Direction of arrival estimation method based on multi-input multi-output radar of unmanned aerial vehicle group-borne electromagnetic vector sensor array

Abstract

The invention provides a direction-of-arrival estimation method based on an unmanned aerial vehicle group-borne electromagnetic vector sensor array multi-input multi-output radar. The method is suitable for air and space target detection of an unmanned aerial vehicle cluster and a small reconnaissance aircraft cluster. One same electromagnetic vector sensor is installed on each unmanned aerial vehicle in a cluster to form an electromagnetic vector sensor array with any array element position, attitude error compensation is performed on a data receiving model of a single sensor, so that all airborne sensors reach a zero attitude, and the unmanned aerial vehicle is in a zero attitude state. An array transmitting data model and an array receiving data model are arranged according to a parallel factor model to obtain three-dimensional tensor data, a bearing matrix is obtained by using a trilinear alternating least square method, and finally DOA estimation is realized by using vector cross multiplication. According to the invention, multi-target DOA estimation of blind array element positions and blind polarization information is realized.

Description

Technical Field

[0001] The present invention relates to the technical fields of signal detection and estimation, and reconnaissance and navigation, and in particular to a method for estimating a direction of arrival of an electromagnetic vector sensor array multi-input multi-output radar based on a swarm of unmanned aerial vehicles. Background Art

[0002] In the field of aerospace target detection, how to complete real-time reconnaissance work faster, more accurately, more reliably, more flexibly and at a lower cost has always been a concern. Today's aerospace target detection usually uses ground base stations, which brings a series of problems, such as large targets that are difficult to conceal and easily become the enemy's main target; high costs, once attacked will cause considerable economic losses; the number of base stations is usually small, and they are easily attacked in electronic warfare, and the reliability is not good enough. In recent years, the continuous improvement of the economy, maneuverability, load and endurance of drones have attracted attention, and drones are increasingly used in long-distance reconnaissance, attack, rescue and other tasks.

[0003] The drone swarm maintains a specific topological structure through the overall formation, and the individual drones have a certain degree of maneuverability, thereby enhancing survivability and improving mission execution efficiency. An electric field vector sensor is installed on each drone, so that the entire drone swarm forms a polarization array, and single-station or multi-station MIMO radar multi-target direction of arrival estimation is performed. The full-aperture multi-target direction of arrival estimation of blind array element position and blind polarization information can be realized without relying on the array element position. The received data is arranged according to the parallel factor model, and the load matrix is ​​obtained using the trilinear alternating least squares method. Summary of the invention

[0004] Purpose of the invention: The technical problem to be solved by the present invention is to overcome the defects of low maneuverability and general survivability of large MIMO radar arrays, and provide a method for estimating the direction of arrival (DOA) of a multiple-input multiple-output (MIMO) radar based on an electromagnetic vector sensor (EMVS) array carried by a drone swarm, comprising the following steps:

[0005] Step 1: Install an electromagnetic vector sensor with the same initial posture on each drone platform. All airborne electromagnetic vector sensors form an electromagnetic vector sensor array, which serves as a receiving array and a transmitting array to receive far-field signals reflected by air and space targets from ground base stations or other drone cluster array elements. All drone nodes transmit the signals obtained by the sensors to the master node in the drone cluster, which processes the received data. Generally speaking, the master node is the node with the strongest computing power in the drone cluster. When the master node is attacked or crashes, the drone cluster elects a new master node. The microcomputer on the master node processes the received data and returns the detection results to the ground station or vehicle-mounted base station.

[0006] Step 2: According to the Parallel Factor (PARAFAC) model, the signals received by the drone cluster are arranged in tensor form, and the trilinear alternating least squares (TALS) method is used for trilinear decomposition to obtain the bearing factor matrix. Finally, the vector cross product (VCP) method is used to estimate the direction of arrival (DOA) of multiple targets.

[0007] In step 1, the electromagnetic vector sensor includes three dipole antennas and three orthogonal magnetic rings, wherein the dipole antennas measure the electric field strength of electromagnetic waves, and the magnetic rings measure the magnetic field strength of electromagnetic waves.

