Angle estimation method for mobile sparse receiving array

Abstract

This invention provides a method for estimating the angle of a mobile sparse receiving array. The method first increases the spacing between elements in various conventional array structures. A periodic signal related to the receiving array's movement speed is emitted from the transmitting end of the MIMO radar, thereby deriving the spatiotemporal invariance of the received signal. Passive aperture synthesis is then used to expand the array aperture at the receiving end. Finally, the received data is processed using methods such as straightening, decimation, tensor smoothing, and parallel factorization to estimate the target angle. This method significantly increases the array's degrees of freedom and further exploits the inherent multidimensional structural information in the data using tensor smoothing. The Khatri-Rao product fully exploits the array aperture of the MIMO radar. Finally, the ESPRIT algorithm is used to calculate and automatically pair the target angle, significantly improving the accuracy of target parameter estimation.

Description

Technical Field

[0001] The present invention relates to the field of MIMO radar, and in particular to an angle estimation method for a MIMO radar, which is suitable for application scenarios where a receiving array operates on a mobile platform. Background Art

[0002] Achieving precise target positioning is of great practical significance in both civilian and military applications. Using bistatic MIMO radar, the receiver can simultaneously obtain the target's angle of departure and angle of arrival, enabling cross-location technology to accurately locate the target without requiring additional distance information. Bistatic MIMO radar also offers advantages such as high resolution, strong anti-interference capabilities, the ability to detect a large number of targets, and the long distance between the transmitting and receiving arrays, resulting in enhanced self-protection capabilities. Over the past decade, this technology has been extensively studied by scholars both domestically and internationally.

[0003] Since the introduction of nested arrays and coprime arrays, the problem of sparse array parameter estimation has flourished. Sparse arrays offer advantages such as higher degrees of freedom and lower mutual coupling for identical physical elements. Consequently, sparse arrays are also used in bistatic MIMO radars to estimate target parameters, thereby increasing degrees of freedom.

[0004] In practical applications, many platforms are mobile. In recent years, researchers have proposed combining sparse arrays with passive aperture synthesis technology to further enhance the array's degrees of freedom and the accuracy of target parameter estimation. Therefore, applying sparse array mobility to improve parameter estimation performance in bistatic MIMO radars has profound research significance. Summary of the Invention

[0005] In order to overcome the shortcomings of the prior art, the present invention provides a method for estimating the angle of a mobile sparse receiving array. In order to further improve the array freedom of a dual-base MIMO radar, the present invention provides a method for estimating the angle of a MIMO radar using a sparse mobile receiving array. The method is to first expand the array element spacing of various traditional array structures (generally about 1-3 times), and transmit a periodic signal related to the moving speed of the receiving array at the transmitting end of the MIMO radar, thereby deriving the spatiotemporal invariance of the received signal, and then using passive aperture synthesis technology to expand the array aperture of the receiving end. Finally, the received data is processed using methods such as straightening, decimation, tensor smoothing, and parallel factor decomposition to achieve the estimation of the target angle.

[0006] The technical solution adopted by the present invention to solve the technical problem includes the following steps:

[0007] Step 1: Establish a receiving signal model for a bistatic MIMO radar in a mobile scenario with a sparse receiving array.

[0008] Step 2: The signals transmitted by each element of the MIMO radar transmit array are orthogonal to each other. When the influence of element mutual coupling is not considered, the data model of the received signal within a pulse is obtained after matched filtering:

[0009]

[0010] Where B=(B t ⊙B r ), ⊙ is the Khatri-Rao product, and are the array manifold matrices of the receiving array and the transmitting array, respectively. The steering vectors of the transmitting array and the receiving array in different directions are:

[0011]

[0012]

[0013] in, and θ k are the wave departure angle and wave arrival angle of the target to be measured respectively;

[0014] Taking into account the Doppler frequency shift caused by the movement of the receiving array, the received signal vector is expressed as:

[0015]

