Two-dimensional DOA and polarization parameter estimation method based on polarization sensitive parallel array

Abstract

The invention relates to a two-dimensional DOA and polarization parameter estimation method based on a polarization sensitive parallel array. The method comprises the following steps: determining parameters of the polarization sensitive parallel array according to the total number of array elements; designing a separated polarization sensitive sparse array according to the polarization sensitive parallel array parameters determined in the step 1; based on the separated polarization sensitive sparse array, a virtual area array is deduced by combining the motion of the array along the normal direction of the array; on the basis of the obtained virtual area array, the degree of freedom of the virtual area array in a differential common array domain of a space domain-polarization domain is solved; and based on the virtual area array, deducing a multi-dimensional parameter estimation algorithm based on ESPRIT according to a virtual array structure, taking the solved degree of freedom as an upper limit of a maximum estimable signal source number of the parameter estimation algorithm, and obtaining two-dimensional DOA and polarization parameter estimation of each signal by using the parameter estimation algorithm. Compared with the prior art, the array has the characteristics of low mutual coupling, high degree of freedom and large aperture, and the parameter estimation method has the advantages of low complexity, automatic parameter matching and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of antenna array signal processing, and in particular to a two-dimensional DOA and polarization parameter estimation method based on a polarization sensitive parallel array. Background Art

[0002] In the past decade, with the gradual promotion of phased arrays in radar, communication, sonar and other systems, array signal processing has received extensive attention and research. Polarization-sensitive array signal processing, as a research hotspot and difficulty in array signal processing, can provide estimates of the direction of arrival and polarization parameters of target signals, which can effectively enhance the target positioning and recognition capabilities of radar, communication, sonar and other systems.

[0003] However, in order to ensure the estimation accuracy of the target signal’s direction of arrival and polarization parameters, conventional polarization-sensitive arrays consume a lot of hardware resources. At the same time, the large number of closely spaced array elements in conventional polarization-sensitive arrays and the co-point multi-polarization antenna configuration on each element often introduce strong mutual coupling effects, thereby reducing the accuracy of parameter estimation. In addition, traditional multidimensional parameter estimation methods often produce high computational complexity for two-dimensional direction of arrival and polarization estimation, which does not meet the real-time processing requirements in real scenarios. The above problems are issues that should be considered and resolved in the process of multidimensional parameter estimation of polarization-sensitive arrays. Summary of the invention

[0004] The purpose of the present invention is to provide a two-dimensional DOA and polarization parameter estimation method based on a vertical motion separated polarization sensitive parallel array, by introducing a vertical motion linear nested polarization sensitive array and a differential co-array of block sub-matrices, the array degree of freedom is improved while the algorithm complexity is reduced.

[0005] The purpose of the present invention can be achieved by the following technical solutions:

[0006] A two-dimensional DOA and polarization parameter estimation method based on a polarization sensitive parallel array comprises the following steps:

[0007] Step 1: Determine the polarization sensitive parallel array parameters according to the total number of array elements;

[0008] Step 2: Design a separated polarization-sensitive sparse array according to the polarization-sensitive parallel array parameters determined in step 1;

[0009] Step 3: Based on the separated polarization-sensitive sparse array designed in step 2, the virtual array is derived by combining the movement of the array along its normal direction;

[0010] Step 4: Based on the virtual array obtained in step 3, the degrees of freedom of the virtual array in the differential common array domain of the spatial domain and the polarization domain are obtained;

[0011] Step 5: Based on the virtual array in step 3, a multidimensional parameter estimation algorithm based on ESPRIT is derived according to the virtual array structure, and the degrees of freedom obtained in step 4 are used as the upper limit of the maximum number of estimable signal sources of the parameter estimation algorithm. The parameter estimation algorithm is used to obtain the two-dimensional DOA and polarization parameter estimates of each signal.

[0012] The polarization-sensitive parallel array parameters include the array structure, the number of array elements and the polarization type of each subarray, wherein the polarization-sensitive parallel array comprises two sparse linear arrays parallel to the y-axis, respectively composed of a dipole antenna and a magnetic ring, and the distance between the two subarrays is d=λ / 2, wherein λ is the wavelength of the signal; the position of the reference array element is set to (0, 0); the array structures of the two subarrays are the same, both having N=N1+N2 array elements, when N is an odd number, N1=(N-1) / 2, N2=(N+1) / 2; when N is an even number, N1=N2=N / 2.

[0013] The sparse linear arrays of the polarization-sensitive parallel arrays are composed of a left sub-array L, a middle sub-array M and a right sub-array R. N1 is the total number of array elements of the left sub-array and the right sub-array, N2 is the number of array elements of the middle sub-array, and the position set is expressed as:

[0014] P=LU M UR,

[0015] in,

[0016]

[0017] Where l represents V 21 , V1(N2) or V 22 The position of any array element in V 21 V is the part of the dense subarray with odd array element positions. 22 is the part of the dense subarray with even array element positions, V1(N2) is the array element position set of the sparse subarray, which is further expressed as:

[0018]

[0019] in, Indicates rounding down.