[0008] In step 1, the electromagnetic wave parameters are represented by spatial arrival parameter descriptors (θ, φ) and polarization ellipse descriptors (γ, η), where the elevation angle θ∈(0, π), the azimuth angle φ∈(0, 2π), the polarization angle γ∈(-π / 2, π / 2), the polarization ellipticity η∈(-π / 4, π / 4), and (θ, φ) represents the arrival direction of the electromagnetic wave; the arrival direction matrix V(θ, φ) and the polarization parameter matrix ξ(γ, η) are defined as follows:

[0009]

[0010] The electromagnetic field guidance vector b is defined as:

[0011]

[0012] Where j is the imaginary part, e represents the natural constant, n x and m x Represent the electric field vector and the magnetic field vector respectively; perform the normalized cross product of the electric field vector and the magnetic field vector to obtain the Poynting vector h:

[0013]

[0014] in is the vector cross product, ||n x || F Indicates n x The Frobenius norm (F-norm) of , u, v, w represent the direction cosines in the direction of electromagnetic wave propagation.

[0015] In step 1, the single sensor posture is described by the rotation vector express in are three rotation angles, T represents matrix transpose; rotation posture matrix b R Can fully represent posture information:

[0016]

[0017] The signal q(t) transmitted by the drone swarm array at time t is expressed as:

[0018] q(t)=V T ω m a T s(t) (5)

[0019] where ω m is the antenna current weight coefficient vector of the mth electromagnetic vector sensor in the array, ω m =[ω m (1) ,ω m (2) ,…,ω m (p) ], where p is the number of sensor units, ω m (p) represents the current gain of the pth unit in the mth electromagnetic vector sensor; defines the Boda constant Then the spatial load vector Where λ represents the wavelength of electromagnetic wave, p m is the installation position coordinate of the sensor in the Cartesian coordinate system, p m =[x m ,y m ,z m ] T , s(t) represents the snapshot waveform of a total of M transmitted signals, s(t) = [s1(t), s2(t), …, s M (t)],s1(t),s2(t),…,s M (t) represents the 1st, 2nd,...,Mth signal snapshot waveforms respectively.

[0020] Step 1 also includes: each airborne electromagnetic vector sensor receives the echo signal x reflected by the kth target at time t m(t)′ is expressed as:

[0021]

[0022] where c k (l) is the complex reflection coefficient of the kth target to the lth pulse signal, is the scattering coefficient matrix, where represents a two-row and two-column complex matrix, V k represents the direction of arrival matrix of the kth target, a k represents the spatial carrying vector of the kth target, The Boda constant h k is the Poynting vector corresponding to the kth target;

[0023] The Beidou or GPS system installed on the drone is used to obtain its own attitude information. Each drone uses its own measured attitude to remove the influence of attitude differences, so that all sensors in the array can achieve the same attitude. m (t)′ multiply on the left The inverse matrix of the electromagnetic vector sensor array receives the signal x at time t m (t) is:

[0024]

[0025] The lth pulse x(l,t) in the received signal received by the electromagnetic vector sensor array after being reflected by K targets is expressed as:

[0026]

[0027] Where n(l,t) is the noise vector of the received signal; when s(t) is the power signal transmitted in an orthogonal coding manner, the electromagnetic vector sensor array receives the mth echo signal x generated by the signal pulse within one cycle. m (l) is:

[0028]

[0029] in, s * (t) represents the conjugate of s(t), n m (l) represents the noise signal;

[0030] The array receives the lth pulse X of the mth echo m (l) is expressed as:

[0031] X m (l) = BD m (A)C T +N m(l) (10)

[0032] Among them, D m (A) means constructing the mth row of A into a diagonal matrix, the spatial response matrix The kth item k ranges from 1 to K, and the polarization domain steering matrix is the radar cross-sectional area coefficient matrix, α k is the radar cross-sectional area coefficient of the kth target, f k is the Doppler frequency generated by the kth target movement, δ is the pulse frequency of the transmitted signal, N m (l) is the noise matrix,

[0033] Step 2 includes: arranging the M echo reception signals received by all electromagnetic vector sensors to obtain L pulse signals reflected by K targets, that is, the reception signal matrix is ​​expressed as:

[0034]

[0035] Where ⊙ is the Khatri-Rao product, N1 to N M Represents the noise matrix corresponding to the rearranged matrix of each row of A, is the additive white Gaussian noise matrix.

