[0005] To achieve the above technical effects, the technical solution of the present invention is as follows:

[0006] A method for real-time direction estimation of an unmanned aerial vehicle, the method comprising the following steps:

[0007] S1. Construct a two-dimensional array composed of two linear uniform arrays, and the linear uniform array is composed of a plurality of array elements;

[0008] S2. Based on the two-dimensional array, calculate the covariance matrix located on the uniform linear array, and map the covariance matrix to a real-domain covariance matrix;

[0009] S3. Determine whether the number of unmanned aerial vehicles is known. If so, take the first K columns of the real-domain covariance matrix to construct a signal subspace matrix, and based on the signal subspace matrix, calculate the noise subspace matrix; if not, calculate the noise subspace matrix based on the real-domain covariance matrix;

[0010] S4. Construct a polynomial of the noise subspace matrix, solve the polynomial to obtain uncoupled solutions near the unit circle, and analyze the uncoupled solutions to obtain the angles between the directions of the unmanned aerial vehicles and the X-axis and the Y-axis respectively;

[0011] S5. Perform matrix transformation processing on the angles to obtain a sorting matrix, and use the sorting matrix to process the angles to obtain a real-time estimation value of the direction of the unmanned aerial vehicle.

[0012] Preferably, the two-dimensional array in S1 includes a uniform linear array in the positive X-axis direction and a uniform linear array in the positive Y-axis direction. The uniform linear array in the positive X-axis direction places an array element every d starting from the origin, and a total of M + 1 array elements are placed; the uniform linear array in the positive Y-axis direction places an array element every d starting from the origin, and a total of M + 1 array elements are placed. The uniform linear array in the positive X-axis direction and the uniform linear array in the positive Y-axis direction share the array element at the origin.

[0013] Preferably, the expression for calculating the covariance matrix located on the uniform linear array in the positive X-axis direction is as follows:

[0014]

[0015] Among them, R xdenotes the covariance matrix on a uniform linear array along the positive X-axis direction, denotes R x the approximate covariance of, denotes the output snapshot data matrix of a uniform linear array along the positive X-axis direction, denotes the set of complex numbers, (M + 1)×T denotes the dimension, T denotes the time point, x(t T ) denotes the output vector of reading x(t) of a uniform linear array along the positive X-axis direction at the time point T, (·) H denotes the conjugate transpose of a matrix, (·) * denotes the conjugate of a matrix, (·) T denotes the transpose of a matrix, J denotes the exchange matrix;

[0016] The expression for calculating the covariance matrix located on the uniform linear array along the positive Y-axis direction is as follows:

[0017]

[0018] where, R y denotes the covariance matrix on a uniform linear array along the positive Y-axis direction, denotes R y the approximate covariance of, denotes the output snapshot data matrix of a uniform linear array along the positive Y-axis direction, y(t T ) denotes the output vector of reading y(t) of a uniform linear array along the positive Y-axis direction at the time point T.

[0019] Preferably, in S2, mapping the covariance matrix to a real-domain covariance matrix includes:

[0020] S21. Define the unitary matrix as the following expression:

[0021]

[0022] where, denotes the imaginary unit, I denotes the identity matrix, [[ID=�3]]

[0023] S22. Use the unitary matrix Q m to map the covariance matrix to a real-domain covariance matrix as follows:

[0024]

[0025] where, denotes the real-domain covariance matrix of a uniform linear array along the positive X-axis direction, the real-domain covariance matrix of a uniform linear array along the positive Y-axis direction, denotes the set of real numbers.

[0026] Preferably, in S3, based on the signal subspace matrix, the expression for calculating the noise subspace matrix is as follows:

[0027]

[0028] where, E x denotes the signal subspace matrix constructed by taking the first K columns of , E y denotes the signal subspace matrix constructed by taking the first K columns of , U x denotes the noise subspace matrix of the uniform linear array along the positive X-axis direction, and U y denotes the noise subspace matrix of the uniform linear array along the positive Y-axis direction.

[0029] Preferably, in S3, based on the real-domain covariance matrix, the expression for calculating the noise subspace matrix is as follows:

[0030]

[0031] where, U x denotes the noise subspace matrix of the uniform linear array along the positive X-axis direction, U y denotes the noise subspace matrix of the uniform linear array along the positive Y-axis direction, and μ represents the minimum value.

[0032] Preferably, S4 specifically includes:

[0033] S41. Define the polynomial of the noise subspace matrix U x of the uniform linear array along the positive X-axis direction as f x (u), and the polynomial of the noise subspace matrix U y of the uniform linear array along the positive Y-axis direction as f y (v). The calculation expressions of f x (u) and f y (v) are as follows respectively:

[0034]

[0035] where, u i and v i represent complex variables, p i and q i represent polynomial coefficients;

[0036] S42. Calculate p i and q i respectively as follows:

[0037]

[0038] Among them, diag(,) represents a diagonal matrix, and sum(.) represents a summation function;

[0039] S43. Solve the polynomials f x (u) = 0 and f y (v) = 0 to obtain uncoupled solutions near the unit circle represents the number of uncoupled solutions;

[0040] S44. Analyze the uncoupled solutions to obtain the angles between the UAV direction and the X-axis and Y-axis as follows:

[0041]

[0042] Among them, represents the angle between the UAV direction and the X-axis, represents the angle between the UAV direction and the Y-axis, arccos represents the inverse cosine function, arg represents the complex argument, λ represents the wavelength, π represents the pi, and d represents the element spacing of the uniform linear array.