[0016] where (s1(t), s2(t), ..., s K (t)) is obtained after matched filtering of the target transmission signal, and L is the number of sampling snapshots, that is, the number of pulses in a CPI coherence interval, t = 1, 2, ..., L;

[0017] Step 3: Since the receiving array moves only half a wavelength and the target is in the far field, the angle of the target is constant. At time t+τ, the received signal is expressed as:

[0018]

[0019] Where τ is the time required for the receiving array to move half a wavelength, satisfying vτ=d;

[0020] Step 4: The received signal vector is:

[0021]

[0022] Since the transmitted signal is a signal with a period of time τ, we have s k (t+τ)=s k(t), so the received signal vector is expressed as:

[0023]

[0024] in is the Hadamard product and vτ=d, so x(t+τ) is expressed as:

[0025]

[0026] in

[0027] Step 5: Then concatenate the received signals x(t) and x(t+τ) to obtain a new array received signal using passive aperture synthesis technology:

[0028] y(t)=(B t ⊙B rc )s(t)+w(t)=B c s(t)+w(t)

[0029] Among them B rc =[b rc (θ1),...,b rc (θ K )] and the new array receiving steering vector is:

[0030]

[0031] Then, the covariance statistics of the array received data y(t) are obtained:

[0032]

[0033] in is the signal covariance matrix is the noise covariance matrix, and Estimated R y ;

[0034] Step 6: Straighten the received covariance data of the array to obtain:

[0035]

[0036] in, And i=vec(I 2MN );

[0037] Eliminate vector r y The redundant items in , and rearrange them to get the signal virtual receiving vector r0:

[0038]

[0039] Where i0 is a column vector with all elements zero except the middle element which is 1, and the virtual transmit and receive array flow types are Type B r0 =[b r0 (θ1),...,b r0 (θ K )], and the virtual receive and transmit steering vectors are:

[0040]

[0041]

[0042] Where M0 = M2(M1+1) and N0 = 3N1(N2+1)+2, it can be seen that the degree of freedom is expanded nearly three times by moving the array;

[0043] Step 7: Next, define two selection matrices to operate on the virtual receive vector r0:

[0044]

[0045]

[0046] in and Through two selection matrices, we get vectors Expressed as:

[0047]

[0048] symbol is the Kronecker product, and B z =(B tz ⊙B rz ), B rz =[b rz (θ1),...,b rz (θ K )],in:

[0049]

[0050]

[0051]

[0052]

[0053] According to the matrix smoothing method, a new virtual covariance matrix is reconstructed:

[0054]

[0055] Step 8: Using the tensor smoothing method, first define the virtual single snapshot receiving tensor as:

[0056]

[0057] in and is a K×K×K unit diagonal tensor;

[0058] Define a fourth-order tensor:

[0059]

[0060] in Represents the outer product, and then use the following formula to get the new virtual covariance matrix R0:

[0061]

[0062] Get R0 = B z C T +N;

[0063] Arrange it to get a third-order tensor Then using parallel factorization, we get

[0064] Step 9: To fully utilize the transmit and receive array apertures of the MIMO radar, and Perform the Khatri-Rao product operation, i.e. To solve for angles using the ESPRIT algorithm, and ( and ) Four selection matrices are defined, and the matrices are selected respectively. The first M0-1 (N0-1) row and the last M0-1 (N0-1) row;

[0065] Step 10: Using the rotation invariance of the array, we can get the following formula:

[0066]

[0067] because Established, of which for The signal subspace obtained after singular value decomposition is a full-rank square matrix, so the matrix Ψ containing the target angle information is t and Ψ rIt is obtained by the following formula:

[0068]

[0069] The symbols represents the Moore-Penrose pseudoinverse, so according to Ψ t =TD t T -1 and Ψ r =TD r T -1 By eigenvalue decomposition, two diagonal matrices D containing target wave departure angle information and wave arrival angle information are obtained. t and D r , and the angle values of the targets can also be automatically matched; finally, according to

[0070]

[0071] Get the angle estimate that can be automatically paired, where kind The matrix D t and D r The kth diagonal element of .

