CN110954859A - L-shaped array-based two-dimensional incoherent distributed non-circular signal parameter estimation method - Google Patents

L-shaped array-based two-dimensional incoherent distributed non-circular signal parameter estimation method Download PDF

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CN110954859A
CN110954859A CN201911159873.6A CN201911159873A CN110954859A CN 110954859 A CN110954859 A CN 110954859A CN 201911159873 A CN201911159873 A CN 201911159873A CN 110954859 A CN110954859 A CN 110954859A
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陈华
刘永红
蔡子熠
方嘉雄
章泽昊
蒋依凡
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Ningbo University
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Abstract

A two-dimensional incoherent distributed non-circular signal parameter estimation method based on L-shaped array is to conjugate the incident signal data received by the L-shaped array and the received data to form a new extended data vector; constructing an extended covariance matrix based on the new extended data vector and performing feature decomposition on the constructed extended covariance matrix to obtain a corresponding signal subspace and a corresponding noise subspace; dividing the X axis and the Z axis of the L-shaped array into two different sub-arrays with the same array element number, respectively obtaining signal subspaces corresponding to the two sub-arrays according to the dividing mode of the two sub-arrays of the X axis, and respectively obtaining signal subspaces corresponding to the two sub-arrays of the Z axis according to the dividing mode of the two sub-arrays of the Z axis; and respectively constructing an information source parameter estimator according to the rank loss principle to estimate two central DOAs of the non-relevant distribution sources, and pairing. The method can solve the more complex two-dimensional model condition, reduce the operation amount and improve the estimation precision of the central DOA.

Description

L-shaped array-based two-dimensional incoherent distributed non-circular signal parameter estimation method
Technical Field
The invention relates to a method for estimating a non-circular signal DOA. In particular to a two-dimensional incoherent distributed non-circular signal parameter estimation method based on an L-shaped array.
Background
Spatial spectrum estimation, also known as direction of arrival (DOA) estimation, has been widely used in many fields such as radar, communication, sonar, and the like, and has been rapidly developed in recent ten years. The research of the spatial spectrum estimation theory has been the focus of academic attention, and the classical spatial spectrum estimation theory is mostly based on the point source assumption. The spatial spectrum estimation algorithm based on the point source does not consider the influence of angular spatial diffusion, and the direction-finding performance is obviously reduced when the spatial spectrum estimation algorithm is applied to a distributed source scene. In distributed source modeling, a non-coherent distributed source model is more consistent with an actual wireless communication scenario than a coherent distributed source model. For the incoherent distributed source model, DSPE and DISPARE algorithms are provided based on the MUSIC algorithm, but the algorithms need multidimensional searching to obtain angle estimation, the calculation is complex, and the instantaneity is poor. To reduce complexity, polynomial-based root finding methods and ESPRIT-like algorithms are applied to non-coherent distributed source scenarios. In two-dimensional DOA estimation, an L-shaped array is very popular, its structure is simple, and estimation using various conditions is used. Compared with the one-dimensional DOA estimation, the two-dimensional DOA estimation needs to estimate a plurality of angle parameters of the information source, the calculation amount is increased, and the calculation complexity is increased. However, at present, two-dimensional incoherent distribution source algorithms are few, and most incoherent distribution source algorithms do not consider the non-circular characteristic of the signal, so that the number of separable signals and the accuracy of DOA estimation need to be improved. Therefore, it is essential to research the two-dimensional incoherent source spatial spectrum estimation technology under the non-circular characteristic.
Disclosure of Invention
The invention aims to solve the technical problem of providing a two-dimensional incoherent distributed non-circular signal parameter estimation method based on an L-shaped array, which can reduce the operation amount and effectively improve the DOA estimation performance.
The technical scheme adopted by the invention is as follows: a two-dimensional incoherent distributed non-circular signal parameter estimation method based on L-shaped array is to conjugate the incident signal data received by the L-shaped array and the received data to form a new extended data vector; constructing an extended covariance matrix based on the new extended data vector, and performing feature decomposition on the constructed extended covariance matrix to obtain a corresponding signal subspace and a corresponding noise subspace; dividing the X axis and the Z axis of the L-shaped array into two different sub-arrays with the same array element number, respectively obtaining signal subspaces corresponding to the two sub-arrays according to the dividing mode of the two sub-arrays of the X axis, and respectively obtaining signal subspaces corresponding to the two sub-arrays of the Z axis according to the dividing mode of the two sub-arrays of the Z axis; and finally, respectively constructing an information source parameter estimator according to the rank loss principle to estimate two center DOAs of the uncorrelated distributed sources, and pairing.
Comprises the following steps:
1) establishing an L-shaped array signal model, wherein the modeling process comprises the following steps: receiving a data vector, an extended covariance matrix, and a feature decomposition of the extended covariance matrix;
2) and estimating the DOA of the information source center, including dividing the L-shaped array, dividing the signal subspace, respectively constructing an information source parameter estimator according to the rank loss principle to estimate two DOAs of the uncorrelated distributed sources, and pairing the two DOAs.