[0020] In order to improve the flexibility of the array, the position of the dense subarray is further optimized, the position of the sparse subarray is kept unchanged, and a movable array set V′ is introduced into the subarray. 21 , V′ 22 , where V′ 21 , V′ 22 Represent the movable sub-array sets of the left sub-array and the right sub-array respectively, as follows:

[0021] V′ 21={N1-3,…,N1-2k1-1,…,0}

[0022] V′ 22 ={N1-2, N1-4,…,N1-2k2,…,0}

[0023] After the movement, a new array ANA-MDS is obtained;

[0024] The array ANA-MDS is discussed in two scenarios: Scenario 1 is to move only some elements of the left subarray, and the operation method is to change V′ 21 Scenario 2 is to move only some of the elements in the right sub-array. The operation method is to transfer V′ 22 If some of the array elements in the left sub-array are transferred to the left sub-array, the position sets P′1 and P′2 of the first sub-array and the second sub-array are:

[0025]

[0026] Among them, in scenario 1, D 21 ={N1, N1-1}∪V′ 21，L , D 22 =V 22 ∪V′ 21，R And V′ 21 =V′ 21 , L ∪V′ 21，R , V′ 21 Divided into V′ 21，R and V′ 21，L , V′ 21，R Represents the set of array elements moved to the right, V′ 21，L Indicates the array element set left on the left; in scenario 2, D 21 =V 21 ∪V′ 22，L , D 22 =V′ 22，R And V′ 22 =V′ 22，L ∪V′ 22，R , V′ 22 Divided into V′ 22，R and V′ 22，L , V′ 22，R represents the set of array elements remaining on the right, V′ 22，L Indicates the set of array elements moved to the left.

[0027] The separated polarization-sensitive sparse array is designed in step 2, specifically:

[0028] Assume that K far-field uncorrelated electromagnetic signals are incident along the y-axis onto the array ANA-MDS consisting of N magnetic rings and N dipole antennas. The total number of antennas is 2N. At time t, the received signal model of the array is:

[0029] x(t)=A αβ，p s(t)+n(t),

[0030] The signal vector s(t) = [s1(t), s2(t), ..., s K (t)], Gaussian white noise vector n(t) = [n1(t), n2(t), ..., n 2N (t)]T, array manifold Spatial Array Manifold A α =[a α，1 , a α，2 , …, a α，K ], airspace steering vector a k is the angle between the kth incident signal and the physical array, P is the position vector of the array ANA-MDS, and the polarization state vector of the magnetic ring array is L = A p，1 , the dipole array polarization state vector is D = A p，2 , the transformation matrix Φ β =diag(φ β，1 ,φ β，2 ,…,φ β，K ) is a diagonal matrix, β k is the angle between the kth incident signal and the normal direction of the physical array; And polarization array manifold θ k represents the pitch angle of the kth signal measured from the positive direction of the z-axis, γ k and η k They represent the polarization angle and polarization phase difference of the corresponding signals respectively.

[0031] In step 3, the virtual array is derived according to the movement of the array along its normal direction, specifically:

[0032] Assuming that the array moves along the vertical direction, i.e., the x-axis, at a speed v, the DOA of each incident signal is considered a fixed value, at time t+mτ, m=1,…,M-1, where τ is a short time interval and M is the number of array movements, the array ANA-MDS mth shift array signal model is expressed as:

[0033]

[0034] in,

[0035] Assume τv=d=λ / 2, then T β，m for:

[0036] Assuming the signal is a narrowband signal and its carrier frequency is f, then s(t) = s(t+mτ)e -j2πf·m·τ , x(t+mτ) can be rewritten as: Among them, x m (t) = x(t+mτ)e -j2πf·m·τ and

[0037] Repeat the shift array M-1 times, combine the original array ANA-MDS with several shift arrays to form a virtual plane array M-ANA-MDS, whose signal model is:

[0038]

[0039] After rearranging the signal model according to the polarization type, it is simplified to:

[0040] in And B αβ，p =A β，p ⊙A β ⊙A α , A β =[a β，1 , …, a β，K ],

[0041] In step 4, the degrees of freedom of the virtual array in the differential common array domain of the spatial domain and the polarization domain are determined based on the covariance matrix of the virtual array, specifically:

[0042] Use step 3 to generate a virtual array moving along its normal direction but The covariance matrix of is: is the noise power, the signal covariance matrix represents the power of the kth signal;

[0043] Covariance matrix Related to dual-polarized planar arrays, using the block model Re-expressed as:

[0044]

[0045] The block matrix It is expressed as,

[0046]

[0047] Where 1≤g, h≤2, 1≤i, j≤M, and 0≤m i , m j ≤M-1, δ(·) represents the discrete impulse function;

[0048] Using the idea of ​​differential co-matrix, the sub-matrix Expanded into a virtual submatrix with more degrees of freedom, we have:

[0049]

[0050] in

[0051]

[0052] in is a virtual array steering vector with a uniform linear array structure.

