A method and system for locating a UAV signal based on two-dimensional DOA estimation

Abstract

The application provides a UAV signal positioning method and system based on two-dimensional DOA estimation, and relates to the technical field of array signal processing. First, based on the steering vector matrix of a receiving array and a two-dimensional incident signal of a UAV, a two-dimensional spatial spectrum function is constructed by using a non-prior source number algorithm based on a propagator. The use of the non-prior source number algorithm avoids the prior estimation of the number of signal sources and reduces the calculation complexity. Within the angle range of the direction angle and the angle range of the pitch angle, the direction angle and the pitch angle are traversed, the peak value of the two-dimensional spatial spectrum function is searched, the direction angle and the pitch angle of the peak value corresponding to the incident signal of the UAV are obtained as the two-dimensional DOA estimation value of the incident signal of the UAV, and 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 incident signal of the UAV are calculated, so that the modeling capability of multidimensional spatial information is enhanced.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of array signal processing, and more particularly to a UAV signal positioning method and system based on two-dimensional DOA estimation. BACKGROUND

[0002] In recent years, with the continuous development of integrated circuit technology and control technology, the civil unmanned aerial vehicle industry has developed rapidly. As civil unmanned aerial vehicles play an increasingly important role in daily life, the problem of supervision has become increasingly prominent. In terms of safety control measures, some unmanned aerial vehicle businesses use real-name activation, set no-fly zones, and limit flight height in certain areas. However, these measures mostly rely on sensors such as GPS on the aircraft body to determine the location of consumers, and consumers can easily break through the flight restriction settings by physically shielding the sensors, resulting in repeated illegal intrusion of unmanned aerial vehicles. Unmanned aerial vehicles that illegally enter without permission pose many safety hazards and pose a serious threat to ground public safety. There have been many safety incidents of unmanned aerial vehicles interfering with normal flight operations at home and abroad, posing a great risk to aviation safety. Therefore, it is crucial to study an effective method for positioning unmanned aerial vehicle signals.

[0003] Direction of Arrival (DOA) technology receives the incident signal of the unmanned aerial vehicle through a sensor array, records the time difference or phase difference of the incident signal of the unmanned aerial vehicle arriving at different array elements, and determines the direction of the signal source of the unmanned aerial vehicle by calculating the relationship between the distance between different array elements, the wavelength of the signal, and the phase difference.

[0004] A one-dimensional DOA estimation method suitable for low signal-to-noise ratio environments is proposed in the prior art. The received signal of a uniform linear array is processed, and the covariance matrix of the received signal is processed to reduce the dimension. At the same time, the eigenvalue of the noise signal is subtracted to achieve the effect of noise reduction, and the coefficients of the weighted matrix are iteratively updated in the convex optimization process of the sparse vector solution to gradually correct the deviation of the angle position. Finally, the estimation error of the angle is reduced, and the DOA estimation accuracy of the compressed sensing algorithm in a low signal-to-noise ratio environment is improved. However, the method of reducing the covariance matrix of the received signal 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 capability of the method for multi-dimensional spatial information. At the same time, the one-dimensional DOA estimation method used in this scheme needs to accurately estimate the number of signal sources in advance, but in actual complex signal environments, the types of signal sources are diverse and dynamic, making it extremely difficult to accurately estimate the number of signal sources, thereby increasing the complexity of the calculation. SUMMARY

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

[0006] In order to achieve the above technical effects, the technical solutions of the present invention are as follows:

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

[0008] S1. Constructing a steering vector matrix for the receiving array;

[0009] S2. Based on the steering vector matrix, the receiving array receives and samples the two-dimensional incident signal from the UAV to obtain an output signal.

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

[0011] S4. Construct the noise subspace based on the decomposed fourth-order cumulant matrix and the propagator-based algorithm without prior signal source number;

[0012] S5. Construct a two-dimensional spatial spectrum function based on the noise subspace, the azimuth angle, and the pitch angle of the UAV;

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

[0014] S7. Calculate the position coordinates of the incident signal from the UAV based on the two-dimensional DOA estimate and the position coordinates of the receiving station where the receiving array is located.

[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 drone, a two-dimensional spatial spectrum function is constructed using a propagator-based a priori source number algorithm. The use of the a priori source number algorithm avoids the a priori estimation of the number of signal sources and reduces the computational complexity. Within the angular range of the azimuth angle and the angular range of the pitch angle, the azimuth angle and the pitch angle are traversed to search for the peak of the two-dimensional spatial spectrum function, and the azimuth angle and pitch angle of the drone incident signal corresponding to the peak are obtained as the two-dimensional DOA estimation value of the drone 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 drone incident signal are calculated, thereby enhancing the modeling capability of multi-dimensional spatial information.