The invention discloses a two-dimensional incoherent distributed non-circular signal parameter estimation method based on an L-shaped array, which is characterized in that under the condition of the L-shaped array, the L-shaped array is divided into two overlapped sub-arrays according to different coordinate axes respectively, the generalized ESPRIT theory is applied, the non-circular information of an incoherent distribution source is fully utilized twice to decouple and estimate multidimensional parameters, and then the center DOA of the two-time estimation is matched.
Drawings
Fig. 1 is a scatter distribution diagram of the parameter θ and the parameter β in the present invention.
Detailed Description
The two-dimensional incoherent distributed non-circular signal parameter estimation method based on the L-shaped array according to the present invention is described in detail with reference to the following embodiments and the accompanying drawings.
The invention relates to a two-dimensional incoherent distributed non-circular signal parameter estimation method based on an L-shaped array, which comprises the steps of conjugating incident signal data received by the L-shaped array and the received data to form a new extended data vector; constructing an extended covariance matrix based on the new extended data vector, and performing feature decomposition on the constructed extended covariance matrix to obtain a corresponding signal subspace and a corresponding noise subspace; dividing the X axis and the Z axis of the L-shaped array into two different sub-arrays with the same array element number, respectively obtaining signal subspaces corresponding to the two sub-arrays according to the division mode of the two sub-arrays of the X axis, and respectively obtaining signal subspaces corresponding to the two sub-arrays of the Z axis according to the division mode of the two sub-arrays of the Z axis; and finally, respectively constructing an information source parameter estimator according to the rank loss principle to estimate two center DOAs of the non-relevant distribution source, and pairing. The method specifically comprises the following steps:
1) establishing an L-shaped array signal model, wherein the modeling process comprises the following steps: a received data vector, an extended covariance matrix, and an eigen decomposition of the extended covariance matrix. Wherein,
(1) the received data vector, comprising:
the L-shaped array is an L-shaped array which is positioned on an X-Z plane and consists of an X-axis array and a Z-axis array, the L-shaped array consists of M array elements of the X-axis and N array elements of the Z-axis, the distance between every two adjacent array elements is d, and in order to ensure non-deviation estimation, the d is lambda/2, and the lambda is the wavelength; setting K incoherent distributed non-circular signals s with far-field narrow-band irrelevancek(t) (K ═ 1,2, …, K) at an angle
Figure BDA0002285772170000021
Incident on said L-shaped array; setting the energy of the distributed source in the incoherent distributed source model to be continuously distributed in space, and in practice, an incident signal irradiates the array along a large number of scattering paths, so that the t-time L-shaped array receiving number vector x (t) is expressed as
Figure BDA0002285772170000022
Wherein
Figure RE-GDA0002379993850000023
Is an (M + N-1) multiplied by 1 dimensional array flow pattern vector;
Figure RE-GDA0002379993850000024
and
Figure RE-GDA0002379993850000025
are two angles of incidence corresponding to the l path of the k non-circular signal; gamma rayk,l(t) represents the complex-valued gain of the corresponding incident path; l iskIs the total number of incident paths of the kth non-circular signal; n (t) ═ n1(t),…,nM+N-1(t)]TIs a mean of 0 and a variance of
Figure RE-GDA0002379993850000026
For non-coherent distributed sources, the complex gain γ of the different propagation pathsk,l(t) is not related, i.e. gammak,l(t) is a zero-mean complex variable independently and identically distributed in the time domain, and the incident angle
Figure RE-GDA0002379993850000027
And
Figure RE-GDA0002379993850000028
can be respectively expressed as
Figure BDA0002285772170000029
Figure BDA0002285772170000031
Wherein, thetakAnd βkAre the two center DOAs of the kth non-circular signal;
Figure BDA0002285772170000032
and
Figure BDA0002285772170000033
is the angle deviation corresponding to two center DOAs of the kth non-circular signal, and is set
Figure BDA0002285772170000034
And
Figure BDA0002285772170000035
respectively obey mean value of 0 and variance of
Figure BDA0002285772170000036
A sum mean of 0 and a variance of
Figure BDA0002285772170000037
The distribution of the gaussian component of (a) is,
Figure BDA0002285772170000038
and
Figure BDA0002285772170000039
is an angular expansion; expanding by adopting an angle of 0-10 degrees; namely, it is
Figure BDA00022857721700000310
And
Figure BDA00022857721700000311
the value is small, and the DOAs of different incident paths corresponding to the same non-circular signal are relatively close to each other.
