CN111983554A - High-precision two-dimensional DOA estimation under non-uniform L array - Google Patents

High-precision two-dimensional DOA estimation under non-uniform L array Download PDF

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CN111983554A
CN111983554A CN202010881593.2A CN202010881593A CN111983554A CN 111983554 A CN111983554 A CN 111983554A CN 202010881593 A CN202010881593 A CN 202010881593A CN 111983554 A CN111983554 A CN 111983554A
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matrix
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王兰美
王乐
周琨
廖桂生
王桂宝
孙长征
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Xidian University
Shaanxi University of Technology
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Shaanxi University of Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
    • G01S3/14—Systems for determining direction or deviation from predetermined direction

Abstract

The invention discloses a high-precision two-dimensional DOA estimation algorithm based on a non-uniform L-shaped array, aiming at the problems of more array elements and complex operation of the L-shaped array. The method can reduce the number of array elements and the complexity and improve the estimation precision at the same time. The implementation mode is as follows: firstly, two non-uniform linear arrays with the same degree of freedom as a 6-array element second-order nested array are expanded into an L-shaped array to receive a received signal; then, a virtual array received data matrix of the two sub-arrays is obtained according to the received data; the signal subspace of the subarrays is obtained by constructing an auxiliary operator, and the operation amount is reduced; and finally, obtaining estimated values of a pitch angle and an azimuth angle by utilizing the idea of an ESPRIT algorithm, and pairing the azimuth angle and the pitch angle. The high-precision estimation method based on the non-uniform L-shaped array can reduce the number of array elements and improve the DOA estimation precision under the condition of unchanged array area, and has lower calculation complexity compared with the traditional method.

Description

High-precision two-dimensional DOA estimation under non-uniform L array
Technical Field
The invention belongs to the field of array signal processing, and relates to a high-precision two-dimensional DOA estimation method under a non-uniform L array.
Background
In the field of array signal processing, the effective aperture of an antenna array is related to the number of array elements and the interval of the array elements, and because the interval of the array elements of the uniform array is the same and generally does not exceed half of the wavelength of an incident target source, the array aperture of the uniform array cannot be effectively improved at a certain time of the number of the array elements, and higher angle resolution and estimation performance cannot be realized in spatial spectrum estimation. The non-uniform array changes the array element spacing, expands the array aperture, and the estimation performance far exceeds that of the uniform array under the same array element number, but the array element spacing of the non-uniform array is unequal and is generally integral multiple of the incident information source wavelength, so that the problem of angle blurring (existence of false peaks) is easily caused. In order to avoid the problem, scholars at home and abroad develop research on the position arrangement of the Array elements of the non-uniform Array, the Array elements are reasonably arranged at intervals, a continuous and uniform linear Array is generated through certain matrix transformation, and then spatial spectrum estimation is carried out through the Array, so that the specific Array just comprises a Minimum Redundant Array (MRA), a Coprime Array (CA) and a Nested Array (NA). Compared with a uniform array with the same array element number, the non-uniform array has higher array freedom degree and higher parameter estimation precision, and can solve the problem that the target source number is larger than the actual physical array element number.
In recent years, a non-uniform array has a larger array degree of freedom and a higher spatial resolution than a uniform array, and is widely used in direction of arrival (DOA) estimation. A non-uniform array structure is adopted to carry out one-dimensional DOA estimation on a space domain target, and under the premise that the number of elements of a uniform linear array is the same, underdetermined DOA estimation that the number of physical array elements is smaller than the number of actual targets can be realized, which cannot be realized for a uniform array. In practical engineering application, in order to realize more accurate positioning, only the pitch angle information of a target is not enough, and therefore, the inhomogeneous linear array is expanded to an L-shaped array on the basis of one-dimensional DOA estimation, so that not only can high-precision estimation of the azimuth angle and the pitch angle of a target source be realized, but also a close-range target can be processed.
In the two-dimensional DOA estimation, when the number of array elements is large and the number of snapshots is large, in order to avoid high calculation complexity caused by matrix decomposition and spectrum search, the invention reduces the operation amount by constructing an auxiliary operator, obtains the DOA estimation algorithm of the pitch angle and the azimuth angle by utilizing the ESPRIT algorithm idea, and performs complexity analysis on the algorithm. Simulation results show that when the non-uniform array of the expanded aperture is used for two-dimensional direction of arrival estimation, high-precision DOA estimation can be realized, and a near-distance target can be processed.
