Unmanned aerial vehicle signal positioning method and system based on two-dimensional DOA estimation

Abstract

The invention provides an unmanned aerial vehicle signal positioning method and system based on two-dimensional DOA estimation, and relates to the technical field of array signal processing.The method comprises the steps that firstly, based on a steering vector matrix of a receiving array and a sampled unmanned aerial vehicle two-dimensional incident signal, a two-dimensional spatial spectrum function is constructed through a propagator-based non-prior-information-source-number algorithm; the prior estimation of the number of signal sources is avoided due to the use of a prior-source-number-free algorithm, and the calculation complexity is reduced; in the angle range of the direction angle and the angle range of the pitch angle, traversing the direction angle and the pitch angle, searching the peak value of the two-dimensional spatial spectrum function, obtaining the azimuth angle and the pitch angle of the unmanned aerial vehicle incident signal corresponding to the peak value, and taking the azimuth angle and the pitch angle as two-dimensional DOA estimation values of the unmanned aerial vehicle incident signal; and finally, based on the two-dimensional DOA estimation value and the position coordinate of the receiving station where the receiving array is located, the position coordinate of the incident signal of the unmanned aerial vehicle is calculated, and the modeling capability of multi-dimensional space information is enhanced.

Description

Technical Field

[0001] The present invention relates to the technical field of array signal processing, and more specifically, to a method and system for positioning unmanned aerial vehicle (UAV) signals based on two-dimensional direction of arrival (DOA) estimation. Background Art

[0002] In recent years, with the continuous development of integrated circuit technology and control technology, the civilian UAV industry has developed rapidly. As civilian UAVs play an increasingly important role in daily life, their regulatory issues have become increasingly prominent. In terms of safety prevention and control measures, some UAV merchants adopt means such as real-name activation, setting no-fly zones, and restricting flight altitudes in specific areas. However, most of these measures rely on sensors such as the body GPS to determine the position of consumers, and consumers can easily crack the flight restrictions by physically shielding the sensors, resulting in repeated occurrences of illegal UAV intrusions. Unauthorized illegal UAV intrusions pose many safety hazards and pose a serious threat to ground public safety. There have been many safety incidents at home and abroad where UAVs interfere with the normal operation of flights, bringing great risks to aviation safety. Therefore, it is crucial to study a method for effectively positioning UAV signals.

[0003] The direction of arrival (DOA) estimation technology receives the incident signals of UAVs through a sensor array, records the time difference or phase difference of the incident signals of UAVs arriving at different array elements, and can determine the direction of the UAV signal source by calculating the relationship between the distances between different array elements, the signal wavelength, and the phase difference.

[0004] In the prior art, a one-dimensional DOA estimation method applicable to a low signal-to-noise ratio environment is proposed. By processing the received signals of a uniform linear array, reducing the dimension of the covariance matrix of the received signals, and subtracting the eigenvalues of the noise signals to achieve a noise reduction effect, and iteratively updating the coefficients of the weighted matrix during the convex optimization process of the sparse vector solution, gradually correcting the deviation of the angular position, and finally reducing the estimation error of the angle to improve the DOA estimation accuracy of compressive sensing algorithms in a low signal-to-noise ratio environment. However, the method of reducing the covariance matrix of the received signals to one dimension to improve the signal-to-noise ratio can only estimate the horizontal azimuth angle and cannot determine the pitch angle and height information of the target, resulting in poor modeling ability for multi-dimensional space information; at the same time, the one-dimensional DOA estimation method used in this scheme requires accurate estimation of the number of signal sources in advance, but in an actual complex signal environment, the types of signal sources are diverse and dynamically changing, making it extremely difficult to accurately estimate the number of signal sources and increasing the computational complexity. Summary of the Invention

[0005] To solve the problems of the current UAV DOA estimation method, such as poor modeling ability for multi-dimensional space information and unknown number of signal sources, the present invention proposes a UAV signal positioning method and system based on two-dimensional DOA estimation, which enhances the modeling ability for multi-dimensional space information, uses an improved propagator algorithm, avoids the prior requirement for the number of signal sources, and reduces the computational complexity.

[0006] To achieve the above technical effects, the technical solution of the present invention is as follows:

[0007] In a first aspect, the present application proposes a UAV signal positioning method based on two-dimensional DOA estimation, including the following steps:

[0008] S1. Construct the steering vector matrix of the receiving array;

[0009] S2. Based on the steering vector matrix, use the receiving array to receive and sample the two-dimensional incident signal of the UAV to obtain the output signal;

[0010] S3. Construct the fourth-order cumulant matrix of the output signal, decompose the fourth-order cumulant matrix, and obtain the decomposed fourth-order cumulant matrix;

[0011] S4. Based on the decomposed fourth-order cumulant matrix and the propagator-based algorithm without prior knowledge of the number of signal sources, construct the noise subspace;

[0012] S5. Based on the noise subspace, the direction angle and the pitch angle of the UAV, construct the two-dimensional spatial spectrum function;

[0013] S6. In the angular range of the direction angle and the angular range of the pitch angle, traverse the direction angle and the pitch angle, search for the peak value of the two-dimensional spatial spectrum function, and obtain the azimuth angle and the pitch angle of the UAV incident signal corresponding to the peak value, as the two-dimensional DOA estimation value of the UAV incident signal;

[0014] S7. Based on the two-dimensional DOA estimation value and the position coordinates of the receiving station where the receiving array is located, calculate the position coordinates of the UAV incident signal.