According to the angle of incidence
Figure BDA00022857721700000312
And
Figure BDA00022857721700000313
the expression (2) is that under the condition of 0-10 angle expansion, the flow pattern vectors are arrayed
Figure BDA00022857721700000314
Is first order Taylor expansion of
Figure BDA00022857721700000315
Wherein,
Figure BDA00022857721700000316
is a (theta)k,βk) To thetakThe partial derivative of (a) of (b),
Figure BDA00022857721700000317
is a (theta)k,βk) Pair βkThe received data vector x (t) is then re-expressed as:
Figure BDA00022857721700000318
wherein:
Figure BDA00022857721700000319
the formula (5) is rewritten as follows
x(t)≈B(θ,β)g(t)+n(t) (7)
Wherein
B(θ,β)＝[A(θ1,β1),A(θ2,β2),…,A(θK,βK)]∈C(M+N-1)×3K(8)
A(θk,βk)＝[a(θk,βk),a′θ(θk,βk),a′β(θk,βk)]∈C(M+N-1)×3(9)
Figure BDA00022857721700000320
gk＝[υk,0(t),υk,1(t),υk,2(t)]∈C3×1(11)
B (theta, β) is a generalized array flow pattern matrix and is related only to the center DOA for obtaining a decoupled estimate of the center DOA, g (t) is a signal vector, and n (t) is a noise vector.
The received signal is a strictly non-circular signal with a non-circular rate of 1, so the signal vector g (t) is rewritten to
g(t)＝Φg0(t) (12)
Wherein, g0(t)∈C3K×1Is a real-valued signal vector;
Figure BDA00022857721700000321
is a diagonal matrix of 3K × 3K dimensions, with the diagonal element ω ═ ω1,ω′θ,1,ω′β,1,…,ωK,ω′θ,K,…,ω′β,K]TNon-circular phase information is included;
(2) the extended data vector comprises:
using the non-circular characteristic of the signal to combine the received data vector x (t) of the uniform linear array with the conjugate x of the received data vector x (t)*(t) forming a new spread data vector y (t):
Figure BDA0002285772170000041
wherein
Figure BDA0002285772170000042
Is an extended generalized flow pattern matrix;
Figure BDA0002285772170000043
is the spread noise vector.
(3) The extended covariance matrix R is:
Figure BDA0002285772170000044
wherein Λ ═ E { g (t) gH(t) is the covariance of the signal vector g (t).
(4) The eigen decomposition of the extended covariance matrix is to perform eigen decomposition on the extended covariance matrix R to divide a subspace, that is, the extended covariance matrix R is obtained by dividing the subspace
Figure BDA0002285772170000045
Wherein, the matrix U of 2(M + N-1) multiplied by 2KsAnd 2(M + N-1) × [2(M + N-1) -2K]Matrix U ofnRespectively a signal subspace and a noise subspace; matrix Λ of 2Ks＝diag{λ1,…,λ2KAnd [2(M + N-1) -2K]×[2(M+N-1)-2K]Of (2) matrix
Figure BDA0002285772170000046
Is a diagonal matrix of the angles,
Figure BDA0002285772170000047
representing eigenvalues of the extended covariance matrix R.
2) And estimating the DOA of the information source center, including dividing the L-shaped array, dividing the signal subspace, respectively constructing an information source parameter estimator according to the rank loss principle to estimate two DOAs of the uncorrelated distributed sources, and pairing the two DOAs. Wherein,
(1) the division of the L-shaped array divides the X axis and the Z axis of the L-shaped array into two sub-arrays with the same array element number for realizing two central DOA estimation, and in order to ensure the optimal estimation accuracy, the array element number of each sub-array of the X axis is M1The number of array elements of each subarray on the Z-axis is N1N-1, and the four sub-arrays respectively contain coordinate values of { x }1,…,xM-1}，{x2,…,xM}，{z1,…,zN-1And { z }2,…,zN}. For convenience of presentation, let us order
Figure BDA0002285772170000048
And
Figure BDA0002285772170000049
showing the positions of two subarray elements on the X-axis,
Figure BDA00022857721700000410
and
Figure BDA00022857721700000411
indicating the position of two sub-array elements of the Z-axis, and x1,m＜x2,m,m＝1,…,M1，z1,n＜z2,n,n＝1,…,N1。
Define the following selection matrix
J1＝[0(M-1)×(N-1)IM-10(M-1)×1]∈C(M-1)×(M+N-1)(17)
J2＝[0(M-1)×(N-1)0(M-1)×1IM-1]∈C(M-1)×(M+N-1)(18)
J3＝[0(N-1)×1IN-10(N-1)×(M-1)]∈C(N-1)×(M+N-1)(19)
J4＝[IN-10(N-1)×10(N-1)×(M-1)]∈C(N-1)×(M+N-1)(20)
From equations (8), (9) and (14), we can obtain:
Figure BDA0002285772170000051
Figure BDA0002285772170000052
Figure BDA0002285772170000053
wherein,
Figure BDA0002285772170000054
Figure BDA0002285772170000055
Figure BDA0002285772170000056
Figure BDA0002285772170000057
Figure BDA0002285772170000058
Ω′β,k＝02(M-1)×2(M-1)(29)
Figure BDA0002285772170000059
a*(θk,βk)，
Figure BDA00022857721700000510
and
Figure BDA00022857721700000511
are respectively a (theta)k,βk)，a′θ(θk,βk) And a'β(θk,βk) Conjugation of (A) to (B), K1＝blkdiag{J1,J1}， K2＝blkdiag{J2,J2According to formulae (21), (22) and (23), giving:
Figure BDA00022857721700000512
Figure BDA00022857721700000513
(2) the division of the signal subspace is determined by a subspace theory and a signal subspace UsExpanded column space and expanded wide-sense flow pattern matrix
Figure BDA00022857721700000514
The column spaces spanned are identical, i.e.