[0036] Step 2 also includes: arranging X into a tensor form according to the parallel factor model:

[0037] Z=I K ×1A×2B×3C+N (12)

[0038] Where Z represents the tensor matrix, I K is a K-order cubic unit tensor, ×1, ×2, ×3 are the n-module products of tensor matrices, is the noise tensor matrix;

[0039] The multi-target DOA estimation problem is solved by minimizing the following cost function:

[0040]

[0041] Formula (11) is a slice rearrangement matrix for the tensor matrix Z. For a three-dimensional tensor, slices are sliced ​​along three directions to obtain three slice rearrangement matrices. For the received signal tensor matrix Z, the slice rearrangement matrices in the other two directions are:

[0042]

[0043] Noise Matrix Noise Matrix

[0044] Formula (13) is equivalent to solving the following problems at the same time:

[0045]

[0046] Using the trilinear alternating least squares method, the iterative expressions of the three factor matrices are:

[0047]

[0048] in represents the pseudo-inverse of the matrix B⊙C; using the trilinear alternating least squares method TALS, the estimated values ​​of the three factor matrices are are the estimated values ​​of A, B, and C after the iteration.

[0049] Step 2 also includes: using The information in is vector cross multiplied to obtain the Poynting vector, thereby obtaining the DOA estimate:

[0050] use express The kth column of and denote the electric field vector and magnetic field vector of the kth target respectively. Combining equation (3), we can get and Perform normalized vector cross multiplication to obtain the Poynting vector corresponding to the kth target

[0051]

[0052] in, They represent the estimated values ​​of u, v, w, φ, and θ corresponding to the k-th target respectively;

[0053] Finally, the DOA estimate of the kth target is obtained through the Poynting vector:

[0054]

[0055] The present invention also provides an electronic device, comprising a processor and a memory, wherein the memory stores program code, and when the program code is executed by the processor, the processor executes the steps of the described method.

[0056] The present invention also provides a storage medium storing a computer program or instruction. When the computer program or instruction is run on a computer, the steps of the method described are executed.

[0057] Compared with the prior art, the present invention adopts the above technical solution and has the following beneficial effects:

[0058] (1) Compared with traditional ground base stations, reconnaissance aircraft, and early warning aircraft, drone swarms have many advantages, such as high reliability, strong survivability, flexibility, not easily obstructed, and low cost. The failure of a small number of nodes in a drone swarm will not seriously affect the reconnaissance mission. At the same time, long-distance detection and tracking can be carried out through multi-batch, controllable number of drone swarms, and multiple reconnaissance results can be integrated, thereby improving the efficiency and effectiveness of reconnaissance.

[0059] (2) GPS and other airborne equipment are used to obtain the attitude information of the UAV, and the attitude information of the UAV is used to process the received signal, thereby eliminating the influence of attitude error on the multi-target DOA estimation. Therefore, it is not necessary to make all UAVs reach the same attitude during measurement, which improves the real-time performance of reconnaissance and reduces the response speed.

[0060] (3) In this method, there is no need to obtain the position information of the drone's onboard sensors and the polarization parameters of the electromagnetic wave in advance for processing the received signal. This method can be used for drone clusters at any location. When the relative position of the drone is unknown or the relative position changes frequently, and the relative position of the array element cannot be accurately recorded, this method can also be used to complete the detection task, which reduces the use conditions and is more in line with the actual use scenario, realizing full-aperture multi-target DOA estimation of blind array element position and blind polarization information. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments, and the above and / or other advantages of the present invention will become more clear.