[0053] In step 4, the degrees of freedom of the array M-ANA-MDS are: DOF ANAWMDSI-MP =M·DOF ANAWMDSI , where DOF ANAWMDSI =2DOF ANAI2 , the degrees of freedom DOF of the classic ANAI2 ANAI2 =2((N1+1)N2+(N1-2))-1, the unilateral degree of freedom of the classic ANAI2 is: L u =(N1+1)N2+(N1-2)-1.

[0054] In step 5, a multidimensional parameter estimation algorithm based on ESPRIT is derived according to the virtual array structure, specifically: based on vτ=λ / 2, the angle β between the incident signal and the normal direction of the physical array is obtained using the concept of ESPRIT, and other parameters are estimated using the eigenvector based on the ESPRIT algorithm;

[0055] Rewrite the virtual covariance matrix in step 4 as in

[0056] Covariance matrix Perform eigendecomposition, expressed as Among them U s is the signal subspace matrix, U n is the noise subspace matrix, ∑ s and∑ n Represent the eigenvalue diagonal matrices corresponding to the signal subspace and the noise subspace respectively;

[0057] According to the ESPRIT concept, the virtual array is separated into two identical overlapping sub-arrays, where the array manifolds of the dipole array and the magnetic toroidal array are in

[0058]

[0059] Among them, I N×M and O N×M Represented as the unit matrix and zero matrix of N×M dimensions respectively;

[0060] Due to the Vandermonde structure, the translation invariance is

[0061]

[0062] and U s In the same subspace, there exists a non-singular matrix T1 such that thereby: C αβ，p = U s T1, where U s = J U s ,

[0063] From the rotational invariance equation of ESPRIT have to:

[0064]

[0065] Ψ=T1Φ β，p T1 -1

[0066] Then, the estimation of polarization angle and polarization phase difference γ, η is expressed as:

[0067]

[0068] Where abs(·) represents the absolute value, and arg(·) represents the phase operation.

[0069] The non-singular matrix T1 is obtained from the above formula, and the other parameters of the k-th signal are expressed as [Φ] k，k The corresponding eigenvector estimate is:

[0070]

[0071] Depend on Can be found

[0072] All estimated parameters of the kth signal are automatically paired according to the one-to-one relationship between eigenvectors and eigenvalues.

[0073] The computational complexity of the multidimensional parameter estimation algorithm is:

[0074] The complexity of the received data covariance matrix obtained from step 4 is approximately equal to O((2(N1+N2)M) 2 L), where L is the number of snapshots;

[0075] From step 5, we can get the complexity of eigenvalue decomposition of ESPRIT algorithm as O(2(((N1+1)N2+(N1-2))(M-1)) 2 ), the complexity of the closed estimate of β is O(2((N1+1)N2+(N1-2))(M-1)K 2 +K 3 );

[0076] Then the total complexity of the multidimensional parameter estimation algorithm is O((2(N1+N2)M) 2 L+2(((N1+1)N2+(N1-2))(M-1)) 2 +2((N1+1)N2+(N1-2))(M-1)K 2 +K 3 ).

[0077] Compared with the prior art, the present invention has the following beneficial effects:

[0078] (1) Different from the traditional array configuration design based on differential co-array, the present invention places antennas with different polarizations at different array element positions and organically combines the differential co-array with the array motion characteristics to achieve an array design with small mutual coupling, large aperture, and multiple degrees of freedom under a limited number of array elements. At the same time, the physical array element positions of the proposed array can be adjusted as required, and its differential co-array is kept as a uniform array structure. The array's degrees of freedom, low mutual coupling, and flexibility are superior to most existing array configurations.

[0079] (2) The parameter estimation method proposed in the present invention can obtain four-dimensional parameters (i.e., two-dimensional DOA and polarization parameters) about the target signal by using ESPRIT only once, and realize self-matching of multiple parameters. Compared with the existing multi-dimensional parameter estimation methods, it has the advantages of low complexity and high estimation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 is a flow chart of the method of the present invention;

[0081] Figure 2 is a schematic diagram of a M-ANA-MDS array in an embodiment;

[0082] Figure 33 is a scatter diagram of four angle parameters based on the M-ANA-MDS array in an embodiment, wherein (3a) represents the relationship between the azimuth angle and the elevation angle, and (3b) represents the relationship between the polarization angle and the polarization angle difference;

[0083] Figure 4 4 is a diagram showing how the root mean square error varies with the signal-to-noise ratio in an embodiment, wherein (4a) shows how the root mean square error of the azimuth angle and the elevation angle varies with the signal-to-noise ratio, and (4b) shows how the root mean square error of the polarization angle and the polarization angle difference varies with the signal-to-noise ratio;

[0084] Figure 5 1 is a graph showing how the root mean square error varies with the number of snapshots in an embodiment, wherein (5a) shows how the root mean square error of the azimuth angle and the elevation angle varies with the number of snapshots, and (5b) shows how the root mean square error of the polarization angle and the polarization angle difference varies with the number of snapshots. DETAILED DESCRIPTION

[0085] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0086] This embodiment provides a two-dimensional DOA and polarization parameter estimation method based on a polarization sensitive parallel array. Figure 1 As shown, the following steps are included:

[0087] Step 1: Determine the polarization sensitive parallel array parameters according to the total number of array elements.

