Method and system for estimating direction of unmanned aerial vehicle in real time

Abstract

The invention provides an unmanned aerial vehicle direction real-time estimation method and system, and relates to the technical field of signal processing, and the method comprises the steps: calculating a covariance matrix located on a uniform linear array based on a two-dimensional array, and mapping the covariance matrix into a real number field covariance matrix; if the number of the unmanned aerial vehicles is known, first K columns of the real number field covariance matrix are taken to construct a signal subspace matrix, and a noise subspace matrix is calculated based on the signal subspace matrix; otherwise, calculating a noise subspace matrix based on the real number field covariance matrix; constructing a polynomial of the noise subspace matrix, solving the polynomial to obtain a non-coupling solution, and analyzing the non-coupling solution to obtain an included angle between the direction of the unmanned aerial vehicle and the X axis and an included angle between the direction of the unmanned aerial vehicle and the Y axis; and performing matrix conversion processing on the included angle to obtain a sorting matrix, and processing the included angle by using the sorting matrix to obtain a real-time estimation value of the direction of the unmanned aerial vehicle. According to the method, the operation complexity is reduced, the algorithm operation time is shortened, the direction estimation time delay is reduced, and real-time local direction estimation is realized.

Description

Technical Field

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

[0002] With the gradual improvement of drone technology and industry, drones have begun to assist in all aspects of social life. However, there are also criminals who use drones to carry out illegal activities, such as using drones to follow and take secret photos, operating drones into confidential areas, drone attacks, etc. Therefore, how to quickly identify drones and estimate their direction is of great significance to preventing and controlling drone attacks.

[0003] UAVs will emit or radiate signals during flight. The direction of the UAV can be obtained by receiving the UAV signal through the array antenna and estimating the direction of arrival (DOA) of the signal. 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 algorithm (MUSIC) proposed by Schmidt RO et al. The main idea of ​​this algorithm is to divide the covariance matrix of the array received data into a signal subspace and an orthogonal noise subspace based on 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 orthogonal characteristics of the two subspaces. To estimate the direction of the UAV, it is necessary to obtain the pitch angle and azimuth angle of the UAV signal DOA, where the pitch angle is the angle between the direction of the UAV and the XY plane, and the azimuth angle is the angle between the projection of the direction of the UAV 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) estimation. Therefore, the prior art uses a two-dimensional MUSIC algorithm based on an "L"-shaped array to perform two-dimensional DOA estimation, but has the following disadvantages: the data of the prior art two-dimensional MUSIC algorithm is complex data, and a single multiplication of complex data involves 4 multiplication operations, which is large in amount of calculation; the prior art extracts the noise subspace by eigenvalue decomposition, but the eigenvalue decomposition operation is complex and the computational cost is much greater than that of general matrix operations; the prior art obtains the estimated value of the drone direction (azimuth and pitch angle) by two-dimensional search, and the estimation accuracy is linked 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 cycles of the search process, which will lead to higher computational complexity, and because the search dimension is two-dimensional, as the step size decreases, the computational complexity increases exponentially; in addition, the application premise of the prior art is that the number of drones is known or correctly estimated. In the face of an unknown number of drones, it is difficult to accurately estimate in real time. Summary of the invention

[0004] In order to solve the problems in the above-mentioned prior art that the computational complexity is high, the algorithm running time is long, the direction estimation has a delay, and it is difficult to achieve real-time direction estimation, the present invention proposes a method and system for real-time estimation of the direction of a UAV, which reduces the computational complexity, reduces the algorithm running time, reduces the direction estimation delay, and achieves real-time direction estimation.

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

[0006] A method for real-time estimation of the direction of a drone, the method comprising the following steps:

[0007] S1. constructing a two-dimensional array consisting of two linear uniform arrays, wherein the linear uniform array consists of a number 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 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;

[0010] S4. construct a polynomial of the noise subspace matrix, solve the polynomial to obtain a non-coupled solution near the unit circle, analyze the non-coupled solution to obtain the angles between the drone direction and the X-axis and the Y-axis respectively;

[0011] S5. Perform matrix conversion processing on the angle to obtain a sorting matrix, and use the sorting matrix to process the angle to obtain a real-time estimated value of the drone direction.