[0043] Preferably, in S5, the matrix transformation process of the angles is performed to obtain a sorting matrix, including:

[0044] S501. Use the angle between the UAV direction and the X-axis to construct the first steering matrix represents the column vector of the first steering matrix; and use the angle between the UAV direction and the Y-axis to construct the second steering matrix represents the column vector of the second steering matrix;

[0045] S502. Based on the first steering matrix and the second steering matrix calculate the cross-covariance matrix of the uniform linear array x(t) along the positive X-axis direction and the uniform linear array y(t) along the positive Y-axis direction as follows:

[0046]

[0047] Among them, R s represents the signal covariance matrix, represents the estimated value of the signal covariance matrix;

[0048] S503. Based on the cross-covariance matrix construct the following minimization problem:

[0049]

[0050] Solve the minimization problem to obtain the optimal matrix Denote the pseudo-inverse of the matrix;

[0051] S505. Convert the optimal matrix into a sorting matrix g(·) represents the conversion function.

[0052] Preferably, using the sorting matrix to process the included angle to obtain a real-time estimated value of the UAV direction includes:

[0053] S511. Use the sorting matrix to calculate the included angle between the UAV direction and the Y-axis and sort them as follows:

[0054]

[0055] where, represents the included angle between the sorted UAV direction and the Y-axis;

[0056] S512. Based on the included angle between the sorted UAV direction and the Y-axis and the included angle between the UAV direction and the X-axis form a UAV included angle pair

[0057] S513. Calculate the real-time estimated value of the UAV direction based on the UAV included angle pair The real-time estimated value of the UAV direction includes an azimuth estimated value and a pitch estimated value The calculation expression of the azimuth estimated value is as follows:

[0058]

[0059] The calculation expression of the pitch estimated value is as follows:

[0060]

[0061] The present invention proposes a real-time UAV direction estimation system, and the system includes:

[0062] A construction module for constructing a two-dimensional array composed of two linear uniform arrays, and the linear uniform array is composed of several array elements;

[0063] A mapping module for calculating a covariance matrix located on the uniform linear array according to the two-dimensional array, and mapping the covariance matrix into a real-domain covariance matrix;

[0064] The noise subspace matrix calculation module is used to determine whether the number of UAVs is known. If so, the first K columns of the real-domain covariance matrix are taken to construct a signal subspace matrix, and based on the signal subspace matrix, a noise subspace matrix is calculated; if not, the noise subspace matrix is calculated based on the real-domain covariance matrix;

[0065] The polynomial solving module is used to construct a polynomial of the noise subspace matrix, solve the polynomial to obtain uncoupled solutions near the unit circle, and analyze the uncoupled solutions to obtain the angles between the UAV directions and the X-axis and Y-axis respectively;

[0066] The direction estimation module is used to perform matrix transformation processing on the angles to obtain a sorting matrix, and use the sorting matrix to process the angles to obtain a real-time estimated value of the UAV direction. Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

[0067] The present invention proposes a method and system for real-time estimation of UAV direction. First, by constructing a two-dimensional array and mapping the covariance matrix on a uniform linear array to the real domain, the operation complexity is significantly reduced; secondly, matrix operations are used to replace eigenvalue decomposition to calculate the noise subspace, reducing the calculation cost of the noise subspace. By judging whether the number of UAVs is known, the calculation method of the noise subspace matrix is switched, and all methods do not require eigenvalue decomposition; then, the two-dimensional array in the XY plane and the two-dimensional signal model containing azimuth and elevation angles are transformed into two one-dimensional signal models, and each model has only one angle variable, which are the angles between the UAV direction and the X-axis and the angle between the UAV direction and the Y-axis respectively; and instead of using the traversal search method, the angle estimation is decoupled by constructing polynomial solving to directly obtain the analytical solution of the angle. Compared with the traversal search process, this process does not need to make a trade-off between accuracy and complexity, and can greatly reduce the complexity and direction estimation delay while maintaining the accuracy unchanged; further, when calculating the noise subspace, it is judged whether the number of UAVs K is known to switch different calculation methods of the noise subspace. The present invention does not require the UAV number K parameter and can correctly perform direction estimation in a complex UAV intrusion scenario. Description of the Drawings

[0068] Figure 1 It represents a flowchart of a method for real-time estimation of UAV direction proposed in an embodiment of the present invention;

[0069] Figure 2 It represents a schematic diagram of the geometric layout of the two-dimensional array proposed in an embodiment of the present invention;

[0070] Figure 3 It represents a schematic diagram of UAV signal acquisition proposed in an embodiment of the present invention;

[0071] Figure 4 Another flowchart showing a method for real-time estimation of the direction of an unmanned aerial vehicle (UAV) proposed in an embodiment of the present invention;

