CN114114139A - DOA and mutual coupling joint estimation method based on nulling constraint - Google Patents

DOA and mutual coupling joint estimation method based on nulling constraint Download PDF

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CN114114139A
CN114114139A CN202111172456.2A CN202111172456A CN114114139A CN 114114139 A CN114114139 A CN 114114139A CN 202111172456 A CN202111172456 A CN 202111172456A CN 114114139 A CN114114139 A CN 114114139A
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mutual coupling
matrix
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doa
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潘玉剑
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Hangzhou Dianzi University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
    • G01S3/14—Systems for determining direction or deviation from predetermined direction

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Abstract

The invention discloses a combined estimation method of DOA and mutual coupling based on nulling constraint, which is particularly used for improving and improving DOA estimation performance when array element mutual coupling exists and simultaneously providing estimation of mutual coupling. The existing method needs prior information of mutual coupling degree, and performance is reduced when the estimated mutual coupling degree is larger than the real mutual coupling degree. The method firstly carries out array arrangement and modeling of received signals in the presence of mutual coupling, then carries out dimension compression based on singular value decomposition, establishes an optimization problem based on zero constraint, solves the optimization problem of zero constraint by adopting an iteration method, and finally carries out DOA and mutual coupling estimation. The method can utilize all array data, and has no aperture loss; prior information of the mutual coupling degree can be omitted, and even if the mutual coupling degree is over-estimated, the performance is not influenced obviously. The method improves the DOA and the mutual coupling estimation precision.

Description

DOA and mutual coupling joint estimation method based on nulling constraint
Technical Field
The invention belongs to the technical field of information, particularly relates to the technical field of array signal processing, particularly relates to array signal processing under the condition of array element mutual coupling, and particularly relates to a DOA and mutual coupling joint estimation method based on nulling constraint.
Background
DOA (direction of arrival positioning technology) is an intra-industry term in the research fields of electronics, communications, radar, sonar, and the like, and acquires distance information and orientation information of a target by processing received echo signals. DOA estimation belongs to an array signal processing technology, is used for estimating the direction of arrival of signals by using a sensor array, and is widely applied to the military and civil technical fields of radar, communication, sonar, medical diagnosis and the like. DOA estimation methods based on parametric modeling are more favored because of their high resolution. However, the performance of such methods is susceptible to array imperfections such as array element amplitude and phase errors, array element cross-coupling, etc. Array element mutual coupling is caused by wave propagation characteristics and is difficult to avoid. Therefore, there is a great deal of interest in studying how to correct mutual coupling.
To correct for mutual coupling, publication 1(z.ye and c.liu, "On the responsiveness of MUSIC direction sizing anti-sensitivity sensor coupling," IEEE transactions On anti-natures and amplification, vol.56, No.2, pp.371-380,2008) removes the array elements at both ends of the array to equivalently eliminate the effect of mutual coupling, and estimates DOA using only the middle subarray. The disadvantage of this method is that the array is not fully utilized and there is a loss of aperture. Publication 2(f. Sellone and A. Serra, "A novel connecting mutual coupling compensation for uniform and linear arrays," IEEE Transactions on signal processing, vol.55, No.2, pp.560-573,2007) corrects mutual coupling using an iterative calculation method with alternately minimizing a cost function. The method has the defect that the corrected spatial spectrum is easy to have false peaks, and the DOA estimation performance is influenced. In addition, the methods of both the publication 1 and the publication 2 require prior information of the mutual coupling degree, and when the estimated mutual coupling degree is larger than the true mutual coupling degree, the performance of both the methods is degraded.
Disclosure of Invention
The present invention aims to provide a joint estimation method of DOA and mutual coupling based on nulling constraint, aiming at the above-mentioned deficiencies of the prior art.