[0012] Preferably, S1 the two-dimensional array comprises a uniform linear array along the positive direction of the X-axis and a uniform linear array along the positive direction of the Y-axis, wherein the uniform linear array along the positive direction of the X-axis takes the origin as the starting point and places an array element at every interval d, with a total of M+1 array elements; the uniform linear array along the positive direction of the Y-axis takes the origin as the starting point and places an array element at every interval d, with a total of M+1 array elements, and the uniform linear array along the positive direction of the X-axis and the uniform linear array along the positive direction of the Y-axis share the array element at the origin.

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

[0014]

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

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

[0017]

[0018] Among them, R y represents 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 a 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) read along the positive direction of the Y axis at time point T.

[0019] Preferably, S2 maps the covariance matrix to a real domain covariance matrix, including:

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

[0021]

[0022] in, represents the imaginary unit, I represents the unit matrix,

[0023] S22. Using the unitary matrix Q m The covariance matrix is ​​mapped to the real domain covariance matrix as follows:

[0024]

[0025] 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.

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

[0027]

[0028] Among them, E x Indicates taking The signal subspace matrix constructed by the first K columns of E y Indicates taking The signal subspace matrix constructed by the first K columns of x represents the noise subspace matrix of the uniform linear array along the positive direction of the X-axis, U y Represents the noise subspace matrix of the uniform linear array along the positive Y-axis.

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

[0030]

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

[0032] Preferably, S4 specifically includes:

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

[0034]

[0035] Among them, u i and v i represents a complex variable, p i and q i represents polynomial coefficients;

[0036] S42. i and q i The calculations are as follows:

[0037]

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

[0039] S43. For polynomial f x (u) = 0 and f y (v) = 0, and the uncoupled solution is obtained near the unit circle. represents the number of uncoupled solutions;

[0040] S44. Determine the uncoupled solution After analysis, we can get the angles between the drone direction and the X-axis and Y-axis as follows:

[0041]

[0042] in, Indicates the angle between the drone direction and the X axis. represents the angle between the drone direction and the Y axis, arccos represents the inverse cosine function, arg represents the complex amplitude, λ represents the wavelength, π represents pi, and d represents the element spacing of the uniform linear array.

[0043] Preferably, the matrix conversion processing of the angle in S5 to obtain a sorting matrix includes:

[0044] S501. Using the angle between the drone direction and the X axis Construct the first steering matrix Represents the column vector of the first steering matrix; and uses the angle between the direction of the drone and the Y axis 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 direction of the X axis and the uniform linear array y(t) along the positive direction of the Y axis as follows:

[0046]

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

[0048] S503. Based on the cross-covariance matrix The minimization problem is constructed as follows:

[0049]

[0050] S504. Solve the minimization problem to obtain the optimal matrix represents the matrix pseudoinverse;

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

[0052] Preferably, the using the sorting matrix to process the angle to obtain a real-time estimate of the direction of the drone includes:

[0053] S511. Using the sorting matrix to calculate the angle between the direction of the drone and the Y axis Sort as follows:

[0054]

[0055] in, Indicates the angle between the sorted drone direction and the Y axis;

[0056] S512. Based on the angle between the sorted drone direction and the Y axis The angle between the drone direction and the X axis Composition of drone angle pairs

[0057] S513. Based on the angle of the drone Calculate a real-time estimate of the direction of the drone, including an azimuth estimate and the pitch angle estimate The azimuth estimate The calculation expression is as follows:

[0058]

[0059] The pitch angle estimate The calculation expression is as follows:

[0060]

[0061] The present invention proposes a real-time estimation system for the direction of an unmanned aerial vehicle, the system comprising:

[0062] A construction module, used to construct a two-dimensional array consisting of two linear uniform arrays, wherein the linear uniform arrays are composed of a plurality of array elements;