[0015] In this technical solution, first, based on the steering vector matrix of the receiving array and the sampled two-dimensional incident signal of the UAV, use the propagator-based algorithm without prior knowledge of the number of signal sources to construct the two-dimensional spatial spectrum function. The use of the algorithm without prior knowledge of the number of signal sources avoids the prior estimation of the number of signal sources and reduces the computational complexity; in the angular range of the direction angle and the angular range of the pitch angle, traverse the direction angle and the pitch angle, search for the peak value of the two-dimensional spatial spectrum function, and obtain the azimuth angle and the pitch angle of the UAV incident signal corresponding to the peak value, as the two-dimensional DOA estimation value of the UAV incident signal. Finally, based on the two-dimensional DOA estimation value and the position coordinates of the receiving station where the receiving array is located, calculate the position coordinates of the UAV incident signal, enhancing the modeling ability for multi-dimensional space information.

[0016] Preferably, the process of constructing the steering vector matrix of the receiving array in step S1 is as follows:

[0017] It is defined that there are k target UAV signal sources distributed in space, which are incident on the receiving array at angles of (θ1, φ1), (θ2, φ2), …, (θ k , φ k ), where θ is the azimuth angle and φ is the elevation angle;

[0018] Suppose the receiving array is an L-shaped array. Among them, there are M x array elements on the X-axis and M y array elements on the Y-axis. The coordinates of the m-th receiving array element are (x m , y m ). The expression of the steering vector a(θ k ) of the receiving array for receiving the k-th target UAV signal source is:

[0019]

[0020] The expression of the steering vector matrix A x on the X-axis is:

[0021]

[0022] The expression of the steering vector matrix A y on the Y-axis is:

[0023]

[0024] Then, the expression of the total steering vector matrix A is:

[0025]

[0026] Preferably, based on the steering vector matrix, the receiving array performs T receiving samplings on the two-dimensional incident signal of the UAV, and the expression of the output signal is:

[0027] X = AS + N

[0028] where the output signal X of the receiving array = [x(1), x(2),..., x(T)], X is an M×T matrix, A represents the total steering vector matrix, A = [a(θ1), a(θ2), …, a(θ k )], S represents the UAV incident signal matrix, S = [s(1), s(2), s(3), …, s(T)], S is a k×T incident signal matrix, and N is the array noise matrix, N is an M×T matrix.

[0029] Preferably, the fourth-order cumulant matrix of the constructed output signal in step S3, the fourth-order cumulant matrix C X has the following expression:

[0030]

[0031] where E{.} represents the mathematical expectation, x(t) represents the t-th column submatrix under the output signal X of the receiving array, represents the Kronecker product, and H represents the conjugate transpose operation of the matrix.

[0032] Preferably, the process of decomposing the fourth-order cumulant matrix in step S3 to obtain the decomposed fourth-order cumulant matrix satisfies the expression:

[0033] C X = BC S B H

[0034] where B is the direction matrix expanded using the fourth-order cumulant, and the i-th column of B is expressed as:

[0035]

[0036] In the decomposed fourth-order cumulant matrix, C S has the following expression:

[0037]

[0038] where s(t) is the signal vector, E{.} represents the mathematical expectation, and * represents the conjugate.

[0039] Preferably, the process of constructing the noise subspace based on the decomposed fourth-order cumulant matrix and the propagator-based algorithm without prior knowledge of the number of signal sources in step S4 is as follows:

[0040] Extract the first k columns U S submatrix of the decomposed fourth-order cumulant matrix C s , where

[0041] If the number of signal sources is known, then is full rank and the rank is k, and directly construct the noise subspace U n , and the expression is:

[0042]

[0043] where H represents the conjugate transpose operation of the matrix, and I M is the M×M identity matrix;

[0044] If the number of signal sources is unknown, then based on the propagator-free a priori signal source number algorithm, the hyperparameter μ is introduced to construct the noise subspace U n , the expression is:

[0045]

[0046] Among them, I M is the M×M identity matrix.

[0047] Preferably, in step S5, a two-dimensional space spectrum function is constructed based on the noise subspace, the direction angle and the pitch angle of the drone, and the expression of the two-dimensional space spectrum function is:

[0048]

[0049] Among them, P(θ,φ) represents the two-dimensional spatial spectrum function; θ is the azimuth angle, φ is the pitch angle, H represents the conjugate transpose operation of the matrix, and a(θ,φ) is the direction vector.