Figure BDA00022857721700000515
Wherein T is a reversible 2 Kx 2K dimensional matrix, and the signal subspace U is divided according to the X axis subarraysFor two signal subspaces U relating to theta only1And U2，U1,U2∈C2(M-1)×2KWherein:
Figure BDA00022857721700000516
Figure BDA0002285772170000061
similarly, dividing the signal subspace U according to the Z-axis subarraysFor two signal subspaces U associated only with β3And U4， U3,U4∈C2(N-1)×2KWherein:
Figure BDA0002285772170000062
Figure BDA0002285772170000063
wherein K3＝blkdiag{J3,J3}，K2＝blkdiag{J3,J3}。
(3) Respectively constructing a source parameter estimator according to a rank loss principle to estimate two center DOAs of an uncorrelated distributed source, wherein the method comprises the following steps:
defining the matrix Ψ (θ) to be
Ψ(θ)＝blkdiag{ejψIM-1,e-jψIM-1} (37)
Where ψ is 2 π dcos θ/λ. Structure D (θ) is
Figure BDA0002285772170000064
Wherein,
Figure BDA0002285772170000065
according to the formula (31), Q (θ) can be rewritten as
Figure BDA0002285772170000066
According to the formula (39), when θ ═ θkMiddle (omega) of Q (theta)k- Ψ (θ)) becomes zero in the (2k-1) th column, thus if θ ═ θ ·kD (theta) yields a rank deficiency, DHThe determinant of (theta) D (theta) becomes zero, so that the estimated value of the non-circular signal center DOA
Figure BDA0002285772170000067
Obtained by searching the maximum K peaks of the following formula:
Figure BDA0002285772170000068
similarly, the matrix Ψ (β) is defined as
Ψ(β)＝blkdiag{ejψIN-1,e-jψIN-1} (41)
Wherein ψ 2 π dcos β/λ configuration D (β) is
Figure BDA0002285772170000069
Wherein,
Figure BDA00022857721700000610
a similar Q (β) can be rewritten as
Figure BDA00022857721700000611
Wherein
Figure BDA0002285772170000071
Θ′θ,k＝02(N-1)×2(N-1)(45)
Figure BDA0002285772170000072
As shown in formula (43), when β is βkIn (Θ) of Q (β)k- Ψ (β)) will become zero at column (2k-1), thus, if β ═ βkD (β) will yield a rank deficiency, DH(β) the determinant of D (β) will become zero, so the estimated value of the noncircular signal center angle β
Figure BDA0002285772170000073
This can be obtained by searching for the maximum K peaks of the following formula:
Figure BDA0002285772170000074
(4) the pairing of the two central DOAs comprises:
in the case of a single source,
Figure BDA0002285772170000075
and
Figure BDA0002285772170000076
obtained by equations (40) and (47), respectively, however, when there are a plurality of incident sources, since the estimation of the central angle theta and the central angle β is performed independently,
Figure BDA0002285772170000077
and
Figure BDA0002285772170000078
not necessarily in a one-to-one correspondence, and thus need not be paired
Figure BDA0002285772170000079
And
Figure BDA00022857721700000710
performing pairing treatment on
Figure BDA00022857721700000711
And
Figure BDA00022857721700000712
and (3) bringing the two-dimensional MUSIC spatial spectrum into, completing pairing by calculating the minimum value of the denominator, and performing pairing processing by adopting the following formula:
Figure BDA00022857721700000713
wherein E isnA noise subspace representing a covariance matrix of the data vector x (t) | | · | | | luminance2Representing a two-norm.
The invention discloses a two-dimensional incoherent distributed non-circular signal parameter estimation method based on an L-shaped array, which considers that the actual received data vector is finite-length, namely the maximum likelihood estimation of an extended covariance matrix is as follows:
Figure BDA00022857721700000714
to pair
Figure BDA00022857721700000715
The characteristic decomposition of (a) is expressed as:
Figure BDA00022857721700000716
wherein,
Figure BDA00022857721700000717
and
Figure BDA00022857721700000718
maximum likelihood estimation of extended covariance matrix
Figure BDA00022857721700000719
Signal subspace and noise subspace, diagonal matrix
Figure BDA00022857721700000720
And
Figure BDA00022857721700000721
maximum likelihood estimation of extended covariance matrix
Figure BDA00022857721700000722
The signal subspace and the noise subspace.