[0063] A mapping module, used 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 drones is known. If so, the first K columns of the real domain covariance matrix are taken to construct a signal subspace matrix, and the noise subspace matrix is ​​calculated based on the signal subspace matrix; if not, the noise subspace matrix is ​​calculated based on the real domain covariance matrix;

[0065] A polynomial solving module is used to construct a polynomial of the noise subspace matrix, solve the polynomial to obtain a non-coupled solution located near the unit circle, and analyze the non-coupled solution to obtain the angles between the drone direction and the X-axis and the Y-axis respectively;

[0066] The direction estimation module is used to perform matrix conversion processing on the angle to obtain a sorting matrix, and use the sorting matrix to process the angle to obtain a real-time estimation value of the direction of the drone. Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0067] The present invention proposes a method and system for real-time estimation of the direction of a drone. Firstly, a two-dimensional array is constructed and the covariance matrix on the uniform linear array is mapped to the real number domain, thereby significantly reducing the computational complexity. Secondly, matrix operations are used to replace eigenvalue decomposition to calculate the noise subspace, thereby reducing the computational cost of the noise subspace. The calculation method of the noise subspace matrix is ​​switched by judging whether the number of drones is known, and all methods do not require eigenvalue decomposition. Then, the two-dimensional array located in the XY plane and the two-dimensional signal model containing the azimuth angle and the pitch angle are converted into two one-dimensional signal models, each of which has only one angle variable. They are the angle between the drone direction and the X-axis, and the angle between the drone direction and the Y-axis, respectively; and instead of using a traversal search method, the angle estimation is decoupled by constructing a polynomial solution to directly obtain an analytical solution of the angle. Compared with the traversal search process, this process does not require 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 determined whether the number of drones K is known to switch the calculation method of different noise subspaces. The present invention does not require the drone number K parameter, and can correctly perform direction estimation in complex drone intrusion scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0070] Figure 3 A schematic diagram showing the signal collection of a UAV proposed in an embodiment of the present invention;

[0071] Figure 4 Another flowchart of a method for real-time estimation of the direction of a UAV proposed in an embodiment of the present invention is shown;

[0072] Figure 5 The figure shows a structural block diagram of a real-time estimation system for the direction of a UAV proposed in an embodiment of the present invention. DETAILED DESCRIPTION

[0073] The drawings are for illustrative purposes only and should not be construed as limiting the present patent;

[0074] It is understandable to those skilled in the art that some well-known contents may be omitted in the drawings;

[0075] In order to facilitate understanding of this embodiment, first, the prior art information of this embodiment is introduced as follows:

[0076] In the prior art, a two-dimensional MUSIC algorithm based on an "L"-shaped array is used to perform two-dimensional DOA estimation, and a brief description of the steps is as follows:

[0077] Set up an "L"-shaped antenna array, with a uniform linear array (ULA, UniformLinearArraY) consisting of M array elements on the X axis and a ULA consisting of M array elements on the Y axis. The two ULAs share the array elements at the origin, forming an "L"-shaped two-dimensional array containing 2M-1 array elements;

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

[0079] Compute 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, Σ is a diagonal matrix with the diagonal elements being the eigenvalues ​​of R arranged from small to large;

[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 drones;

[0082] Substitute the DOA range azimuth angle θ∈[0,360) and elevation angle φ∈[0,90) into the spatial spectrum formula A traversal search is performed to obtain the spatial spectrum surface. 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, and a single multiplication of complex data involves 4 multiplication operations, which is a large amount of calculation; the prior art extracts the noise subspace through eigenvalue decomposition, but the eigenvalue decomposition operation is complex and the calculation cost is much greater than the general matrix operation; the prior art obtains the estimated value of the drone direction (azimuth and pitch angle) through two-dimensional search, and the estimation accuracy is linked 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 cycles in the search process, which will lead to higher computational complexity. Therefore, the prior art needs to make a trade-off between accuracy and computational complexity. And because the search dimension of the prior art is two-dimensional, as the step size decreases, the computational complexity increases exponentially. After the prior art performs eigenvalue decomposition, it is necessary to take MK eigenvectors to form the noise subspace matrix U n Therefore, the application of the existing technology is based on the premise that the number of drones K is known or correctly estimated, otherwise the existing technology will not work properly. However, in actual scenarios, the invading drones are released by the enemy, so the number is unknown; and because drones can take off and land at any time, and some drones will crash or be shot down during the invasion process, the number of drones K changes frequently and is difficult to estimate accurately.