[0072] In step 1, the transmitting array of the bistatic MIMO radar has M array elements, the receiving array has N array elements, and there are K far-field uncorrelated targets to be measured in space; the transmitting array is a classic nested array, wherein subarray 1 has M1 array elements and subarray 2 has M2 array elements; the receiving array is a sparse array obtained by expanding the array element spacing of the classic nested array, wherein subarray 1 has N1 array elements and subarray 2 has N2 array elements, and the receiving array moves uniformly along a straight line at a constant speed v; the schematic diagram of the array structure is shown in Figure 2 , and the array element positions of the transmitting array and the receiving array are:

[0073]

[0074]

[0075] Where d = λ / 2, λ is the carrier wavelength of the received signal.

[0076] The beneficial effects of the present invention are as follows: the present invention introduces a mobile sparse array in the receiving end of a bistatic MIMO radar, greatly improving the array degree of freedom of the system, and further utilizing the multidimensional structural information inherent in the data by using a tensor smoothing method. The array aperture of the MIMO radar is fully utilized by using the Khatri-Rao product, and finally the target angle is solved and automatically matched by the ESPRIT algorithm, thereby greatly improving the parameter estimation accuracy of the target. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 This is a flow chart of an angle estimation method based on a mobile sparse receiving array.

[0078] Figure 2 This is a schematic diagram of the direction finding of a dual-base MIMO radar system, where Figure 2 (a) is a schematic diagram of the dual-base MIMO radar transmitter. Figure 2 (b) is a schematic diagram of the mobile receiving end of the dual-base MIMO radar.

[0079] Figure 3 It is a schematic diagram of the maximum number of identifiable targets for different methods. Figure 3 (a) is the result of angle estimation of 12 targets when the receiver uses the classic nested array. Figure 3 (b) is the result of angle estimation of 40 targets when the receiver uses a moving sparse array.

[0080] Figure 4 It is the result of the root mean square error of the angle estimation of the three targets using different methods as the signal-to-noise ratio changes.

[0081] Figure 5 It is the result of the root mean square error of the angle estimation of the three targets using different methods changing with the number of snapshots. DETAILED DESCRIPTION

[0082] The present invention will be further described below with reference to the accompanying drawings and examples.

[0083] The present invention applies a mobile sparse array to dual-base MIMO to improve the degree of freedom of the system, and further improves the estimation accuracy of parameters through a tensor smoothing method.

[0084] like Figure 1 As shown, the present invention provides a method for estimating the angle of a mobile sparse receiving array, comprising the steps of:

[0085] Step 1: Set initialization parameters;

[0086] like Figure 2 Schematic diagram of a bistatic MIMO radar direction-finding system. In this scheme, the MIMO radar's transmit array is configured as a classic nested array, with subarray 1 having M1 elements and subarray 2 having M2 elements. The transmit elements transmit completely orthogonal signals. The receive array is a sparse array obtained by expanding the element spacing of the classic nested array. Subarray 1 has N1 elements and subarray 2 has N2 elements. The receive array moves uniformly along a straight line at a constant velocity v.

[0087] Step 2: Build a tensor signal model to receive data

[0088] The transmitting end transmits a periodic signal that is the time required for the receiving array to move half a wavelength. The received signal is obtained by using the passive aperture synthesis technology and the covariance statistics are obtained.

[0089]

[0090] Then, a new tensor receiving model is obtained through operations such as straightening, extraction, tensor smoothing and rearrangement.

[0091]

[0092] Then using parallel factorization we can get

[0093] Step 3: Use the Khatri-Rao product operation to get right Perform singular value decomposition to obtain the signal subspace

[0094] Step 4: Use the ESPRIT algorithm to obtain two diagonal matrices D containing the target wave departure angle information and wave arrival angle information t and D r .

[0095] Step 5: Finally, pass the target direction estimation formula

[0096]

[0097] Get the automatically paired target angle estimate.

