CN107576951B - Direction-of-arrival estimation method based on nested electromagnetic vector sensor array - Google Patents

Direction-of-arrival estimation method based on nested electromagnetic vector sensor array Download PDF

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CN107576951B
CN107576951B CN201710902384.XA CN201710902384A CN107576951B CN 107576951 B CN107576951 B CN 107576951B CN 201710902384 A CN201710902384 A CN 201710902384A CN 107576951 B CN107576951 B CN 107576951B
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axis direction
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CN107576951A (en
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杨明磊
陈伯孝
丁进
孙磊
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Xidian University
Xian Cetc Xidian University Radar Technology Collaborative Innovation Research Institute Co Ltd
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Xian Cetc Xidian University Radar Technology Collaborative Innovation Research Institute Co Ltd
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Abstract

The invention discloses a method for estimating a direction of arrival based on a nested electromagnetic vector sensor array, which mainly solves the problems that mutual coupling among all electromagnetic components of the electromagnetic vector sensor array is serious and the hardware of the electromagnetic vector sensor array is complex to realize in the prior art. The realization process is as follows: constructing a nested electromagnetic vector sensor array; utilizing an ESPRIT algorithm to obtain a fuzzy estimation value of the cosine of the target direction; pairing fuzzy estimation values of the cosine of the target direction; obtaining an unambiguous estimation value of the cosine of the target direction by using a vector cross product algorithm of a single separated electromagnetic vector sensor; and carrying out deblurring on the fuzzy estimation value of the cosine of the target direction, and carrying out triangular operation to obtain a two-dimensional estimation value of the direction of arrival of the space target. The invention reduces the mutual coupling among all electromagnetic components and the complexity of hardware realization, expands the aperture of the whole array, improves the angle measurement precision, and can be used for the angle positioning of a radar to a target.

Description

Direction-of-arrival estimation method based on nested electromagnetic vector sensor array
Technical Field
The invention belongs to the technical field of signal processing, and particularly relates to a direction of arrival estimation method which can be used for angle positioning of a target by a radar.
Background
The electromagnetic vector sensor array radar is a new system radar with great potential which is proposed for adapting to modern war. Compared with a conventional array, the electromagnetic vector sensor array can sense electromagnetic components of incident waves in different directions, so that more information such as polarization and the like can be extracted, and the performance of signal multi-dimensional parameter estimation and signal detection can be further improved by combining polarization domain information with spatial domain information. Therefore, in recent decades, the estimation of the target space angle based on the electromagnetic vector sensor array has received much attention. The electromagnetic vector sensor which consists of three orthogonal electric dipoles and three orthogonal magnetic rings with coincident phase centers can measure three-dimensional electric field components and three-dimensional magnetic field components of incident signals and is called as a concurrent electromagnetic vector sensor. For such a concurrent electromagnetic vector sensor, professor k.t.wong proposes a new DOA estimation method for the electromagnetic vector sensor, a vector cross product algorithm, which may not involve frequency domain information and phase differences between antennas, and thus is used for DOA estimation of narrow-band and wide-band signals. However, such a concurrent electromagnetic vector sensor with coincident phase centers requires very strict electromagnetic isolation between the electromagnetic components, which is not easily realized in hardware. For this purpose, separate electromagnetic vector sensors are proposed, which spatially separate the components by a distance in order to reduce the mutual coupling of the components and the complexity of the hardware implementation. However, since each component of the separated electromagnetic vector sensor is spatially separated and a phase shift factor is introduced, the target DOA cannot be estimated by directly using a vector cross product algorithm.
In 2011, professor k.t.wong proposes a separated electromagnetic vector sensor based on a parallel line structure, and successfully realizes application of a vector cross product DOA estimation algorithm in the separated electromagnetic vector sensor, but the method has relatively strict requirements on array element positions, and only discusses the case of the vector cross product algorithm in a single separated electromagnetic vector sensor, and does not discuss the application of the vector cross product algorithm in an array.
Because the array angle measurement precision is in direct proportion to the array aperture, for a common uniform linear array ULA, the array element spacing is not more than lambda/2, and the array aperture is limited to a certain extent. In contrast, p.p.vaidyanathan proposes a nested array, which is composed of two or more uniform linear sub-arrays with different array element distances, and the array element distances of the other sub-arrays except the first sub-array are far greater than λ/2, the mutual coupling between each array unit is small, and under the condition of the same number of array units, the array aperture is larger than the uniform linear array ULA, and the angle measurement precision is higher. Previous studies have focused on the case where the array elements are single polarized antennas, the collected electromagnetic information is not complete, and the case of using a separate electromagnetic vector sensor as the antenna elements of a nested array has not been discussed.
In 2014, Keyong Han proposed an array combining a concurrent electromagnetic vector sensor and a uniform linear array ULA, and realized the estimation of a target DOA by using a tensor method, but because an array unit of the array is the concurrent electromagnetic vector sensor, the mutual coupling among components of the electromagnetic vector sensor is large, and is influenced by the array aperture and the array element spacing of the uniform linear array not more than lambda/2, the mutual coupling among the electromagnetic vector sensors seriously influences the estimation performance of the target DOA, and in addition, the method estimates the DOA of the target by using the tensor, and the calculated amount is relatively large.
In summary, both the single separated electromagnetic vector sensor and the nested array can correctly estimate the direction of arrival of the target, but both have certain limitations, and the application of the electromagnetic vector sensor to the array in the common form causes the accuracy of estimation of the direction of arrival of the target to be reduced due to the influence of mutual coupling between components of the electromagnetic vector sensor and mutual coupling between the electromagnetic vector sensors.
Disclosure of Invention
In view of the above-mentioned deficiencies of the prior art, the present invention provides a method for estimating a direction of arrival based on a nested electromagnetic vector sensor array, so as to reduce mutual coupling between electromagnetic vector sensors and improve estimation accuracy of a target direction of arrival.