[0085] In summary, the existing technology has high computational complexity, long algorithm running time, and time delay in direction estimation, making it difficult to achieve real-time direction estimation. In addition, the high flying speed of the drone will lead to a large deviation between the direction estimation result and the actual position of the drone. In order to solve the above problems, the present invention proposes a method and system for real-time estimation of the direction of a drone. The following is a symbolic description table of the technical solution design of the present invention:

[0086] Table 1 Symbols

[0087]

[0088] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0089] Example 1

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

[0091] S1. constructing a two-dimensional array consisting of two linear uniform arrays, wherein the linear uniform array consists of a number of array elements;

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

[0093] See also Figure 3 , the two-dimensional array collects drone signals. Assuming there are K drones, the wavelength of the signal emitted is denoted as λ, and the drone signal is denoted as {s1(t),s2(t),…,s K (t)}, the signal powers are The angles between the directions of K drones and the X-axis are {ω1,ω2,…,ω K}, and the angle with the Y axis is {β1,β2,…,β K}, the azimuth is recorded as {θ1,θ2,…,θ K}, the pitch angle is recorded as {φ1,φ2,…φ K}, the received signal model can be expressed as:

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

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

[0096] The output of the uniform linear array along the positive direction of the X-axis is recorded as The output of the uniform linear array along the positive direction of the Y axis is recorded as Then the uniform linear array x(t) along the positive direction of the X-axis and the uniform linear array y(t) along the positive direction of the Y-axis 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] in and is a one-dimensional guiding matrix; and is the 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, the covariance of the two uniform linear array output vectors in the "L"-shaped two-dimensional array is first calculated:

[0102]

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

[0104]

[0105] Among them, R x represents the covariance matrix of the uniform linear array along the positive direction of the X axis, Represents R x The approximate covariance of represents the output snapshot data matrix of a uniform linear array along the positive direction of the X-axis, represents a complex set, (M+1)×T represents the dimension, T represents the time point, x(t T ) represents the output vector of the uniform linear array x(t) along the positive direction of the X-axis read at time point T, (·) H represents the conjugate transpose of the matrix, (·) * represents matrix conjugation, (·) T represents matrix transpose, J represents exchange matrix;

[0106] The expression for calculating the covariance matrix of the uniform linear array along the positive direction of the Y axis is as follows:

[0107]

[0108] Among them, 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 a 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 direction of the Y axis by orthogonal projection as follows:

[0119]

[0120] Among them, E x Indicates taking The signal subspace matrix constructed by the first K columns of E y Indicates taking The signal subspace matrix constructed by the first K columns of x represents the noise subspace matrix of the uniform linear array along the positive direction of the X-axis, U y Represents the noise subspace matrix of the uniform linear array along the positive Y-axis.

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

[0122]

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

[0124] S4. construct a polynomial of the noise subspace matrix, solve the polynomial to obtain a non-coupled solution near the unit circle, analyze the non-coupled solution to obtain the angles between the drone direction and the X-axis and the Y-axis respectively;

[0125] In S4, since the noise subspace matrix is ​​orthogonal to the steering vector, we have So the specific steps of S4 include:

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

[0127]

[0128] Among them, u i and v i represents a complex variable, p i and q i represents polynomial coefficients;

[0129] S42. i and q i The calculations are as follows:

[0130]

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

[0132] S43. For polynomial f x (u) = 0 and f y (v) = 0, and the uncoupled solution is obtained 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 polynomial. Due to the conjugate symmetry of the polynomial coefficients, the solutions obtained are mutually coupled (the mutually coupled solutions have the same complex argument), so M uncoupled solutions can be obtained, of which only The uncoupled solutions are located near the unit circle (i.e., the modulus is 1), and Remember this The solution is This facilitates subsequent calculations.