[0050] Preferably, in step S7, the position coordinates of the incident signal of the drone are calculated based on the two-dimensional DOA estimation value of the incident signal of the drone and the position coordinates of the receiving station where the receiving array is located, and the process is:

[0051] If the number of receiving stations is 2, define the coordinates of the two receiving stations A and B as: (x1, y1, z1) and (x2, y2, z2) respectively;

[0052] Define the distances from the drone incident signal to the two receiving stations A and B as r1 and r2 respectively;

[0053] The two-dimensional DOA estimates of the incident signal from the UAV are (θ1, φ1) and (θ2, φ2);

[0054] The position coordinates of the incident signal of the drone are calculated based on the two receiving stations A and B respectively. For receiving station A, the expression for calculating the position coordinates (x, y, z) of the incident signal of the drone is:

[0055]

[0056] For receiving station B, the expression for calculating the position coordinates (x, y, z) of the incident signal of the drone is:

[0057]

[0058] Combining expressions (1) and (2), we get the expression:

[0059] CX=D

[0060] in,

[0061]

[0062] Using the minimum sum of squared errors min||CX - D|| 2 Solve the output signal X of the receiving array, and the expression for the solution of X is:

[0063] X = (A T A) -1 A T B

[0064] After obtaining X, the position coordinates (x, y, z) of the target signal are obtained.

[0065] Preferably, based on the two-dimensional DOA estimation value of the UAV incident signal and the position coordinates of the receiving station in step S7, positioning the position coordinates of the UAV incident signal further includes:

[0066] If the number of receiving stations is M, M > 2, then using the target information provided by the receiving stations, the target information includes the direction angles θ1 to θ M of the UAV incident signal, the elevation angles φ1 to φ M of the UAV incident signal, and the distances r1 to r M at which the UAV incident signal arrives at the receiving stations, and based on the data fusion technology, the position coordinates (x, y, z) of the UAV incident signal are obtained.

[0067] In a second aspect, the present application also proposes a UAV signal positioning system based on two-dimensional DOA estimation. The system is used to execute the method described above and includes:

[0068] A steering vector model construction unit for constructing a steering vector matrix of the receiving array;

[0069] An array output signal generation unit for receiving and sampling the two-dimensional incident signal of the UAV by the receiving array based on the steering vector matrix to obtain an output signal;

[0070] A fourth-order cumulant matrix decomposition unit for constructing a fourth-order cumulant matrix of the output signal of the receiving array, and decomposing the fourth-order cumulant matrix to obtain the decomposed fourth-order cumulant matrix;

[0071] A noise subspace construction unit for constructing a noise subspace based on the decomposed fourth-order cumulant matrix and the propagator-based algorithm without prior source number;

[0072] A two-dimensional spatial spectrum function construction unit for constructing a two-dimensional spatial spectrum function based on the noise subspace, the direction angle and the elevation angle of the UAV;

[0073] The DOA estimation unit is used to traverse the direction angle and the elevation angle within the angular range of the direction angle and the angular range of the elevation angle, search for the peak value of the two-dimensional spatial spectrum function, and obtain the azimuth angle and the elevation angle of the UAV incident signal corresponding to the spatial spectrum peak, which are used as the two-dimensional DOA estimation values of the UAV incident signal;

[0074] The UAV position coordinate calculation unit is used to calculate the position coordinates of the UAV incident signal based on the two-dimensional DOA estimation value and the position coordinates of the receiving station where the receiving array is located.

[0075] Compared with the prior art, the beneficial effects of the technical solution of the present invention are as follows:

[0076] The present invention provides a UAV signal positioning method and system based on two-dimensional DOA estimation. First, based on the steering vector matrix of the receiving array and the sampled two-dimensional UAV incident signal, a two-dimensional spatial spectrum function is constructed by using the propagator-based algorithm without prior knowledge of the number of signal sources. The use of the algorithm without prior knowledge of the number of signal sources avoids the prior estimation of the number of signal sources and reduces the computational complexity. Within the angular range of the direction angle and the angular range of the elevation angle, the direction angle and the elevation angle are traversed to search for the peak value of the two-dimensional spatial spectrum function, and the azimuth angle and the elevation angle of the UAV incident signal corresponding to the peak value are obtained as the two-dimensional DOA estimation values of the UAV incident signal. Finally, based on the two-dimensional DOA estimation value and the position coordinates of the receiving station where the receiving array is located, the position coordinates of the UAV incident signal are calculated, enhancing the modeling ability of multi-dimensional spatial information. Description of the Drawings

[0077] Figure 1 It represents a schematic flow chart of a UAV signal positioning method based on two-dimensional DOA estimation proposed in Embodiment 1 of the present invention;

[0078] Figure 2 It represents a schematic diagram of the L-shaped receiving array proposed in Embodiment 2 of the present invention;

[0079] Figure 3 It represents a schematic diagram of the principle of determining the position coordinates of the UAV incident signal based on the receiving station and the two-dimensional DOA estimation value of the UAV incident signal proposed in Embodiment 2 of the present invention;

[0080] Figure 4 It represents a structural diagram of a UAV signal positioning system based on two-dimensional DOA estimation proposed in Embodiment 3 of the present invention. Detailed Embodiments

[0081] The drawings are only for illustrative purposes and should not be construed as a limitation of this patent;

[0082] For better illustration of this embodiment, some parts of the drawings are omitted, enlarged or reduced, and do not represent the actual size;

[0083] For those skilled in the art, it is understandable that some well-known content descriptions in the drawings may be omitted.