[0088] The polarization-sensitive parallel array parameters include the array structure, number of array elements and polarization type of each subarray.

[0089] Nested array is a classic sparse array. To further improve the freedom of nested array, predecessors proposed ANAI array. To improve the flexibility of array arrangement, the present invention adds a movable array set on the basis of ANAI array and proposes a new array ANA-MDS (augment nested array with movable dense subarrayI), which is specifically expressed as follows.

[0090] The array proposed in the present invention is a planar array structure, such as Figure 2 As shown. It consists of subarray 1 and subarray 2, that is, two sparse linear arrays parallel to the y-axis. Subarray 1 and subarray 2 have the same number of antennas but different polarization types. Subarray 1 consists of dipole antennas parallel to the z-axis, and subarray 2 consists of magnetic rings with their normal directions parallel to the z-axis.

[0091] The spacing between adjacent array elements in each subarray in the x-axis direction conforms to the array distribution model of ANAI-2. The distance between two subarrays is d = λ / 2, where λ is the wavelength of the signal; the position of the reference array element is set to (0,0). The array structure of the two subarrays is the same, with N = N1 + N2 array elements. When N is an odd number, N1 = (N-1) / 2, N2 = (N+1) / 2; when N is an even number, N1 = N2 = N / 2.

[0092] Sub-matrix 1 and sub-matrix 2 are composed of left sub-matrix L, middle sub-matrix M and right sub-matrix R. The number of array elements in the middle sub-matrix M is N2 and the array element spacing is (N1+1)d. The total number of array elements in the left sub-matrix L and the right sub-matrix R is N1. The position set is expressed as:

[0093] P=LU M UR,

[0094] in,

[0095]

[0096] Where l represents V 21 , V1(N2) or V 22 The position of any array element in V 21 V is the part of the dense subarray with odd array element positions. 22 is the part of the dense subarray with even array element positions, V1(N2) is the array element position set of the sparse subarray, which is further expressed as:

[0097]

[0098] in, Indicates rounding down.

[0099] Taking sub-matrix 1 as an example, sub-matrix 1 has N1+N2 array elements, which are composed of left sub-matrix L1, middle sub-matrix M1 and right sub-matrix R1. The position set P1 is expressed as,

[0100] P1=L1∪M1∪R1

[0101] Described in detail

[0102] Similarly, sub-array 2 has N1+N2 array elements, which are also composed of left sub-array L2, middle sub-array M2 and right sub-array R2. The array element position P2 is

[0103] P2=L2∪M2∪R2

[0104] Here L2=L1, M2=M1, R2=R1.

[0105] In order to improve the flexibility of the array, the position of the dense subarray is further optimized, the position of the sparse subarray is kept unchanged, and a movable array set V′ is introduced into the subarray. 21 , V′ 22 , the array positions of the left and right subarrays are further optimized to obtain the movable ANAI-2 array ANA-MDS (augment nested array with movable dense subarray I). 21 , V′ 22 Represent the movable sub-array sets of the left sub-array and the right sub-array respectively, as follows:

[0106] V′ 21 ={N1-3,…,N1-2k1-1,…,0}

[0107] V′ 22 ={N1-2, N1-4,…,N1-2k2,…,0}

[0108] After the movement, a new array ANA-MDS (augment nested array with movable densesubarray) is obtained.

[0109] The array ANA-MDS is discussed in two scenarios: Scenario 1 is when it is difficult to place all the elements of the left subarray in the real scene, and V′ can be randomly taken out. 21 Scenario 2 is when it is difficult to place all the elements of the right sub-array in the real scene, and V′ can be randomly taken out. 22 That is, scenario 1 is to move only some of the elements of the left sub-array. The operation method is to move V′ 21 Scenario 2 is to move only some of the elements in the right sub-array. The operation method is to transfer V′ 22 If some of the array elements in the left sub-array are transferred to the left sub-array, the position sets P′1 and P′2 of the first sub-array and the second sub-array are:

[0110]

[0111] Among them, in scenario 1, D 21 ={N1, N1-1}∪V′ 21，L , D 22 =V 22 ∪V′ 21，R And V′ 21 =V′ 21，L ∪V′ 21，R , V′ 21 Divided into V′ 21，R and V′ 21，L , V′ 21，RRepresents the set of array elements moved to the right, V′ 21，L Indicates the array element set left on the left; in scenario 2, D 21 =V 21 ∪V′ 22，L , D 22 =V′ 22，R And V′ 22 =V′ 22，L ∪V′ 22，R , V′ 22 Divided into V′ 22，R and V′ 22，L , V′ 22，R represents the set of array elements remaining on the right, V′ 22，L Indicates the set of array elements moved to the left.

[0112] After the move, the position set P′1 of submatrix 1 is composed of the left submatrix L′1, the middle submatrix M′1 ​​and the right submatrix R′1:

[0113]

[0114] Similarly, the items in the position set P′2 of sub-array 2 after the move are

[0115]

[0116] Step 2: According to the polarization-sensitive parallel array parameters determined in step 1, a separated polarization-sensitive sparse array is designed.