In order to achieve the purpose, the electromagnetic vector sensor and the nested array are combined according to respective advantages of the electromagnetic vector sensor and the nested array, and the technical scheme is as follows:
1) constructing a nested electromagnetic vector sensor array:
given the number N of array units, N is the first1The array units are arranged along a certain direction by taking D as the array element interval, the obtained uniform linear array ULA is used as a first subarray C1 of the nested electromagnetic vector sensor array, and the last n is2The array units are arranged along the same direction by taking mD as the array element spacing, and a uniform linear array ULA is obtained and is used as a second sub-array C2 of the nested electromagnetic vector sensor array, wherein m is n1+1 and having n1+n2One for each array elementThe method comprises the following steps of (1) obtaining a nested electromagnetic vector sensor array A by a separated electromagnetic vector sensor, wherein D is larger than lambda/2, and lambda is the wavelength of electromagnetic waves;
2) dividing received data X (t) of the nested electromagnetic vector sensor array into X according to a first sub-array C1 and a second sub-array C21(t) and X2(t) two parts;
3) receiving data X for two parts1(t) and X2(t) respectively estimating two groups of fuzzy target y-axis direction cosine estimated values by using rotation invariant subspace ESPRIT algorithm
Figure BDA0001423340730000031
And
Figure BDA0001423340730000032
and the signal subspaces Es respectively corresponding to the two groups of estimation values1And Es2Wherein K is the target number;
4) for two groups of target y-axis direction cosine estimated values estimated in the step 3)
Figure BDA0001423340730000033
And
Figure BDA0001423340730000034
pairing is carried out, and the signal subspace Es corresponding to the estimated value is paired according to the pairing sequence1And Es2Matching to obtain an estimated value of an array flow pattern matrix of the nested electromagnetic vector sensor array;
5) performing phase compensation on the guide vectors of the rest array units except the reference array unit in the estimated value of the array flow pattern matrix, and synthesizing the guide vectors of the rest compensated array units to the guide vector of the separated electromagnetic vector sensor at the reference array unit to obtain the synthesized guide vector of the separated electromagnetic vector sensor at the reference array unit;
6) using the guide vectors of the separated electromagnetic vector sensors at the synthesized reference array unit obtained in the step 5), and obtaining a group of target y-axis direction cosine estimates with lower precision and no ambiguity through a vector cross product algorithmValue of
Figure BDA0001423340730000035
And a set of x-axis direction cosine estimates
Figure BDA0001423340730000036
And two sets of fuzzy target x-axis direction cosine estimated values
Figure BDA0001423340730000037
And
Figure BDA0001423340730000038
7) obtaining two groups of fuzzy target y-axis direction cosine estimated values in the step 4)
Figure BDA0001423340730000039
And step 6) obtaining two groups of fuzzy target x-axis direction cosine estimated values
Figure BDA00014233407300000310
Performing ambiguity resolution to obtain a group of ambiguity-free high-precision target x-axis direction cosine estimated values
Figure BDA00014233407300000311
And a group of target y-axis direction cosine high-precision estimated values without ambiguity
Figure BDA00014233407300000312
8) High-precision cosine estimation value of target x-axis direction without ambiguity
Figure BDA00014233407300000313
And a target y-axis direction cosine high-precision estimated value without ambiguity
Figure BDA00014233407300000314
Performing trigonometric operation to obtain the two-dimensional space direction-of-arrival information of the target
Figure BDA00014233407300000315
Wherein
Figure BDA00014233407300000316
Is an estimate of the azimuth angle of the ith target,
Figure BDA00014233407300000317
is the pitch angle estimate for the ith target.
Compared with the existing array structure and the existing algorithm, the method has the following advantages:
1) compared with an even linear array, the array unit arrangement mode of the array adopts a nested array structure, has larger array aperture under the condition of the same array unit number, and has higher angle measurement precision;
2) compared with the common electromagnetic vector sensor array, each array unit of the array is a separated electromagnetic vector sensor, and the distance between the array units is larger, so that the mutual coupling between electromagnetic components in received signals and the complexity of hardware of the electromagnetic vector sensor are reduced;
3) compared with the existing algorithm of the electromagnetic vector sensor array, the method has the advantages that the calculation amount and complexity are reduced on the basis of keeping the characteristics of the utilization of all electromagnetic information of each array unit and the simultaneous estimation of a plurality of targets.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a schematic of the geometry of a single split electromagnetic vector sensor of the present invention;
FIG. 3 is a schematic diagram of an array configuration in accordance with the present invention;
FIG. 4 is a diagram illustrating simulation results of one estimation of a target two-dimensional direction of arrival angle using the present invention;
FIG. 5 is a comparison of RMS error versus SNR for cosine estimates in different directions in accordance with the present invention;
FIG. 6 is a graph comparing the root mean square error and the signal-to-noise ratio of the angle estimates of the two-dimensional directions of arrival of the targets of the array of the present invention and two arrays of uniform linear electromagnetic vector sensors, where the number of array units of the two arrays of uniform linear electromagnetic vector sensors is the same as the array of the present invention, and the array unit spacing is D and mD, respectively;
FIG. 7 is a graph comparing the root mean square error and snapshot number of the angle estimates of the two-dimensional directions of arrival of the targets of the array of the present invention and two arrays of uniform linear electromagnetic vector sensors, where the number of array units of the two arrays of uniform linear electromagnetic vector sensors is the same as the array of the present invention, and the array unit spacing is D and mD, respectively;
fig. 8 is a graph comparing the root mean square error of the angle estimation values of the two-dimensional directions of arrival of the targets of the array according to the present invention and two uniform linear electromagnetic vector sensor arrays with the array element spacing relationship of the first sub-array C1, where the number of array elements of the two uniform linear electromagnetic vector sensor arrays is the same as that of the array according to the present invention, and the array element spacing is D and mD, respectively.
Detailed Description
The following further describes the implementation and effects of the present invention with reference to the drawings.
Referring to fig. 1, the implementation steps of the invention are as follows:
step 1, designing a nested electromagnetic vector sensor array according to a single separated electromagnetic vector sensor.
Referring to fig. 2, the single split electromagnetic vector sensor is divided into: six components, delta, of an electric dipole Ex parallel to the x-axis, an electric dipole Ey parallel to the y-axis, an electric dipole Ez parallel to the z-axis, a magnetic loop Hx perpendicular to the x-axis, a magnetic loop Hy perpendicular to the y-axis and a magnetic loop Hz perpendicular to the z-axisx,yDenotes the spacing between Ex and Ey, and the spacing between Hx and Hy is also equal to Δx,y，Δy,zRepresents the distance between Ey and Ez, and the distance between Hy and Hz is also equal to deltay,z；
The number N of the array units is given, the positions of the array units are designed according to the structure of the nested array, and all the array units are divided into a front part and a rear part: a first sub-array C1 and a second sub-array C2, wherein:
using front n1The array units take D as the space between the array unitsA uniform linear array ULA is constructed in the y-axis direction as a first sub-array C1, the array elements of which are located at [0, D,2D1-1)D]Taking the array unit with the position of 0 as a reference array unit;
with the remainder of n2The array units take mD as the spacing between the array units, and a uniform linear array ULA is constructed in the same direction after the first subarray C1 as a second subarray C2, and the positions of the array units are as follows:
[n1D,(n1+m)D,(n1+2m)D,...,(n1+(n2-1)m)D]wherein m is n1+1 and having n1+n2N, D is greater than λ 2, λ is the electromagnetic wavelength;
placing the N separate electromagnetic vector sensors according to the array unit positions of the nested array, and obtaining the nested electromagnetic vector sensor array, as shown in FIG. 3, wherein the array units of the nested array are positioned as follows: [0, D, 2D., (n.)1-1)D,n1D,(n1+m)D,(n1+2m)D,...,(n1+(n2-1)m)D]。
And 2, obtaining receiving data X (t) of the nested electromagnetic vector sensor array according to the constructed nested electromagnetic vector sensor array.