[0134] S44. Determine the uncoupled solution After analysis, we can get the angles between the drone direction and the X-axis and Y-axis as follows:

[0135]

[0136] in, Indicates the angle between the drone direction and the X axis. represents the angle between the drone direction and the Y axis, arccos represents the arccosine function, arg represents the complex amplitude, λ represents the wavelength, π represents the circumference, and d represents the element spacing of the uniform linear array; indivual and Although each of them is obtained, the matching relationship between them is unknown. At this time, there is a sorting matrix make Make Match.

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

[0138] In S5, the angle is subjected to matrix transformation to obtain a sorting matrix, including:

[0139] S501. Using the angle between the drone direction and the X axis Construct the first steering matrix Represents the column vector of the first steering matrix; and uses the angle between the direction of the drone and the Y axis Construct the second steering matrix represents the column vector of the second steering matrix;

[0140] Where R x The approximate covariance of can be expressed as the model make but First calculate the initial cross-covariance matrix of x(t) and y(t)

[0141]

[0142] make Then the initial cross-covariance matrix Perform transformation according to step S502;

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

[0144]

[0145] Among them, R s represents the signal covariance matrix, represents the estimate of the signal covariance matrix;

[0146] S503. Based on the cross-covariance matrix The minimization problem is constructed as follows:

[0147]

[0148] S504. Solve the minimization problem to obtain the optimal matrix represents the matrix pseudoinverse;

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

[0150] In S505, the optimal matrix The maximum modulus value of each row is set to 1, the remaining values ​​are set to 0, and Pass in the conversion function g(·) to get the sorting matrix

[0151] The step of processing the angle using the sorting matrix to obtain a real-time estimate of the direction of the drone includes:

[0152] S511. Using the sorting matrix to calculate the angle between the direction of the drone and the Y axis Sort as follows:

[0153]

[0154] in, Indicates the angle between the sorted drone direction and the Y axis;

[0155] S512. Based on the angle between the sorted drone direction and the Y axis The angle between the drone direction and the X axis Composition of drone angle pairs

[0156] S513. Based on the angle of the drone Calculate a real-time estimate of the direction of the drone, including an azimuth estimate and the pitch angle estimate The azimuth estimate The calculation expression is as follows:

[0157]

[0158] The pitch angle estimate The calculation expression is as follows:

[0159]

[0160] In this embodiment, first, the covariance matrix output data of the uniform linear array constituting the two-dimensional array is mapped to the real number domain, so as to reduce the complexity of the multiplication operation in the subsequent steps, and reduce the complexity scale of the subsequent real number operation to 1 / 4 of the original scale; secondly, the noise subspace is calculated by using the matrix multiplication operation, and the eigenvalue decomposition is not used to reduce the computational cost of the noise subspace; then, a two-dimensional array signal model is established by using the one-dimensional steering vector, and the matching algorithm is used to decouple the original azimuth and pitch angle two-dimensional DOA estimation into two one-dimensional DOA estimations; and instead of using the search method, the DOA estimation value is obtained by constructing a polynomial and directly solving it. 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; when further calculating the noise subspace, it is determined whether the number of drones is known to switch different noise subspace calculation methods. When the number of targets is unknown, the noise subspace is calculated using a quasi-orthogonal projection algorithm. The algorithm does not require a signal source number parameter and can correctly estimate the direction in complex drone intrusion scenarios.