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

[0017] It is defined that there are k target unmanned aerial vehicle signal sources distributed in the space, which respectively incident into the receiving array at angles of (θ1, φ1), (θ2, φ2), …, (θ k ,φ k ), θ is the direction angle, and φ is the pitch angle;

[0018] Suppose that the receiving array is an L-shaped array, wherein 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 ), and the expression of the steering vector a(θ k ) of the kth target unmanned aerial vehicle signal source received by the receiving array 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 receives the two-dimensional incident signals of the unmanned aerial vehicle T times to obtain the expression of the output signal:

[0027] X=AS+N

[0028] Wherein, the output signal X of the receiving array is [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 unmanned aerial vehicle incident signal matrix, S=[s(1), s(2), s(3), …, s(T)], S is a k×T incident signal matrix, and N is an array noise matrix, N is an M×T matrix.

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

[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 The expression is:

[0037]

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

[0039] Preferably, the noise subspace is constructed based on the decomposed fourth-order cumulant matrix and the propagator-based a priori source number algorithm in step S4, and the process is as follows:

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

[0041] 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:

[0042]

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

[0044] If the number of signal sources is unknown, a hyperparameter μ is introduced based on the propagator-free source number algorithm without prior knowledge of the source number to construct the noise subspace U n , the expression is:

[0045]

[0046] where I M is an MxM identity matrix.

[0047] Preferably, step S5 constructs a two-dimensional spatial spectrum function based on the noise subspace, the direction angle and the pitch angle of the unmanned aerial vehicle, and the expression of the two-dimensional spatial spectrum function is:

[0048]

[0049] 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.

[0050] Preferably, step S7 calculates the position coordinates of the incident signal of the unmanned aerial vehicle based on the two-dimensional DOA estimation value of the incident signal of the unmanned aerial vehicle 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, the coordinates of the two receiving stations A and B are defined as (x1,y1,z1) and (x2,y2,z2), respectively.

[0052] The distances of the incident signal of the unmanned aerial vehicle to the two receiving stations A and B are defined as r1 and r2, respectively.

[0053] The two-dimensional DOA estimation values of the incident signal of the unmanned aerial vehicle are (θ1,φ1) and (θ2,φ2), respectively.

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

[0055]

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

[0057]

[0058] By combining expressions (1) and (2), the expression is obtained:

[0059] CX=D

[0060] where

[0061]

[0062] 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:

[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, the step S7 of locating 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 further includes:

[0066] 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 drone incident signal φ1~φ M , the distance from the drone incident signal to the receiving station r1~r M , based on data fusion technology, the position coordinates (x, y, z) of the UAV incident signal are obtained.

[0067] In a second aspect, the present application further proposes a drone signal positioning system based on two-dimensional DOA estimation, wherein the system is used to perform the method described above, including:

[0068] A steering vector model building unit, used to build a steering vector matrix of a receiving array;

[0069] 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 the steering vector matrix to obtain an output signal;

[0070] A fourth-order cumulant matrix decomposition unit is 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;

[0071] A noise subspace construction unit is used to construct a noise subspace based on the decomposed fourth-order cumulant matrix and a propagator-based a priori signal source number algorithm;

[0072] A two-dimensional spatial spectrum function construction unit is used to construct a two-dimensional spatial spectrum function based on the noise subspace, the direction angle and the pitch angle of the UAV;

[0073] 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 pitch angle, search for the peak of the two-dimensional spatial spectrum function, and obtain the azimuth angle and pitch angle of the UAV incident signal corresponding to the spatial spectrum peak as the two-dimensional DOA estimation value 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:

[0076] The present invention proposes 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 incident signal of the UAV, a two-dimensional spatial spectrum function is constructed using a propagator-based a priori signal source number algorithm. The use of the a priori signal source number algorithm avoids the a priori estimation of the number of signal sources and reduces the computational complexity. Within the angular range of the azimuth angle and the angular range of the pitch angle, the azimuth angle and the pitch angle are traversed to search for the peak of the two-dimensional spatial spectrum function, and the azimuth angle and pitch angle of the UAV incident signal corresponding to the peak are obtained 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, the position coordinates of the UAV incident signal are calculated, thereby enhancing the modeling capability of multi-dimensional spatial information. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 A schematic diagram showing a flow chart of a UAV signal positioning method based on two-dimensional DOA estimation proposed in Example 1 of the present invention;