[0084] The technical solution of the present invention will be further described below in conjunction with the drawings and embodiments.

[0085] The description of the positional relationship in the drawings is only for illustrative purposes and should not be construed as a limitation of this patent;

[0086] Embodiment 1

[0087] This embodiment proposes a method for positioning an unmanned aerial vehicle (UAV) signal based on two-dimensional direction-of-arrival (DOA) estimation. The flowchart of the implementation process of this method is shown in Figure 1 as Figure 1 shown, and includes the following steps:

[0088] S1. Construct the steering vector matrix of the receiving array;

[0089] S2. Based on the steering vector matrix, use the receiving array to receive and sample the two-dimensional incident signal of the UAV to obtain the output signal;

[0090] S3. Construct the fourth-order cumulant matrix of the output signal, decompose the fourth-order cumulant matrix, and obtain the decomposed fourth-order cumulant matrix;

[0091] S4. Based on the decomposed fourth-order cumulant matrix and the propagator-based algorithm without prior knowledge of the number of signal sources, construct the noise subspace;

[0092] S5. Based on the noise subspace, the direction angle and pitch angle of the UAV, construct the two-dimensional spatial spectrum function;

[0093] S6. Within the angular range [0°, 360°] of the direction angle and the angular range [0°, 90°] of the pitch angle, traverse the direction angle and pitch angle, search for the peak value of the two-dimensional spatial spectrum function, and obtain the azimuth angle and pitch angle of the UAV incident signal corresponding to the peak value, as the two-dimensional DOA estimation value of the UAV incident signal;

[0094] S7. Based on the two-dimensional DOA estimation value and the position coordinates of the receiving station where the receiving array is located, calculate the position coordinates of the UAV incident signal.

[0095] In this embodiment, first, based on the steering vector matrix of the receiving array and the sampled two-dimensional incident signals of the UAV, a two-dimensional spatial spectrum function is constructed using the propagator-based algorithm without prior knowledge of the number of signal sources. The use of the algorithm without prior knowledge of the number of signal sources avoids the prior estimation of the number of signal sources and reduces the computational complexity. Within the angular range of the azimuth angle and the elevation angle, the azimuth angle and the elevation angle are traversed to search for the peak value of the two-dimensional spatial spectrum function, and the azimuth angle and the elevation angle of the UAV incident signal corresponding to the peak value are obtained as the two-dimensional DOA estimation values of the UAV incident signal. Finally, based on the two-dimensional DOA estimation values and the position coordinates of the receiving station where the receiving array is located, the position coordinates of the UAV incident signal are calculated, enhancing the modeling ability for multi-dimensional spatial information.

[0096] Embodiment 2

[0097] In this embodiment, the process of constructing the steering vector matrix of the receiving array in step S1 is as follows:

[0098] It is defined that there are k target UAV signal sources distributed in space, and they are incident on the receiving array at angles of (θ1, φ1), (θ2, φ2), …, (θ k , φ k ), where θ is the azimuth angle and φ is the elevation angle;

[0099] Suppose the receiving array is an L-shaped array, and the schematic diagram of the L-shaped array is as shown in Figure 2 Figure, where there are M x array elements on the X-axis and M y array elements on the Y-axis. The coordinates of the m-th receiving array element are (x m , y m ). The expression for the steering vector a(θ k ) of the receiving array for receiving the k-th target UAV signal source is:

[0100]

[0101] The expression for the steering vector matrix A x on the X-axis is:

[0102]

[0103] The expression for the steering vector matrix A y on the Y-axis is:

[0104]

[0105] Then, the expression for the total steering vector matrix A is:

[0106]

[0107] Specifically, the receiving array includes, but is not limited to, an L-shaped array.

[0108] In this embodiment, based on the steering vector matrix, the receiving array performs T times of receiving sampling on the two-dimensional incident signal of the UAV, and the expression of the output signal is obtained as:

[0109] X = AS + N

[0110] Among them, the output signal X of the receiving array is X = [x(1), x(2),..., x(T)], X is an M×T matrix, A represents the total steering vector matrix, A = [a(θ1), a(θ2), …, a(θ k )], S represents the UAV incident signal matrix, S = [s(1), s(2), s(3), …, s(T)], S is a k×T incident signal matrix, N is the array noise matrix, and N is an M×T matrix.