[0161] Example 2

[0162] See also Figure 4 This embodiment describes the steps of a method for real-time estimation of the direction of a drone proposed in the above embodiment, which specifically includes the following steps:

[0163] Step 1: Use 2M+1 array elements to arrange an "L"-shaped two-dimensional array;

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

[0165]

[0166]

[0167] Step 3: Convert the covariance R x and R y Mapping to the real domain covariance matrix and

[0168]

[0169] Step 4: Determine whether the number of drones 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: Get the real domain covariance matrix and The first K columns of E are constructed 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 coefficient p i ,i=0,…,2M and q i ,i=0,…,2M

[0175]

[0176] Step 6: Solve the polynomial f x (u) = 0 and f y (v) = 0, and the uncoupled solution is obtained near the unit circle.

[0177] Step 7: Analyze the angle between the drone direction and the X and Y axes

[0178]

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

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

[0181] Step 10: Calculate the optimal matrix And converted into a sorting matrix

[0182] Step 11: Sort by

[0183]

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

[0185]

[0186] The steps of a method for real-time estimation of the direction of a drone 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, so that the algorithm proposed in the present invention can quickly obtain the drone direction estimation result with real-time performance, including:

[0188] 1) The covariance matrix in the complex domain is mapped to the real domain using a unitary matrix. The scale of real number operations is one-fourth of that of complex numbers. However, the existing technology directly processes data in the complex domain, which results in a large amount of operations.

[0189] 2) Matrix multiplication is used to calculate the noise subspace. The calculation method of the noise subspace matrix is ​​switched by judging whether the number of drones K is known. All methods do not require eigenvalue decomposition. However, the existing technology needs to extract the noise subspace matrix through eigenvalue decomposition with high computational complexity.

[0190] 3) The two-dimensional array in the XY plane and the two-dimensional signal model containing the azimuth and elevation angles are converted into two one-dimensional signal models, each of which has only one angle variable, ω and β; after solving ω and β respectively, the two angles are matched through the sorting matrix; and when solving the two one-dimensional signal models again, the traversal search method is not used, but the polynomial model is established and solved to directly obtain the analytical solution of the angle. In contrast, the existing technology not only requires a search traversal to calculate the spatial spectrum, but the search process is two-dimensional, which will bring a huge amount of calculations.

[0191] Second, the present invention can select different noise subspace matrix calculation methods by judging whether the number of drones is known. When the number of drones is unknown, the present invention uses a quasi-projection matrix to calculate the noise subspace. The introduction of this algorithm makes it unnecessary to use the number of drones K as a parameter in the direction estimation process. Therefore, when the number of drones is unknown, the present invention can still correctly estimate the DOA. In the prior art, the number of signal sources is required to be known or correctly estimated, otherwise the prior art cannot achieve DOA estimation. However, in actual scenarios, the invading drones are released by the enemy, so the number is unknown; and because drones can take off and land at any time, and some drones will crash or be shot down during the invasion process, the number of drones K changes frequently and is difficult to estimate accurately.

[0192] Example 3

[0193] See also Figure 5 This embodiment proposes a real-time estimation system for the direction of a UAV, the system comprising:

[0194] A building module, used for building a two-dimensional array consisting of a plurality of array elements;

[0195] A mapping module, used 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;

[0196] The noise subspace matrix calculation module is used to determine whether the number of drones is known. If so, the first K columns of the real domain covariance matrix are taken to construct a signal subspace matrix, and the noise subspace matrix is ​​calculated based on the signal subspace matrix; if not, the noise subspace matrix is ​​calculated based on the real domain covariance matrix;

[0197] A polynomial solving module is used to construct a polynomial of the noise subspace matrix, solve the polynomial to obtain a non-coupled solution located near the unit circle, and analyze the non-coupled solution to obtain the angles between the drone direction and the X-axis and the Y-axis respectively;

[0198] The direction estimation module is used to perform matrix conversion processing on the angle to obtain a sorting matrix, and process the sorting matrix to obtain a real-time estimation value of the direction of the drone.