The method comprises the following steps:
step (1), modeling of received signals when array arrangement and mutual coupling exist:
arranging uniform linear arrays, wherein the number of array elements is M, and the distance between adjacent array elements is d; k wavelengths are λ from θ1,θ2,…,θKNarrow-band signals in the direction are incident to the uniform linear array and receive N snapshots, and modeling is carried out on a plurality of pieces of snapshot receiving data: Y-CAS + E, Y-Y [ Y1]，y[2]，…，y[N]]The signal matrix S ═ S [1 ]]，s[2]，…，s[N]]The noise matrix E ═ epsilon [1 ═ n]，ε[2]，…，ε[N]]C is a mutual coupling matrix, and C is Toeplitz ([1, C)1,c2,…,cP,0,…,0]) Toeplitz (. circle.) denotes the generation of a Toeplitz matrix, c1,c2,…,cPP represents the mutual coupling degree as a mutual coupling parameter;
wherein, the received data of the array at the nth snapshot is modeled as:
Figure BDA0003293889140000021
n is 1,2, …, N; wherein,
Figure BDA0003293889140000022
representing a complex set, flow pattern matrix A ═ a (θ)1),a(θ2),…,a(θK)]，a(θ1),a(θ2),…,a(θK) Representing a steering vector, the kth narrowband signal steering vector a (θ)k) The m-th element of (a)m(θk)＝exp[j(m-1)uk]，k＝1,2,…,K，m＝1,2,…,M，
Figure BDA0003293889140000023
uk＝2πd cos(θk)/λ；s[n]Is a signal vector of ε [ n ]]Is a noise vector.
Step (2) dimension compression is carried out based on singular value decomposition:
performing singular value decomposition on Y, and performing dimensionality compression on Y to obtain Y
Figure BDA0003293889140000024
VsA matrix is represented which is composed of right singular vectors corresponding to K maximum singular values of Y.
Step (3) establishing an optimization problem based on the nulling constraint:
the optimization problem is represented as:
Figure BDA0003293889140000025
wherein | · | purple sweet2Denotes a 2 norm, vectorization of Z ═ vec (Z) ·, vec () denotes stacking vectorization of matrices by columns, IKWhich represents an identity matrix of order K,
Figure BDA0003293889140000026
denotes the Kronecker product, the mutual coupling matrix C ═ Toeplitz ([1, C)T,0,...,0]) The mutual coupling vector c ═ c1,c2,...,cP′]TP' represents an estimated value of the mutual coupling, an auxiliary parameter
Figure BDA0003293889140000027
ηkA vector of M (K-1) to Mk elements, K being 1,2T,γT,hT]T(ii) a Multi-block shooting matrix
Figure BDA0003293889140000028
Figure BDA0003293889140000029
To construct the operators of the Toeplitz matrix,
Figure BDA00032938891400000210
is eta, is the ith row and the jth column element ofnI-j + K +1 th element of (M-K), i-1, 2, …, (M-K), j-1, 2, …, (K +1), a nulling filter
Figure BDA00032938891400000211
Omega is a constant vector; s.t. represents a constraint, (.)H、(·)TRespectively representing taking a conjugate transpose and transpose.
And (4) solving an optimization problem of the nulling constraint by adopting an iterative method:
first of all, initializing
Figure BDA00032938891400000212
Wherein c is0＝0P′，0P′Zero vector representing P' × 1, initial value γ of γ0And an initial value h of h0Obtaining by assuming no mutual coupling of the arrays and performing TLS-ESTTRIT-like method on Z; then iterative computation is carried out, and upsilon is obtained in the process of q +1 iterationq+1＝υq+ Δ upsilon, q ≧ 0, wherein
Figure BDA0003293889140000031
For the result obtained by the q iteration calculation, Delta upsilon is a search vectorThe method is obtained by solving the following linear quadratic optimization problem:
Figure BDA0003293889140000032
wherein, f vector
Figure BDA0003293889140000033
Cross coupling matrix obtained by q iteration
Figure BDA0003293889140000034
g vector
Figure BDA0003293889140000035
f vector Jacobian matrix
Figure BDA0003293889140000036
g vector Jacobian matrix
Figure BDA0003293889140000037
Multi-block Q matrix
Figure BDA0003293889140000038
Namely, it is
Figure BDA0003293889140000039
Is gammaqThe M (k-1) th to Mk th elements of (b),
Figure BDA00032938891400000310
[·].,1:P′representing the first P' column of the matrix constituting a new matrix, Toeplitz matrix
Figure BDA00032938891400000311
Hankel matrix
Figure BDA00032938891400000312
Figure BDA00032938891400000313
Is composed of
Figure BDA00032938891400000314
1, and so on;
Figure BDA00032938891400000315
to construct another operator of the Toeplitz matrix,
Figure BDA00032938891400000316
ith action of
Figure BDA00032938891400000317
i is 1,2, …, (M-K), and Γ is the inverse angle identity matrix.