[0117] Assume that K far-field uncorrelated electromagnetic signals are incident along the y-axis onto the array ANA-MDS consisting of N magnetic rings and N dipole antennas. The total number of antennas is 2N, and the array structure is as follows: Figure 2 As shown. At time t, the array's received signal model is:

[0118] x(t)=A αβ，p s(t)+n(t),

[0119] The signal vector s(t) = [s1(t), s2(t), ..., s K (t)], Gaussian white noise vector n(t) = [n1(t), n2(t), ..., n 2N (t)] T , array manifold Spatial Array Manifold A α =[a α，1 , a α，2 , …, a α，K ], airspace steering vector a kis the angle between the kth incident signal and the physical array, P is the position vector of the array ANA-MDS, and the polarization state vector of the magnetic ring array (i.e., subarray 2) is L=A p,1 , the polarization state vector of the dipole array (i.e., subarray 1) is D = A p,2 , defined by the polarization array flow pattern. The transformation matrix Φ β =diag(φ β,1 ,φ β,2 ,…,φ β,K ) is a diagonal matrix, β k is the angle between the kth incident signal and the normal direction of the physical array. The polarization array flow pattern is recorded as And polarization array manifold θ k represents the pitch angle of the kth signal measured from the positive direction of the z-axis, γ k and η k They represent the polarization angle and polarization phase difference of the corresponding signals respectively.

[0120] The two-dimensional DOA of each signal is obtained by the following formula:

[0121]

[0122] in, Represents the azimuth of the k signals measured from the positive direction of the z-axis. k and β k Represent the angles between the corresponding signal and the y-axis and x-axis respectively.

[0123] Step 3: Based on the separated polarization-sensitive sparse array designed in step 2, the virtual array is derived by combining the movement of the array along its normal direction.

[0124] Assume that the array moves along the vertical direction, i.e., the x-axis, at a speed v. Due to the short-distance movement, the DOA of each incident signal is considered to be a fixed value. At time t+mτ, m=1,…,M-1, where τ is the short time interval and M is the number of array movements, the original array ANA-MDS mth shift array signal model is expressed as:

[0125]

[0126] in,

[0127] Assume τv=d=λ / 2, then T β,m for:

[0128] Since the signal is assumed to be a narrowband signal, its carrier frequency is f, then s(t) = s(t + mτ)e -j2πf·m·τ, x(t+mτ) can be rewritten as: Among them, x m (t) = x(t+mτ)e -j2πf·m·τ and

[0129] Repeat the shift array M-1 times, combine the original array ANA-MDS with several shift arrays to form a virtual plane array M-ANA-MDS, whose signal model is:

[0130]

[0131] After rearranging the signal model according to the polarization type, it is simplified to:

[0132] in And B αβ,p =A β,p ⊙A β ⊙A α , A β =[a β,1 ,…,a β,K ],

[0133] Step 4: Based on the virtual array obtained in step 3, the degrees of freedom of the virtual array in the differential common array domain of the spatial domain and the polarization domain are obtained.

[0134] Use step 3 to generate a virtual array moving along its normal direction but The covariance matrix of is: is the noise power, the signal covariance matrix represents the power of the kth signal.

[0135] Because the covariance matrix It is related to the dual-polarization planar array. Therefore, in order to simplify the algorithm complexity, the virtual array is split into two parts according to the polarization type, namely the dipole virtual array and the magnetic ring virtual array. Re-expressed as:

[0136]

[0137] The block matrix represents the cross-covariance matrix formed by the g-th sub-matrix in the i-th array and the h-th sub-matrix in the j-th array, expressed as,

[0138]

[0139] Among them, 1≤g,h≤2, 1≤i,j≤M, and 0≤m i ,m j ≤M-1, δ(·) represents the discrete impulse function.

[0140] Using the idea of ​​differential co-matrix, the sub-matrix Expanded into a virtual submatrix with more degrees of freedom, we have:

[0141]

[0142] in

[0143]

[0144] in is a virtual array steering vector with a uniform linear array structure.

[0145] From the degrees of freedom of ANA-MDS and the differential common array of M-ANA-MDS, we can know that the degrees of freedom of the array M-ANA-MDS are: DOF ANAWMDSI-MP =M·DOF ANAWMDSI , where ANA-MDS, DOF in scenario 1 ANAWMDSI =2DOF ANAI2 , the degrees of freedom DOF of the classic ANAI2 ANAI2 =2((N1+1)N2+(N1-2))-1, the unilateral degree of freedom of the classic ANAI2 is: L u =(N1+1)N2+(N1-2)-1. In scenario 2, the degrees of freedom of ANA-MDS change with the change of the moving array element. The closed form expression of the degrees of freedom is DOF ANAI2 =2((N1+1)N2+(N1-2)-2m)-1, Where m is the number of movable array elements. The array degrees of freedom can be regarded as the upper bound of the maximum number of estimable signal sources in the parameter estimation algorithm.

[0146] Step 5: Based on the virtual array in step 3, a multidimensional parameter estimation algorithm based on ESPRIT is derived according to the virtual array structure, and the degrees of freedom obtained in step 4 are used as the upper limit of the maximum number of estimable signal sources of the parameter estimation algorithm. The parameter estimation algorithm is used to obtain the two-dimensional DOA and polarization parameter estimates of each signal.