[0078] Figure 2 A schematic diagram showing an L-shaped receiving array proposed in Example 2 of the present invention;

[0079] Figure 3 A schematic diagram illustrating the principle of determining the position coordinates of a UAV incident signal based on two-dimensional DOA estimates of a receiving station and a UAV incident signal, as proposed in Example 2 of the present invention;

[0080] Figure 4 The figure shows a structural diagram of a UAV signal positioning system based on two-dimensional DOA estimation proposed in Example 3 of the present invention. DETAILED DESCRIPTION

[0081] The accompanying drawings are for illustrative purposes only and are not to be construed as limiting this patent;

[0082] In order to better illustrate this embodiment, some parts of the drawings may be omitted, enlarged, or reduced, and do not represent the actual size;

[0083] It is understandable to those skilled in the art that descriptions of certain well-known contents may be omitted in the drawings.

[0084] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0085] The positional relationships described in the drawings are for illustrative purposes only and should not be construed as limiting this patent;

[0086] Example 1

[0087] This embodiment proposes a UAV signal positioning method based on two-dimensional DOA estimation. The implementation process of this method is shown in FIG. Figure 1 ,like Figure 1 As shown, the following steps are included:

[0088] S1. Constructing a steering vector matrix for the receiving array;

[0089] S2. Based on the steering vector matrix, the receiving array receives and samples the two-dimensional incident signal from the UAV to obtain an output signal.

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

[0091] S4. Construct the noise subspace based on the decomposed fourth-order cumulant matrix and the propagator-based algorithm without prior signal source number;

[0092] S5. Construct a two-dimensional spatial spectrum function based on the noise subspace, the azimuth angle, and the pitch angle of the UAV;

[0093] S6. Search for the peak of the two-dimensional spatial spectrum function within the azimuth angle range [0°, 360°] and the elevation angle range [0°, 90°], and obtain the azimuth and elevation angles of the incident UAV signal corresponding to the peak as the two-dimensional DOA estimate of the incident UAV signal.

[0094] S7. Calculate the position coordinates of the incident signal from the UAV based on the two-dimensional DOA estimate and the position coordinates of the receiving station where the receiving array is located.

[0095] In this embodiment, first, based on the steering vector matrix of the receiving array and the sampled two-dimensional incident signal of the drone, a two-dimensional spatial spectrum function is constructed using a propagator-based a priori source number algorithm. The use of the a priori source number algorithm avoids the a priori estimation of the number of signal sources and reduces the computational complexity. Within the angular range of the azimuth angle and the angular range of the pitch angle, the azimuth angle and the pitch angle are traversed to search for the peak of the two-dimensional spatial spectrum function, and the azimuth angle and pitch angle of the drone incident signal corresponding to the peak are obtained as the two-dimensional DOA estimation value of the drone 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 drone incident signal are calculated, thereby enhancing the modeling capability of multi-dimensional spatial information.

[0096] Example 2

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

[0098] 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, φ is the elevation angle;

[0099] Assume that the receiving array is an L-shaped array. The schematic diagram of the L-shaped array is as follows: Figure 2 As shown, there is M on the X axis 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 steering vector a(θ k ) is:

[0100]

[0101] Steering vector matrix A on the X axis x The expression is:

[0102]

[0103] Steering vector matrix A on the Y axis y The expression is:

[0104]

[0105] Then, the expression of 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 reception sampling on the two-dimensional incident signal of the drone, and the expression of the output signal is obtained as follows:

[0109] X=AS+N

[0110] Where, 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.

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

[0112]

[0113] 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.

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

[0115] C X =BC S B H

[0116] Where B is the direction matrix expanded using the fourth-order cumulant, and the i-th column of B is expressed as:

[0117]

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

[0119]

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

[0121] In this embodiment, the noise subspace is constructed based on the decomposed fourth-order cumulant matrix and the propagator-based a priori source number algorithm in step S4. The process is as follows:

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

[0123] 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:

[0124]

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

[0126] If the number of signal sources is unknown, then based on the propagator-free source number algorithm, the hyperparameter μ is introduced to construct the noise subspace U n , the expression is:

[0127]

[0128] Among them, I M is the M×M identity matrix.

[0129] In this embodiment, step S5 constructs a two-dimensional spatial spectrum function based on the noise subspace, the direction angle and the pitch angle of the drone. The expression of the two-dimensional spatial spectrum function is:

[0130]

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

[0132] In this embodiment, the process of calculating the position coordinates of the drone incident signal 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 in step S7 is as follows:

[0133] 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; Figure 3 The schematic diagram of the process is shown in Figure 1, where 1 represents receiving station A, 2 represents the location coordinates of the incident signal from the drone, and 3 represents receiving station B.