Step (5) DOA and mutual coupling estimation:
after iterative convergence, a convergence solution is obtained
Figure BDA00032938891400000318
Figure BDA00032938891400000319
Is an estimate of the mutual coupling vector,
Figure BDA00032938891400000320
is an estimate of the value of y,
Figure BDA00032938891400000321
is an estimate of the value of h,
Figure BDA00032938891400000322
will be provided with
Figure BDA00032938891400000323
Bringing in
Figure BDA00032938891400000324
Obtaining a polynomial, solving K roots of the polynomial to obtain x1,x2,...,xKThen DOA is estimated as
Figure BDA00032938891400000325
K1, 2,. K; wherein, the angle (·) takes a plurality of amplitude main values; according to
Figure BDA00032938891400000326
Obtaining an estimated cross-coupling matrix
Figure BDA00032938891400000327
Preferably, the value of ω in step (3) is an initial value of h in the iterative calculation of step (4), that is, ω is h0。
Compared with the prior art, the method has the following beneficial effects:
firstly, the method can utilize all array data, and aperture loss does not exist; secondly, the method does not need prior information of the mutual coupling degree, and even if the mutual coupling degree is over-estimated, the performance is not obviously influenced; thirdly, the DOA and mutual coupling estimation accuracy of the method is high.
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FIG. 1 is a general flow diagram of the process of the present invention;
FIG. 2 is a diagram illustrating DOA estimation performance comparison between the method of the present invention and other methods under different cross-coupling estimation values;
FIG. 3 is a graph showing the DOA estimation performance of the present invention compared to other methods at different SNR;
FIG. 4 is a graph showing the comparison of mutual coupling estimation performance between the method of the present invention and other methods under different SNR;
FIG. 5 is a graph showing a comparison of DOA estimation performance with other methods at different fast beat numbers according to the present invention;
FIG. 6 is a graph showing the comparison of the performance of the mutual coupling estimation of the present invention with other methods at different fast beat numbers.
Detailed Description
The following describes the embodiments and effects of the present invention in further detail with reference to the accompanying drawings.
As shown in fig. 1, a joint estimation method of DOA and mutual coupling based on nulling constraint includes the following specific steps:
step (1), modeling of received signals when array arrangement and mutual coupling exist:
laying outUniform linear arrays, the number of array elements is M, and the distance between adjacent array elements is d; k wavelengths are λ from θ1,θ2,…,θKNarrow-band signals in the direction are incident to the uniform linear array and receive N snapshots, and modeling is carried out on a plurality of pieces of snapshot receiving data: Y-CAS + E, Y-Y [ Y1]，y[2]，…，y[N]]The signal matrix S ═ S [1 ]]，s[2]，…，s[N]]The noise matrix E ═ epsilon [1 ═ n]，ε[2]，…，ε[N]]C is a mutual coupling matrix, C has symmetric Toeplitz properties for uniform linear arrays, and C ═ Toeplitz ([1, C)1,c2,…,cP,0,…,0]) Toeplitz (. circle.) denotes the generation of a Toeplitz matrix, c1,c2,…,cPFor the mutual coupling parameter, P represents the mutual coupling degree.
Wherein, the received data of the array at the nth snapshot is modeled as:
Figure BDA0003293889140000041
n is 1,2, …, N; wherein,
Figure BDA0003293889140000042
representing a complex set, flow pattern matrix A ═ a (θ)1),a(θ2),…,a(θK)]，a(θ1),a(θ2),…,a(θK) Representing a steering vector, the kth narrowband signal steering vector a (θ)k) The m-th element of (a)m(θk)＝exp[j(m-1)uk]，k＝1,2,…,K，m＝1,2,…,M，
Figure BDA0003293889140000043
uk＝2πd cos(θk)/λ；s[n]Is a signal vector of ε [ n ]]For the noise vector, the noise is set to zero mean gaussian white noise.