[0062] Figure 1 Schematic diagram of electromagnetic vector sensor.

[0063] Figure 2 Schematic diagram of multi-target DOA estimation using electromagnetic vector sensor arrays carried by drone swarms. DETAILED DESCRIPTION

[0064] The embodiment of the present invention provides a method for estimating a direction of arrival based on a multi-input multi-output radar of an electromagnetic vector sensor array carried by a swarm of drones, comprising the following steps:

[0065] Step 1, establishing a single-station electromagnetic vector sensor array data transmission and reception model;

[0066] The electromagnetic vector sensor used in the embodiment of the present invention is composed of three dipole antennas and three orthogonal magnetic rings. Figure 1 As shown, the dipole antenna measures the electric field strength of the electromagnetic wave, and the magnetic ring measures the magnetic field strength of the electromagnetic wave. Figure 2As shown, a full electric field vector sensor is installed on each drone in the drone formation. The drone group uses one of the nodes or the main node as the origin of the Cartesian coordinate system. All airborne electromagnetic vector sensors EMVS form an electromagnetic vector sensor EMVS array as a signal transceiver unit. This embodiment only takes a single-station MIMO-EMVS array as an example to introduce the model and algorithm. In actual applications, multiple drone clusters can be used as signal stations to perform multi-target DOA detection tasks of multi-station MIMO-EMVS arrays. Since the detection target distance is usually far, the return signal is considered to be a far-field signal in this embodiment, so the drone cluster can be regarded as a point in space, that is, the target DOA is determined by taking the position of the main node in the cluster as the base station position.

[0067] The electromagnetic wave parameters are represented by spatial arrival parameter descriptors (θ, φ) and polarization ellipse descriptors (γ, η), where the elevation angle θ∈(0, π), the azimuth angle φ∈(0, 2π), the polarization angle γ∈(-π / 2, π / 2), the polarization ellipticity η∈(-π / 4, π / 4), and (θ, φ) represent the direction of arrival (DOA) of the electromagnetic wave. The direction of arrival matrix V(θ, φ) and the polarization parameter matrix ξ(γ, η) are defined as:

[0068]

[0069] The electromagnetic field guidance vector is defined as:

[0070]

[0071] where n x and m x Represent the electric field vector and magnetic field vector respectively. Perform the normalized cross product of the electric field vector and the magnetic field vector to obtain the Poynting vector h:

[0072]

[0073] in is the vector cross product (VCP), ||n x || F Indicates n x The Frobenius norm (F-norm), u, v, w represent the direction cosines in the direction of electromagnetic wave propagation, and the Poynting vector can describe the direction of arrival of the electromagnetic wave.

[0074] The electromagnetic vector sensor is rigidly mounted on the drone, so the sensor attitude is the same as the drone attitude. According to the three-dimensional space rotation theory, the attitude of a single sensor is represented by a rotation vector descriptor. in For three rotation angles, the rotation attitude matrix can fully represent the attitude information:

[0075]

[0076] The UAV swarm array transmission signal is expressed as:

[0077] q(t)=V T ω m a T s(t) (5)

[0078] where ω m is the antenna current weight coefficient vector of the mth electromagnetic vector sensor in the array, ω m =[ω m (1) ,ω m (2) ,…,ω m (p) ], characterizes the current gain of each unit in the electromagnetic vector sensor, where p is the number of sensor units. For example, for the electromagnetic vector sensor in this method, the number of sensor units is 6. a is the spatial bearing vector in p m =[x m ,y m ,z m ] T is the installation position coordinate of the sensor in the Cartesian coordinate system. When the UAV formation performs tracking and detection tasks, the position change of the UAV is usually not obvious, and the position information is usually known. When encountering enemy attacks or passing through complex environments, the cluster needs to frequently re-form and change the position of each node. Therefore, the algorithm in this paper can still achieve multi-target DOA estimation without the need for sensor position information in the array. s(t)=[s1(t),s2(t),…,s M (t)] are the snapshot waveforms of M transmitted signals, s1(t),s2(t),…,s M (t) represents the 1st, 2nd,...,Mth signal snapshot waveforms respectively.