The embodiment of the L-shaped array-based two-dimensional incoherent distributed non-circular signal parameter estimation method considers the L-shaped array, the distance between adjacent array elements is half wavelength, and a snapshot number of 1000 is adopted to a covariance matrix
Figure RE-GDA00023799938500000723
And (6) estimating. Assuming that the X-axis array element of the L-type array is M-8, the Z-axis array element is N-8, and the variance of the path gain of each source
Figure RE-GDA00023799938500000724
Propagation path for each source
Figure RE-GDA00023799938500000725
Under the condition of Gaussian white noise, four incoherent distributed non-circular signals with irrelevant far-field narrow bands arrive at the array, and the centers DOA are respectively (theta)1,β1)＝(50°,85°)，(θ2,β2)＝(75°,60°)，(θ3,β3) Equal to (90 °,70 °) and (θ)4,β4) The angular spread is all 0.1 °, and the non-circular phase is (90 °,60 °,30 °,22.5 °) (65 °,95 °). At a signal-to-noise ratio of 20dB, a parameter theta of the proposed algorithm is givenkAnd βkThe scattering distribution chart of (2) shows the results in FIG. 1. As can be seen from fig. 1, the two central DOAs can be accurately resolved.

Claims (10)

1. A two-dimensional incoherent distributed non-circular signal parameter estimation method based on L-shaped array is characterized in that incident signal data received by the L-shaped array and the received data are conjugated to form a new extended data vector; constructing an extended covariance matrix based on the new extended data vector, and performing feature decomposition on the constructed extended covariance matrix to obtain a corresponding signal subspace and a corresponding noise subspace; dividing the X axis and the Z axis of the L-shaped array into two different sub-arrays with the same array element number, respectively obtaining signal subspaces corresponding to the two sub-arrays according to the dividing mode of the two sub-arrays of the X axis, and respectively obtaining signal subspaces corresponding to the two sub-arrays of the Z axis according to the dividing mode of the two sub-arrays of the Z axis; and finally, respectively constructing an information source parameter estimator according to the rank loss principle to estimate two center DOAs of the non-relevant distribution source, and pairing.
2. The L-shaped array based two-dimensional incoherent distributed non-circular signal parameter estimation method according to claim 1, characterized by comprising the following steps:
1) establishing an L-shaped array signal model, wherein the modeling process comprises the following steps: receiving a data vector, an extended covariance matrix, and a feature decomposition of the extended covariance matrix;
2) and estimating the DOA of the information source center, including dividing the L-shaped array, dividing the signal subspace, respectively constructing an information source parameter estimator according to the rank loss principle to estimate two DOAs of the uncorrelated distributed sources, and pairing the two DOAs.
3. The method of claim 2, wherein the receiving the data vector in step 1) comprises:
the L-shaped array is positioned on an X-Z plane and consists of an X-axis array and a Z-axis array, the L-shaped array consists of M array elements of the X axis and N array elements of the Z axis, the distance between every two adjacent array elements is d, and in order to ensure non-deviation estimation, the d is lambda/2, and the lambda is the wavelength; setting K incoherent distributed non-circular signals s with far-field narrow-band irrelevancek(t), K is 1,2, …, K, at an angle
Figure FDA0002285772160000011
Incident on said L-shaped array; setting the energy of the distributed source in the incoherent distributed source model to be continuously distributed in space, and in practice, incident signals irradiate the array along a large number of scattering paths, so that t time L-shaped array received data vector x (t) is expressed as
Figure FDA0002285772160000012
Wherein
Figure FDA0002285772160000013
Is an (M + N-1) multiplied by 1 dimensional array flow pattern vector;
Figure FDA0002285772160000014
and
Figure FDA0002285772160000015
are two angles of incidence corresponding to the l path of the k non-circular signal; gamma rayk,l(t) represents the complex-valued gain of the corresponding incident path; l iskIs the total number of incident paths of the kth non-circular signal; n (t) ═ n1(t),…,nM+N-1(t)]TIs a mean of 0 and a variance of
Figure FDA0002285772160000016
For non-coherent distributed sources, the complex gain γ of the different propagation pathsk,l(t) is not related, i.e. gammak,l(t) is a zero-mean complex variable independently and identically distributed in the time domain,
angle of incidence
Figure FDA0002285772160000017
And
Figure FDA0002285772160000018
are respectively represented as
Figure FDA0002285772160000019
Figure FDA0002285772160000021
Wherein, thetakAnd βkAre the two center DOAs of the kth non-circular signal;
Figure FDA0002285772160000022
and
Figure FDA0002285772160000023
is the angle deviation corresponding to two center DOAs of the kth non-circular signal, and is set
Figure FDA0002285772160000024
And
Figure FDA0002285772160000025
respectively obey mean value of 0 and variance of
Figure FDA0002285772160000026
A sum mean of 0 and a variance of
Figure FDA0002285772160000027
The distribution of the gaussian component of (a) is,
Figure FDA0002285772160000028
and
Figure FDA0002285772160000029
for angular expansion, use is made of an angular expansion of 0-10, i.e.