2.1) obtaining a guide vector of a nested electromagnetic vector sensor array as
Figure BDA0001423340730000051
Where a denotes the steering vector of the split electromagnetic vector sensor at the reference array element, which is expressed as follows:
Figure BDA0001423340730000061
wherein the content of the first and second substances,
Figure BDA0001423340730000062
(ex,ey,ez) Representing the components of the electric field received in the x, y and z axes, respectively, (h)x,hy,hz) Respectively representing the x-axis, y-axis and z-axis received magnetic field components, phi ∈ [0,2 π), theta ∈ [0, π ∈ ]]Respectively representing the azimuth angle and the pitch angle of an incident signal, wherein the azimuth angle is the positive included angle between the signal and an x axis, the pitch angle is the positive included angle between the signal and a z axis, and gamma belongs to [0, pi/2 ]]，η∈[-π,π]Denotes the auxiliary angle and phase difference of polarization of the incident signal, u ═ sin θ cos θ denotes the cosine of the incident signal along the x axis, v ═ sin θ sin Φ denotes the cosine of the incident signal along the y axis, w ═ cos θ denotes the cosine of the incident signal along the z axis, ⊙ denotes the Hadamard product, (x ═ sin θ denotes the cosine of the incident signal along the z axis, andh,yh,zh) Representing the position coordinates of a magnetic ring Hx which is arranged perpendicular to the x axis of the separated electromagnetic vector sensor at the reference array unit;
2.2) obtaining the receiving data X (t) of the array according to the guide vector of the nested electromagnetic vector sensor array:
assuming that K mutually uncorrelated narrow-band target signals are incident on the array, the overall array received signal model can be expressed as:
Figure BDA0001423340730000063
wherein, blDenotes a steering vector corresponding to the l-th signal, wherein l is 1,2
Figure BDA0001423340730000064
And is uncorrelated with the incident signal, B ═ B1,b2,...,bl,...,bK]For an array flow pattern matrix, the signal vector is s (t) ═ s1(t),s2(t),...,sl(t),...,sK(t)]T，sl(t) represents the l-th incident signal, ()TRepresenting the transpose of the vector, t representing the sampling time t ═ t1,t2,...,tLAnd L represents the number of fast beats.
Step 3, obtaining the array unit positions of the two sub-arrays C1 and C2 respectivelyCovariance matrix of received data to first subarray C1 and second subarray C2
Figure BDA0001423340730000071
And
Figure BDA0001423340730000072
according to the division of two sub-arrays C1 and C2, the data X (t) received by the array is (t) equal to X (t)1),X(t2),...,X(tL)]Is divided into X1(t)＝[X1(t1),X1(t2),...,X1(tL)]And X2(t)＝[X2(t1),X2(t2),...,X2(tL)]Two parts, obtaining covariance matrix of the two groups of received data by maximum likelihood estimation
Figure BDA0001423340730000073
And
Figure BDA0001423340730000074
()Hrepresenting the conjugate transpose of the matrix.
Step 4, covariance matrix of received data according to the first subarray C1 and the second subarray C2
Figure BDA0001423340730000075
And
Figure BDA0001423340730000076
obtaining a signal subspace matrix Es of the first sub-matrix C11And a signal subspace matrix Es of the second sub-array C22。
Covariance matrix of received data for first sub-matrix C1
Figure BDA0001423340730000077
Decomposing the eigenvalues, and forming a signal subspace matrix Es of a first sub-matrix C1 by using the eigenvectors corresponding to the largest K eigenvalues1；
Covariance matrix of received data for second sub-matrix C2
Figure BDA0001423340730000078
Decomposing the eigenvalues, and forming a signal subspace matrix Es of a second sub-matrix C2 by using the eigenvectors corresponding to the largest K eigenvalues2。
Step 5, according to the signal subspace matrix Es of the first subarray C11Obtaining a group of periodically fuzzy y-axis direction cosine estimated values by utilizing an ESPRIT algorithm of a rotation invariant subspace
Figure BDA0001423340730000079
5.1) order alIndicating the steering vector of the split electromagnetic vector sensor at the reference array element to the ith target,
Figure BDA00014233407300000710
representing the first sub-array C1 front n1-a steering vector of 1 array element to the ith target,
Figure BDA00014233407300000711
representing n after the first sub-array C11-a steering vector of 1 array element to the ith target;
for a single target, the first n of the first sub-array C11-1 array element and last n1The spatial rotation invariance of 1 array element is reflected on the steering vector, which is of the form:
Figure BDA0001423340730000081
5.2) order
Figure BDA0001423340730000082
Is the first sub-array C1 front n1An array flow pattern matrix corresponding to 1 array unit,
Figure BDA0001423340730000083
n after the first subarray C11-an array flow pattern matrix corresponding to 1 array unit;
for all targets, the first n of the first sub-array C11-1 array element and last n1Spatial rotation invariance deformation of 1 array element into matrix form:
Figure BDA0001423340730000084
wherein the content of the first and second substances,
Figure BDA0001423340730000085
a rotation invariant factor matrix which is a first sub-matrix C1;
5.3) according to the property that the signal subspace is the same as the space formed by the guide vector, obtaining the following relation:
Es1＝B1T1
wherein B is1An array flow pattern matrix, T, representing a first sub-array C11Is a rotation invariant factor matrix with the first sub-matrix C1
Figure BDA0001423340730000086
A corresponding unique non-singular matrix;
will relation
Figure BDA0001423340730000087
Substituted into Es1＝B1T1The following relationship is obtained:
Figure BDA0001423340730000088
wherein, Es1,2Representing n after the first sub-array C11-1 signal subspace matrix, Es, corresponding to the array elements1,1Representing the first sub-array C1 front n1-a signal subspace matrix corresponding to 1 array element and having
Figure BDA0001423340730000089
5.4) Signal subspace matrix Es according to the first sub-matrix C11Separating out the first n1-1 signal subspace matrix Es for an array element1,1And after n1-1 signal subspace matrix Es for an array element1,2According to the relational expression
Figure BDA00014233407300000810
Obtaining a first intermediate variable
Figure BDA00014233407300000811
5.5) pairs
Figure BDA00014233407300000812
Performing eigenvalue decomposition, wherein the eigenvalue is the rotation invariant factor matrix of the first sub-matrix C1
Figure BDA00014233407300000813
According to the condition that D is more than lambda/2, a group of periodically fuzzy y-axis direction cosine estimated values are obtained by using a total least square method:
Figure BDA00014233407300000814
step 6, according to the signal subspace matrix Es of the second subarray C22Obtaining a group of periodically fuzzy y-axis direction cosine estimated values by utilizing an ESPRIT algorithm of a rotation invariant subspace
Figure BDA0001423340730000091
6.1) order
Figure BDA0001423340730000092
Is front n2-a steering vector of 1 array element to the ith target,
Figure BDA0001423340730000093
is a rear n2-a steering vector of 1 array element to the ith target;
for a single target, the first n of the second sub-array C22-1 array element and a second sub-array C2 after n2The spatial rotation invariance of 1 array element is reflected on the steering vector, which is of the form:
Figure BDA0001423340730000094
6.2) order
Figure BDA0001423340730000095
Is the first n of the second sub-array C22An array flow pattern matrix corresponding to 1 array unit,
Figure BDA0001423340730000096
n after the second sub-array C22-an array flow pattern matrix corresponding to 1 array unit;
for all targets, the first n of the second sub-array C22-1 array element and a second sub-array C2 and n2Spatial rotation invariance deformation of 1 array element into matrix form:
Figure BDA0001423340730000097
wherein the content of the first and second substances,
Figure BDA0001423340730000098
a rotation invariant factor matrix which is a second sub-matrix C2;
6.3) according to the property that the signal subspace is the same as the space spanned by the guide vectors, the following relation is obtained:
Es2＝B2T2，
wherein B is2An array flow pattern matrix, T, representing a second sub-array C22Is a rotation invariant factor matrix with a second sub-matrix C2
Figure BDA0001423340730000099
A corresponding unique non-singular matrix;
will relation
Figure BDA00014233407300000910
Substitution into Es2＝B2T2The following relationship is obtained:
Figure BDA00014233407300000911
wherein, Es2,2Representing n after the second sub-array C22-1 signal subspace matrix, Es, corresponding to the array elements2,1Representing the first n of the second sub-array C22-a signal subspace matrix corresponding to 1 array element and having
Figure BDA00014233407300000912
6.4) Signal subspace matrix Es according to the second sub-matrix C22Separating the front n of the second sub-array C22-1 signal subspace matrix Es for an array element2,1And n after the second sub-array C22-1 signal subspace matrix Es for an array element2,2According to the relational expression
Figure BDA0001423340730000101
Obtaining a second intermediate variable
Figure BDA0001423340730000102
6.5) pairs
Figure BDA0001423340730000103
Performing eigenvalue decomposition, wherein the eigenvalue is the rotation invariant factor matrix of the second sub-matrix C2
Figure BDA0001423340730000104
According to the condition that mD is more than D and more than lambda/2, a group of periodically fuzzy y-axis direction cosine estimated values are obtained by using a total least square method:
Figure BDA0001423340730000105
step 7, according to
Figure BDA0001423340730000106
And
Figure BDA0001423340730000107
diagonal element pair of
Figure BDA0001423340730000108
And
Figure BDA0001423340730000109
and (6) pairing.
