CN113341371A - DOA estimation method based on L array and two-dimensional ESPRIT algorithm - Google Patents

DOA estimation method based on L array and two-dimensional ESPRIT algorithm Download PDF

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CN113341371A
CN113341371A CN202110596959.6A CN202110596959A CN113341371A CN 113341371 A CN113341371 A CN 113341371A CN 202110596959 A CN202110596959 A CN 202110596959A CN 113341371 A CN113341371 A CN 113341371A
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林仕文
周亚文
邹炜钦
李万春
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University of Electronic Science and Technology of China
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    • 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
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Abstract

The invention belongs to the technical field of radar signal processing, and particularly relates to a DOA estimation method based on an L-array and a two-dimensional ESPRIT algorithm. The invention provides a DOA estimation method based on an L array and a two-dimensional ESPRIT algorithm. The invention has the advantages that the large matrix is constructed by utilizing the L-array, the obtained matrix is simple in form, the lower calculation complexity is kept in the subsequent direction finding process, meanwhile, the influence of a statistic independent noise source is effectively removed, and the resolution capability and the statistic performance in the Gaussian noise environment are improved.

Description

DOA estimation method based on L array and two-dimensional ESPRIT algorithm
Technical Field
The invention belongs to the technical field of radar signal processing, and particularly relates to a DOA estimation method based on an L-array and a two-dimensional ESPRIT algorithm.
Background
In radar signal processing, direction of arrival (DOA) estimation of target radar radiation source signals based on L-array realization is always a research focus, however, with the increasingly dense modern electromagnetic spectrum, higher and higher pulse density and application of high-power electronic equipment, the electromagnetic environment is more and more complex, the traditional DOA estimation method based on MUSIC algorithm faces the problems of low direction finding precision and high calculation complexity, meanwhile, most of researches of the methods are only suitable for one-dimensional DOA estimation, direction finding capability of two-dimensional angles in actual space is deficient, and realization of two-dimensional DOA estimation on L-array is still a relatively large challenge. Therefore, it is urgent to find new technologies and means, and there is an urgent need to improve the signal processing capability and direction-finding accuracy of the radar receiving array.
The principle of the ESPRIT algorithm lies in that the rotation invariant characteristic of a data covariance matrix signal subspace is used for solving information such as the incident angle of a signal, and due to the fact that spectral peak searching is not needed, the complexity and the calculated amount of the ESPRIT algorithm are greatly reduced compared with those of an MUSIC algorithm, and the ESPRIT algorithm is widely applied to DOA estimation. For two-dimensional direction finding based on an L array, some two-dimensional ESPRIT methods are proposed in the past, but the methods have the problems of complex structural form and high calculation amount, noise influence cannot be well inhibited, the relation between performance and calculation cost cannot be well balanced when radar signals are processed, and large errors always exist in array direction finding results.
Disclosure of Invention
The invention aims to solve the problems and provides a DOA estimation method based on an L array and a two-dimensional ESPRIT algorithm.
The technical scheme of the invention is as follows:
dividing an L array into four sub-arrays, processing target signal receiving data in space, calculating cross covariance matrixes among three sub-arrays without shared array elements in the L array, forming a large matrix for L array sub-space decomposition by using the three cross covariance matrixes, obtaining two rotation matrixes according to rotation invariance, processing the two matrixes based on a two-dimensional ESPRIT algorithm, obtaining characteristic values of the two rotation matrixes through characteristic decomposition, pairing the characteristic values, finally solving to obtain azimuth angles and elevation angles of signals, and finishing two-dimensional DOA estimation.
The signal receiving model based on the L array of the invention is shown in figure 1, signal si(t) vector for direction of arrival (DOA)
Figure BDA0003091485480000021