Figure FDA00022857721600000210
And
Figure FDA00022857721600000211
the more value is takenSmall, the closer the DOA values of different incident paths corresponding to the same non-circular signal are;
according to the angle of incidence
Figure FDA00022857721600000212
And
Figure FDA00022857721600000213
the expression (2) is that under the condition of 0-10 angle expansion, the flow pattern vectors are arrayed
Figure FDA00022857721600000214
Is first order Taylor expansion of
Figure FDA00022857721600000215
Wherein,
Figure FDA00022857721600000216
is a (theta)k,βk) To thetakThe partial derivative of (a) of (b),
Figure FDA00022857721600000217
is a (theta)k,βk) Pair βkThe received data vector x (t) is then re-expressed as:
Figure FDA00022857721600000218
wherein:
Figure FDA00022857721600000219
the formula (5) is rewritten as follows
x(t)≈B(θ,β)g(t)+n(t) (7)
Wherein
B(θ,β)＝[A(θ1,β1),A(θ2,β2),…,A(θK,βK)]∈C(M+N-1)×3K(8)
A(θk,βk)＝[a(θk,βk),a′θ(θk,βk),a′β(θk,βk)]∈C(M+N-1)×3(9)
Figure FDA00022857721600000220
gk＝[υk,0(t),υk,1(t),υk,2(t)]∈C3×1(11)
B (theta, β) is a generalized array flow pattern matrix and is related only to the center DOA for obtaining a decoupled estimate of the center DOA, (g (t) is a signal vector, n (t) is a noise vector;
the received signal is a strictly non-circular signal with a non-circular rate of 1, so the signal vector g (t) is rewritten to
g(t)＝Φg0(t) (12)
Wherein, g0(t)∈C3K×1Is a real-valued signal vector;
Figure FDA00022857721600000221
is a diagonal matrix of 3K × 3K dimensions, with the diagonal element ω ═ ω1,ω′θ,1,ω′β,1,…,ωK,ω′θ,K,…,ω′β,K]TIncluding non-circular phase information.
4. The method according to claim 2, wherein the expanding the data vector in step 1) comprises:
using the non-circular characteristic of the signal to combine the received data vector x (t) of the uniform linear array with the conjugate x of the received data vector x (t)*(t) forming a new spread data vector y (t):
Figure FDA0002285772160000031
wherein
Figure FDA0002285772160000032
To expand generalized flow matrix;
Figure FDA0002285772160000033
is the spread noise vector.
5. The method according to claim 2, wherein the extended covariance matrix R in step 1) is:
Figure FDA0002285772160000034
wherein Λ ═ E { g (t) gH(t) is the covariance of the signal vector g (t).
6. The method of claim 2, wherein the eigen decomposition of the extended covariance matrix in step 1) is to perform eigen decomposition on the extended covariance matrix R to divide a subspace, i.e. the L-shaped array based two-dimensional incoherent distributed non-circular signal parameter estimation method
Figure RE-FDA0002379993840000035
Wherein, the matrix U of 2(M + N-1) multiplied by 2KsAnd 2(M + N-1) × [2(M + N-1) -2K]Matrix U ofnRespectively a signal subspace and a noise subspace; 2 Kx 2K matrix Σs＝diag{λ1,…,λ2KAnd [2(M + N-1) -2K]×[2(M+N-1)-2K]Matrix Σ ofn＝diag{λ2K+1,…,λ2(M+N-1)Is a diagonal matrix and is,
Figure RE-FDA0002379993840000036
representing eigenvalues of the extended covariance matrix R.