[0072] Figure 5 A block diagram showing the structure of a system for real-time estimation of the direction of an unmanned aerial vehicle (UAV) proposed in an embodiment of the present invention. Detailed implementation manners

[0073] The accompanying drawings are only for illustrative purposes and should not be construed as limitations on this patent;

[0074] For those skilled in the art, it is understandable that some well-known content descriptions in the accompanying drawings may be omitted;

[0075] For the convenience of understanding this embodiment, first, the prior art information of this embodiment is introduced as follows:

[0076] In the prior art, the two-dimensional MUSIC algorithm based on an "L"-shaped array is used for two-dimensional DOA estimation. A brief description of its steps is as follows:

[0077] Set up an "L"-shaped antenna array, with a uniform linear array (ULA, Uniform Linear Array) composed of M elements on the X-axis and a ULA composed of M elements on the Y-axis. The two ULAs share the element at the origin to form a two-dimensional array in the shape of an "L" containing 2M - 1 elements;

[0078] Read the array output T times at different times to obtain the output data

[0079] Calculate the covariance matrix of the array output

[0080] Perform eigenvalue decomposition on the covariance matrix EIG(R) = UΣU H , where U is the eigenvector matrix and Σ is a diagonal matrix whose diagonal elements are the eigenvalues of R arranged in ascending order;

[0081] Take the first 2M - 1 - K column vectors of the eigenvector matrix to form the noise subspace matrix U n ∈C (2M-1)×(2M-1-K) , where K is the number of UAVs;

[0082] Substitute the azimuth angle θ ∈ [0, 360) and elevation angle φ ∈ [0, 90] within the DOA range into the spatial spectrum formula Perform a traversal search to obtain the spatial spectrum surface, and the search values θ and φ corresponding to the peak positions of the surface are the DOA estimation values.

[0083] The prior art has the following disadvantages:

[0084] The data of the prior art is complex data. A single multiplication of complex data involves 4 multiplication operations, resulting in a large amount of computation. The prior art extracts the noise subspace through eigenvalue decomposition, but the eigenvalue decomposition has a high computational complexity and a computational cost much greater than that of general matrix operations. The prior art obtains the estimated values of the UAV direction (azimuth and pitch angle) through two-dimensional search. The estimation accuracy is related to the search step size. The smaller the search step size, the higher the accuracy. However, the smaller the search step size, the greater the number of loops in the search process, which will lead to a higher computational complexity. Therefore, the prior art needs to make a trade-off between accuracy and computational complexity. And since the search dimension of the prior art is two-dimensional, as the step size shrinks, the computational complexity increases exponentially. After performing eigenvalue decomposition in the prior art, it is necessary to take M-K eigenvectors to form the noise subspace matrix U n , so the prerequisite for the application of the prior art is that the number K of UAVs is known or correctly estimated, otherwise the prior art will not be able to operate properly. However, in actual scenarios, the intruding UAVs are released by the opponent, so the number is unknown; and since the UAVs can take off and land at any time, and some UAVs will also crash or be shot down during the intrusion process, the number K of UAVs changes frequently and is difficult to accurately estimate.

[0085] In summary, the prior art has a high computational complexity, a long algorithm running time, a time delay in direction estimation, and it is difficult to achieve real-time direction estimation. Coupled with the fast flight speed of the UAV, there will be a large deviation between the direction estimation result and the real position of the UAV. To solve the above problems, the present invention proposes a method and system for real-time estimation of UAV direction. The following is a symbol description table for the technical solution design of the present invention:

[0086] Table 1 Symbol Description Table

[0087]

[0088] The technical solution of the present invention will be further described below with reference to the drawings and embodiments.

[0089] Embodiment 1

[0090] As Figure 1 shown, the present invention proposes a method for real-time estimation of UAV direction, and the method includes the following steps:

[0091] S1. Construct a two-dimensional array composed of two linear uniform arrays, and the linear uniform array is composed of several array elements;

[0092] In S1, refer to Figure 2, the two-dimensional array is in an "L" shape. The two-dimensional array includes a uniformly linear array along the positive X-axis direction and a uniformly linear array along the positive Y-axis direction. In the uniformly linear array along the positive X-axis direction, an element is placed every interval d starting from the origin, and a total of M + 1 elements are placed. The coordinates of the elements can be expressed as {(kd, 0)|k = 0, …, M}, where d is the unit spacing of the elements, generally set to half the wavelength of the received signal; in the uniformly linear array along the positive Y-axis direction, an element is placed every interval d starting from the origin, and a total of M + 1 elements are placed. The uniformly linear array along the positive X-axis direction and the uniformly linear array along the positive Y-axis direction share the element at the origin, and the coordinates of the elements can be expressed as {(0, kd)|k = 0, …, M}. The uniformly linear array has a total of 2M + 1 elements.