[0079] For receiving signals, the platform attitude is an important factor that cannot be ignored. The echo signal received by each airborne sensor after being reflected by the kth target is expressed as:

[0080]

[0081] where c k (l) is the complex reflection coefficient of the kth target to the lth pulse signal, is the scattering coefficient matrix, The Boda constant m=1,2,···,k,h kis the Poynting vector corresponding to the kth target. The Beidou or GPS system installed on the drone is used to obtain its own attitude information. Each drone uses its own measured attitude to remove the influence of attitude differences, so that all sensors in the array can achieve the same attitude (zero attitude), that is, for x m (t)′ multiply on the left The inverse matrix of . So the EMVS array receives the signal:

[0082]

[0083] Since the accuracy of the attitude estimated by the navigation system is limited, the transmission signal model that removes the attitude information has a certain error. This error can be reduced by increasing the number of drones, increasing the number of snapshots, and increasing the signal-to-noise ratio. Especially for drone swarms, increasing the number of drones is an efficient and economical way. Another method is to make each drone actively reach the same attitude when receiving signals and performing DOA estimation. The lth pulse of the received signal received by the EMVS array on the drone swarm after being reflected by K targets is expressed as:

[0084]

[0085] n(l,t) is the noise vector of the received signal. When s(t) is the power signal transmitted in an orthogonal coding manner, the mth echo signal generated by the EMVS array receiving a signal pulse within a cycle is:

[0086]

[0087] in,

[0088] The lth pulse of the mth echo received by the array is expressed as:

[0089]

[0090] Among them, D m (A) means that the mth row of A is constructed as a diagonal matrix, and the spatial response matrix k ranges from 1 to K, and the polarization domain steering matrix is the radar cross section (RCS) matrix, α k is the RCS coefficient of the kth target, f k is the Doppler frequency generated by the kth target movement, δ is the pulse frequency, is the noise matrix.

[0091] Step 2: Parallel factorization and DOA estimation

[0092] Arrange the M echo reception signals received by all electromagnetic vector sensors to obtain L pulse signals reflected by K targets:

[0093]

[0094] Where ⊙ is the Khatri-Rao product, N1 to N M Represents the noise matrix corresponding to the rearranged matrix of each row of A, is the additive white Gaussian noise matrix. According to the parallel factor model, X is arranged into a tensor form:

[0095] Z=I K ×1A×2B×3C+N (12)

[0096] Among them I K is a K-order cubic unit tensor, ×1, ×2, ×3 are the n-module products of tensor matrices, is the noise tensor matrix. Therefore, the multi-target DOA estimation problem can be solved by minimizing the following cost function:

[0097]

[0098] Formula (11) is a slice rearrangement matrix of the tensor matrix Z. Similarly, the slice rearrangement matrices in the other two directions are as follows:

[0099] Y=[B⊙C]A T +N y (14)

[0100] Z=[C⊙A]B T +N z (15)

[0101] Noise Matrix

[0102] Formula (13) is equivalent to solving the following problems at the same time:

[0103]

[0104] The trilinear alternating least squares (TALS) method is used to solve this problem. Its core concept is: when updating a factor matrix, it depends on the estimated values ​​of the other two factor matrices in the previous iteration and is updated by the least squares (LS) method. The goal of each iteration is to minimize the cost function until the entire algorithm reaches a convergence state. The iterative expression of the three factor matrices is:

[0105]

[0106] in represents the pseudo-inverse of the matrix B⊙C. Using the TALS method, the estimated values ​​of the three factor matrices are Finally, using The information in the vector is cross-multiplied to obtain the Poynting vector and then the DOA estimate. express The kth column of , noting formula (2), Depend on and Composition, that is Combining formula (3), and Perform normalized vector cross multiplication to obtain the Poynting vector corresponding to the kth target

[0107]

[0108] in, They respectively represent the estimated values ​​of u, v, w, φ, and θ corresponding to the k-th target.