[0111] In this embodiment, the fourth-order cumulant matrix of the output signal constructed in step S3, and the expression of the fourth-order cumulant matrix C X is:

[0112]

[0113] Among them, E{.} represents the mathematical expectation, x(t) represents the t-th column sub-matrix under the output signal X of the receiving array, represents the Kronecker product, and H represents the conjugate transpose operation of the matrix.

[0114] In this embodiment, the process of decomposing the fourth-order cumulant matrix described in step S3 to obtain the decomposed fourth-order cumulant matrix satisfies the expression:

[0115] C X = BC S B H

[0116] Among them, B is the direction matrix extended after using the fourth-order cumulant, and the i-th column of B is expressed as:

[0117]

[0118] In the decomposed fourth-order cumulant matrix, the expression of C S is:

[0119]

[0120] Among them, s(t) is the signal vector, E{.} represents the mathematical expectation, and * represents the conjugate.

[0121] In this embodiment, for the process of constructing the noise subspace based on the decomposed fourth-order cumulant matrix and the propagator-based algorithm for the number of sources without prior knowledge, the steps are as follows:

[0122] Extract the first k columns U S of the decomposed fourth-order cumulant matrix C s submatrix, where

[0123] If the number of signal sources is known, then it is full rank and the rank is k, and directly construct the noise subspace U n , and the expression is:

[0124]

[0125] where H represents the conjugate transpose operation of the matrix, and I M is the M×M identity matrix;

[0126] If the number of signal sources is unknown, then based on the propagator-based algorithm for the number of sources without prior knowledge, introduce the hyperparameter μ and construct the noise subspace U n , and the expression is:

[0127]

[0128] where I M is the M×M identity matrix.

[0129] In this embodiment, for the process of constructing the two-dimensional spatial spectrum function based on the noise subspace, the direction angle and pitch angle of the UAV, the expression of the two-dimensional spatial spectrum function is:

[0130]

[0131] where P(θ,φ) represents the two-dimensional spatial spectrum function; θ is the azimuth angle, φ is the pitch angle, H represents the conjugate transpose operation of the matrix, and a(θ,φ) is the direction vector.

[0132] In this embodiment, for the process of calculating the position coordinates of the UAV incident signal based on the two-dimensional DOA estimation value of the UAV incident signal and the position coordinates of the receiving station where the receiving array is located, the steps are as follows:

[0133] If the number of receiving stations is 2, define the coordinates of two receiving stations A and B as: (x1,y1,z1) and (x2,y2,z2); Figure 3 is the schematic diagram of the principle of this process, where 1 represents receiving station A, 2 represents the position coordinates of the UAV incident signal, and 3 represents receiving station B;

[0134] Define the distances from the UAV incident signal to the two receiving stations A and B as r1 and r2 respectively;

[0135] The two-dimensional DOA estimates of the incident signal from the UAV are (θ1, φ1) and (θ2, φ2);

[0136] The position coordinates of the incident signal of the drone are calculated based on the two receiving stations A and B respectively. For receiving station A, the expression for calculating the position coordinates (x, y, z) of the incident signal of the drone is:

[0137]

[0138] For receiving station B, the expression for calculating the position coordinates (x, y, z) of the incident signal of the drone is:

[0139]

[0140] Combining expressions (1) and (2), we get the expression:

[0141] CX=D

[0142] in,

[0143]

[0144] Using the minimization of the sum of squared errors min||CX-D|| 2 Solve for the output signal X of the receiving array, and the solution expression of X is:

[0145] X=(A T A) -1 A T B

[0146] After obtaining X, the position coordinates (x, y, z) of the target signal are obtained.

[0147] In this embodiment, the step S7, based on the two-dimensional DOA estimation value of the drone incident signal and the position coordinates of the receiving station, locates the position coordinates of the drone incident signal, and further includes:

[0148] If the number of receiving stations is M, M>2, the target information provided by the receiving station is used, and the target information includes the direction angles θ1~θ M 、The pitch angle of the incident signal of the drone is φ1~φ M , the distance from the incident signal of the drone to the receiving station is r1~r M , based on data fusion technology, the position coordinates (x, y, z) of the incident signal of the UAV are obtained.