[0098] Figure 3 The signal-to-noise ratio (SNR) is 5 dB, the number of sampling snapshots is L = 100, and the radar cross-section (RCS) amplitude is α = [1, 1, 1] T The target's Doppler shift is uniformly distributed within the range f = (200, 950) / 2000. The transmitting array is a uniform linear array with M = 3 elements, and the receiving arrays are a classic nested array with N1 = 2 and a moving sparse array with N2 = 2, respectively. Schematic diagrams of the estimation results for 12 and 40 targets, respectively, are shown for two different receiving arrays. Figure 3 The transmitting arrays of the MIMO radar are all set to uniform linear arrays, while the receiving arrays use a classic nested array and a sparse moving array of the experiment of this invention. It can be seen that the method in this paper can estimate the parameters of more targets compared with the uncorrected method.

[0099] Figure 4 Select the number of targets as 3 and the Doppler frequency as f = [200, 400, 850] T / 2000, the directions of the targets are When the number of sampling snapshots is L=200, the transmitting array is selected as a classic nested array with array elements M1=2 and M2=3, and the receiving array is selected as a classic nested array with N1=2 and N2=3. The root mean square error variation diagram of the matrix reconstruction ESPRIT algorithm (ESPRIT), the matrix smoothing parallel factor algorithm (MS-PARAFAC), and the tensor smoothing parallel factor algorithm (TS-PARAFAC) proposed in the present invention under different signal-to-noise ratios (SNRs) is used.

[0100] Figure 4 This is the direction estimation error curve under different signal-to-noise ratios when the number of sampling snapshots is selected as L=200 in the experiment of the present invention. It can be seen that compared with the matrix model algorithm and the parallel factor decomposition algorithm based on matrix smoothing, the method of the present invention has higher estimation accuracy.

[0101] Figure 5 Select the number of targets as 3 and the Doppler frequency as f = [200, 400, 850] T / 2000, the target directions are When the signal-to-noise ratio is selected as SNR=5dB, the root mean square error change diagram of the matrix reconstruction ESPRIT algorithm (ESPRIT), the matrix smoothing parallel factor algorithm (MS-PARAFAC), and the tensor smoothing parallel factor algorithm (TS-PARAFAC) proposed in the present invention under different sampling fast numbers L is shown.

[0102] Figure 5 This is the direction estimation error curve under different sampling snapshot numbers when the signal-to-noise ratio SNR=5dB is selected in the experiment of the present invention. It can be seen that the method of the present invention has higher accuracy than the matrix model algorithm and the parallel factor decomposition algorithm based on matrix smoothing.

[0103] In summary, applying a mobile sparse array to the receiving end of a bistatic MIMO radar can greatly improve the array freedom of the system and increase the maximum number of identifiable targets of the system. The use of a tensor smoothing algorithm can further improve the target estimation accuracy.