Step (2) dimension compression is carried out based on singular value decomposition:
performing singular value decomposition on Y, and performing dimensionality compression on Y to obtain Y
Figure BDA0003293889140000044
VsA matrix is represented which is composed of right singular vectors corresponding to K maximum singular values of Y.
Step (3) establishing an optimization problem based on the nulling constraint:
the optimization problem is represented as:
Figure BDA0003293889140000051
wherein | · | purple sweet2Denotes a 2 norm, vectorization of Z ═ vec (Z) ·, vec () denotes stacking vectorization of matrices by columns, IKWhich represents an identity matrix of order K,
Figure BDA0003293889140000052
denotes the Kronecker product, the mutual coupling matrix C ═ Toeplitz ([1, C)T,0,...,0]) The mutual coupling vector c ═ c1,c2,...,cP′]TP' represents an estimated value of the mutual coupling, an auxiliary parameter
Figure BDA0003293889140000053
ηkA vector of M (K-1) to Mk elements, K being 1,2T,γT,hT]T(ii) a Multi-block shooting matrix
Figure BDA0003293889140000054
Figure BDA0003293889140000055
To construct the operators of the Toeplitz matrix,
Figure BDA0003293889140000056
is eta, is the ith row and the jth column element ofnI-j + K +1 th element of (M-K), i-1, 2, …, (M-K), j-1, 2, …, (K +1), a nulling filter
Figure BDA0003293889140000057
Omega is a constant vector and takes the value as the initial value h of h in iterative computation0(ii) a s.t. represents a constraint, (.)H、(·)TRespectively representing taking a conjugate transpose and transpose.
Step (4) solving an optimization problem of the nulling constraint by adopting an iteration method;
firstly, the methodInitialization
Figure BDA0003293889140000058
Wherein c is0＝0P′，0P′Zero vector representing P' × 1, initial value γ of γ0And an initial value h of h0Obtaining by assuming no mutual coupling of the arrays and performing TLS-ESTTRIT-like method on Z; then iterative computation is carried out, and upsilon is obtained in the process of q +1 iterationq+1＝υq+ Δ upsilon, q ≧ 0, wherein
Figure BDA0003293889140000059
And (3) for a result obtained by the q-th iteration calculation, wherein the Delta upsilon is a search vector and is obtained by solving the following linear quadratic optimization problem:
Figure BDA00032938891400000510
wherein, f vector
Figure BDA00032938891400000511
Cross coupling matrix obtained by q iteration
Figure BDA00032938891400000512
g vector
Figure BDA00032938891400000513
f vector Jacobian matrix
Figure BDA00032938891400000514
g vector Jacobian matrix
Figure BDA00032938891400000515
Multi-block Q matrix
Figure BDA00032938891400000516
Namely, it is
Figure BDA00032938891400000517
Is gammaqThe M (k-1) th to Mk th elements of (b),
Figure BDA00032938891400000518
[·].,1:P′the first P' column representing the fetch matrix constitutes a new matrix,
Figure BDA00032938891400000519
respectively a Toeplitz matrix and a Hankel matrix,
Figure BDA0003293889140000061
Figure BDA0003293889140000062
is composed of
Figure BDA0003293889140000063
1, and so on;
Figure BDA0003293889140000064
to construct another operator of the Toeplitz matrix,
Figure BDA0003293889140000065
ith action of
Figure BDA0003293889140000066
i is 1,2, …, (M-K), and Γ is the inverse angle identity matrix.
Step (5) DOA and mutual coupling estimation:
after iterative convergence, a convergence solution is obtained
Figure BDA0003293889140000067
Figure BDA0003293889140000068
Is an estimate of the mutual coupling vector,
Figure BDA0003293889140000069
is an estimate of the value of y,
Figure BDA00032938891400000610
is an estimate of the value of h,
Figure BDA00032938891400000611
will be provided with
Figure BDA00032938891400000612
Bringing in
Figure BDA00032938891400000613
Obtaining a polynomial, solving K roots of the polynomial to obtain x1,x2,...,xKThen DOA is estimated as
Figure BDA00032938891400000614
K1, 2,. K; wherein, the angle (·) takes a plurality of amplitude main values; according to
Figure BDA00032938891400000615
Obtaining an estimated cross-coupling matrix
Figure BDA00032938891400000616
The effect of the method of the invention is verified by combining the simulation example.