[0134] Define the distances between the drone incident signal and the two receiving stations A and B as r1 and r2 respectively;

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

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

[0137]

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

[0139]

[0140] By combining the expressions (1) and (2), the expression is obtained:

[0141] CX=D

[0142] wherein,

[0143]

[0144] By minimizing the error square sum min||CX-D||, the output signal X of the receiving array is solved, and the expression for the solution of X is: 2

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

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

[0147] In the embodiment, the positioning of 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 in step S7 further includes:

[0148] If the number of receiving stations is M, M>2, the target information provided by the receiving stations is used, and the target information includes the direction angles θ1-θM of the UAV incident signal, the elevation angles φ1-φM of the UAV incident signal, and the distances r1-rM of the UAV incident signal to the receiving stations, and the position coordinates (x, y, z) of the UAV incident signal are obtained based on the data fusion technology. M M M

[0149] Embodiment 3

[0150] As Figure 4 ​​​​As shown, this application proposes a UAV signal positioning system based on two-dimensional DOA estimation, including:

[0151] The steering vector model construction unit is used to construct the steering vector matrix of the receiving array. The process is as follows:

[0152] 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, φ is the elevation angle;

[0153] 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 steering vector a(θ k ) is:

[0154]

[0155] Steering vector matrix A on the X axis x The expression is:

[0156]

[0157] Steering vector matrix A on the Y axis y The expression 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] The array output signal generation unit is used to receive and sample the two-dimensional incident signal of the UAV using the receiving array based on the steering vector matrix, and the expression of the output signal is:

[0163] X=AS+N

[0164] Where, 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 a UAV incident signal matrix, S = [s(1), s(2), s(3), …, s(T)], S is a k x T incident signal matrix, N is an array noise matrix, N is an M x T matrix;

[0165] The fourth-order cumulant matrix decomposition unit is configured 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.

[0166] The fourth-order cumulant matrix of the output signal is constructed, and the fourth-order cumulant matrix C X is expressed as:

[0167]

[0168] wherein E{.} represents mathematical expectation, x(t) represents the tth column sub-matrix of the output signal X of the receiving array, represents a Kronecker product, and H represents a conjugate transpose operation of a matrix.

[0169] The process of decomposing the fourth-order cumulant matrix to obtain the decomposed fourth-order cumulant matrix satisfies an expression:

[0170] C X = BC S B H

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

[0172]

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

[0174]

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

[0176] The noise subspace construction unit is configured to construct a noise subspace based on the decomposed fourth-order cumulant matrix and based on a non-priori source number algorithm based on a propagator, and the process is:

[0177] The first k columns U S sub-matrix of the decomposed fourth-order cumulant matrix C s are extracted, wherein

[0178] If the number of signal sources is known, the rank of U is k, and the noise subspace U is directly constructed.n , the expression is:

[0179]

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

[0181] If the number of signal sources is unknown, then based on the propagator-free source number algorithm, the hyperparameter μ is introduced to construct the noise subspace U n , the expression is:

[0182]

[0183] Among them, 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:

[0185]

[0186] Where P(θ,φ) represents the two-dimensional spatial spectrum function; θ is the azimuth angle, φ is the elevation 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 azimuth angle and the pitch angle within the azimuth angle range of [0°, 360°] and the pitch angle range of [0°, 90°], search for the peak of the two-dimensional spatial spectrum function, and obtain the azimuth and pitch angle of the UAV incident signal corresponding to the spatial spectrum peak 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, define the coordinates of the two receiving stations A and B as (x1, y1, z1) and (x2, y2, z2) respectively;

[0190] Define the distances between the drone incident signal and the two receiving stations A and B as r1 and r2 respectively;

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

[0192] The position coordinates of the incident signal of the UAV 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 UAV is:

[0193]

[0194] For receiving station B, the expression for calculating the position coordinates (x, y, z) of the incident signal from 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 drone incident signal φ1~φ M , the distance from the drone incident signal to the receiving station r1~r M , based on data fusion technology, the position coordinates (x, y, z) of the UAV incident signal 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 on 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 from the drone are calculated using the dynamic fusion state equation based on Kalman filtering. The specific steps include:

[0209] Define the UAV 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] Among them, x k-1 is the predicted value of the UAV's position at time k-1, F is the state transfer matrix, w k is the process noise matrix;

[0212] The target information (r M ,φ M ,θ M ) is converted into Cartesian coordinates and input into the Kalman filter to obtain the observation value z of the drone's position coordinates k , the expression is:

[0213] z k =Hx k +v k

[0214] Among them, x k is the predicted value of the UAV's position at time k, H is the observation matrix, v k is the observation noise matrix.