[0093] See Figure 3 , the two-dimensional array collects UAV signals. Suppose there are K UAVs, the wavelength of the signals transmitted outward is denoted as λ, and the UAV signals are denoted as {s1(t), s2(t), …, s K (t)}, and the signal powers are respectively Denote the angles between the directions of the K UAVs and the X-axis as {ω1, ω2, …, ω K}, the angles with the Y-axis as {β1, β2, …, β K}, the azimuth angles as {θ1, θ2, …, θ K}, and the elevation angles as {φ1, φ2, …φ K}. Then the received signal model can be expressed as:

[0094] z(t) = Cs(t) + n(t)

[0095] where is the output vector, x0(t) is the output of the element at the origin, x i (t) is the output of the element with coordinates (id, 0), y i (t) is the output of the element with coordinates (0, id); is the signal vector; is the Gaussian additive white noise vector, and the noise power is denoted as is the two-dimensional array steering vector, is the one-dimensional steering vector after removing the origin, is the one-dimensional steering vector.

[0096] Denote the output of the uniformly linear array along the positive X-axis direction as Denote the output of the uniformly linear array along the positive Y-axis direction as Then the uniformly linear array x(t) along the positive X-axis direction and the uniformly linear array y(t) along the positive Y-axis direction can be expressed as the following model:

[0097] x(t) = A x s(t) + n x (t)

[0098] y(t) = A y s(t) + n y (t)

[0099] where and is a one - dimensional steering matrix; and is a noise vector.

[0100] S2. Based on the two - dimensional array, calculate the covariance matrix located on the uniform linear array, and map the covariance matrix to a real - domain covariance matrix;

[0101] In S2, first calculate the covariance of the output vectors of the two uniform linear arrays in the "L" - shaped two - dimensional array respectively:

[0102]

[0103] Then, in actual use, use the second - order statistics to calculate the expression of the covariance matrix located on the uniform linear array along the positive X - axis as follows:

[0104]

[0105] where R x represents the covariance matrix on the uniform linear array along the positive X - axis, represents the approximate covariance of R x of, represents the output snapshot data matrix of the uniform linear array along the positive X - axis, represents the set of complex numbers, (M + 1)×T represents the dimension, T represents the time point, x(t T ) represents the output vector of reading x(t) of the uniform linear array along the positive X - axis at the time point T, (·) H represents the conjugate transpose of the matrix, (·) * represents the conjugate of the matrix, (·) T represents the transpose of the matrix, J represents the exchange matrix;

[0106] Calculate the expression of the covariance matrix located on the uniform linear array along the positive Y - axis as follows:

[0107]

[0108] where R yrepresents the covariance matrix of the uniform linear array along the positive direction of the Y axis, Represents R y The approximate covariance of represents the output snapshot data matrix of the uniform linear array along the positive direction of the Y axis, y(t T ) represents the output vector of the uniform linear array y(t) along the positive direction of the Y axis read at time point T. S2 maps the covariance matrix to a real domain covariance matrix;

[0109] S21. Define the unitary matrix The following expression:

[0110]

[0111] in, represents the imaginary unit, I represents the unit matrix,

[0112] S22. Using the unitary matrix Q m The covariance matrix is mapped to the real domain covariance matrix as follows:

[0113]

[0114] in, represents the real domain covariance matrix of the uniform linear array along the positive direction of the X axis, The real domain covariance matrix of the uniform linear array along the positive Y-axis, represents the set of real numbers.

[0115] S3. Determine whether the number of drones is known. If so, take the first K columns of the real domain covariance matrix to construct a signal subspace matrix, and calculate the noise subspace matrix based on the signal subspace matrix; if not, calculate the noise subspace matrix based on the real domain covariance matrix;

[0116] In S3, when the number of drones K is known, the real domain covariance matrix is taken The first K columns of the signal subspace matrix are constructed Based on the signal subspace matrix E x , calculate the noise subspace matrix of the uniform linear array along the positive direction of the X axis by orthogonal projection as follows:

[0117]

[0118] Similarly, take The first K columns construct the signal subspace matrix E y , based on the signal subspace matrix E y, calculate the noise subspace matrix of the uniform linear array along the positive Y-axis direction through orthogonal projection as follows:

[0119]

[0120] where, E x denotes the signal subspace matrix constructed by taking the first K columns of , E y denotes the signal subspace matrix constructed by taking the first K columns of , U x denotes the noise subspace matrix of the uniform linear array along the positive X-axis direction, U y denotes the noise subspace matrix of the uniform linear array along the positive Y-axis direction.

[0121] When the number of UAVs K is unknown, based on the real-domain covariance matrix and , the expression for calculating the noise subspace matrix through pseudo-orthogonal projection is as follows:

[0122]

[0123] where, U x denotes the noise subspace matrix of the uniform linear array along the positive X-axis direction, U y denotes the noise subspace matrix of the uniform linear array along the positive Y-axis direction, μ represents the minimum value, and generally can be set to μ = 10 -3 .