[0149] Example 3

[0150] like Figure 4As shown in the figure, the present application proposes a UAV signal positioning system based on two-dimensional DOA estimation, including:

[0151] A steering vector model construction unit for constructing the steering vector matrix of the receiving array. The process is as follows:

[0152] Define that there are k target UAV signal sources distributed in space, which respectively enter the receiving array at angles of (θ1, φ1), (θ2, φ2), …, (θ k , φ k ). θ is the direction angle and φ is the elevation angle;

[0153] Assume that the receiving array is an L-shaped array. Among them, there are M x array elements on the X-axis and M y array elements on the Y-axis. The coordinates of the mth receiving array element are (x m , y m ). The expression of the steering vector a(θ k ) of the receiving array for receiving the kth target UAV signal source is:

[0154]

[0155] The expression of the steering vector matrix A x on the X-axis is:

[0156]

[0157] The expression of the steering vector matrix A y on the Y-axis is:

[0158]

[0159] Then, the expression of the total steering vector matrix A is:

[0160]

[0161] Specifically, the receiving array includes but is not limited to an L-shaped array;

[0162] An array output signal generation unit for receiving and sampling the two-dimensional incident signal of the UAV based on the steering vector matrix by using the receiving array, and the expression of the output signal obtained is:

[0163] X = AS + N

[0164] Among them, the output signal X of the receiving array = [x(1), x(2),..., x(T)], X is an M×T matrix, A represents the total steering vector matrix, A = [a(θ1), a(θ2), …, a(θ k)], S represents the incident signal matrix of the UAV, S = [s(1), s(2), s(3), …, s(T)], S is a k×T incident signal matrix, N is the array noise matrix, and N is an M×T matrix;

[0165] The fourth-order cumulant matrix decomposition unit is used to construct the fourth-order cumulant matrix of the output signal of the receiving array, and decompose the fourth-order cumulant matrix to obtain the decomposed fourth-order cumulant matrix;

[0166] For the construction of the fourth-order cumulant matrix of the output signal, the fourth-order cumulant matrix C X The expression is:

[0167]

[0168] where E{.} represents the mathematical expectation, x(t) represents the t-th column submatrix under the output signal X of the receiving array, represents the Kronecker product, and H represents the conjugate transpose operation of the matrix;

[0169] For the decomposition of the fourth-order cumulant matrix to obtain the decomposed fourth-order cumulant matrix, the process satisfies the expression:

[0170] C X = BC S B H

[0171] where B is the direction matrix extended using the fourth-order cumulant, and the i-th column of B is expressed as:

[0172]

[0173] In the decomposed fourth-order cumulant matrix, C S The expression is:

[0174]

[0175] where s(t) is the signal vector, E{.} represents the mathematical expectation, and * represents the conjugate;

[0176] The noise subspace construction unit is used to construct the noise subspace based on the decomposed fourth-order cumulant matrix and the propagator-based algorithm without prior knowledge of the number of signal sources. The process is as follows:

[0177] Extract the first k columns U S submatrix of the decomposed fourth-order cumulant matrix C s where,

[0178] If the number of signal sources is known, then is full rank and the rank is k, and directly construct the noise subspace Un , the expression is:

[0179]

[0180] where H represents the conjugate transpose operation of the matrix, and I M is the M×M identity matrix;

[0181] If the number of signal sources is unknown, for the propagator-based algorithm without prior knowledge of the number of signal sources, a hyperparameter μ is introduced to construct the noise subspace U n , the expression is:

[0182]

[0183] where I M is the M×M identity matrix;

[0184] The two-dimensional spatial spectrum function construction unit is used to construct the expression of the two-dimensional spatial spectrum function based on the noise subspace, the direction angle and the pitch angle of the UAV, and the expression is:

[0185]

[0186] where P(θ,φ) represents the two-dimensional spatial spectrum function; θ is the azimuth angle, φ is the pitch angle, H represents the conjugate transpose operation of the matrix, and a(θ,φ) is the direction vector;

[0187] The DOA estimation unit is used to traverse the direction angle and the pitch angle within the angular range [0°, 360°] of the direction angle and the angular range [0°, 90°] of the pitch angle, search for the peak value of the two-dimensional spatial spectrum function, and obtain the azimuth angle and the pitch angle of the UAV incident signal corresponding to the spatial spectrum peak value as the two-dimensional DOA estimation value of the UAV incident signal;

[0188] The UAV position coordinate calculation unit is used to calculate the position coordinates of the UAV incident signal based on the two-dimensional DOA estimation value and the position coordinates of the receiving station where the receiving array is located. The process is as follows:

[0189] If the number of receiving stations is 2, the coordinates of two receiving stations A and B are defined as: (x1, y1, z1) and (x2, y2, z2);

[0190] The distances from the UAV incident signal to the two receiving stations A and B are defined as r1 and r2 respectively;

[0191] The two-dimensional DOA estimation values of the UAV incident signal are (θ1, φ1) and (θ2, φ2) respectively;

[0192] Calculate the position coordinates of the UAV incident signal based on the two receiving stations A and B respectively. For receiving station A, the expression for calculating the position coordinates (x, y, z) of the UAV incident signal is:

[0193]

[0194] For receiving station B, the expression for calculating the position coordinates (x, y, z) of the incident signal of the drone is:

[0195]

[0196] Combining expressions (1) and (2), we get the expression:

[0197] CX=D

[0198] in,

[0199]

[0200] Using the minimization of the sum of squared errors min||CX-D|| 2 Solve for the output signal X of the receiving array, and the solution expression of X is:

[0201] X=(A T A) -1 A T B

[0202] After obtaining X, the position coordinates (x, y, z) of the target signal are obtained;

[0203] If the number of receiving stations is M, M>2, the target information provided by the receiving station is used, and the target information includes the direction angles θ1~θ M 、The pitch angle of the incident signal of the drone is φ1~φ M , the distance from the incident signal of the drone to the receiving station is r1~r M , based on data fusion technology, the position coordinates (x, y, z) of the incident signal of the UAV are obtained.