[0147] Based on vτ=λ / 2, the angle β between the incident signal and the normal direction of the physical array can be obtained using the concept of ESPRIT, and then other parameters can be estimated using the eigenvector based on the ESPRIT algorithm.

[0148] Rewrite the virtual covariance matrix in step 4 as in

[0149] Covariance matrix Perform eigendecomposition, expressed as Among them U s is the signal subspace matrix, U n is the noise subspace matrix, Σ s and Σ n Represent the diagonal matrices of eigenvalues ​​corresponding to the signal subspace and the noise subspace respectively.

[0150] According to the ESPRIT concept, the virtual array is separated into two identical overlapping sub-arrays, where the array manifolds of the dipole array and the magnetic toroidal array are in

[0151]

[0152] Among them, I N×M and O N×M Represented as the unit matrix and zero matrix of N×M dimensions respectively.

[0153] Due to the Vandermonde structure, the translation invariance is

[0154]

[0155] because and U s are in the same subspace, so there exists a non-singular matrix T1 such that This results in: C αβ,p = U s T1, where U s = J U s .

[0156] From the rotational invariance equation of ESPRIT We can get:

[0157]

[0158] Then we can get:

[0159]

[0160] Further we can get:

[0161]

[0162] Then, the estimation of polarization angle and polarization phase difference γ,η is expressed as:

[0163]

[0164] Where abs(·) represents the absolute value, and arg(·) represents the phase operation.

[0165] The non-singular matrix T1 is obtained from the above formula. The other parameters of the k-th signal can be used [Φ] k,k The corresponding eigenvector estimate is:

[0166]

[0167] Depend on Can be found

[0168] All estimated parameters of the kth signal are automatically paired according to the one-to-one relationship between eigenvectors and eigenvalues.

[0169] According to the above steps, the computational complexity of the multidimensional parameter estimation algorithm can be obtained as:

[0170] The complexity of the received data covariance matrix obtained from step 4 is approximately equal to O((2(N1+N2)M) 2 L), where L is the number of snapshots;

[0171] From step 5, we can get the complexity of eigenvalue decomposition of ESPRIT algorithm as O(2(((N1+1)N2+(N1-2))(M-1)) 2 ), the complexity of the closed estimate of β is O(2((N1+1)N2+(N1-2))(M-1)K 2 +K 3 );

[0172] Then the total complexity of the multidimensional parameter estimation algorithm is O((2(N1+N2)M) 2 L+2(((N1+1)N2+(N1-2))(M-1)) 2 +2((N1+1)N2+(N1-2))(M-1)K 2 +K 3 ).

[0173] This embodiment illustrates the effects of the proposed array and method through simulation experiments.

[0174] Simulation experiment 1:

[0175] The simulation conditions are set as follows: the array element positions of the two subarrays of the proposed array along the y-axis are [0 1 3 4 9 141921]. Four uncorrelated signals are selected, and their elevation angle, azimuth angle, polarization angle and polarization angle difference are

[0176] and The spatial noise is Gaussian white noise, the signal-to-noise ratio is set to 5 dB, the number of snapshots is 1500, and the number of Monte Carlo iterations is 300. Figure 3 The figure shows the estimation results of the parameters of the four signals based on the proposed estimation method of the proposed array. It can be seen from the figure that the parameter estimation values ​​obtained by 300 Monte Carlo tests are all close to the true values, which shows the effectiveness of the proposed array and method.

[0177] Simulation experiment 2:

[0178] The number of array elements in the proposed array and the comparison array is 16. The comparison array is a common second-order polarization nested sensitive array. The comparison array uses the BOMP algorithm to estimate the two-dimensional DOA and polarization parameters of the signal. Three uncorrelated signals are selected, and their elevation angle, azimuth angle, polarization angle and polarization angle difference are and (60°, 77.2°, 39°, 70°), the number of Monte Carlo experiments is 300. Figure 4 The root mean square error (RMSE) of the estimation results is shown as a function of the signal-to-noise ratio, with the number of snapshots being 2000. It can be seen from the figure that the estimation results of the parameters of the proposed method based on the proposed array are better than those of the BOMP algorithm based on the comparison array. Figure 5 The variation of RMSE with the number of snapshots is shown, and the signal-to-noise ratio is set to 5 dB. It can be seen from the figure that for both 2D DOA and polarization parameters, the RMSE of the proposed method based on the proposed array is lower than the RMSE of the BOMP algorithm based on the comparison array, which fully demonstrates the superior performance of the proposed array and the proposed method.