[0124] S4. Construct a polynomial of the noise subspace matrix, solve the polynomial to obtain the uncoupled solutions near the unit circle, and analyze the uncoupled solutions to obtain the angles between the UAV directions and the X-axis and Y-axis respectively;

[0125] In S4, since the noise subspace matrix is orthogonal to the steering vector, there is Therefore, the specific steps of S4 include:

[0126] S41. Define the polynomial of the noise subspace matrix U x of the uniform linear array along the positive X-axis direction as f x (u), and the polynomial of the noise subspace matrix U y of the uniform linear array along the positive Y-axis direction as f y (v). The calculation expressions of f x (u) and f y (v) are as follows respectively:

[0127]

[0128] Among them, u i and v i represent complex variables, and p i and q i represent polynomial coefficients;

[0129] S42. Calculate p i and q i respectively as follows:

[0130]

[0131] Among them, diag(,) represents a diagonal matrix, and sum(.) represents a summation function;

[0132] S43. Solve the polynomials f x (u) = 0 and f y (v) = 0 to obtain uncoupled solutions near the unit circle represents the number of uncoupled solutions;

[0133] In S43, since both polynomials are of degree 2M, 2M solutions can be obtained for each. Due to the conjugate symmetry of the polynomial coefficients, the obtained solutions are pairwise coupled (the coupled solutions have the same complex argument). Therefore, M uncoupled solutions can be obtained, and only uncoupled solutions are near the unit circle (i.e., the modulus is 1), and denote these solutions as for subsequent calculations.

[0134] S44. Analyze the uncoupled solutions to obtain the angles between the UAV direction and the X-axis and Y-axis as follows:

[0135]

[0136] Among them, represents the angle between the UAV direction and the X-axis, represents the angle between the UAV direction and the Y-axis, arccos represents the inverse cosine function, arg represents the complex argument, λ represents the wavelength, π represents the pi, and d represents the element spacing of the uniform linear array; at this time number of and Although obtained separately, the matching relationship between them is unknown. At this time, there is a sorting matrix such that makes match.

[0137] S5. Perform matrix transformation processing on the included angle to obtain a sorting matrix, and use the sorting matrix to process the included angle to obtain a real-time estimated value of the UAV direction.

[0138] In S5, the performing matrix transformation processing on the included angle to obtain a sorting matrix includes:

[0139] S501. Utilize the included angle between the UAV direction and the X-axis to construct a first guiding matrix denote the column vectors of the first guiding matrix; and utilize the included angle between the UAV direction and the Y-axis to construct a second guiding matrix denote the column vectors of the second guiding matrix;

[0140] where the approximate covariance of R x can be expressed as the model Let then First, calculate the initial cross-covariance matrix of x(t) and y(t)

[0141]

[0142] Let then transform the initial cross-covariance matrix according to the steps of S502;

[0143] S502. Based on the first guiding matrix and the second guiding matrix the cross-covariance matrix of the uniform linear array x(t) along the positive X-axis direction and the uniform linear array y(t) along the positive Y-axis direction is expressed as follows:

[0144]

[0145] where, R s denotes the signal covariance matrix, denotes the estimated value of the signal covariance matrix;

[0146] S503. Based on the cross-covariance matrix construct the following minimization problem:

[0147]

[0148] S504. Solve the minimization problem to obtain the optimal matrix denote the matrix pseudo-inverse;

[0149] S505. Transform the optimal matrix into a sorting matrix g(·) represents the transformation function.

[0150] In S505, the optimal matrix sets the maximum modulus value of each row to 1, and the remaining values to 0, and passes it into the transformation function g(·) to obtain the sorting matrix

[0151] Using the sorting matrix to process the included angle to obtain the real-time estimated value of the UAV direction includes:

[0152] S511. Using the sorting matrix to sort the included angle between the UAV direction and the Y-axis as follows:

[0153]

[0154] where represents the sorted included angle between the UAV direction and the Y-axis;

[0155] S512. Based on the sorted included angle between the UAV direction and the Y-axis and the included angle between the UAV direction and the X-axis to form a UAV included angle pair

[0156] S513. Based on the UAV included angle pair calculate the real-time estimated value of the UAV direction, and the real-time estimated value of the UAV direction includes the azimuth angle estimated value and the pitch angle estimated value The calculation expression of the azimuth angle estimated value is as follows:

[0157]

[0158] The calculation expression of the pitch angle estimated value is as follows:

[0159]

[0160] In this embodiment, first, the covariance matrix output data of the uniform linear array that constitutes the two-dimensional array is mapped to the real number domain to reduce the complexity of multiplication operations in subsequent steps, and the complexity scale of subsequent real number operations is reduced to 1 / 4 of the original scale; second, matrix multiplication operations are used to calculate the noise subspace without using eigenvalue decomposition, reducing the computational cost of the noise subspace; then, a two-dimensional array signal model is established using a one-dimensional steering vector, and a matching algorithm is used to decouple the original azimuth and elevation two-dimensional DOA estimation into two one-dimensional DOA estimations; and instead of using a search method, the DOA estimation value is obtained by constructing a polynomial and directly solving. Compared with the search process, this process does not require a trade-off between accuracy and complexity, and can greatly reduce the complexity while maintaining the accuracy unchanged; further, when calculating the noise subspace, different noise subspace calculation methods are switched by judging whether the number of UAVs is known. When the number of targets is unknown, the quasi-orthogonal projection algorithm is used to calculate the noise subspace. This algorithm does not require the signal source number parameter and can correctly estimate the direction in a complex UAV intrusion scenario.