[0199] In this embodiment, firstly, by constructing a two-dimensional array and mapping the covariance matrix to the real number domain, the computational complexity is significantly reduced; secondly, matrix operation is used instead of eigenvalue decomposition to calculate the noise subspace, which reduces the computational cost of the noise subspace, and the calculation method of the noise subspace matrix is ​​switched by judging whether the number of drones is known, and all methods do not need to perform eigenvalue decomposition; then, the two-dimensional array located in the XY plane and the two-dimensional signal model containing the azimuth angle and the pitch angle are converted into two one-dimensional signal models, each model has only one angle variable, which is the angle between the drone direction and the X-axis and the angle between the drone direction and the Y-axis; and instead of using the traversal search method, the angle estimation is decoupled by constructing a polynomial solution 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 keeping the accuracy unchanged; further, when calculating the noise subspace, it is judged whether the number of drones K is known to switch different noise subspace calculation methods. The present invention does not require the number of drones K parameter, and can correctly perform direction estimation in complex drone intrusion scenarios.

[0200] Obviously, the above embodiments of the present invention are only examples for clearly illustrating the present invention, and are not intended to limit the implementation methods of the present invention. For those skilled 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 list all implementation methods here. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should 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 a drone, characterized in that: The method comprises the following steps: S1. constructing a two-dimensional array consisting of two linear uniform arrays, wherein the linear uniform array consists 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 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; S4. construct a polynomial of the noise subspace matrix, solve the polynomial to obtain a non-coupled solution near the unit circle, analyze the non-coupled solution to obtain the angles between the drone direction and the X-axis and the Y-axis respectively; S5. Perform matrix conversion processing on the angle to obtain a sorting matrix, and use the sorting matrix to process the angle to obtain a real-time estimated value of the drone direction.

2. The method for real-time estimation of the direction of a UAV according to claim 1, characterized in that: S1 The two-dimensional array includes a uniform linear array along the positive direction of the X-axis and a uniform linear array along the positive direction of the Y-axis. The uniform linear array along the positive direction of the X-axis takes the origin as the starting point and places an array element every interval d, with a total of M+1 array elements; the uniform linear array along the positive direction of the Y-axis takes the origin as the starting point and places an array element every interval d, with a total of M+1 array elements. The uniform linear array along the positive direction of the X-axis and the uniform linear array along the positive direction of the Y-axis share the array element at the origin.

3. The method for real-time estimation of the direction of a UAV according to claim 2, characterized in that: The expression for calculating the covariance matrix of the uniform linear array along the positive direction of the X-axis is as follows: Among them, R x represents the covariance matrix of the uniform linear array along the positive direction of the X axis, Represents R x The approximate covariance of represents the output snapshot data matrix of a uniform linear array along the positive direction of the X-axis, represents a complex set, (M+1)×T represents the dimension, T represents the time point, x(t T ) represents the output vector of the uniform linear array x(t) along the positive direction of the X-axis read at time point T, (·) H represents the conjugate transpose of the matrix, (·) * represents matrix conjugation, (·) T represents matrix transpose, J represents exchange matrix; The expression for calculating the covariance matrix of the uniform linear array along the positive direction of the Y axis is as follows: Among them, R y represents 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 a 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) read along the positive direction of the Y axis at time point T.

4. The method for real-time estimation of the direction of a UAV according to claim 3, characterized in that: S2, mapping the covariance matrix to a real domain covariance matrix, comprises: S21. Define the unitary matrix The following expression: in, represents the imaginary unit, I represents the unit matrix, S22. Using the unitary matrix Q m The covariance matrix is ​​mapped to the real domain covariance matrix as follows: 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.

5. The method for real-time estimation of the direction of a UAV according to claim 4, characterized in that: In S3, based on the signal subspace matrix, the expression for calculating the noise subspace matrix is ​​as follows: Among them, E x Indicates taking The signal subspace matrix constructed by the first K columns of E y Indicates taking The signal subspace matrix constructed by the first K columns of x represents the noise subspace matrix of the uniform linear array along the positive direction of the X-axis, U y Represents the noise subspace matrix of the uniform linear array along the positive Y-axis.