[0204] The specific implementation process can be as follows:

[0205] Perform data preprocessing and synchronization. The specific steps include:

[0206] Use the NTP protocol to align timestamps for data from multiple receiving stations;

[0207] Convert the local coordinate system of each receiving station to the WGS-84 geographic coordinate system;

[0208] The position coordinates (x, y, z) of the incident signal of the UAV are calculated using the dynamic fusion state equation based on Kalman filtering. The specific steps include:

[0209] Define the drone motion model as a uniform speed model and predict the position x at the next moment kk|k-1 , the expression is:

[0210] x k|k-1 = Fx k-1 + w k

[0211] Wherein, x k-1 is the predicted value of the position of the UAV at time k-1, F is the state transition matrix, and w k is the process noise matrix;

[0212] Convert the target information (r M , φ M , θ M ) provided by each receiving station into Cartesian coordinates and input them into the Kalman filter to obtain the observed value z k of the position coordinates of the UAV, and the expression is:

[0213] z k = Hx k + v k

[0214] Wherein, x k is the predicted value of the position of the UAV at time k, H is the observation matrix, and v k is the observation noise matrix.

[0215] The embodiments are only examples for clearly illustrating the present invention, and are not intended to limit 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 list all implementation manners here. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included within the protection scope of the claims of the present invention.

Claims

1. A UAV signal positioning method based on two-dimensional DOA estimation, characterized in that: The following steps are involved: S1. Constructing a steering vector matrix of a receiving array; S2. Based on the steering vector matrix, the receiving array is used to receive and sample the two-dimensional incident signal of the UAV to obtain an output signal; S3. Construct a fourth-order cumulant matrix of the output signal, decompose the fourth-order cumulant matrix, and obtain a decomposed fourth-order cumulant matrix; S4. Based on the decomposed fourth-order cumulant matrix and the propagator-based algorithm without a priori signal source number, the noise subspace is constructed; S5. Construct a two-dimensional spatial spectrum function based on the noise subspace, the direction angle and pitch angle of the UAV; S6. Within the angle range of the azimuth angle and the angle range of the pitch angle, traverse the azimuth angle and the pitch angle, search for the peak value of the two-dimensional spatial spectrum function, and obtain the azimuth angle and the pitch angle of the UAV incident signal corresponding to the peak value as the two-dimensional DOA estimation value of the UAV incident signal; S7. Calculate the position coordinates of the incident signal of the UAV based on the two-dimensional DOA estimation value and the position coordinates of the receiving station where the receiving array is located.

2. The method for positioning a UAV signal based on two-dimensional DOA estimation according to claim 1, characterized in that: The process of constructing the steering vector matrix of the receiving array in step S1 is as follows: There are k target drone signal sources distributed in the defined space, with (θ1, φ1), (θ2, φ2), …, (θ k ,φ k ) is incident on the receiving array at an angle of θ, θ is the azimuth angle, and φ is the elevation angle; Assume that the receiving array is an L-shaped array, where there are M x There are M elements on the Y axis. y The coordinates of the mth receiving element are (x m ,y m ), the receiving array receives the guidance vector a(θ k ) is: Steering vector matrix A on the X axis x The expression is: Steering vector matrix A on the Y axis y The expression is: Then, the expression of the total steering vector matrix A is:

3. The method for positioning UAV signals based on two-dimensional DOA estimation according to claim 2, characterized in that: Based on the steering vector matrix, the receiving array is used to receive and sample the two-dimensional incident signal of the UAV T times, and the expression of the output signal is obtained as follows: X=AS+N Wherein, the output signal of the receiving array X = [x(1), x(2), ..., x(T)], X is an M×T matrix, A represents the total steering vector matrix, A = [a(θ1), a(θ2), ..., a(θ k )], S represents the UAV incident signal matrix, S = [s(1), s(2), s(3), …, s(T)], S is the k × T incident signal matrix, N is the array noise matrix, and N is an M × T matrix.

4. The method for positioning UAV signals based on two-dimensional DOA estimation according to claim 3 is characterized in that: The fourth-order cumulant matrix of the output signal constructed in step S3, the fourth-order cumulant matrix C X The expression is: Where E{.} represents the mathematical expectation, x(t) represents the t-th column submatrix under the output signal X of the receiving array, represents the Kronecker product and H represents the conjugate transpose operation of the matrix.