[0161] Embodiment 2

[0162] See Figure 4 , this embodiment describes the steps of an embodiment of a method for real-time UAV direction estimation proposed in the above embodiment, specifically including the following steps:

[0163] Step 1: Arrange a "L"-shaped two-dimensional array using 2M + 1 array elements;

[0164] Step 2: Calculate the covariance matrices R x and R y of the two uniform linear arrays located on the X-axis and Y-axis respectively;

[0165]

[0166]

[0167] Step 3: Map the covariance matrices R x and R y to the real number domain covariance matrices and

[0168]

[0169] Step 4: Judge whether the number of UAVs K is known. If it is known, execute Step 4.1 and skip Step 4.2; if it is unknown, skip Step 4.1 and execute Step 4.2

[0170] Step 4.1: Take the real number domain covariance matrices and Construct \(E\) for the first \(K\) columns respectively x and \(E\) y , calculate the noise subspace matrix \(U\) x and \(U\) y

[0171]

[0172] Step 4.2: Calculate the noise subspace matrix \(U\) x and \(U\) y

[0173]

[0174] Step 5: Calculate the polynomial coefficients \(p\) i , \(i = 0,\cdots,2M\) and \(q\) i , \(i = 0,\cdots,2M\)

[0175]

[0176] Step 6: Solve the polynomials \(f\) x (u)=0 and \(f\) y (v)=0, and obtain the uncoupled solutions near the unit circle

[0177] Step 7: Analyze the angles between the UAV direction and the \(X\)-axis and \(Y\)-axis

[0178]

[0179] Step 8: Construct the first steering matrix and the second steering matrix

[0180] Step 9: Calculate the cross-covariance matrix

[0181] Step 1: Calculate the optimal matrix and convert it to a sorted matrix

[0182] Step 11: Sort to obtain

[0183]

[0184] Step 12: Calculate the azimuth angle and the pitch angle

[0185]

[0186] The steps of a method for real-time estimation of the direction of an unmanned aerial vehicle (UAV) proposed in this embodiment have the following advantages:

[0187] First, multiple methods are used to reduce the computational complexity. Reducing the computational complexity means reducing the amount of calculation, enabling the algorithm proposed in the present invention to quickly obtain the UAV direction estimation result, with real-time performance, including:

[0188] 1) Use a unitary matrix to map the covariance matrix in the complex domain to the real domain. The scale of real arithmetic operations is one-fourth of that of complex numbers; while the prior art directly processes data in the complex domain with a large amount of computation.

[0189] 2) Use matrix multiplication operations to calculate the noise subspace, and switch the calculation method of the noise subspace matrix by determining whether the number of UAVs K is known. All methods do not require eigenvalue decomposition; while the prior art needs to extract the noise subspace matrix through eigenvalue decomposition with high computational complexity.

[0190] 3) Transform the two-dimensional array located in the XY plane and the two-dimensional signal model containing azimuth and elevation angles into two one-dimensional signal models. Each model has only one angle variable, namely ω and β; after solving ω and β respectively, match the two included angles through a sorting matrix; and when solving the two one-dimensional signal models, instead of using the traversal search method, establish a polynomial model and solve it to directly obtain the analytical solution of the angle. In contrast, the prior art not only needs to perform a search traversal to calculate the spatial spectrum, but also this search process is two-dimensional, which will bring a huge amount of computation.

[0191] Second, the present invention can select different calculation methods for the noise subspace matrix by determining whether the number of UAVs is known. When the number of UAVs is unknown, the present invention uses a class of projection matrices to calculate the noise subspace. The introduction of this algorithm enables the direction estimation process not to use the number of UAVs K as a parameter. Therefore, the present invention can still correctly estimate the direction of arrival (DOA) when the number of UAVs is unknown. In the prior art, it is required that the number of signal sources is known or has been correctly estimated, otherwise the prior art cannot achieve DOA estimation. However, in actual scenarios, the invading UAVs are released by the opposing party, so the number is unknown; and since UAVs can take off and land at any time, and some UAVs will also crash or be shot down during the invasion process, the number of UAVs K changes frequently and is difficult to accurately estimate.

[0192] Embodiment 3

[0193] See Figure 5 , this embodiment proposes a real-time UAV direction estimation system, and the system includes:

[0194] A construction module for constructing a two-dimensional array composed of a plurality of array elements;

[0195] A mapping module, configured to calculate a covariance matrix located on the uniform linear array according to the two-dimensional array, and map the covariance matrix into a real-domain covariance matrix;

[0196] A noise subspace matrix calculation module, configured to determine whether the number of drones is known. If so, take the first K columns of the real-domain covariance matrix to construct a signal subspace matrix, and calculate a noise subspace matrix based on the signal subspace matrix; if not, calculate the noise subspace matrix based on the real-domain covariance matrix;

[0197] A polynomial solving module, configured to construct a polynomial of the noise subspace matrix, solve the polynomial to obtain uncoupled solutions near the unit circle, and analyze the uncoupled solutions to obtain the angles between the drone directions and the X-axis and the Y-axis respectively;

[0198] A direction estimation module, configured to perform matrix transformation processing on the angles to obtain a sorting matrix, and process the sorting matrix to obtain a real-time estimated value of the drone direction.