Represents: wherein theta is an azimuth angle and ranges from theta epsilon (-pi, pi) to be defined as an included angle between a projection of the direction of arrival on the xoy plane and the positive x half axis,
Figure BDA0003091485480000022
is elevation angle, range is
Figure BDA0003091485480000023
Defined as the angle between the projection of the direction of arrival on the yoz plane and the positive z-axis. The distance between adjacent array elements is d.
In order to simplify the analysis process and ensure the reasonability of the constructed mathematical model, the signal receiving model based on the L array is based on the following assumptions: (1) the amplitude phase error of an array element channel of the receiving antenna array is not considered; (2) the array receiving signals are narrow-band signals sent by far-field point sources, the center frequencies of the signals are the same and known, and the wavelength lambda of the signals is more than twice of the array element spacing d, namely lambda is more than or equal to 2 d; (3) the phase of the received signal is random, and special conditions under the condition of known signal part prior information such as strict non-circular signals and the like are not considered.
As shown in fig. 2, the uniform L array may be divided into four sub-arrays: the first M array elements on the X axis form a subarray X1The last M array elements form a subarray X2(ii) a The first M array elements on the Y axis form a subarray Y1And the last M array elements form a subarray Y2。
Subarrays X1、X2And Y1、Y2The received data matrices are respectively:
Figure BDA0003091485480000024
wherein x isl、ylArray element reception denoted by the reference symbols l (l ═ 0,1,2, …, M +1) for array X and array Y, respectivelyThe data of (1).
The DOA estimation method based on the L array and the two-dimensional ESPRIT mainly comprises the following steps:
s1, using subarray X1、X2And Y1、Y2The received data matrix is constructed to obtain three cross covariance matrices:
Figure BDA0003091485480000025
due to subarray X1And Y2Subarray X2And Y1Subarray X2And Y2There is no shared array element between them, and the noise received by each array element is independent, so there is no noise item in the three cross covariance matrixes.
S2, stacking the three cross covariance matrixes in the step S1 into a large matrix CLThe matrix is constructed in the form of
Figure BDA0003091485480000031
S3, for the large matrix C constructed in the step S2LPerforming singular value decomposition, and obtaining estimation E of the signal subspace by taking a matrix formed by eigenvectors corresponding to the first N large eigenvalues as the estimation of the signal subspaceS。
Figure BDA0003091485480000032
Wherein E is1、E2And E3To form a matrix ESThree M × M dimensional block matrices;
s4, calculating two rotation matrixes psiXAnd ΨYThe calculation formula is
Figure BDA0003091485480000033
Figure BDA0003091485480000034
Performing characteristic decomposition on the two rotation matrixes to obtain
Figure BDA0003091485480000035
Figure BDA0003091485480000036
Wherein λ is1,…,λNAnd gamma1,…,γNAre respectively the rotation matrices ΨXAnd ΨYCharacteristic value of (phi)XAnd phiYIs a matrix of eigenvalues, T1And T2Is formed by the rotation matrix ΨXAnd ΨYThe feature vectors of (a) constitute an orthogonal matrix.
S5, performing two-dimensional angle parameter pairing based on two-dimensional ESPRIT algorithm, and determining two rotation matrixes psiXAnd ΨYThe corresponding relation between the characteristic values comprises the following specific steps:
s51, constructing an estimation matrix
Figure BDA0003091485480000037
The structure form is as follows:
Figure BDA0003091485480000038
s52 extraction matrix
Figure BDA0003091485480000041
Diagonal element u of1,…,uNAnd taking a plurality of phase angles for the elements, and sequencing the diagonal elements from large to small according to the size of the phase angles to obtain the sequenced diagonal elements
Figure BDA0003091485480000042
Take the matrix ΨYCharacteristic value gamma1,…,γNAnd according to the magnitude of the phase angle, the gamma is measured from large to small1,…,γNSorting is carried out to obtain the sorted characteristic value sequence
Figure BDA0003091485480000043
Obtaining the pairing relation according to the sequenced serial numbers
Figure BDA0003091485480000044
S53, according to the diagonal elements in the step S52
Figure BDA0003091485480000045
And matrix T1Adjusting psi according to the corresponding relation of the medium feature vectorsXOrder of characteristic value (if
Figure BDA0003091485480000046
In a matrix
Figure BDA0003091485480000047
The row sequence in (1) is j, then its corresponding eigenvector is matrix T1Corresponding to the jth column vector of (2), corresponding to ΨXHas a characteristic value ofj) To obtain the adjusted matrix ΨXCharacteristic value of