6. The method for real-time estimation of the direction of a UAV according to claim 4, characterized in that: In S3, based on the real domain covariance matrix, the expression for calculating the noise subspace matrix is ​​as follows: Among them, U x represents the noise subspace matrix of the uniform linear array along the positive direction of the X-axis, U y represents the noise subspace matrix of the uniform linear array along the positive direction of the Y axis, and μ represents the minimum value.

7. The method for real-time estimation of the direction of a UAV according to claim 5 or 6, characterized in that: S4 specifically includes: S41. Define the noise subspace matrix U of the uniform linear array along the positive direction of the X-axis x The polynomial is f x (u), the noise subspace matrix U of the uniform linear array along the positive direction of the Y axis y The polynomial is f y (v), f x (u) and f y The calculation expressions of (v) are as follows: Among them, u i and v i represents a complex variable, p i and q i represents polynomial coefficients; S42. i and q i The calculations are as follows: Among them, diag(,) represents a diagonal matrix, and sum(.) represents a summation function; S43. For polynomial f x (u) = 0 and f y (v) = 0, and the uncoupled solution is obtained near the unit circle. represents the number of uncoupled solutions; S44. Determine the uncoupled solution After analysis, we can get the angles between the drone direction and the X-axis and Y-axis as follows: in, Indicates the angle between the drone direction and the X axis. represents the angle between the drone direction and the Y axis, arccos represents the inverse cosine function, arg represents the complex amplitude, λ represents the wavelength, π represents pi, and d represents the element spacing of the uniform linear array.

8. The method for real-time estimation of the direction of a UAV according to claim 7, characterized in that: S5 performs matrix transformation processing on the angle to obtain a sorting matrix, including: S501. Using the angle between the drone direction and the X axis Construct the first steering matrix Represents the column vector of the first steering matrix; and uses the angle between the direction of the drone and the Y axis Construct the second steering matrix represents the column vector 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 x(t) along the positive direction of the X axis and the uniform linear array y(t) along the positive direction of the Y axis It is expressed as follows: Among them, R s represents the signal covariance matrix, represents the estimate of the signal covariance matrix; S503. Based on the cross-covariance matrix The minimization problem is constructed as follows: S504. Solve the minimization problem to obtain the optimal matrix represents the matrix pseudoinverse; S505. Convert the optimal matrix into a sorting matrix g(·) represents the conversion function.

9. The method for real-time estimation of the direction of a UAV according to claim 8, characterized in that: The step of processing the angle using the sorting matrix to obtain a real-time estimate of the direction of the drone includes: S511. Using the sorting matrix to calculate the angle between the direction of the drone and the Y axis Sort as follows: in, Indicates the angle between the sorted drone direction and the Y axis; S512. Based on the angle between the sorted drone direction and the Y axis The angle between the drone direction and the X axis Composition of drone angle pairs S513. Based on the angle of the drone Calculate a real-time estimate of the direction of the drone, including an azimuth estimate and the pitch angle estimate The azimuth estimate The calculation expression is as follows: The pitch angle estimate The calculation expression is as follows:

10. A real-time estimation system for the direction of an unmanned aerial vehicle, characterized in that: The system comprises: A construction module, used to construct a two-dimensional array consisting of two linear uniform arrays, wherein the linear uniform arrays are composed of a plurality of array elements; A mapping module, used 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; The noise subspace matrix calculation module is used to determine whether the number of drones is known. If so, the first K columns of the real domain covariance matrix are taken to construct a signal subspace matrix, and the noise subspace matrix is ​​calculated based on the signal subspace matrix; if not, the noise subspace matrix is ​​calculated based on the real domain covariance matrix; A polynomial solving module is used to construct a polynomial of the noise subspace matrix, solve the polynomial to obtain a non-coupled solution located near the unit circle, and analyze the non-coupled solution to obtain the angles between the drone direction and the X-axis and the Y-axis respectively; The direction estimation module is used to perform matrix conversion processing on the angle to obtain a sorting matrix, and use the sorting matrix to process the angle to obtain a real-time estimated value of the drone direction.

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