[0215] The embodiments are provided merely to illustrate the present invention and are not intended to limit the embodiments of the present invention. Those skilled in the art will appreciate that other variations or modifications may be made based on the above description. It is not necessary and impossible to enumerate all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention are intended to be included within the scope of protection of the claims.

Claims

1. A UAV signal positioning method based on two-dimensional DOA estimation, characterized in that: The following steps are involved: S1. Construct the steering vector matrix of the receiving array. The process is: 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, 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 steering 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: Where, A=[a(θ1),a(θ2),…,a(θ k )]; S2. Based on the steering vector matrix, the receiving array receives and samples the two-dimensional incident signal from the UAV to obtain an output signal. S3. Construct a fourth-order cumulant matrix of the output signal, decompose the fourth-order cumulant matrix to obtain a decomposed fourth-order cumulant matrix; S4. Construct the noise subspace based on the decomposed fourth-order cumulant matrix and the propagator-based algorithm without prior signal source number; S5. Construct a two-dimensional spatial spectrum function based on the noise subspace, the azimuth angle, and the pitch angle of the UAV; S6. Within the angular range of the azimuth angle and the angular range of the pitch angle, search for the peak of the two-dimensional spatial spectrum function, and obtain the azimuth and pitch angle of the UAV incident signal corresponding to the peak as the two-dimensional DOA estimate of the UAV incident signal; S7. Based on the two-dimensional DOA estimate and the position coordinates of the receiving station where the receiving array is located, the position coordinates of the incident signal from the UAV are calculated as follows: 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 between the drone incident signal and 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 UAV 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 UAV is: For receiving station B, the expression for calculating the position coordinates (x, y, z) of the incident signal from 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 Where B is the direction matrix expanded by using the fourth-order cumulant, B=[b1,b2,b3,...,b i ], column i of B i The expression is: After obtaining X, the position coordinates (x, y, z) of the target signal are obtained.

2. The method for positioning UAV signals based on two-dimensional DOA estimation according to claim 1, characterized in that: Based on the steering vector matrix, the receiving array is used to perform T reception sampling on the two-dimensional incident signal of the UAV, and the expression of the output signal is obtained as follows: X=AS+N Where, 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.

3. The method for positioning UAV signals based on two-dimensional DOA estimation according to claim 2, 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.

4. The method for positioning UAV signals based on two-dimensional DOA estimation according to claim 3, 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 Where B is the direction matrix expanded 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: Where s(t) is the signal vector, E{.} represents the mathematical expectation, and * represents conjugation.

5. The method for positioning UAV signals based on two-dimensional DOA estimation according to claim 4, 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 as follows: 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 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.

6. The method for positioning UAV signals based on two-dimensional DOA estimation according to claim 5, characterized in that: In step S5, a two-dimensional spatial spectrum function is constructed based on the noise subspace, the direction angle and the pitch angle of the UAV. The expression of the two-dimensional spatial spectrum function is: Where P(θ,φ) represents a two-dimensional spatial spectrum function; θ is the azimuth angle, φ is the elevation angle, H represents the conjugate transpose operation of the matrix, and a(θ,φ) is the direction vector.

7. The method for positioning UAV signals based on two-dimensional DOA estimation according to claim 6, characterized in that: Step S7 locates the position coordinates of the drone incident signal based on the two-dimensional DOA estimation value of the drone incident signal and the position coordinates of the receiving station, and also 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 drone incident signal φ1~φ M , the distance from the drone incident signal to the receiving station r1~r M , based on data fusion technology, the position coordinates (x, y, z) of the UAV incident signal are obtained.

8. A UAV signal positioning system based on two-dimensional DOA estimation, characterized by: The system is used to perform the method according to any one of claims 1 to 7, comprising: A steering vector model building unit, used to build 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 the steering vector matrix to obtain an output signal; A fourth-order cumulant matrix decomposition unit is 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 is used to construct a noise subspace based on the decomposed fourth-order cumulant matrix and a propagator-based a priori signal source number algorithm; A two-dimensional spatial spectrum function construction unit is used to construct a two-dimensional spatial 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 pitch angle, search for the peak of the two-dimensional spatial spectrum function, and obtain the azimuth angle and pitch angle of the UAV incident signal corresponding to the spatial spectrum peak 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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