Due to the fact that
Figure BDA00014233407300001010
And
Figure BDA00014233407300001011
are two relatively independent processes, so they are not automatically paired, and therefore need to be deblurred before they can be used
Figure BDA00014233407300001012
And
Figure BDA00014233407300001013
and (6) pairing.
Due to the fact that
Figure BDA00014233407300001014
Is based on
Figure BDA00014233407300001015
Diagonal line element of
Figure BDA00014233407300001016
Is generated at the first sub-array C1 due to the phase difference of the first target due to the spacing D between the array elements
Figure BDA00014233407300001017
The obtained material has the advantages of high yield,
Figure BDA00014233407300001018
the sequence of the sequence numbers of the objects in the sequence table
Figure BDA00014233407300001019
The arrangement sequence of each target serial number in the diagonal elements is the same;
Figure BDA00014233407300001020
is based on
Figure BDA00014233407300001021
Diagonal line element
Figure BDA00014233407300001022
Is generated in the second sub-array C2 due to the phase difference of the first target due to the spacing mD between the array elements
Figure BDA00014233407300001023
The obtained material has the advantages of high yield,
Figure BDA00014233407300001024
the sequence of the sequence numbers of the objects in the sequence table
Figure BDA00014233407300001025
The arrangement order of the target serial numbers in the diagonal elements is the same, so that the target serial numbers can be arranged in the same order
Figure BDA00014233407300001026
And
Figure BDA00014233407300001027
the pairing problem is converted into
Figure BDA00014233407300001028
Diagonal elements of and
Figure BDA00014233407300001029
the pairing problem of diagonal elements.
Figure BDA00014233407300001030
Pair ofAngle line elements and
Figure BDA00014233407300001031
is implemented according to the m-times relationship between the array cell pitch mD of the second sub-array C2 and the array cell pitch D of the first sub-array C1, which includes the following steps:
7.1) set the true phase difference of a target at the first sub-array C1 due to the array element spacing D to Λ1＝2g1π+φ1Wherein phi1Is Λ1The phase difference, g, that can be actually measured1Is Λ1Phi and phi1The period fuzzy number of the phase difference is set as Λ, and the phase difference of the target at the second sub-array C2 caused by the array unit distance mD is set as2＝2g2π+φ2，φ2Is Λ2The phase difference that can be actually measured is phi2，g2Is Λ2Phi and phi2The number of periodic ambiguities that differ therebetween;
obtaining the m lambda according to the m-time relation between the array unit spacing mD of the second subarray C2 and the array unit spacing D of the first subarray C11＝Λ2The relational expression of (1);
7.2) by the relation m Λ1＝Λ2The following equation is obtained:
m×(2g1π+φ1)＝2g2π+φ2，
the equation is transformed to obtain the following transformed relation:
mφ1＝2π(g2-mg1)+φ2
according to the deformed relation and the property of the exponential function, obtaining the following relation:
Figure BDA0001423340730000111
7.3) according to the relation
Figure BDA0001423340730000112
To pair
Figure BDA0001423340730000113
Diagonal line element of
Figure BDA0001423340730000114
Are all made to the power of m and sequentially and
Figure BDA0001423340730000115
diagonal line element of
Figure BDA0001423340730000116
Comparing one by one, selecting the pairing with the minimum difference value to obtain
Figure BDA0001423340730000117
Diagonal elements of and
Figure BDA0001423340730000118
the pairing order of the diagonal elements of (1);
7.4) according to the obtained
Figure BDA0001423340730000119
Diagonal elements of and
Figure BDA00014233407300001110
the order of the pairs of diagonal elements, and the cosine estimated values of the two sets of target y-axis directions
Figure BDA00014233407300001111
And
Figure BDA00014233407300001112
the sequence of the sequence numbers of the targets is reordered to finish the pair
Figure BDA00014233407300001113
And
Figure BDA00014233407300001114
the pairing of (1).