Disclosure of Invention
The invention aims to provide a high-precision two-dimensional DOA estimation method under a non-uniform L array.
A high-precision two-dimensional DOA estimation method under a non-uniform L array comprises the following steps:
the method comprises the following steps: constructing a non-uniform L-shaped array, and solving a virtual sub-array U and a differential matrix corresponding to the non-uniform sub-array
Figure BDA0002654278870000026
Two non-uniform sub-arrays are respectively arranged on an x axis and a z axis, and the positions of array elements are both omega ═ d1,d2,d3,d4,d5,d6]＝[0,d,4d,7d,9d,11d]The L-type non-uniform array shown in fig. 2 is formed, the array element number "0" at the origin is used as a reference array element and is shared by two sub-arrays, and the positions of the virtual sub-array elements corresponding to the x-axis and z-axis non-uniform sub-arrays with the array element numbers of 6 are all U [ -11d, -10d, -9d, -8d, -7d, -6d, -5d, -4d, -3d, -2d, -1d,0, d,2d,3d,4d,5d,6d,7d,8d,9d,10d,11d]，
Figure BDA0002654278870000021
λ is the electromagnetic wave wavelength. Differential matrix corresponding to non-uniform array
Figure BDA0002654278870000022
Comprises the following steps:
Figure BDA0002654278870000023
step two: taking the non-uniform L-shaped array constructed in the step one as a receiving signal array, enabling K far-field, narrow-band and incoherent signals to be incident on the array, and calculating a covariance matrix R by using receiving signals X (t), Z (t) and x-axis and z-axisx＝E[X(t)X(t)H]And Rz＝E[Z(t)Z(t)H]。
Wherein the x-axis received signal is X (t) AθS(t)+Nx(t) the z-axis reception signal is z (t) GφS(t)+Nz(t)，Aθ＝[a(θ1),...,a(θk),...,a(θK)]Array manifold matrix composed of steering vectors in x-axis direction, Gφ＝[g(φ1),...,g(φk),...,g(φK)]A manifold matrix formed by guide vectors in the z-axis direction; s (t) ═ s1(t),s2(t),...,sk(t),...,sK(t)]TSet of target source signals, Nx(t)，Nz(t) represents x-axis and z-axis channel noise respectively,
Figure BDA0002654278870000024
dmthe position of the mth array element of the x-axis non-uniform array is m, which is 1,2, 6,
Figure BDA0002654278870000025
dζthe Zeta array element position is the Zeta array element position of the z-axis non-uniform array, wherein the Zeta is 1,2kIs the angle between the kth incident signal and the positive half axis of the x-axis, called the azimuth angle, phikIs the angle between the kth incident signal and the positive half axis of the z-axis, called the pitch angle, thetak∈[0°,180°]，φk∈[0°,180°]. From Rx＝E[X(t)X(t)H]∈C6×6And Rz＝E[Z(t)Z(t)H]∈C6×6Solving the data covariance matrix as Rx，Rz，[·]TIs a transpose of a matrix [ ·]HFor complex conjugate transposition, E [. cndot.)]Is a statistical mean.
Step three: for covariance matrix Rx，RzPerforming vectorizationProcessing to obtain data vector r before removing redundancyxAnd rzPicking r from the index setxAnd rzTo obtain virtual array received data of x-axis and z-axis sub-arrays
Figure BDA0002654278870000031
Data vector r of data vector before redundancy removalx＝vec(Rx)，rz＝vec(Rz) Vec (-) denotes a vectorization operation on a matrix, i.e. arranging the matrix elements column by column into a column vector, differencing the matrix vector
Figure BDA0002654278870000032
Will not mix the matrix vector
Figure BDA0002654278870000033
The elements equal to those in the virtual array element position vector U are taken out and form a new vector from large to small
Figure BDA0002654278870000034
When in use
Figure BDA0002654278870000035
When a plurality of elements are the same as one element in U, only one element is taken out, and the rest elements are discarded to obtain
Figure BDA0002654278870000036
Figure BDA0002654278870000037
Simultaneously recording the 23 elements in the column vector
Figure BDA0002654278870000038
In (3), finding r from the index setxAnd rzThe effective data of the corresponding position in the data base to obtain the final virtual array receiving data
Figure BDA0002654278870000039
Step four: constructing an auxiliary operator to obtain an x-axis sub-array signal subspace, and obtaining the azimuth angle of a target source through an ESPRIT algorithm;
(4a) receiving data by a virtual array
Figure BDA00026542788700000310
And a selection matrix JiObtaining a full rank matrix W;
will be provided with
Figure BDA00026542788700000311
Is divided into
Figure BDA00026542788700000312
The number of sub-matrices is,
Figure BDA00026542788700000313
obtaining a full rank matrix by superposition of the submatrices
Figure BDA00026542788700000314
Order to
Figure BDA00026542788700000315
Wherein
Figure BDA00026542788700000316
To select the matrix, i 1, 12,
Figure BDA00026542788700000317
(4b) calculating an auxiliary operator Q and a signal subspace E according to the full rank matrix WS；
The full rank matrix W is divided into [ W ═ W1 T,W2 T]Wherein
Figure BDA00026542788700000318
Consists of the first K rows of W,
Figure BDA00026542788700000319
from W
Figure BDA00026542788700000320
Line composition, auxiliary operators
Figure BDA00026542788700000321
According to the relational expression
Figure BDA00026542788700000322
Obtaining a signal subspace ES，IKRepresenting a K × K identity matrix.