Claims

1. A method for angle estimation of a mobile sparse receiving array, characterized in that The steps include: Step 1: Establish a receiving signal model for a bistatic MIMO radar in a mobile scenario with a sparse receiving array. In step 1, the transmitting array of the bistatic MIMO radar has M array elements, the receiving array has N array elements, and there are K far-field uncorrelated targets to be measured in space; the transmitting array is a classic nested array, wherein subarray 1 has M1 array elements and subarray 2 has M2 array elements; the receiving array is a sparse array obtained by expanding the array element spacing of the classic nested array, wherein subarray 1 has N1 array elements and subarray 2 has N2 array elements, and the receiving array moves uniformly along a straight line at a constant speed v; Step 2: The signals transmitted by each element of the MIMO radar transmit array are orthogonal to each other. When the influence of element mutual coupling is not considered, the data model of the received signal within a pulse is obtained after matched filtering: Where B=(B t ⊙B r ), ⊙ is the Khatri-Rao product, and are the array manifold matrices of the receiving array and the transmitting array, respectively. The steering vectors of the transmitting array and the receiving array in different directions are: in, and θ k are the wave departure angle and wave arrival angle of the target to be measured respectively; Taking into account the Doppler frequency shift caused by the movement of the receiving array, the received signal vector is expressed as: where (s1(t),s2(t),…,s K (t)) is obtained after matched filtering of the target transmission signal, and L is the number of sampling snapshots, that is, the number of pulses in a CPI coherence interval, t = 1, 2, …, L; λ is the carrier wavelength of the received signal; Step 3: Since the receiving array moves only half a wavelength and the target is in the far field, the angle of the target is constant. At time t+τ, the received signal is expressed as: Where τ is the time required for the receiving array to move half a wavelength, satisfying vτ=d; Step 4: The received signal vector is: Since the transmitted signal is a signal with a period of time τ, we have s k (t+τ)=s k (t), so the received signal vector is expressed as: in is the Hadamard product and vτ=d, so x(t+τ) is expressed as: in Step 5: Then concatenate the received signals x(t) and x(t+τ) to obtain a new array received signal using passive aperture synthesis technology: y(t)=(B t ⊙B rc )s(t)+w(t)=B c s(t)+w(t) Among them B rc =[b rc (θ1),…,b rc (θ K )] and the new array receiving steering vector is: Then, the covariance statistics of the array received data y(t) are obtained: in is the signal covariance matrix is the noise covariance matrix, and Estimated R y ; Step 6: Straighten the received covariance data of the array to obtain: in, And i=vec(I 2MN ); Eliminate vector r y The redundant items in , and rearrange them to get the signal virtual receiving vector r0: Where i0 is a column vector with all elements zero except the middle element which is 1, and the virtual transmit and receive array flow types are and B r0 =[b r0 (θ1),…,b r0 (θ K )], and the virtual receive and transmit steering vectors are: Where M0 = M2(M1+1) and N0 = 3N1(N2+1)+2, it can be seen that the degree of freedom is expanded nearly three times by moving the array; Step 7: Define two selection matrices to operate on the virtual receive vector r0: in and Through two selection matrices, we get vectors Expressed as: symbol is the Kronecker product, and B z =(B tz ⊙B rz ), B rz =[b rz (θ1),…,b rz (θ K )],in: According to the matrix smoothing method, a new virtual covariance matrix is reconstructed: Step 8: Using the tensor smoothing method, first define the virtual single snapshot receiving tensor as: in And I K is a K×K×K unit diagonal tensor; Define a fourth-order tensor: in Represents the outer product, and then use the following formula to get the new virtual covariance matrix R0: Get R0 = B z C T +N; Arrange it to get a third-order tensor Y=I K ×1B tz ×2B rz ×3C+N, and then use parallel factorization to get Step 9: To fully utilize the transmit and receive array apertures of the MIMO radar, and Perform the Khatri-Rao product operation, i.e. To solve for angles using the ESPRIT algorithm, and Four selection matrices are defined, and Select the matrices respectively The first M0-1 row and the last M0-1 row, and and Select the matrices respectively The first N0-1 rows and the last N0-1 rows; Step 10: Using the rotation invariance of the array, we can get the following formula: because Established, of which for The signal subspace obtained after singular value decomposition is a full-rank square matrix, so the matrix Ψ containing the target angle information is t and Ψ r It is obtained by the following formula: The symbols represents the Moore–Penrose pseudoinverse, so according to Ψ t =TD t T -1 and Ψ r =TD r T -1 By eigenvalue decomposition, two diagonal matrices D containing target wave departure angle information and wave arrival angle information are obtained. t and D r , and the angle values of the targets can also be automatically matched; finally, according to Get the angle estimate that can be automatically paired, where and The matrix D t and D r The kth diagonal element of .

2. The method for angle estimation of a mobile sparse receiving array according to claim 1, wherein: The array element positions of the transmitting array and the receiving array are: D t ={0,1,…,(M1-1),M1,…,(M1+1)M2-1}d <h2 style=";text-align:left;direction:ltr">D<h2 style=";text-align:left;direction:ltr"> r <h2 style=";text-align:left;direction:ltr"> ={0,1,…,3(N1-1),…,6N1,…,(3N2+3)N1}d Where d = λ / 2, λ is the carrier wavelength of the received signal.

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