7. The method as claimed in claim 2, wherein the dividing of the L-shaped array in step 2) divides the X-axis and the Z-axis of the L-shaped array into two sub-arrays with the same number of elements to realize two central DOA estimation, and the number of elements in each sub-array of the X-axis is set to M to ensure the best estimation accuracy1The number of array elements of each subarray on the Z-axis is N1N-1, and the four sub-arrays respectively contain coordinate values of { x }1,…,xM-1}，{x2,…,xM}，{z1,…,zN-1And { z }2,…,zN}; for convenience of representation, let
Figure FDA0002285772160000037
And
Figure FDA0002285772160000038
showing the positions of two subarray elements on the X-axis,
Figure FDA0002285772160000039
and
Figure FDA00022857721600000310
indicating the position of two sub-array elements of the Z-axis, and x1,m＜x2,m,m＝1,…,M1，z1,n＜z2,n,n＝1,…,N1；
Define the following selection matrix
J1＝[0(M-1)×(N-1)IM-10(M-1)×1]∈C(M-1)×(M+N-1)(17)
J2＝[0(M-1)×(N-1)0(M-1)×1IM-1]∈C(M-1)×(M+N-1)(18)
J3＝[0(N-1)×1IN-10(N-1)×(M-1)]∈C(N-1)×(M+N-1)(19)
J4＝[IN-10(N-1)×10(N-1)×(M-1)]∈C(N-1)×(M+N-1)(20)
From equations (8), (9) and (14), we can obtain:
Figure FDA0002285772160000041
Figure FDA0002285772160000042
Figure FDA0002285772160000043
wherein,
Figure FDA0002285772160000044
Figure FDA0002285772160000045
Figure FDA0002285772160000046
Figure FDA0002285772160000047
Figure FDA0002285772160000048
Ω′β,k＝02(M-1)×2(M-1)(29)
Figure FDA0002285772160000049
a*(θk,βk)，
Figure FDA00022857721600000410
and
Figure FDA00022857721600000411
are respectively a (theta)k,βk)，a′θ(θk,βk) And a'β(θk,βk) Conjugation of (A) to (B), K1＝blkdiag{J1,J1}，K2＝blkdiag{J2,J2According to formulae (21), (22) and (23), giving:
Figure FDA00022857721600000412
Figure FDA00022857721600000413
8. the L-shaped array based two-dimensional incoherent distributed non-circular signal parameter estimation method according to claim 2, wherein the signal subspace is divided in the step 2) according to subspace theory and signal subspace UsExpanded column space and extended generalized flow pattern matrix
Figure FDA0002285772160000051
The column spaces spanned are identical, i.e.
Figure FDA0002285772160000052
Wherein T is a reversible 2 Kx 2K dimensional matrix, and the signal subspace U is divided according to the X axis subarraysFor two signal subspaces U relating to theta only1And U2，U1,U2∈C2(M-1)×2KWherein:
Figure FDA0002285772160000053
Figure FDA0002285772160000054
similarly, dividing the signal subspace U according to the Z-axis subarraysFor two signal subspaces U associated only with β3And U4，U3,U4∈C2(N-1)×2KWherein:
Figure FDA0002285772160000055
Figure FDA0002285772160000056
wherein K3＝blkdiag{J3,J3}，K2＝blkdiag{J3,J3}。
9. The method as claimed in claim 2, wherein the step 2) of constructing a source parameter estimator according to the rank loss principle to estimate two central DOAs of the uncorrelated distributed sources comprises:
defining the matrix Ψ (θ) to be
Ψ(θ)＝blkdiag{ejψIM-1,e-jψIM-1} (37)
Wherein ψ is 2 π dcos θ/λ; structure D (θ) is
Figure FDA0002285772160000057
Wherein,
Figure FDA0002285772160000058
according to the formula (31), Q (theta) is rewritten as
Figure FDA0002285772160000059
According to the formula (39), when θ ═ θkMiddle (omega) of Q (theta)k- Ψ (θ)) becomes zero in the (2k-1) th column, thus if θ ═ θ ·kD (theta) yields a rank deficiency, DHThe determinant of (theta) D (theta) becomes zero, so that the estimated value of the non-circular signal center DOA
Figure FDA00022857721600000510
Obtained by searching the maximum K peaks of the following formula:
Figure FDA00022857721600000511
similarly, the matrix Ψ (β) is defined as
Ψ(β)＝blkdiag{ejψIN-1,e-jψIN-1} (41)
Wherein ψ 2 π dcos β/λ configuration D (β) is
Figure FDA0002285772160000061
Wherein,
Figure FDA0002285772160000062
a similar Q (β) can be rewritten as
Figure FDA0002285772160000063
Wherein
Figure FDA0002285772160000064
Θ′θ,k＝02(N-1)×2(N-1)(45)
Figure FDA0002285772160000065
As shown in formula (43), when β is βkIn (Θ) of Q (β)k- Ψ (β)) becomes zero at column (2k-1), thus, if β ═ βkD (β) will yield a rank deficiency, DH(β) since the determinant of D (β) becomes zero, the estimated value of the noncircular signal center angle β
Figure FDA0002285772160000066
Obtained by searching the maximum K peaks of the following formula:
Figure FDA0002285772160000067
10. the method for estimating parameters of two-dimensional incoherent distributed non-circular signals based on L-shaped array as claimed in claim 2, wherein said pairing two central DOAs in step 2) comprises:
in the case of a single source,
Figure FDA0002285772160000068
and
Figure FDA0002285772160000069
obtained by equations (40) and (47), respectively, however, when there are a plurality of incident sources, since the estimation of the central angle theta and the central angle β is performed independently,
Figure FDA00022857721600000610
and
Figure FDA00022857721600000611
not necessarily in a one-to-one correspondence, and thus need not be paired
Figure FDA00022857721600000612
And
Figure FDA00022857721600000613
performing pairing treatment on
Figure FDA00022857721600000614
And
Figure FDA00022857721600000615
and (3) bringing the two-dimensional MUSIC spatial spectrum into, completing pairing by calculating the minimum value of the denominator, and performing pairing processing by adopting the following formula:
Figure FDA00022857721600000616
wherein E isnA noise subspace representing a covariance matrix of the received data vector x (t) | | · | | luminance2Representing a two-norm.