[0179] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning, or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A two-dimensional DOA and polarization parameter estimation method based on a polarization sensitive parallel array, characterized in that: The following steps are involved: Step 1: Determine the polarization sensitive parallel array parameters according to the total number of array elements; Step 2: Design a separated polarization-sensitive sparse array according to the polarization-sensitive parallel array parameters determined in step 1; Step 3: Based on the separated polarization-sensitive sparse array designed in step 2, the virtual array is derived by combining the movement of the array along its normal direction; Step 4: Based on the virtual array obtained in step 3, the degrees of freedom of the virtual array in the differential common array domain of the spatial domain and the polarization domain are obtained; Step 5: Based on the virtual array in step 3, a multidimensional parameter estimation algorithm based on ESPRIT is derived according to the virtual array structure, and the degrees of freedom obtained in step 4 are used as the upper limit of the maximum number of estimable signal sources of the parameter estimation algorithm. The parameter estimation algorithm is used to obtain the two-dimensional DOA and polarization parameter estimates of each signal.

2. The method for estimating two-dimensional DOA and polarization parameters based on a polarization sensitive parallel array according to claim 1, characterized in that: The polarization-sensitive parallel array parameters include the array structure, the number of array elements and the polarization type of each subarray, wherein the polarization-sensitive parallel array comprises two sparse linear arrays parallel to the y-axis, respectively composed of a dipole antenna and a magnetic ring, and the distance between the two subarrays is d=λ / 2, wherein λ is the wavelength of the signal; the position of the reference array element is set to (0,0); the array structures of the two subarrays are the same, both having N=N1+N2 array elements, when N is an odd number, N1=(N-1) / 2, N2=(N+1) / 2; when N is an even number, N1=N2=N / 2.

3. The method for estimating two-dimensional DOA and polarization parameters based on a polarization sensitive parallel array according to claim 2, characterized in that: The sparse linear arrays of the polarization-sensitive parallel arrays are composed of a left sub-array L, a middle sub-array M and a right sub-array R. N1 is the total number of array elements of the left sub-array and the right sub-array, N2 is the number of array elements of the middle sub-array, and the position set is expressed as: P = L ∪ M ∪ R, in, Where l represents V 21 , V1(N2) or V 22 The position of any array element in V 21 V is the part of the dense subarray with odd array element positions. 22 is the part of the dense subarray with even array element positions, V1(N2) is the array element position set of the sparse subarray, which is further expressed as: in, Indicates rounding down.

4. The method for estimating two-dimensional DOA and polarization parameters based on a polarization sensitive parallel array according to claim 3, characterized in that: In order to improve the flexibility of the array, the position of the dense subarray is further optimized, the position of the sparse subarray is kept unchanged, and a movable array set V′ is introduced into the subarray. 21 , V′ 22 , where V′ 21 , V′ 22 Represent the movable sub-array sets of the left sub-array and the right sub-array respectively, as follows: In 21 ={N1-3,…,N1-2k1-1,…,0} IN' 22 ={N1-2,N1-4,…,N1-2k2,…,0} After the movement, a new array ANA-MDS is obtained; The array ANA-MDS is discussed in two scenarios: Scenario 1 is to move only some elements of the left subarray, and the operation method is to change V′ 21 Scenario 2 is to move only some of the elements in the right sub-array. The operation method is to transfer V′ 22 If some of the array elements in the left sub-array are transferred to the left sub-array, the position sets P′1 and P′2 of the first sub-array and the second sub-array are: Among them, in scenario 1, D 21 ={N1,N1-1}∪V′ 21,L , D 22 =V 22 ∪V′ 21,R And V′ 21 =V′ 21,L ∪V′ 21,R , V′ 21 Divided into V′ 21,R and V′ 21,K , V′ 21,R Represents the set of array elements moved to the right, V′ 21,L Indicates the array element set left on the left; in scenario 2, D 21 =V 21 ∪V′ 22,L , D 22 =V′ 22,R And V′ 22 =V′ 22,L ∪V′ 22,R , V′ 22 Divided into V′ 22,R and V′ 22,L , V′ 22,R represents the set of array elements remaining on the right, V′ 22,L Indicates the set of array elements moved to the left.

5. The method for estimating two-dimensional DOA and polarization parameters based on a polarization sensitive parallel array according to claim 4, characterized in that: The separated polarization-sensitive sparse array is designed in step 2, specifically: Assume that K far-field uncorrelated electromagnetic signals are incident along the y-axis onto the array ANA-MDS consisting of N magnetic rings and N dipole antennas. The total number of antennas is 2N. At time t, the received signal model of the array is: x(t)=A αβ,p s(t)+n(t), The signal vector s(t) = [s1(t), s2(t), …, s K (t)], Gaussian white noise vector n(t) = [n1(t),n2(t),…,n 2N (t)] T , array manifold Spatial Array Manifold A α =[a α,1 ,a α,2 ,…,a α,K ], airspace steering vector a k is the angle between the kth incident signal and the physical array, P is the position vector of the array ANA-MDS, and the polarization state vector of the magnetic ring array is L = A p,1 , the dipole array polarization state vector is D = A p,2 , the transformation matrix Φ β =diag(φ β,1 ,φ β,2 ,…,φ β,K ) is a diagonal matrix, β k is the angle between the kth incident signal and the normal direction of the physical array; And polarization array manifold θ k represents the pitch angle of the kth signal measured from the positive direction of the z-axis, γ k and η k They represent the polarization angle and polarization phase difference of the corresponding signals respectively.