(4c) Space of signal words ESIs divided into ES1And ES2Obtaining the azimuth angle of the target source by using an ESPRIT algorithm
Figure BDA00026542788700000323
Space of signal words ESIs divided into ES1＝Jg1ESAnd ES2＝Jg2ESAnd is composed of
Figure BDA00026542788700000324
By performing a feature decomposition on Ψ, i.e., [ V, Uq]Eig (Ψ), wherein V and UqRepresenting the eigenvectors and eigenvalues of the matrix Ψ, respectively, and eig (·) is the eigen-decomposition of the matrix, then the estimate of the azimuth is:
Figure BDA0002654278870000041
wherein
Figure BDA0002654278870000042
Figure BDA0002654278870000043
To represent
Figure BDA0002654278870000044
And
Figure BDA0002654278870000045
a dimension unit matrix;
Figure BDA0002654278870000046
to represent
Figure BDA0002654278870000047
And
Figure BDA0002654278870000048
a zero-dimensional matrix. v. ofkkElements representing the kth row and kth column of the diagonal matrix V, if order
Figure BDA0002654278870000049
The estimate of the azimuth of the signal is
Figure BDA00026542788700000410
Step five: constructing an auxiliary operator to obtain a z-axis sub-array signal subspace, and obtaining the pitch angle of the target source through the idea of an ESPRIT algorithm
Figure BDA00026542788700000411
The specific method is the same as the step four.
Step six: for the azimuth angle obtained in the step four
Figure BDA00026542788700000412
And the pitch angle obtained in the step five
Figure BDA00026542788700000413
Carrying out pairing;
(6a) the estimated values of the azimuth angle and the pitch angle are respectively
Figure BDA00026542788700000414
And
Figure BDA00026542788700000415
the corresponding array manifold matrix is
Figure BDA00026542788700000416
And
Figure BDA00026542788700000417
k ═ 1,2,. K;
(6b) computing matrices
Figure BDA00026542788700000418
Find the position n corresponding to the largest element in the matrix psi, then
Figure BDA00026542788700000419
And
Figure BDA00026542788700000420
is matched, order
Figure BDA00026542788700000421
Figure BDA00026542788700000422
And
Figure BDA00026542788700000423
respectively corresponding to azimuth angle and pitch angle of the same signal, wherein
Figure BDA00026542788700000424
Figure BDA00026542788700000425
Is that
Figure BDA00026542788700000426
The (c) th row of (a),
Figure BDA00026542788700000427
Rxz＝E[X(t)ZH(t)]cross covariance matrices of data received for the x-axis and z-axis sub-arrays of the algorithm of the present invention.
In the foregoing steps, K denotes the number of signal sources, K is 1,2, K denotes the reference number of the signal source, m is 1,2, 6 denotes the reference number of the x-axis array element position,
Figure BDA00026542788700000428
the reference number indicating the position of the z-axis array element, p 1,2, 36 indicates the element number in the difference matrix, i 1, 2...,12 denotes the reference numeral of the virtual array receiving data sub-matrix.
1. The invention expands the non-uniform array with the same degree of freedom as the second-order nested array to the L array, and utilizes the array to carry out two-dimensional DOA estimation, thereby achieving the expected effect.
2. The invention reduces the operand by constructing the auxiliary operator, estimates the pitch angle and the azimuth angle by using the projection operator method, reduces the algorithm complexity, reduces the operand and has high estimation precision.