Step 8, according to the signal subspace matrix Es of the first subarray C11And a second sub-arraySignal subspace matrix Es of C22And
Figure BDA00014233407300001115
and
Figure BDA00014233407300001116
the result of the combination of the guide vectors of all the electromagnetic vector sensors except the reference array unit onto the guide vector at the reference array unit is obtained
Figure BDA00014233407300001117
And
Figure BDA00014233407300001118
8.1) pairs
Figure BDA00014233407300001119
And
Figure BDA00014233407300001120
after the feature decomposition, the feature vectors form a nonsingular matrix T1And T2According to
Figure BDA00014233407300001121
And
Figure BDA00014233407300001122
are respectively paired with the pairing result of
Figure BDA00014233407300001123
And
Figure BDA00014233407300001124
column vector and non-singular matrix T1And T2According to the relation between the signal subspace matrix and the array flow pattern matrix in the ESPRIT algorithm
Figure BDA00014233407300001125
And
Figure BDA00014233407300001126
obtaining an array flow pattern matrix B1And B2Is estimated value of
Figure BDA00014233407300001127
And
Figure BDA00014233407300001128
8.2) performing phase compensation on the guide vectors of all the electromagnetic vector sensors except the electromagnetic vector sensor at the reference array unit so as to perform coherent addition, thereby synthesizing the guide vectors of the separated electromagnetic vector sensors at the reference array unit, wherein the compensation amount is a phase shift factor of each electromagnetic vector sensor, and the result that the guide vectors of all the electromagnetic vector sensors except the reference array unit are synthesized on the guide vectors at the reference array unit is obtained:
Figure BDA0001423340730000121
Figure BDA0001423340730000122
wherein, c1And c2Are the complex constants of the difference between the first and second,
Figure BDA0001423340730000123
step 9, according to
Figure BDA0001423340730000124
And
Figure BDA0001423340730000125
with vector cross product algorithm, a group of estimation values with low u precision and no ambiguity is obtained
Figure BDA0001423340730000126
And higher accuracy but periodically ambiguous estimates of two sets u
Figure BDA0001423340730000127
And
Figure BDA0001423340730000128
and a set of less accurate but unambiguous estimates of v
Figure BDA0001423340730000129
9.1) pairs
Figure BDA00014233407300001210
And
Figure BDA00014233407300001211
the normalized vector cross product of the electric field component and the magnetic field component is performed separately, and the result is as follows:
Figure BDA00014233407300001212
Figure BDA00014233407300001213
order to
Figure BDA00014233407300001214
As a final cross product of vectors of the separate electromagnetic vector sensors at the reference array element, by plThe constitution of (1):
Figure BDA00014233407300001215
obtaining u, v, w estimated values with lower precision but no ambiguity:
Figure BDA0001423340730000131
wherein | represents an absolute value;
9.2) order
Figure BDA0001423340730000132
To obtain
Figure BDA0001423340730000133
According to
Figure BDA0001423340730000134
Obtaining two groups of high-precision estimated values of the cosine u of the direction of the target along the x axis and with periodical ambiguity
Figure BDA0001423340730000135
And
Figure BDA0001423340730000136
Figure BDA0001423340730000137
Figure BDA0001423340730000138
step 10, according to
Figure BDA0001423340730000139
To pair
Figure BDA00014233407300001310
And
Figure BDA00014233407300001311
performing deblurring to obtain high-precision and non-fuzzy estimated value of v
Figure BDA00014233407300001312
10.1) lower precision but unambiguous y-axis direction cosine estimate
Figure BDA00014233407300001313
Estimation of cosine in y-axis direction with high solution precision but periodic ambiguityEvaluating value
Figure BDA00014233407300001314
The first, more accurate and unambiguous, estimate of v
Figure BDA00014233407300001315
The following fuzzy equation gives:
Figure BDA00014233407300001316
wherein the content of the first and second substances,
Figure BDA00014233407300001317
Figure BDA00014233407300001318
which means that the rounding is made up,
Figure BDA00014233407300001319
represents rounding down;
10.2) mixing
Figure BDA00014233407300001320
As the cosine estimated value in the y-axis direction with higher solution precision but periodic ambiguity
Figure BDA00014233407300001321
The final high-precision and unambiguous estimate of v
Figure BDA00014233407300001322
The following fuzzy equation gives:
Figure BDA0001423340730000141
wherein the content of the first and second substances,
Figure BDA0001423340730000142
step 11, according to
Figure BDA0001423340730000143
To pair
Figure BDA0001423340730000144
And
Figure BDA0001423340730000145
carrying out deblurring to obtain a high-precision and non-fuzzy estimated value of u
Figure BDA0001423340730000146
11.1) lower precision but unambiguous cosine estimate of the x-axis direction
Figure BDA0001423340730000147
As the cosine estimated value in the x-axis direction with high solution precision but periodic ambiguity
Figure BDA0001423340730000148
The first accurate and unambiguous estimation of u
Figure BDA0001423340730000149
The following fuzzy equation gives:
Figure BDA00014233407300001410
wherein the content of the first and second substances,
Figure BDA00014233407300001411
11.2) will
Figure BDA00014233407300001412
As the cosine estimated value in the x-axis direction with higher solution precision but periodic ambiguity
Figure BDA00014233407300001413
The final high-precision and unambiguous estimation of u
Figure BDA00014233407300001414
The following fuzzy equation gives:
Figure BDA00014233407300001415
wherein the content of the first and second substances,
Figure BDA00014233407300001416
step 12, according to the high-precision non-fuzzy high-precision estimated value of u
Figure BDA00014233407300001417
High precision unambiguous estimation of sum v
Figure BDA00014233407300001418
Obtaining the azimuth angle and pitch angle estimated values of the target
Figure BDA00014233407300001419
To pair
Figure BDA00014233407300001420
And
Figure BDA00014233407300001421
the following trigonometric operations are performed:
Figure BDA00014233407300001422
obtaining two-dimensional direction of arrival estimation information of target
Figure BDA00014233407300001423
Wherein
Figure BDA00014233407300001424
Is an estimate of the azimuth angle of the ith target,
Figure BDA00014233407300001425
is the pitch angle estimate for the ith target.
The effects of the present invention are further illustrated by the following computer simulation.
1. Simulation conditions
Assuming that the number of array cells is 10, an array is constructed according to step 1 in the above embodiment, with the array cell positions being [0,1,2,3,4,5,11,17,23,29], the first sub-array C1 being composed of array cells [0,1,2,3,4], the second sub-array C2 being composed of array cells [5,11,17,23,29], and with the array cell pitch of C1 being 6 λ, the array cell pitch of C2 is 36 λ.
A separate electromagnetic vector sensor is arranged at each array unit; for any one of the split electromagnetic vector sensors, the distance between the three electric dipoles is Δx,y＝Δy,zSetting the separated electromagnetic vector sensor at the reference array unit as a separated electromagnetic vector sensor with an electric dipole Ey positioned at the original point, wherein the coordinate of a magnetic ring Hx vertical to the x axis is
Figure BDA0001423340730000151
The constructed nested electromagnetic vector sensor array is shown in fig. 3.
The method is characterized in that K is 3 irrelevant targets in the same distance unit, the azimuth angles of the targets are phi (42 degrees, 55 degrees and 28 degrees), the pitch angles are theta (20 degrees, 60 degrees and 45 degrees), the polarization auxiliary angles are gamma (45 degrees, 30 degrees and 55 degrees), the polarization phase difference is η (90 degrees, 120 degrees and 70 degrees), the fast beat number is L (200 degrees), the signal-to-noise ratio is SNR (15 dB), and 200 Monte-Carlo experiments are carried out.
2. Emulated content
Simulation 1: the effectiveness of the invention was simulated.
Under the above simulation conditions, the two-dimensional direction of arrival of the target is estimated, and the estimation result is shown in fig. 4.
It can be seen from fig. 4 that the present invention can correctly estimate two-dimensional direction-of-arrival angle information, i.e., the azimuth angle and the pitch angle of the target.
Simulation 2: the invention simulates the relation between the root mean square error and the signal-to-noise ratio of cosine estimated values in different directions.
Under the simulation conditions, the SNR is set as a set of values, and the relationship between the root mean square error and the SNR of the cosine estimation values in different directions of the present invention is simulated, and the result is shown in fig. 5.
As can be seen from fig. 5, since the aperture expansion of the array according to the present invention in the y-axis direction is much larger than the aperture expansion in the x-axis direction, when the snr is higher than the snr threshold for deblurring, the estimation accuracy of the cosine v in the y-axis direction is higher than the estimation accuracy of the cosine u in the x-axis direction.
Simulation 3: the relationship between the root mean square error and the signal-to-noise ratio of the target two-dimensional direction-of-arrival angle estimation values of the array of the present invention and the two uniform linear electromagnetic vector sensor arrays shown in fig. 3 is simulated respectively.