Figure BDA0003091485480000048
And the pairing relationship is
Figure BDA0003091485480000049
S54, obtaining a matrix psi according to the two groups of pairing relations obtained in the steps S52 and S53XAnd ΨYThe matching relation between the characteristic values of (1) is
Figure BDA00030914854800000410
S6, calculating the numerical solution of the two-dimensional direction of arrival of the target radiation source signal by using the characteristic values paired in the step S5
Figure BDA00030914854800000411
Completing two-dimensional DOA estimation:
Figure BDA00030914854800000412
wherein,
Figure BDA00030914854800000413
Figure BDA00030914854800000414
Figure BDA00030914854800000415
for the azimuth estimate of the ith signal,
Figure BDA00030914854800000416
for the elevation estimation of the ith signal, the functions "arctan (-) and" arcsin (-) represent the arctan function and the arcsin (-) respectively.
The invention has the advantages that the large matrix is constructed by utilizing the L-array, the obtained matrix is simple in form, the lower calculation complexity is kept in the subsequent direction finding process, meanwhile, the influence of a statistic independent noise source is effectively removed, and the resolution capability and the statistic performance in the Gaussian noise environment are improved.
Drawings
Fig. 1 is a schematic diagram of L-array signal reception;
FIG. 2 is a schematic diagram of the division of an L-array subarray;
FIG. 3 is a graph of RMSE versus SNR;
FIG. 4 is a graph of RMSE versus subarray element number;
fig. 5 is a simulation run time versus subarray element number curve.
Detailed Description
The performance of the present invention will be explained below with reference to the drawings and simulations.
And carrying out simulation verification on the method provided by the invention by utilizing Matlab. Computer simulation environment: microsoft Windows 10 operating system, Matlab 2020a software, AMD R7-4800U processor (supporting AVX instruction set), 16GB DDR4-3200 memory.
DOA direction finding estimation performance of the method
Simulation 1: the direction precision of the method changes along with the signal-to-noise ratio
The total number of L array elements in the space is 13, the number of the array elements of the four sub-arrays is 7, the length of simulation signal data is 500 snapshots, and the incoming wave direction of the signals is (60 degrees and 60 degrees). The variation curve of the angle estimation RMSE with the SNR obtained by 1000 Monte-Carlo experiments under different signal-to-noise ratios is shown in FIG. 3.
Conclusion analysis: from the simulation result, the novel L-array ESPRIT method has the advantages of higher estimation precision of the direction of arrival, less loss on performance and better direction finding effect.
Simulation 2: the direction precision of the method is changed along with the number of array elements of the receiving array subarrays
In an L-shaped array in space, the array element numbers of four sub-arrays are all M, the length of simulation data is 200 snapshots, the signal-to-noise ratio is-10 dB, the incoming wave direction of signals is (60 degrees and 60 degrees), and 500 Monte-Carlo experiments are carried out under different sub-array numbers M to obtain a variation curve of RMSE of the ESPRIT algorithm along with the sub-array element numbers M, which is shown in figure 4.
Conclusion analysis: the results in fig. 4 show that the statistical performance of the method of the present invention increases with the number of subarray elements.
(II) run time of the method of the invention
Simulation 1: simulation time of method
The array elements of four sub-arrays are M, the incoming wave direction of the signal is (30 degrees and 30 degrees), the length of the simulation data is 500 snapshots, and the signal-to-noise ratio is 0 dB. The method is simulated to obtain the simulation duration of the Monte-Carlo experiment of 1000 times of the algorithm under different subarray array elements.
The simulation time length data is drawn into a curve graph to obtain a variation curve of the simulation time length of the algorithm along with the array element number of the subarray, which is shown in fig. 5.
Conclusion analysis: from the result of fig. 5, as the number of the subarray elements increases, the time length of the algorithm of the present invention also increases, but the increase range is small, which shows that the present invention has the advantages of low calculation cost, low calculation complexity and calculation superiority.
By integrating the simulation results, the method provided by the invention achieves better balance between the calculation cost and the estimation performance.