6. The method for estimating two-dimensional DOA and polarization parameters based on a polarization sensitive parallel array according to claim 5, characterized in that: In step 3, the virtual array is derived according to the movement of the array along its normal direction, specifically: Assuming that the array moves along the vertical direction, i.e., the x-axis, at a speed v, the DOA of each incident signal is considered a fixed value. At time t+mτ, m=1,…,M-1, where τ is a short time interval and M is the number of array movements, the array ANA-MDS mth shift array signal model is expressed as: in, Assume τv=d=λ / 2, then T β,m for: Assuming the signal is a narrowband signal and its carrier frequency is f, then s(t) = s(t+mτ)e -j2πf·m·τ , x(t+mτ) can be rewritten as: Among them, x m (t) = x(t+mτ)e -j2πf·m·τ and Repeat the shift array M-1 times, combine the original array ANA-MDS with several shift arrays to form a virtual plane array M-ANA-MDS, whose signal model is: After rearranging the signal model according to the polarization type, it is simplified to: Among them And B αβ,p = A β,p ⊙A β ⊙A α , A β =[a β,1 ,…,a β,K ], 7. The method for estimating two-dimensional DOA and polarization parameters based on a polarization sensitive parallel array according to claim 6, characterized in that: In step 4, the degrees of freedom of the virtual array in the differential common array domain of the spatial domain and the polarization domain are determined based on the covariance matrix of the virtual array, specifically: Use step 3 to generate a virtual array moving along its normal direction but The covariance matrix of is: is the noise power, the signal covariance matrix represents the power of the kth signal; Covariance matrix Related to dual-polarized planar arrays, using the block model Re-expressed as: The block matrix It is expressed as, Among them, 1≤g,h≤2, 1≤i,j≤M, and 0≤m i ,m j ≤M-1, δ(·) represents the discrete impulse function; Using the idea of ​​differential co-matrix, the sub-matrix Expanded into a virtual submatrix with more degrees of freedom, we have: in in is a virtual array steering vector with a uniform linear array structure.

8. The method for estimating two-dimensional DOA and polarization parameters based on a polarization sensitive parallel array according to claim 7, characterized in that: In step 4, the degrees of freedom of the array M-ANA-MDS are: DOF ANAWMDSI-MP =M·DOF ANAWMDSI , where DOF ANAWMDSI =2DOF ANAI2 , the degrees of freedom DOF of the classic ANAI2 ANAI2 =2((N1+1)N2+(N1-2))-1, the unilateral degree of freedom of the classic ANAI2 is: L u =(N1+1)N2+(N1-2)-1.

9. The method for estimating two-dimensional DOA and polarization parameters based on a polarization sensitive parallel array according to claim 8, characterized in that: In step 5, a multidimensional parameter estimation algorithm based on ESPRIT is derived according to the virtual array structure, specifically: based on vτ=λ / 2, the angle β between the incident signal and the normal direction of the physical array is obtained using the concept of ESPRIT, and other parameters are estimated using the eigenvector based on the ESPRIT algorithm; Rewrite the virtual covariance matrix in step 4 as in Covariance matrix Perform eigendecomposition, expressed as Among them U s is the signal subspace matrix, U n is the noise subspace matrix, Σ s and Σ n Represent the eigenvalue diagonal matrices corresponding to the signal subspace and the noise subspace respectively; According to the ESPRIT concept, the virtual array is separated into two identical overlapping sub-arrays, where the array manifolds of the dipole array and the magnetic toroidal array are in Among them, I N×M and O N×M Represented as the unit matrix and zero matrix of N×M dimensions respectively; Due to the Vandermonde structure, the translation invariance is and U s In the same subspace, there exists a non-singular matrix T1 such that thereby: C αβ,p = U s T1, where U s = J U s , From the rotational invariance equation of ESPRIT have to: Ψ=T1Φ β,p T1 -1 Then, the estimation of polarization angle and polarization phase difference γ,η is expressed as: Where abs(·) means to find the absolute value, and arg(·) means to find the phase operation; The non-singular matrix T1 is obtained from the above formula, and the other parameters of the k-th signal are expressed as [Φ] k,k The corresponding eigenvector estimate is: Depend on Can be found All estimated parameters of the kth signal are automatically paired according to the one-to-one relationship between eigenvectors and eigenvalues.

10. The method for estimating two-dimensional DOA and polarization parameters based on a polarization sensitive parallel array according to claim 9, characterized in that: The computational complexity of the multidimensional parameter estimation algorithm is: The complexity of the received data covariance matrix obtained from step 4 is approximately equal to O((2(N1+N2)M) 2 L), where L is the number of snapshots; From step 5, we can get the complexity of eigenvalue decomposition of ESPRIT algorithm as O(2(((N1+1)N2+(N1-2))(M-1)) 2 ), the complexity of the closed estimate of β is O(2((N1+1)N2+(N1-2))(M-1)K 2 +K 3 ); Then the total complexity of the multidimensional parameter estimation algorithm is O((2(N1+N2)M) 2 L+2(((N1+1)N2+(N1-2))(M-1)) 2 +2((N1+1)N2+(N1-2))(M-1)K 2 +K 3 ).

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