Under the simulation conditions, the number of array units of the two uniform linear electromagnetic vector sensor arrays is the same as that of the array of the invention shown in fig. 3, the array element spacing of the array is D and mD, the SNR is a set of values, the relationship between the root mean square error and the SNR of the target two-dimensional direction of arrival angle estimation values of the array of the invention and the two uniform linear electromagnetic vector sensor arrays shown in fig. 3 is simulated, and the simulation result is shown in fig. 6, wherein fig. 6(a) is a comparison graph of the relationship between the root mean square error and the SNR of the azimuth angle estimation values of the array of the invention and the two uniform linear electromagnetic vector sensor arrays shown in fig. 3, and fig. 6(b) is a comparison graph of the relationship between the root mean square error and the SNR of the pitch angle estimation values of the array of the invention and the two uniform linear electromagnetic vector sensor arrays.
As can be seen from fig. 6(a) and 6(b), when the snr is lower than the snr threshold for ambiguity resolution, ambiguity resolution fails, and the azimuth and the pitch of the target cannot be correctly estimated, and after the snr increases to the snr threshold for ambiguity resolution, the angle measurement performance is rapidly optimized, and the angle measurement accuracy increases with the increase of the snr.
In addition, compared with the two uniform linear electromagnetic vector sensor arrays, the array of the invention shown in fig. 3 has a lower ambiguity resolution signal-to-noise ratio threshold, and when the signal-to-noise ratio is higher than the ambiguity resolution signal-to-noise ratio threshold, the angle measurement accuracy of the array of the invention shown in fig. 3 is higher than that of the other two arrays under the condition of the same signal-to-noise ratio.
And (4) simulation: the relationship between the root mean square error and the fast beat number of the angle estimation values of the target two-dimensional directions of arrival of the array of the invention and the two uniform linear electromagnetic vector sensor arrays shown in fig. 3 is simulated.
Under the above simulation conditions, the number of array units of the two uniform linear electromagnetic vector sensor arrays is the same as that of the array of the present invention shown in fig. 3, the array unit spacing of the array is D and mD, and the snapshot number L is a set of values, and the relationship between the root mean square error and the snapshot number of the target two-dimensional direction of arrival angle estimation values of the array of the present invention and the two uniform linear electromagnetic vector sensor arrays shown in fig. 3 is simulated, and the simulation result is shown in fig. 7, where fig. 7(a) is a comparison graph of the relationship between the root mean square error and the snapshot number of the azimuth angle estimation values of the array of the present invention and the two uniform linear electromagnetic vector sensor arrays shown in fig. 3, and fig. 7(b) is a comparison graph of the relationship between the root mean square error and the snapshot number of the pitch angle estimation values of the array of the present invention and the two uniform linear.
As can be seen from fig. 7(a) and 7(b), the angular accuracy of the array of the present invention shown in fig. 3 improves with an increase in the number of fast beats, and the angular accuracy of the array of the present invention shown in fig. 3 is higher than that of the other two arrays for the same number of fast beats.
And (5) simulation: the root mean square error of the angle estimates of the target two-dimensional directions of arrival of the inventive array and the two uniform linear electromagnetic vector sensor arrays shown in fig. 3 was simulated in relation to the array element spacing D of the first sub-array C1.
Under the above simulation conditions, assuming that the number of array units of the two uniform linear electromagnetic vector sensor arrays is the same as that of the array of the present invention shown in fig. 3, the array unit pitches of the arrays are D and mD, respectively, and the array unit pitch D of the first sub-array C1 is a set of values, the relationship between the root mean square error of the target two-dimensional space estimation angles of the array of the present invention and the two uniform linear electromagnetic vector sensor arrays shown in fig. 3 and D is simulated, and the simulation result is shown in fig. 8, where fig. 8(a) is a comparison graph of the root mean square error of the azimuth angle estimation values of the array of the present invention and the two uniform linear electromagnetic vector sensor arrays shown in fig. 3 and D, and fig. 8(b) is a comparison graph of the root mean square error of the pitch angle estimation values of the array of the present invention and the two uniform linear electromagnetic vector sensor.
As can be seen from fig. 8(a) and 8(b), within a certain range, as the array cell pitch D of the first sub-array C1 increases, the angle measurement accuracy of the array of the present invention shown in fig. 3 remains substantially unchanged, because the angle measurement accuracy is mainly determined by the array cell pitch mD of the second sub-array C2, and the array cell pitch mD of the second sub-array C2 exceeds the array cell pitch threshold, and the angle measurement accuracy of the uniform linear electromagnetic vector sensor array with the array cell pitch mD being the array cell pitch cannot be increased as the array cell pitch D of the first sub-array C1 increases, so as the array cell pitch D of the first sub-array C1 increases, the angle measurement accuracy of the array of the present invention shown in fig. 3 remains substantially unchanged. As D increases, the array element pitch D of the sub-array C1 exceeds the array element pitch threshold, and the angle measurement accuracy of the array of the present invention shown in fig. 3 deteriorates rapidly and stays in a low range quickly.
In addition, the array pitch threshold of the array of the present invention shown in fig. 3 is higher than that of two uniform linear electromagnetic vector sensor arrays, and under the same array unit pitch D, the array unit pitch mD of the uniform linear electromagnetic vector sensor array with mD as the array unit pitch is larger than the array unit pitch threshold, and the angle measurement accuracy is kept in a lower range, whereas for the uniform linear electromagnetic vector sensor array with D as the array unit pitch, if D is not larger than the array unit pitch threshold, but because the aperture of the array is relatively small, the angle measurement accuracy is relatively low, and if D is larger than the array unit pitch threshold, the angle measurement accuracy is also rapidly deteriorated and kept in a lower range. The angle measurement accuracy of the inventive array shown in fig. 3 is higher than that of two uniform linear electromagnetic vector sensor arrays at the same array element pitch D of the first sub-array C1 when D is not higher than the array element pitch threshold.
In conclusion, the invention comprehensively utilizes the advantages of the electromagnetic vector sensor and the nested array, reduces the mutual coupling of all components of the electromagnetic vector sensor and the complexity on hardware, enlarges the aperture of the whole array, can provide two-dimensional angle estimation information for a space target and improves the angle measurement performance of the array.