[0109] Finally, the DOA estimate of the kth target is obtained through the Poynting vector:

[0110]

[0111] The present invention provides a method for estimating the direction of arrival of a drone-based electromagnetic vector sensor array multi-input multi-output radar. There are many methods and ways to implement the technical solution. The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, without departing from the principle of the present invention, several improvements and modifications can be made, and these improvements and modifications should also be regarded as the scope of protection of the present invention. All components not specified in this embodiment can be implemented by existing technologies.

Claims

1. A method for estimating the direction of arrival of a drone-based electromagnetic vector sensor array multi-input multi-output radar, characterized in that: The following steps are involved: Step 1: Install an electromagnetic vector sensor with the same initial posture on each UAV platform. All airborne electromagnetic vector sensors form an electromagnetic vector sensor array, which serves as a receiving array and a transmitting array to receive far-field signals reflected by air and space targets from ground base stations or other UAV cluster array elements. All UAV nodes transmit the signals obtained by the sensors to the master node in the UAV cluster. Step 2: According to the parallel factor model, the signals received by the drone cluster are arranged in tensor form, and the trilinear alternating least squares method is used to perform trilinear decomposition to obtain the bearing factor matrix. Finally, the vector cross multiplication method is used to estimate the direction of arrival (DOA) of multiple targets.

2. The method according to claim 1, characterized in that In step 1, the electromagnetic vector sensor includes three dipole antennas and three orthogonal magnetic rings, wherein the dipole antennas measure the electric field strength of electromagnetic waves, and the magnetic rings measure the magnetic field strength of electromagnetic waves.

3. The method according to claim 2, characterized in that In step 1, the electromagnetic wave parameters are represented by spatial arrival parameter descriptors (θ, φ) and polarization ellipse descriptors (γ, η), where the elevation angle θ∈(0, π), the azimuth angle φ∈(0, 2π), the polarization angle γ∈(-π / 2, π / 2), the polarization ellipticity η∈(-π / 4, π / 4), and (θ, φ) represents the arrival direction of the electromagnetic wave; the arrival direction matrix V(θ, φ) and the polarization parameter matrix ξ(γ, η) are defined as follows: The electromagnetic field guidance vector b is defined as: Where j is the imaginary part, e represents the natural constant, n x and m x Represent the electric field vector and magnetic field vector respectively; perform the normalized cross product of the electric field vector and the magnetic field vector to obtain the Poynting vector h: in is the vector cross product, ||n x || F Indicates n x The Frobenius norm of , u, v, w represent the direction cosines in the direction of electromagnetic wave propagation.

4. The method according to claim 3, characterized in that In step 1, the single sensor posture is described by the rotation vector express in are three rotation angles, T represents matrix transpose; rotation posture matrix b R Can fully represent posture information: The signal q(t) transmitted by the drone swarm array at time t is expressed as: q(t)=V T ω m a T s(t) (5) where ω m is the antenna current weight coefficient vector of the mth electromagnetic vector sensor in the array, ω m =[ω m (1) ,ω m (2) ,…,ω m (p) ], where p is the number of sensor units, ω m (p) represents the current gain of the pth unit in the mth electromagnetic vector sensor; defines the Boda constant Then the spatial load vector Where λ represents the wavelength of electromagnetic wave, p m is the installation position coordinate of the sensor in the Cartesian coordinate system, p m =[x m ,y m ,z m ] T , s(t) represents the snapshot waveform of a total of M transmitted signals, s(t) = [s1(t), s2(t), …, s M (t)],s1(t),s2(t),…,s M (t) represents the 1st, 2nd,...,Mth signal snapshot waveforms respectively.