Claims (1)

1. A DOA estimation method based on L array and two-dimensional ESPRIT algorithm is used for establishing a signal receiving model based on L array, signal si(t) vector for direction of arrival (DOA)
Figure FDA0003091485470000011
Wherein theta is an azimuth angle and ranges from theta epsilon (-pi, pi), and is defined as an included angle between a projection of the direction of arrival on the xoy plane and the positive x-half axis,
Figure FDA0003091485470000012
is elevation angle, range is
Figure FDA0003091485470000013
The included angle between the projection of the direction of arrival on the yoz plane and the positive z-axis is defined, and the distance between adjacent array elements is d; the uniform L array is divided into four sub-arrays: the first M array elements on the X axis form a subarray X1The last M array elements form a subarray X2(ii) a The first M array elements on the Y axis form a subarray Y1And the last M array elements form a subarray Y2(ii) a Subarrays X1、X2And Y1、Y2The received data matrices are respectively:
Figure FDA0003091485470000014
wherein xl、ylData received by array elements denoted by l of array X and array Y, respectively, where l is 0,1,2, …, M + 1;
the DOA estimation method is characterized by comprising the following steps:
s1, using subarray X1、X2And Y1、Y2The received data matrix is constructed to obtain three cross covariance matrices:
Figure FDA0003091485470000015
due to subarray X1And Y2Subarray X2And Y1Subarray X2And Y2There is no shared array element between them, and the noise received by each array element is independent, so there is no noise item in the three cross covariance matrixes;
s2, stacking the three cross covariance matrixes in the step S1 into a matrix CLThe matrix is constructed in the form of
Figure FDA0003091485470000016
S3, matching the matrix C constructed in the step S2LPerforming singular value decomposition, and obtaining estimation E of the signal subspace by taking a matrix formed by eigenvectors corresponding to the first N eigenvalues as the estimation of the signal subspaceS：
Figure FDA0003091485470000021
Wherein E is1、E2And E3To form a matrix ESThree M × M dimensional block matrices;
s4, calculating two rotation matrixes psiXAnd ΨYThe calculation formula is
Figure FDA0003091485470000022
Figure FDA0003091485470000023
Performing characteristic decomposition on the two rotation matrixes to obtain
Figure FDA0003091485470000024
Figure FDA0003091485470000025
Wherein λ is1,…,λNAnd gamma1,…,γNAre respectively the rotation matrices ΨXAnd ΨYCharacteristic value of (phi)XAnd phiYIs a matrix of eigenvalues, T1And T2Is formed by the rotation matrix ΨXAnd ΨYAn orthogonal matrix composed of the feature vectors of (a);
s5, performing two-dimensional angle parameter pairing based on two-dimensional ESPRIT algorithm, and determining two rotation matrixes psiXAnd ΨYThe corresponding relation between the characteristic values comprises the following specific steps:
s51, constructing an estimation matrix
Figure FDA0003091485470000026
The structure form is as follows:
Figure FDA0003091485470000027
s52 extraction matrix
Figure FDA0003091485470000028
Diagonal element u of1,…,uNAnd taking a plurality of phase angles for the elements, and sequencing the diagonal elements from large to small according to the size of the phase angles to obtain the sequenced diagonal elements
Figure FDA0003091485470000029
Take the matrix ΨYCharacteristic value gamma1,…,γNAnd according to the magnitude of the phase angle, the gamma is measured from large to small1,…,γNSorting is carried out to obtain the sorted characteristic value sequence
Figure FDA00030914854700000210
Obtaining the pairing relation according to the sequenced serial numbers
Figure FDA0003091485470000031
S53, according to the diagonal elements in the step S52
Figure FDA0003091485470000032
And matrix T1Adjusting psi according to the corresponding relation of the medium feature vectorsXThe order of the characteristic values is adjusted in such a way that if
Figure FDA0003091485470000033
In a matrix
Figure FDA0003091485470000034
The row sequence in (1) is j, then its corresponding eigenvector is matrix T1Corresponding to the jth column vector of (2), corresponding to ΨXHas a characteristic value ofjTo obtain the adjusted matrix ΨXCharacteristic value of
Figure FDA0003091485470000035
And the pairing relationship is
Figure FDA0003091485470000036
S54, obtaining a matrix psi according to the two groups of pairing relations obtained in the steps S52 and S53XAnd ΨYThe matching relation between the characteristic values of (1) is
Figure FDA0003091485470000037
S6, calculating the numerical solution of the two-dimensional direction of arrival of the target radiation source signal by using the characteristic values paired in the step S5
Figure FDA0003091485470000038
Completing two-dimensional DOA estimation:
Figure FDA0003091485470000039
wherein,
Figure FDA00030914854700000310
Figure FDA00030914854700000311
Figure FDA00030914854700000312
for the azimuth estimate of the ith signal,
Figure FDA00030914854700000313
for the elevation estimation of the ith signal, the functions "arctan (-) and" arcsin (-) represent the arctan function and the arcsin (-) respectively.
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