3. The model of the invention uses less signals with array element estimation quantity higher than the array element quantity, thereby reducing the cost and having practical application value.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of a simplified array embodying the present invention;
FIG. 3 is a diagram of the method of the present invention and an L-shaped uniform array pattern;
FIG. 4 is a diagram of a two-dimensional DOA estimation result of an airspace target according to the method of the present invention;
FIG. 5 is a graph of the total RMS error as a function of signal-to-noise ratio for the method of the invention and other methods;
Detailed Description
In order to make the aforementioned and other objects, features and advantages of the present invention more apparent, embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
The invention aims to provide a high-precision two-dimensional DOA estimation method under a non-uniform L array.
In order to achieve the purpose, the invention adopts the following technical solutions:
the method comprises the following steps: constructing a non-uniform L-shaped array, and solving a virtual sub-array U and a differential matrix corresponding to the non-uniform sub-array
Figure BDA0002654278870000054
Two non-uniform sub-arrays are respectively arranged on an x axis and a z axis, and the positions of array elements are both omega ═ d1,d2,d3,d4,d5,d6]＝[0,d,4d,7d,9d,11d]The L-type non-uniform array shown in fig. 2 is formed, the array element number "0" at the origin is used as a reference array element and is shared by two sub-arrays, and the positions of the virtual sub-array elements corresponding to the x-axis and z-axis non-uniform sub-arrays with the array element numbers of 6 are all U [ -11d, -10d, -9d, -8d, -7d, -6d, -5d, -4d, -3d, -2d, -1d,0, d,2d,3d,4d,5d,6d,7d,8d,9d,10d,11d]，
Figure BDA0002654278870000051
λ is the electromagnetic wave wavelength. Differential matrix corresponding to non-uniform array
Figure BDA0002654278870000052
Comprises the following steps:
Figure BDA0002654278870000053
step two: taking the non-uniform L-shaped array constructed in the step one as a receiving signal array, enabling K far-field, narrow-band and incoherent signals to be incident on the array, and calculating a covariance matrix R by using receiving signals X (t), Z (t) and x-axis and z-axisx＝E[X(t)X(t)H]And Rz＝E[Z(t)Z(t)H]。
Wherein the x-axis received signal is X (t) AθS(t)+Nx(t) the z-axis reception signal is z (t) GφS(t)+Nz(t)，Aθ＝[a(θ1),...,a(θk),...,a(θK)]Array manifold matrix composed of steering vectors in x-axis direction, Gφ＝[g(φ1),...,g(φk),...,g(φK)]A manifold matrix formed by guide vectors in the z-axis direction; s (t) ═ s1(t),s2(t),...,sk(t),...,sK(t)]TSet of target source signals, Nx(t)，Nz(t) represents x-axis and z-axis channel noise respectively,
Figure BDA0002654278870000061
dmthe position of the mth array element of the x-axis non-uniform array is m, which is 1,2, 6,
Figure BDA0002654278870000062
dζthe Zeta array element position is the Zeta array element position of the z-axis non-uniform array, wherein the Zeta is 1,2kIs the angle between the kth incident signal and the positive half axis of the x-axis, called the azimuth angle, phikIs the angle between the kth incident signal and the positive half axis of the z-axis, called the pitch angle, thetak∈[0°,180°]，φk∈[0°,180°]. From Rx＝E[X(t)X(t)H]∈C6×6And Rz＝E[Z(t)Z(t)H]∈C6×6Solving the data covariance matrix as Rx，Rz，[·]TIs a transpose of a matrix [ ·]HFor complex conjugate transposition, E [. cndot.)]Is a statistical mean.