5. The method according to claim 4, characterized in that Step 1 also includes: each airborne electromagnetic vector sensor receives the echo signal x reflected by the kth target at time t m (t)′ is expressed as: where c k (l) is the complex reflection coefficient of the kth target to the lth pulse signal, is the scattering coefficient matrix, where represents a two-row and two-column complex matrix, V k represents the direction of arrival matrix of the kth target, a k represents the spatial carrying vector of the kth target, The Boda constant h k is the Poynting vector corresponding to the kth target; The Beidou or GPS system installed on the drone is used to obtain its own attitude information. Each drone uses its own measured attitude to remove the influence of attitude differences, so that all sensors in the array can achieve the same attitude. m (t)′ multiply on the left The inverse matrix of the electromagnetic vector sensor array receives the signal x at time t m (t) is: The lth pulse x(l,t) in the received signal received by the electromagnetic vector sensor array after being reflected by K targets is expressed as: Where n(l,t) is the noise vector of the received signal; when s(t) is the power signal transmitted in an orthogonal coding manner, the electromagnetic vector sensor array receives the mth echo signal x generated by the signal pulse within one cycle. m (l) is: in, s * (t) represents the conjugate of s(t), n m (l) represents the noise signal; The array receives the lth pulse X of the mth echo m (l) is expressed as: X m (l)=BD m (A)C T +N m (l) (10) Among them, D m (A) means constructing the mth row of A into a diagonal matrix, the spatial response matrix The kth item k ranges from 1 to K, and the polarization domain steering matrix is the radar cross-sectional area coefficient matrix, α k is the radar cross-sectional area coefficient of the kth target, f k is the Doppler frequency generated by the kth target movement, δ is the pulse frequency of the transmitted signal, N m (l) is the noise matrix, 6. The method according to claim 5, characterized in that Step 2 includes: arranging the M echo reception signals received by all electromagnetic vector sensors to obtain L pulse signals reflected by K targets, that is, the reception signal matrix is ​​expressed as: Where ⊙ is the Khatri-Rao product, N1 to N M Represents the noise matrix corresponding to the rearranged matrix of each row of A, is the additive white Gaussian noise matrix.

7. The method according to claim 6, characterized in that Step 2 also includes: arranging X into a tensor form according to the parallel factor model: Z=I K ×1A×2B×3C+N (12) Where Z represents the tensor matrix, I K is a K-order cubic unit tensor, ×1, ×2, ×3 are the n-module products of tensor matrices, is the noise tensor matrix; The multi-target DOA estimation problem is solved by minimizing the following cost function: Formula (11) is a slice rearrangement matrix for the tensor matrix Z. For a three-dimensional tensor, slices are sliced ​​along three directions to obtain three slice rearrangement matrices. For the received signal tensor matrix Z, the slice rearrangement matrices in the other two directions are: Y=[B⊙C]A T +N y (14) Z=[C⊙A]B T +N z (15) Noise Matrix Noise Matrix Formula (13) is equivalent to solving the following problems at the same time: Using the trilinear alternating least squares method, the iterative expressions of the three factor matrices are: in represents the pseudo-inverse of the matrix B⊙C; using the trilinear alternating least squares method TALS, the estimated values ​​of the three factor matrices are are the estimated values ​​of A, B, and C after the iteration.

8. The method according to claim 7, characterized in that Step 2 also includes: using The information in is vector cross multiplied to obtain the Poynting vector, thereby obtaining the DOA estimate: use express The kth column of and denote the electric field vector and magnetic field vector of the kth target respectively. Combining equation (3), we can get and Perform normalized vector cross multiplication to obtain the Poynting vector corresponding to the kth target in, They represent the estimated values ​​of u, v, w, φ, and θ corresponding to the k-th target respectively; Finally, the DOA estimate of the kth target is obtained through the Poynting vector:

9. An electronic device, characterized in that: The method comprises a processor and a memory, wherein the memory stores program codes, and when the program codes are executed by the processor, the processor executes the steps of the method according to any one of claims 1 to 8.

10. A storage medium, characterized in that: A computer program or instruction is stored, and when the computer program or instruction is run on a computer, the steps of the method according to any one of claims 1 to 8 are executed.

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