[0199] In this embodiment, firstly, by constructing a two-dimensional array and mapping the covariance matrix to the real domain, the operation complexity is significantly reduced; secondly, matrix operations are used to replace eigenvalue decomposition to calculate the noise subspace, reducing the calculation cost of the noise subspace. The calculation method of the noise subspace matrix is switched by determining whether the number of drones is known, and all methods do not require eigenvalue decomposition; then, the two-dimensional array in the XY plane and the two-dimensional signal model containing azimuth and elevation angles are transformed into two one-dimensional signal models, each model has only one angle variable, which are the angles between the drone directions and the X-axis and the Y-axis respectively; and instead of using the traversal search method, angle estimation decoupling is realized by constructing polynomial solving, and the analytical solution of the angle is directly obtained. Compared with the traversal search process, this process does not need to make a trade-off between accuracy and complexity, and can greatly reduce the complexity and direction estimation delay while maintaining the accuracy unchanged; further, when calculating the noise subspace, the calculation method of different noise subspaces is switched by determining whether the number of drones K is known. The present invention does not require the drone number K parameter and can correctly perform direction estimation in a complex drone intrusion scenario.

[0200] Obviously, the above embodiments of the present invention are only examples for clearly illustrating the present invention, rather than limiting the implementation manners of the present invention. For those of ordinary skill in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to enumerate all implementation manners here. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included in the protection scope of the claims of the present invention.

Claims

1. A method for real-time estimation of the direction of an unmanned aerial vehicle, characterized in that, The method includes the following steps: S1. Construct a two-dimensional array composed of two uniform linear arrays, where each uniform linear array is composed of a number of array elements; S2. Based on the two-dimensional array, calculate the covariance matrix located on the uniform linear array, and map the covariance matrix to a real-domain covariance matrix; S3. Determine whether the number of UAVs is known. If so, take the first columns to construct a signal subspace matrix, and calculate a noise subspace matrix based on the signal subspace matrix; if not, calculate the noise subspace matrix based on the real-domain covariance matrix; S4. Construct a polynomial of the noise subspace matrix, solve the polynomial to obtain uncoupled solutions near the unit circle, and analyze the uncoupled solutions to obtain the angles between the UAV direction and the X-axis and Y-axis respectively; S5. Perform matrix transformation processing on the angles to obtain a sorting matrix, and use the sorting matrix to process the angles to obtain a real-time estimated value of the UAV direction; The two-dimensional array described in S1 includes a uniform linear array in the positive X-axis direction and a uniform linear array in the positive Y-axis direction. The uniform linear array in the positive X-axis direction places an element every d starting from the origin, where d is the unit spacing of the elements, and a total of M + 1 elements are placed; the uniform linear array in the positive Y-axis direction places an element every and a total of M + 1 elements are placed. The uniform linear array in the positive X-axis direction and the uniform linear array in the positive Y-axis direction share the element at the origin; The expression for calculating the covariance matrix located on the uniform linear array in the positive X-axis direction is as follows: Among them, represents the covariance matrix on a uniform linear array along the positive X-axis direction, represents the approximate covariance of represents the output snapshot data matrix of a uniform linear array along the positive X-axis direction, represents the set of complex numbers, represents the dimension, T represents the time point, represents reading the output vector of a uniform linear array along the positive X-axis direction at the time point T of represents the conjugate transpose of a matrix, represents the conjugate of a matrix, represents the transpose of a matrix, represents the permutation matrix; The expression for calculating the covariance matrix located on the uniform linear array in the positive Y-axis direction is as follows: Among them, represents the covariance matrix on the uniform linear array in the positive Y-axis direction, represents the approximate covariance of, represents the output snapshot data matrix of the uniform linear array in the positive Y-axis direction, represents reading the output vector of the uniform linear array in the positive Y-axis direction at time point T ​ 2. The real-time direction estimation method of the drone according to claim 1, characterized in that What S2 described as mapping the covariance matrix to a real-domain covariance matrix includes: S21. Define a unitary matrix The following expression: Among them, represents the imaginary unit, represents the identity matrix, ; S22. Using the unitary matrix Map the covariance matrix to a covariance matrix in the real number field as follows: Among them, represents the real-domain covariance matrix of a uniform linear array along the positive X-axis direction, the real-domain covariance matrix of a uniform linear array along the positive Y-axis direction, represents the set of real numbers.

3. The real-time direction estimation method of the drone according to claim 2, wherein The expression for calculating the noise subspace matrix based on the signal subspace matrix described in S3 is as follows: Among them, represents the signal subspace matrix constructed by taking the first columns of ; represents the signal subspace matrix constructed by taking the first columns of ; represents the noise subspace matrix of the uniform linear array along the positive X-axis direction, represents the noise subspace matrix of the uniform linear array along the positive Y-axis direction.

4. The real-time estimation method for the direction of the drone according to claim 3, characterized in that, The expression for calculating the noise subspace matrix based on the real-domain covariance matrix described in S3 is as follows: Among them, represents the noise subspace matrix of a uniform linear array along the positive X-axis direction, represents the noise subspace matrix of a uniform linear array along the positive Y-axis direction, represents the minimum value.