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Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112327244A (en) * 2020-10-22 2021-02-05 中国电子科技集团公司第五十四研究所 L-shaped array-based two-dimensional incoherent distributed target parameter estimation method
CN113238184A (en) * 2021-05-17 2021-08-10 宁波大学 Two-dimensional DOA estimation method based on non-circular signals
CN113341371A (en) * 2021-05-31 2021-09-03 电子科技大学 DOA estimation method based on L array and two-dimensional ESPRIT algorithm
CN113376568A (en) * 2021-05-14 2021-09-10 南京航空航天大学 Circular array DOA estimation method based on subspace orthogonal compensation
CN113378103A (en) * 2021-06-02 2021-09-10 哈尔滨工程大学 Dynamic tracking method for coherent distribution source under strong impact noise

Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20070155192A1 (en) * 2005-12-16 2007-07-05 Shiann Shiun Jeng Module and method for estimating signal direction of arrival
US20110050500A1 (en) * 2009-09-01 2011-03-03 Fujitsu Limited Method of estimating direction of arrival and apparatus thereof
CN103954931A (en) * 2014-04-28 2014-07-30 西安交通大学 Method for locating far field and near field mixed signal sources
CN106842115A (en) * 2017-01-25 2017-06-13 天津大学 The two-dimentional direction-finding method of principle is damaged based on ROOT MUSIC algorithms and order
CN107167763A (en) * 2017-04-21 2017-09-15 天津大学 Far and near field mixed signal Wave arrival direction estimating method based on not rounded characteristic
CN109407047A (en) * 2018-09-19 2019-03-01 江苏大学 A kind of amplitude phase error calibration and Wave arrival direction estimating method based on order damage rooting
JP2019090749A (en) * 2017-11-16 2019-06-13 富士通株式会社 Arrival direction estimating device and arrival direction estimating method

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20070155192A1 (en) * 2005-12-16 2007-07-05 Shiann Shiun Jeng Module and method for estimating signal direction of arrival
US20110050500A1 (en) * 2009-09-01 2011-03-03 Fujitsu Limited Method of estimating direction of arrival and apparatus thereof
CN103954931A (en) * 2014-04-28 2014-07-30 西安交通大学 Method for locating far field and near field mixed signal sources
CN106842115A (en) * 2017-01-25 2017-06-13 天津大学 The two-dimentional direction-finding method of principle is damaged based on ROOT MUSIC algorithms and order
CN107167763A (en) * 2017-04-21 2017-09-15 天津大学 Far and near field mixed signal Wave arrival direction estimating method based on not rounded characteristic
JP2019090749A (en) * 2017-11-16 2019-06-13 富士通株式会社 Arrival direction estimating device and arrival direction estimating method
CN109407047A (en) * 2018-09-19 2019-03-01 江苏大学 A kind of amplitude phase error calibration and Wave arrival direction estimating method based on order damage rooting

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
NIZAR TAYEM等: ""Two-Dimensional DOA Estimation Using Cross-Correlation Matrix With L-Shaped Array"", 《IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS》 *
陈华: "窄带阵列信号的二维测向技术研究", 《中国博士学位论文全文数据库信息科技辑》 *

Cited By (10)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112327244A (en) * 2020-10-22 2021-02-05 中国电子科技集团公司第五十四研究所 L-shaped array-based two-dimensional incoherent distributed target parameter estimation method
CN112327244B (en) * 2020-10-22 2022-06-24 中国电子科技集团公司第五十四研究所 L-shaped array-based two-dimensional incoherent distributed target parameter estimation method
CN113376568A (en) * 2021-05-14 2021-09-10 南京航空航天大学 Circular array DOA estimation method based on subspace orthogonal compensation
CN113376568B (en) * 2021-05-14 2023-12-29 南京航空航天大学 Circular array DOA estimation method based on subspace orthogonal compensation
CN113238184A (en) * 2021-05-17 2021-08-10 宁波大学 Two-dimensional DOA estimation method based on non-circular signals
CN113238184B (en) * 2021-05-17 2023-10-13 宁波大学 Two-dimensional DOA estimation method based on non-circular signal
CN113341371A (en) * 2021-05-31 2021-09-03 电子科技大学 DOA estimation method based on L array and two-dimensional ESPRIT algorithm
CN113341371B (en) * 2021-05-31 2022-03-08 电子科技大学 DOA estimation method based on L array and two-dimensional ESPRIT algorithm
CN113378103A (en) * 2021-06-02 2021-09-10 哈尔滨工程大学 Dynamic tracking method for coherent distribution source under strong impact noise
CN113378103B (en) * 2021-06-02 2023-05-05 哈尔滨工程大学 Dynamic tracking method for coherent distribution source under strong impulse noise

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