Step three: for covariance matrix Rx，RzVectorization processing is carried out to obtain a data vector r before redundancy removalxAnd rzPicking r from the index setxAnd rzTo obtain virtual array received data of x-axis and z-axis sub-arrays
Figure BDA0002654278870000063
Data vector r of data vector before redundancy removalx＝vec(Rx)，rz＝vec(Rz) Vec (·) denotes a vectorization operation on a matrix, that is, matrix elements are arranged in a column vector (for example, if the size of a matrix beta is 3 × 2, the inside of the matrix is vectorized by vec (b), and then the original size is extended to 3 × 2 to 6 × 1, and a specific expression form after vectorization is vec (b) [ (b) ═ b [, b [ ]11,b21,b31,b12,b22,b32]T) Difference matrix vectorMeasurement of
Figure BDA0002654278870000064
Will not mix the matrix vector
Figure BDA0002654278870000065
The same elements in the virtual array element position vector U are taken out and form a new vector from large to small
Figure BDA0002654278870000066
When in use
Figure BDA0002654278870000067
When a plurality of elements are the same as one element in U, only one element is taken out, and the rest elements are discarded to obtain
Figure BDA0002654278870000068
Figure BDA0002654278870000069
Simultaneously recording the 23 elements in the column vector
Figure BDA00026542788700000610
In (3), finding r from the index setxAnd rzThe effective data of the corresponding position in the data base to obtain the final virtual array receiving data
Figure BDA00026542788700000611
Step four: constructing an auxiliary operator to obtain an x-axis sub-array signal subspace, and obtaining the azimuth angle of a target source through an ESPRIT algorithm;
(4a) receiving data by a virtual array
Figure BDA00026542788700000612
And a selection matrix JiObtaining a full rank matrix W;
will be provided with
Figure BDA00026542788700000613
SegmentationIs composed of
Figure BDA00026542788700000614
The number of sub-matrices is,
Figure BDA00026542788700000615
obtaining a full rank matrix by superposition of the submatrices
Figure BDA00026542788700000616
Order to
Figure BDA00026542788700000617
Wherein
Figure BDA00026542788700000618
To select the matrix, i 1, 12,
Figure BDA00026542788700000619
(4b) calculating an auxiliary operator Q and a signal subspace E according to the full rank matrix WS；
The full rank matrix W is divided into [ W ═ W1 T,W2 T]Wherein
Figure BDA0002654278870000071
Consists of the first K rows of W,
Figure BDA0002654278870000072
from W
Figure BDA0002654278870000073
Line composition, auxiliary operators
Figure BDA0002654278870000074
According to the relational expression
Figure BDA0002654278870000075
Obtaining a signal subspace ES，IKRepresenting a K × K identity matrix.
(4c) Space of signal words ESIs divided into ES1And ES2By using ESPRIT algorithm to obtain the azimuth angle of the target source
Figure BDA0002654278870000076
Space of signal words ESIs divided into ES1＝Jg1ESAnd ES2＝Jg2ESAnd is composed of
Figure BDA0002654278870000077
By performing a feature decomposition on Ψ, i.e., [ V, Uq]Eig (·) is a matrix eigendecomposition, where V and UqRepresenting the eigenvectors and eigenvalues of the matrix Ψ, respectively, the estimate of the azimuth angle is:
Figure BDA0002654278870000078
wherein
Figure BDA0002654278870000079
Figure BDA00026542788700000710
To represent
Figure BDA00026542788700000711
And
Figure BDA00026542788700000712
a dimension unit matrix;
Figure BDA00026542788700000713
to represent
Figure BDA00026542788700000714
And
Figure BDA00026542788700000715
a zero-dimensional matrix. v. ofkkElements representing the kth row and kth column of the diagonal matrix V, if order
Figure BDA00026542788700000716
The estimate of the azimuth of the signal is
Figure BDA00026542788700000717
Step five: constructing an auxiliary operator to obtain a z-axis sub-array signal subspace, and obtaining the pitch angle of the target source through the idea of an ESPRIT algorithm
Figure BDA00026542788700000718
The specific method is the same as the step four.
Step six: for the azimuth angle obtained in the step four
Figure BDA00026542788700000719
And the pitch angle obtained in the step five
Figure BDA00026542788700000720
Carrying out pairing;
(6a) the estimated values of the azimuth angle and the pitch angle are respectively
Figure BDA00026542788700000721
And
Figure BDA00026542788700000722
the corresponding array manifold matrix is
Figure BDA00026542788700000723
And
Figure BDA00026542788700000724
k ═ 1,2,. K;
(6b) computing matrices
Figure BDA00026542788700000725
Find the position n corresponding to the largest element in the matrix psi, then
Figure BDA00026542788700000726
And
Figure BDA00026542788700000727
is matched, order
Figure BDA00026542788700000728
Figure BDA00026542788700000729
And
Figure BDA00026542788700000730
respectively corresponding to azimuth angle and pitch angle of the same signal, wherein
Figure BDA00026542788700000731
Figure BDA00026542788700000732
Is that
Figure BDA00026542788700000733
The (c) th row of (a),
Figure BDA00026542788700000734
Rxz＝E[X(t)ZH(t)]cross covariance matrices of data received for the x-axis and z-axis sub-arrays of the algorithm of the present invention.