5. The method for positioning UAV signals based on two-dimensional DOA estimation according to claim 4 is characterized in that: The process of decomposing the fourth-order cumulant matrix in step S3 to obtain the decomposed fourth-order cumulant matrix satisfies the expression: C X =BC S B H Among them, B is the direction matrix expanded after using the fourth-order cumulant, and the i-th column of B is expressed as: In the decomposed fourth-order cumulant matrix, C S The expression is: Among them, s(t) is the signal vector, E{.} represents the mathematical expectation, and * represents conjugation.

6. The method for positioning UAV signals based on two-dimensional DOA estimation according to claim 5, characterized in that: The noise subspace is constructed based on the decomposed fourth-order cumulant matrix and the propagator-based a priori source number algorithm described in step S4. The process is: Extract the decomposed fourth-order cumulant matrix C S The first k columns of U s submatrix, where If the number of signal sources is known, then Full rank and rank is k, directly construct the noise subspace U n , the expression is: Where H represents the conjugate transpose operation of the matrix, I M is the M×M identity matrix; If the number of signal sources is unknown, then based on the propagator-free a priori signal source number algorithm, the hyperparameter μ is introduced to construct the noise subspace U n , the expression is: Among them, I M is the M×M identity matrix.

7. The method for positioning UAV signals based on two-dimensional DOA estimation according to claim 6, characterized in that: In step S5, a two-dimensional space spectrum function is constructed based on the noise subspace, the direction angle and the pitch angle of the drone. The expression of the two-dimensional space spectrum function is: Among them, P(θ,φ) represents the two-dimensional spatial spectrum function; θ is the azimuth angle, φ is the pitch angle, H represents the conjugate transpose operation of the matrix, and a(θ,φ) is the direction vector.

8. The method for positioning UAV signals based on two-dimensional DOA estimation according to claim 7, characterized in that: In step S7, based on the two-dimensional DOA estimation value of the drone incident signal and the position coordinates of the receiving station where the receiving array is located, the position coordinates of the drone incident signal are calculated, and the process is: If the number of receiving stations is 2, define the coordinates of the two receiving stations A and B as: (x1, y1, z1) and (x2, y2, z2) respectively; Define the distances from the drone incident signal to the two receiving stations A and B as r1 and r2 respectively; The two-dimensional DOA estimates of the incident signal from the UAV are (θ1, φ1) and (θ2, φ2); The position coordinates of the incident signal of the drone are calculated based on the two receiving stations A and B respectively. For receiving station A, the expression for calculating the position coordinates (x, y, z) of the incident signal of the drone is: For receiving station B, the expression for calculating the position coordinates (x, y, z) of the incident signal of the drone is: Combining expressions (1) and (2), we get the expression: CX=D in, Using the minimization of the sum of squared errors min||CX-D|| 2 Solve for the output signal X of the receiving array, and the solution expression of X is: X=(A T A) -1 A T B After obtaining X, the position coordinates (x, y, z) of the target signal are obtained.

9. The method for positioning UAV signals based on two-dimensional DOA estimation according to claim 8, characterized in that: The step S7 locates the position coordinates of the incident signal of the drone based on the two-dimensional DOA estimation value of the incident signal of the drone and the position coordinates of the receiving station, and further includes: If the number of receiving stations is M, M>2, the target information provided by the receiving station is used, and the target information includes the direction angles θ1~θ M 、The pitch angle of the incident signal of the drone is φ1~φ M , the distance from the incident signal of the drone to the receiving station is r1~r M , based on data fusion technology, the position coordinates (x, y, z) of the incident signal of the UAV are obtained.

10. A UAV signal positioning system based on two-dimensional DOA estimation, characterized in that: The system is used to execute the method according to any one of claims 1 to 9, comprising: A steering vector model building unit, used for building a steering vector matrix of a receiving array; An array output signal generating unit is used to receive and sample the two-dimensional incident signal of the UAV using a receiving array based on a steering vector matrix to obtain an output signal; A fourth-order cumulant matrix decomposition unit, used to construct a fourth-order cumulant matrix of the output signal of the receiving array, decompose the fourth-order cumulant matrix, and obtain a decomposed fourth-order cumulant matrix; A noise subspace construction unit, used to construct a noise subspace based on the decomposed fourth-order cumulant matrix and a propagator-based a priori source number algorithm; A two-dimensional space spectrum function construction unit is used to construct a two-dimensional space spectrum function based on the noise subspace, the direction angle and the pitch angle of the UAV; The DOA estimation unit is used to traverse the azimuth angle and the pitch angle within the angular range of the azimuth angle and the angular range of the pitch angle, search for the peak value of the two-dimensional spatial spectrum function, and obtain the azimuth angle and the pitch angle of the UAV incident signal corresponding to the spatial spectrum peak value as the two-dimensional DOA estimation value of the UAV incident signal; The UAV position coordinate calculation unit is used to calculate the position coordinates of the UAV incident signal based on the two-dimensional DOA estimation value and the position coordinates of the receiving station where the receiving array is located.

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