Claims (8)

1. A method for estimating a direction of arrival based on a nested electromagnetic vector sensor array comprises the following steps:
1) constructing a nested electromagnetic vector sensor array:
given the number N of array units, N is the first1The array units are arranged along a certain direction by taking D as the array element interval, the obtained uniform linear array ULA is used as a first subarray C1 of the nested electromagnetic vector sensor array, and the last n is2The array units are arranged along the same direction by taking mD as the array element spacing, and a uniform linear array ULA is obtained and is used as a second sub-array C2 of the nested electromagnetic vector sensor array, wherein m is n1+1 and having n1+n2Each array unit is provided with a separated electromagnetic vector sensor to obtain a nested electromagnetic vector sensor array A, D is larger than lambda/2, and lambda is the wavelength of electromagnetic waves;
2) dividing received data X (t) of the nested electromagnetic vector sensor array into X according to a first sub-array C1 and a second sub-array C21(t) and X2(t) two parts;
3) receiving data X for two parts1(t) and X2(t) respectively estimating two groups of fuzzy target y-axis direction cosine estimated values by using rotation invariant subspace ESPRIT algorithm
Figure FDA0002263172740000011
And
Figure FDA0002263172740000012
and the signal subspaces Es respectively corresponding to the two groups of estimation values1And Es2Wherein K is the target number;
4) two groups of target y-axis direction cosine estimated values estimated in the step 3)
Figure FDA0002263172740000013
And
Figure FDA0002263172740000014
pairing is carried out, and the signal subspace Es corresponding to the estimated value is paired according to the pairing sequence1And Es2Matching to obtain an estimated value of an array flow pattern matrix of the nested electromagnetic vector sensor array;
5) performing phase compensation on the guide vectors of the array units except the reference array unit in the estimated value of the array flow pattern matrix obtained in the step 4), and synthesizing the guide vectors of the array units except the reference array unit after compensation onto the guide vector of the separated electromagnetic vector sensor at the reference array unit to obtain the synthesized guide vector of the separated electromagnetic vector sensor at the reference array unit;
6) using the guide vectors of the separated electromagnetic vector sensors at the synthesized reference array unit obtained in the step 5), and obtaining a group of target y-axis direction cosine estimated values with lower precision and without ambiguity through a vector cross product algorithm
Figure FDA0002263172740000015
And a set of x-axis direction cosine estimates
Figure FDA0002263172740000016
And two sets of fuzzy target x-axis direction cosine estimated values
Figure FDA0002263172740000017
And
Figure FDA0002263172740000018
7) two groups of fuzzy target y-axis direction cosine estimated values obtained in the step 4) after pairing
Figure FDA0002263172740000021
And step 6) obtainingTo two groups of fuzzy target x-axis direction cosine estimated values
Figure FDA0002263172740000022
Performing ambiguity resolution to obtain a group of ambiguity-free high-precision target x-axis direction cosine estimated values
Figure FDA0002263172740000023
And a group of target y-axis direction cosine high-precision estimated values without ambiguity
Figure FDA0002263172740000024
8) High-precision cosine estimation value of target x-axis direction without ambiguity
Figure FDA0002263172740000025
And a target y-axis direction cosine high-precision estimated value without ambiguity
Figure FDA0002263172740000026
Performing trigonometric operation to obtain the two-dimensional space direction-of-arrival information of the target
Figure FDA0002263172740000027
Wherein
Figure FDA0002263172740000028
Is an estimate of the azimuth angle of the ith target,
Figure FDA0002263172740000029
is the pitch angle estimate for the ith target.
2. The method as claimed in claim 1, wherein the data X is received for two parts in step 3)1(t) and X2(t) respectively estimating two groups of fuzzy target y-axis direction cosine estimated values by using rotation invariant subspace ESPRIT algorithm
Figure FDA00022631727400000210
And
Figure FDA00022631727400000211
the method comprises the following steps:
3a) receiving data X according to a first sub-array C11(t) and received data X of the second sub-array C22(t) calculating covariance matrices of the two sets of received data, respectively
Figure FDA00022631727400000212
And
Figure FDA00022631727400000213
Figure FDA00022631727400000214
Figure FDA00022631727400000215
wherein, X1(t)＝[X1(t1),X1(t2),...X1(ti)...,X1(tL)]，
X2(t)＝[X2(t1),X2(t2),...X2(ti)...,X2(tL)]L, L is the snapshot number;
3b) separately for the covariance matrices obtained in 3a)
Figure FDA00022631727400000216
And
Figure FDA00022631727400000217
decomposing the eigenvalues, and respectively taking the eigenvectors corresponding to the largest K eigenvalues in the eigenvalues to form a signal subspace matrix Es of the first sub-matrix C11And a signal subspace matrix Es of the second sub-array C22；
3c) Signal subspace Es according to the first sub-array C1 obtained in 3b)1Separating out the first n1-1 signal subspace matrix Es for an array element1,1And after n1-1 signal subspace matrix Es for an array element1,2Obtaining Es according to the rotation invariant subspace ESPRIT algorithm1,1And Es1,2The following relationships:
Figure FDA0002263172740000031
Figure FDA0002263172740000032
wherein the content of the first and second substances,
Figure FDA0002263172740000033
is the first intermediate variable which is the variable,
Figure FDA0002263172740000034
being the rotation invariant factor matrix of the first sub-matrix C1,
Figure FDA0002263172740000035
vlthe true y-axis cosine of the ith target, i.e., 1, 2.. K, j is an imaginary unit, and diag [. cndot.]Representing the construction of a square matrix, T, with elements in the vector as diagonal elements1Is a rotation invariant factor matrix with the first sub-matrix C1
Figure FDA0002263172740000036
A corresponding unique non-singular matrix;
3d) solving for in 3c) using a total least squares method
Figure FDA0002263172740000037
Obtaining a relational expression
Figure FDA0002263172740000038
To pair
Figure FDA0002263172740000039
Performing eigenvalue decomposition, wherein the eigenvalue is
Figure FDA00022631727400000310
And obtaining a group of high-precision and periodically fuzzy target y-axis direction cosine estimated values according to the condition that D is more than lambda/2:
Figure FDA00022631727400000311
3e) signal subspace Es according to the second sub-array C2 obtained in 3b)2Separating out the first n2-1 signal subspace matrix Es for an array element2,1And after n2-1 signal subspace matrix Es for an array element2,2Obtaining Es according to the rotation invariant subspace ESPRIT algorithm2,1And Es2,2The following relationships:
Figure FDA00022631727400000312
Figure FDA00022631727400000313
wherein the content of the first and second substances,
Figure FDA00022631727400000314
is the second intermediate variable which is the variable,
Figure FDA00022631727400000315
for the rotation invariant factor matrix of the second sub-matrix C2,
Figure FDA00022631727400000316
T2is a rotation invariant factor matrix with a second sub-matrix C2
Figure FDA00022631727400000317
A corresponding unique non-singular matrix;
3f) solving for in 3e) using a total least squares method
Figure FDA0002263172740000041
Obtaining a relational expression
Figure FDA0002263172740000042
To pair
Figure FDA0002263172740000043
Performing eigenvalue decomposition, wherein the eigenvalue is
Figure FDA0002263172740000044
And obtaining a set of target y-axis direction cosine estimated values with higher precision and periodic ambiguity according to the condition that mD is more than D and more than lambda/2:
Figure FDA0002263172740000045
3. the method of claim 1, wherein two sets of target y-axis direction cosine estimates are processed in step 4)
Figure FDA0002263172740000046
And
Figure FDA0002263172740000047
and (3) pairing according to the following rules:
4a) rotation invariant factor matrix according to the first sub-matrix C1
Figure FDA0002263172740000048
Diagonal line element of
Figure FDA0002263172740000049
Is generated at the first sub-array C1 due to the phase difference of the first target due to the spacing D between the array elements
Figure FDA00022631727400000410
The estimated value of the cosine of the y-axis direction of the first target is
Figure FDA00022631727400000411
Wherein
Figure FDA00022631727400000412
The sequence of the sequence numbers of the objects in the sequence table
Figure FDA00022631727400000413
The arrangement sequence of each target serial number in the diagonal elements is the same;
4b) rotation invariant factor matrix according to a second sub-matrix C2
Figure FDA00022631727400000414
Diagonal line element of
Figure FDA00022631727400000415
Is generated in the second sub-array C2 due to the phase difference of the first target due to the spacing mD between the array elements
Figure FDA00022631727400000416
The estimated value of the cosine of the y-axis direction of the first target is
Figure FDA00022631727400000417
Wherein
Figure FDA00022631727400000418
The sequence of the sequence numbers of the objects in the sequence table
Figure FDA00022631727400000419
Of the diagonal elements ofThe arrangement sequence is the same;
4c) according to the following rule pair
Figure FDA00022631727400000420
Diagonal elements of and
Figure FDA00022631727400000421
pairing of diagonal elements of (1):
4c1) let the true phase difference of a target at the first sub-array C1 due to the array cell spacing D be Λ1＝2g1π+φ1Wherein phi1Is Λ1The phase difference, g, that can be actually measured1Is Λ1Phi and phi1The number of periodic ambiguities that differ therebetween;
4c2) let us say that the true phase difference of the target at the second sub-array C2 due to the array cell spacing mD is Λ2＝2g2π+φ2，φ2Is Λ2The phase difference, g, that can be actually measured2Is Λ2Phi and phi2The number of periodic ambiguities that differ therebetween;
4c3) obtaining the m lambda according to the m-time relation between the array unit spacing mD of the second subarray C2 and the array unit spacing D of the first subarray C11＝Λ2From which the following equation is derived:
m×(2g1π+φ1)＝2g2π+φ2
the equation is transformed to obtain the following transformed relation:
mφ1＝2π(g2-mg1)+φ2
according to the deformed relation and the property of the exponential function, obtaining the following relation:
Figure FDA0002263172740000051
4c4) according to the relational expression
Figure FDA0002263172740000052
Will be provided with
Figure FDA0002263172740000053
Diagonal line element of
Figure FDA0002263172740000054
Are all made m times, sequentially and
Figure FDA0002263172740000055
diagonal line element of
Figure FDA0002263172740000056
Comparing one by one, selecting the pairing with the minimum difference value to obtain
Figure FDA0002263172740000057
Diagonal elements of and
Figure FDA0002263172740000058
the pairing order of the diagonal elements of (1);
4d) obtained according to 4c)
Figure FDA0002263172740000059
Diagonal elements of and
Figure FDA00022631727400000510
the order of the pairs of diagonal elements, and the cosine estimated values of the two sets of target y-axis directions
Figure FDA00022631727400000511
And
Figure FDA00022631727400000512
and (6) pairing.