In the foregoing steps, K denotes the number of signal sources, K is 1,2, K denotes the reference number of the signal source, m is 1,2, 6 denotes the reference number of the x-axis array element position,
Figure BDA00026542788700000735
the index number indicating the position of the array element in the z-axis, p 1, 2., 36 indicates the index number of the element in the difference matrix, and i 1, 2., 12 indicates the index number of the sub-matrix of the received data of the virtual array.
The invention uses the non-uniform array of the expanded aperture for the two-dimensional direction of arrival estimation, not only can realize the reduction of the array element number under the condition of unchanged array area, but also avoids the high calculation complexity caused by matrix decomposition and spectrum search.
Simulation 1: the L-shaped non-uniform array shown in FIG. 2 is used as a receiving array, and x-axis and z-axis sub-arraysAll have 6 array elements with the array element positions of [0, d,4d,7d,9d,11d]Simulating the non-uniform L array and the uniform L array, providing a two-dimensional array directional diagram of 2 arrays, and enabling the incident pitch angle and the incident azimuth angle to be (theta)0,φ0) The SNR is 10dB, the snapshot number is 200, and the array pattern is shown in fig. 3 (0 ° ).
It can be seen from fig. 3 that under the same array element number, the main lobe beam width of the non-uniform L array is smaller than that of the uniform L array, which shows that the non-uniform L array adopted by the present invention has not only the estimation performance of the nested array but also does not need to be composed of two or more uniform linear sub-arrays under the condition that the array area is not changed, and is more flexible than the nested array in the aspect of array arrangement; compared with a uniform L array, the DOA estimation capability of the array is stronger because the array used by the invention has narrower beam width and better array pointing capability.
Simulation 2: the L-shaped non-uniform array shown in FIG. 2 is used as a receiving array, each of the x-axis and z-axis sub-arrays has 6 array elements, and the array element positions are [0, d,4d,7d,9d,11d ]]The direction recognition is performed for 4 target sources in the space K, and the angles of arrival at the array are (θ)1,φ1)＝(130°,80°)，(θ2,φ2)＝(70°40°)，(θ3,φ3)＝(45°,65°)，(θ4,φ4) The simulation experiment was performed under the conditions of SNR 0dB and fast beat 500 (90 °,102 °), and the simulation results are shown in fig. 4.
From fig. 4, it can be seen that the algorithm provided by the invention can correctly identify 4 airspace targets under low signal-to-noise ratio, has small angular deviation, and has good estimation accuracy.
Simulation 3: the L-shaped non-uniform array shown in FIG. 2 is used as a receiving array, each of the x-axis and z-axis sub-arrays has 6 array elements, and the array element positions are [0, d,4d,7d,9d,11d ]]The algorithm of the invention and the root finding MUSIC algorithm, the Joint SVD algorithm and the CMM-ESPRIT algorithm are adopted to carry out direction identification on 2 target sources in the space K, and the angles of the target sources reaching the array are (theta)1,φ1)＝(130°,80°)，(θ2,φ2) Ring with fast beat number L2000, signal-to-noise ratio of 0dB to 25dB (70 deg., 40 deg.)In the environment, 200 times of experiments are carried out to count the root mean square error, and the simulation result is shown in fig. 5.
It is clear from fig. 5 that the root mean square error of the algorithm provided by the present invention is small, the DOA estimation performance is better than that of other algorithms, and the method of the present invention has lower computational complexity, so the actual application capability of the algorithm provided by the present invention is stronger.