5. The real-time estimation method for the direction of the unmanned aerial vehicle according to claim 3 or 4, characterized in that S4 specifically includes: S41. Define the noise subspace matrix of the uniform linear array along the positive X-axis direction The polynomial of is The polynomial of the noise subspace matrix of the uniform linear array along the positive Y-axis direction is and The calculation expressions of are as follows respectively: Among them, and represent complex variables, and represent polynomial coefficients; S42. For and calculate respectively as follows: Among them, represents a diagonal matrix, represents a summation function; S43. Solve the polynomials = 0 and = 0 to obtain the uncoupled solutions near the unit circle , denotes the number of uncoupled solutions; S44. Analyze the non-coupled solution to obtain the following angles between the directions of the UAV and the X-axis and Y-axis respectively: Among them, represents the angle between the UAV direction and the X-axis, represents the angle between the UAV direction and the Y-axis, represents the arccosine function, arg represents the complex amplitude angle, represents the wavelength, represents pi, d represents the element spacing of the uniform linear array.

6. The method for real-time estimation of the direction of the unmanned aerial vehicle according to claim 5, wherein, What S5 described as performing matrix transformation processing on the angles to obtain a sorting matrix includes: S501. Use the included angle between the direction of the drone and the X-axis to construct the first steering matrix , where represents the column vectors of the first steering matrix; and use the included angle between the direction of the drone and the Y-axis to construct the second steering matrix , where represents the column vectors of the second steering matrix; S502. Based on the first steering matrix and the second steering matrix , the cross-covariance matrix of the uniform linear array along the positive X-axis direction and the uniform linear array along the positive Y-axis direction is expressed as follows: Among them, represents the signal covariance matrix, represents the estimated value of the signal covariance matrix; S503. Based on the cross-covariance matrix Construct the following minimization problem: Solve the minimization problem to obtain the optimal matrix , denotes the Moore-Penrose pseudoinverse of the matrix; S505. Convert the optimal matrix into a sorting matrix , represents a conversion function.

7. The method for real-time estimation of the direction of an unmanned aerial vehicle according to claim 6, wherein What is described as using the sorting matrix to process the angles to obtain a real-time estimated value of the UAV direction includes: S511. Sort the included angle between the direction of the drone and the Y-axis by using the sorting matrix as follows: Among them, represents the angle between the sorted direction of the drone and the Y-axis; S512. Based on the angle between the sorted drone direction and the Y-axis and the angle between the drone direction and the X-axis , form a drone angle pair ; S513. Based on the included angle of the UAV , calculate the real-time estimated value of the UAV direction, and the real-time estimated value of the UAV direction includes the azimuth estimated value and the pitch estimated value . The calculation expression of the azimuth estimated value is as follows: The estimated pitch angle value has the following calculation expression: 。 8. A real-time direction estimation system for an unmanned aerial vehicle, characterized in that, The system includes: A construction module for constructing a two-dimensional array composed of two uniform linear arrays, where each uniform linear array is composed of a number of array elements; A mapping module for calculating the covariance matrix located on the uniform linear array according to the two-dimensional array and mapping the covariance matrix to a real-domain covariance matrix; A noise subspace matrix calculation module, which is used to determine whether the number of drones is known. If so, the first columns are taken to construct a signal subspace matrix, and based on the signal subspace matrix, a noise subspace matrix is calculated; if not, a noise subspace matrix is calculated based on the real-domain covariance matrix; A polynomial solving module for constructing a polynomial of the noise subspace matrix, solving the polynomial to obtain uncoupled solutions near the unit circle, and analyzing the uncoupled solutions to obtain the angles between the UAV direction and the X-axis and Y-axis respectively; A direction estimation module for performing matrix transformation processing on the angles to obtain a sorting matrix and using the sorting matrix to process the angles to obtain a real-time estimated value of the UAV direction; The two-dimensional array includes a uniform linear array in the positive X-axis direction and a uniform linear array in the positive Y-axis direction. The uniform linear array in the positive X-axis direction places an element every d starting from the origin, where d is the unit spacing of the elements, and a total of M + 1 elements are placed; the uniform linear array in the positive Y-axis direction places an element every and a total of M + 1 elements are placed. The uniform linear array in the positive X-axis direction and the uniform linear array in the positive Y-axis direction share the element at the origin; The expression for calculating the covariance matrix located on the uniform linear array in the positive X-axis direction is as follows: Among them, represents the covariance matrix on a uniform linear array along the positive X-axis direction, represents the approximate covariance of represents the output snapshot data matrix of a uniform linear array along the positive X-axis direction, represents the set of complex numbers, represents the dimension, T represents the time point, represents reading the output vector of a uniform linear array along the positive X-axis direction at the time point T of represents the conjugate transpose of a matrix, represents the conjugate of a matrix, represents the transpose of a matrix, represents the permutation matrix; The expression for calculating the covariance matrix located on the uniform linear array in the positive Y-axis direction is as follows: Among them, represents the covariance matrix on the uniformly linear array in the positive Y-axis direction, represents the approximate covariance of represents the output snapshot data matrix of the uniformly linear array in the positive Y-axis direction, represents reading the output vector of the uniformly linear array in the positive Y-axis direction at time point T ​

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