4. The method as claimed in claim 1, wherein the signal subspaces Es corresponding to the estimation values are paired according to the pairing order in step 4)1And Es2Matching is carried out according to the following rules:
according to the signal subspace matrix Es1And the rotation invariant factor matrix of the first sub-matrix C1
Figure FDA00022631727400000513
The one-to-one correspondence of the arrangement order of the target sequence numbers in the diagonal elements and the signal subspace matrix Es2And the rotation invariant factor matrix of the second sub-matrix C2
Figure FDA00022631727400000514
The one-to-one correspondence of the arrangement order of the target sequence numbers in the diagonal elements of (1) and the signal subspace matrix Es corresponding to the estimated value1And Es2The array order of the column vectors is according to two groups of target y-axis direction cosine estimated values
Figure FDA00022631727400000515
And
Figure FDA00022631727400000516
the matching sequence of (2) is reordered to realize a signal subspace Es corresponding to the estimated value1And Es2Is matched.
5. The method according to claim 1 or 2, wherein the phase compensation is performed on the steering vectors of the rest of the array units except the reference array unit in the estimated value of the array flow pattern matrix in step 5), and the result of synthesizing the steering vectors of all the electromagnetic vector sensors except the reference array unit onto the steering vector at the reference array unit is obtained according to the following formula:
Figure FDA0002263172740000061
Figure FDA0002263172740000062
wherein, c1And c2Are the complex constants of the difference between the first and second,
Figure FDA0002263172740000063
Figure FDA0002263172740000064
to pass through
Figure FDA0002263172740000065
The calculated estimate of the array flow pattern matrix of the first sub-array C1,
Figure FDA0002263172740000066
to pass through
Figure FDA0002263172740000067
An estimate of the array flow pattern matrix of the second sub-array C2 is calculated.
6. The method of claim 1, wherein said step 6) is performed as follows:
6a) steering vectors for separate electromagnetic vector sensors at a synthesized reference array
Figure FDA0002263172740000068
And
Figure FDA0002263172740000069
respectively making normalized vector cross products of the electric field component and the magnetic field component, including:
Figure FDA00022631727400000610
Figure FDA00022631727400000611
order to
Figure FDA00022631727400000612
As a final cross product of vectors of the separate electromagnetic vector sensors at the reference array unit;
6b) by plThe coarse u, v, w estimation values with low precision and no ambiguity are obtained:
Figure FDA0002263172740000071
wherein | represents an absolute value;
6c) order to
Figure FDA0002263172740000072
To obtain
Figure FDA0002263172740000073
According to
Figure FDA0002263172740000074
Obtaining two groups of high-precision estimated values of the cosine u of the direction of the target along the x axis and with periodical ambiguity
Figure FDA0002263172740000075
And
Figure FDA0002263172740000076
Figure FDA0002263172740000077
Figure FDA0002263172740000078
7. the method of claim 1, wherein said step 7) is performed as follows:
7a) the low-precision and non-fuzzy y-axis direction cosine estimated value
Figure FDA0002263172740000079
As the cosine estimated value in the y-axis direction with high solution precision but periodic ambiguity
Figure FDA00022631727400000710
The first, more accurate and unambiguous, estimate of v
Figure FDA00022631727400000711
The following fuzzy equation gives:
Figure FDA00022631727400000712
wherein the content of the first and second substances,
Figure FDA00022631727400000713
Figure FDA00022631727400000714
which means that the rounding is made up,
Figure FDA00022631727400000715
represents rounding down;
7b) will be provided with
Figure FDA00022631727400000716
As the cosine estimated value in the y-axis direction with higher solution precision but periodic ambiguity
Figure FDA00022631727400000717
The final high-precision and unambiguous estimate of v
Figure FDA00022631727400000718
Derived from the following fuzzy equation：
Figure FDA00022631727400000719
Wherein the content of the first and second substances,
Figure FDA0002263172740000081
7c) the cosine estimated value of the X-axis direction with lower precision but without ambiguity
Figure FDA0002263172740000082
As the cosine estimated value in the x-axis direction with high solution precision but periodic ambiguity
Figure FDA0002263172740000083
The first accurate and unambiguous estimation of u
Figure FDA0002263172740000084
The following fuzzy equation gives:
Figure FDA0002263172740000085
wherein the content of the first and second substances,
Figure FDA0002263172740000086
7d) will be provided with
Figure FDA0002263172740000087
As the cosine estimated value in the x-axis direction with higher solution precision but periodic ambiguity
Figure FDA0002263172740000088
The final high-precision and unambiguous estimation of u
Figure FDA0002263172740000089
Blur from the followingThe equation yields:
Figure FDA00022631727400000810
wherein the content of the first and second substances,
Figure FDA00022631727400000811
8. the method of claim 1, wherein the high precision estimation of the x-axis direction cosine of the target without blur in step 8)
Figure FDA00022631727400000812
And a target y-axis direction cosine high-precision estimated value without ambiguity
Figure FDA00022631727400000813
Performing a trigonometric operation by:
Figure FDA00022631727400000814
Figure FDA00022631727400000815
is the two-dimensional direction-of-arrival estimation information of the ith target, wherein
Figure FDA00022631727400000816
Is an estimate of the azimuth angle of the ith target,
Figure FDA00022631727400000817
is the pitch angle estimate for the ith target.
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