Although the present invention has been described with reference to a preferred embodiment, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (5)

1. A high-precision two-dimensional DOA estimation method under a non-uniform L array comprises the following steps:
the method comprises the following steps: constructing a non-uniform L-shaped array, and solving a virtual sub-array U and a differential matrix P corresponding to the non-uniform sub-array;
two non-uniform sub-arrays are respectively arranged on an x axis and a z axis, and the positions of array elements are both omega ═ d1,d2,d3,d4,d5,d6]＝[0,d,4d,7d,9d,11d]The L-type non-uniform array shown in fig. 2 is formed, the array element number "0" at the origin is used as a reference array element and is shared by two sub-arrays, and the positions of the virtual sub-array elements corresponding to the x-axis and z-axis non-uniform sub-arrays with the array element numbers of 6 are all U [ -11d, -10d, -9d, -8d, -7d, -6d, -5d, -4d, -3d, -2d, -1d,0, d,2d,3d,4d,5d,6d,7d,8d,9d,10d,11d]，
Figure FDA0002654278860000011
Lambda is electromagnetic wave wavelength, and the differential matrix corresponding to the non-uniform array
Figure FDA0002654278860000012
Comprises the following steps:
Figure FDA0002654278860000013
step two: taking the non-uniform L-shaped array constructed in the step one as a receiving signal array, enabling K far-field, narrow-band and incoherent signals to be incident on the array, and calculating a covariance matrix R by using receiving signals X (t), Z (t) and x-axis and z-axisx＝E[X(t)X(t)H]And Rz＝E[Z(t)Z(t)H]；
Step three: for covariance matrix Rx，RzVectorization processing is carried out to obtain a data vector r before redundancy removalxAnd rzPicking r from the index setxAnd rzTo obtain virtual array received data of x-axis and z-axis sub-arrays
Figure FDA0002654278860000014
Step four: constructing an auxiliary operator to obtain an x-axis sub-array signal subspace, and obtaining the azimuth angle of a target source through an ESPRIT algorithm;
step five: constructing an auxiliary operator to obtain a z-axis sub-array signal subspace, and obtaining the pitch angle of the target source through the idea of an ESPRIT algorithm
Figure FDA0002654278860000015
The concrete method is the same as the step four;
step six: for the azimuth angle obtained in the step four
Figure FDA0002654278860000016
And the pitch angle obtained in the step five
Figure FDA0002654278860000017
And (6) pairing.
2. According to the rightThe method for estimating the two-dimensional DOA with high precision under the nonuniform L array according to claim 1, wherein in the second step, the nonuniform L-shaped array constructed in the first step is used as a receiving signal array, K far-field, narrow-band and incoherent signals are incident on the array, and a covariance matrix R is calculated by using the receiving signals X (t) and Z (t) of the x-axis and the z-axisx＝E[X(t)X(t)H]And Rz＝E[Z(t)Z(t)H]；
The x-axis received signal is X (t) ═ AθS(t)+Nx(t) the z-axis reception signal is z (t) GφS(t)+Nz(t)，Aθ＝[a(θ1),...,a(θk),...,a(θK)]Array manifold matrix composed of steering vectors in x-axis direction, Gφ＝[g(φ1),...,g(φk),...,g(φK)]A manifold matrix formed by guide vectors in the z-axis direction; s (t) ═ s1(t),s2(t),...,sk(t),...,sK(t)]TSet of target source signals, Nx(t)，Nz(t) represents x-axis and z-axis channel noise respectively,
Figure FDA0002654278860000021
dmthe position of the mth array element of the x-axis non-uniform array is m, which is 1,2, 6,
Figure FDA0002654278860000022
dζthe Zeta array element position is the Zeta array element position of the z-axis non-uniform array, wherein the Zeta is 1,2kIs the angle between the kth incident signal and the positive half axis of the x-axis, called the azimuth angle, phikIs the angle between the kth incident signal and the positive half axis of the z-axis, called the pitch angle, thetak∈[0°,180°]，φk∈[0°,180°]From Rx＝E[X(t)X(t)H]∈C6×6And Rz＝E[Z(t)Z(t)H]∈C6×6Solving the data covariance matrix as Rx，Rz，[·]TIs a transpose of a matrix [ ·]HFor complex conjugate transposition, E [. cndot.)]Is a statistical mean.
3. The method of claim 1The high-precision two-dimensional DOA estimation method under the nonuniform L array comprises a covariance matrix R in the step threex，RzVectorization processing is carried out to obtain a data vector r before redundancy removalxAnd rzPicking r from the index setxAnd rzTo obtain virtual array received data of x-axis and z-axis sub-arrays
Figure FDA0002654278860000023
Data vector r of data vector before redundancy removalx＝vec(Rx)，rz＝vec(Rz) Vec (·) denotes a vectorization operation on a matrix, that is, matrix elements are arranged in a column vector (for example, if the size of a matrix beta is 3 × 2, the inside of the matrix is vectorized by vec (b), and then the original size is extended to 3 × 2 to 6 × 1, and a specific expression form after vectorization is vec (b) [ (b) ═ b [, b [ ]11,b21,b31,b12,b22,b32]T) Difference matrix vector
Figure FDA0002654278860000024
Will not mix the matrix vector
Figure FDA0002654278860000025
The same elements in the virtual array element position vector U are taken out and form a new vector from large to small
Figure FDA0002654278860000026
When in use
Figure FDA0002654278860000027
When a plurality of elements are the same as one element in U, only one element is taken out, and the rest elements are discarded to obtain
Figure FDA0002654278860000028
Figure FDA0002654278860000029
Simultaneously recording the 23 elements in the column vector
Figure FDA00026542788600000210
In (3), finding r from the index setxAnd rzThe effective data of the corresponding position in the data base to obtain the final virtual array receiving data
Figure FDA00026542788600000211
4. The method for estimating the high-precision two-dimensional DOA under the nonuniform L array according to claim 1, wherein an auxiliary operator is constructed in the fourth step to obtain an x-axis sub-array signal subspace, and an azimuth angle of a target source is obtained through an ESPRIT algorithm;
(4.1) receiving data from the virtual array
Figure FDA0002654278860000031
And a selection matrix JiObtaining a full rank matrix W;
will be provided with
Figure FDA0002654278860000032
Is divided into
Figure FDA0002654278860000033
The number of sub-matrices is,
Figure FDA0002654278860000034
obtaining a full rank matrix by superposition of the submatrices
Figure FDA0002654278860000035
Order to
Figure FDA0002654278860000036
Wherein
Figure FDA0002654278860000037
To select a matrix，i＝1,...,12，
Figure FDA0002654278860000038
(4.2) calculating an auxiliary operator Q and a signal subspace E according to the full rank matrix WS；
The full rank matrix W is divided into [ W ═ W1 T,W2 T]Wherein
Figure FDA0002654278860000039
Consists of the first K rows of W,
Figure FDA00026542788600000310
from W
Figure FDA00026542788600000311
Line composition, auxiliary operators
Figure FDA00026542788600000312
According to the relational expression
Figure FDA00026542788600000313
Obtaining a signal subspace ES，IKAn identity matrix representing K;
(4.3) space E of signal wordsSIs divided into ES1And ES2Obtaining the azimuth angle of the target source by using an ESPRIT algorithm
Figure FDA00026542788600000314
Space of signal words ESIs divided into ES1＝Jg1ESAnd ES2＝Jg2ESAnd is composed of
Figure FDA00026542788600000315
By performing a feature decomposition on Ψ, i.e., [ V, Uq]Eig (·) denotes a matrix eigendecomposition, where V and UqRespectively representing eigenvectors and bits of the matrix ΨEigenvalues, then the estimate of the azimuth is:
Figure FDA00026542788600000316
wherein
Figure FDA00026542788600000317
Figure FDA00026542788600000318
To represent
Figure FDA00026542788600000319
And
Figure FDA00026542788600000320
the dimension-unit matrix is a matrix of the dimension units,
Figure FDA00026542788600000321
to represent
Figure FDA00026542788600000322
And
Figure FDA00026542788600000323
dimensional zero matrix, vkkElements representing the kth row and kth column of the diagonal matrix V, if order
Figure FDA00026542788600000324
The estimate of the azimuth of the signal is
Figure FDA00026542788600000325
5. The method for high-precision two-dimensional DOA estimation under nonuniform L-array according to claim 1, wherein the azimuth angles obtained in the step four are six pairs
Figure FDA00026542788600000326
And the pitch angle obtained in the step five
Figure FDA00026542788600000327
Carrying out pairing;
(5.1) estimated values of azimuth and pitch angles, respectively
Figure FDA00026542788600000328
And
Figure FDA00026542788600000329
the corresponding array manifold matrix is
Figure FDA00026542788600000330
And
Figure FDA00026542788600000331
k ═ 1,2,. K;
(5.2) calculating the matrix
Figure FDA00026542788600000332
Find the position n corresponding to the largest element in the matrix psi, then
Figure FDA00026542788600000333
And
Figure FDA00026542788600000334
is matched, order
Figure FDA00026542788600000335
Figure FDA00026542788600000336
And
Figure FDA00026542788600000337
respectively corresponding to azimuth angle and pitch angle of the same signal, wherein
Figure FDA00026542788600000338
Figure FDA00026542788600000339
Is that
Figure FDA00026542788600000340
The (c) th row of (a),
Figure FDA0002654278860000041
Rxz＝E[X(t)ZH(t)]cross covariance matrices of data received for the x-axis and z-axis sub-arrays of the algorithm of the present invention.
CN202010881593.2A 2020-08-28 2020-08-28 High-precision two-dimensional DOA estimation under non-uniform L array Pending CN111983554A (en)

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