Simulation example 1: setting the number of uniform linear array elements as M10, d lambda/2, the mutual coupling degree of array elements as 2 and the mutual coupling parameter as c1＝0.5+0.4j，c20.1-0.03 j. Let K be 2 incident signals and DOA be θ1＝89°+Δθ1，θ2＝105°+Δθ2，Δθ1And Δ θ2At [ -0.5 DEG, 0.5 DEG ]]The inner parts are uniformly distributed. The signal-to-noise ratio is set to 15dB and the number of snapshots is set to 100. The mutual coupling estimate is scanned from 2 to 9. The performance difference in root mean square error of the DOA estimation is compared between the method of the present invention and the methods of documents 1 and 2 in the background art. The comparison results, averaged over 500 monte carlo trials, are shown in figure 2. Since the mutual coupling estimation value of the method of document 1 can only take 3 at maximum, a portion exceeding 3 has no result. As can be seen from FIG. 2, under the condition of mutual coupling overestimation, the performance of the method of the present invention is not significantly affected, and the root mean square error of the DOA estimation is still less than theta10.1 deg.. The other two methods are greatly affected.
Simulation example 2: the number of fast beats is set to 50, the signal-to-noise ratio is swept from-10 dB to 15dB, and the rest of the simulation conditions are the same as the previous ones. The estimated performance difference of each method for DOA and mutual coupling is compared. In order to provide a performance reference, the results for cramer lower limit (CRB) are also provided. CRB can be found in literature: z. -M.Liu and Y. -Y.ZHou, "A unified frame and space Bayesian activity for direction-of-arrival estimation in the presence of array activities," IEEE Transactions on Signal Processing, vol.61, No.15, pp.3786-3798,2013. The simulation results are shown in fig. 3 and 4. As can be seen from the figure, for the estimation of DOA and mutual coupling, the root mean square error of each signal-to-noise ratio reaches the minimum, and the estimation precision is the highest. And when the signal-to-noise ratio is 5dB, the method of the invention estimates the DOA to reach the CRB.
Simulation example 3: the signal-to-noise ratio was set to 5dB, the fast beat number was swept from 10 to 100, and the rest of the simulation conditions were the same as described above. The estimated performance difference of each method for DOA and mutual coupling is compared. The simulation results are shown in fig. 5 and 6. As can be seen from the figure, for the estimation of DOA and mutual coupling, the root mean square error of each fast beat reaches the minimum, and the estimation precision is the highest. And when the number of snapshots is 40, the estimation of DOA by the method of the invention reaches CRB.
The above description is only exemplary of the preferred embodiment and should not be taken as limiting the invention, as any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (2)

1. A joint estimation method of DOA and mutual coupling based on nulling constraint is characterized by comprising the following steps:
step (1), modeling of received signals when array arrangement and mutual coupling exist:
arranging uniform linear arrays, wherein the number of array elements is M, and the distance between adjacent array elements is d; k wavelengths are λ from θ1,θ2,…,θKNarrow-band signals in the direction are incident to the uniform linear array and receive N snapshots, and modeling is carried out on a plurality of pieces of snapshot receiving data: Y-CAS + E, Y-Y [ Y1]，y[2]，…，y[N]]The signal matrix S ═ S [1 ]]，s[2]，…，s[N]]The noise matrix E ═ epsilon [1 ═ n]，ε[2]，…，ε[N]]C is a mutual coupling matrix, and C is Toeplitz ([1, C)1,c2,…,cP,0,…,0]) Toeplitz (. circle.) denotes the generation of a Toeplitz matrix, c1,c2,…,cPP represents the mutual coupling degree as a mutual coupling parameter;
wherein, the received data of the array at the nth snapshot is modeled as:
Figure FDA0003293889130000011
wherein,
Figure FDA0003293889130000012
representing a complex set, flow pattern matrix A ═ a (θ)1),a(θ2),…,a(θK)]，a(θ1),a(θ2),…,a(θK) Representing a steering vector, the kth narrowband signal steering vector a (θ)k) The m-th element of (a)m(θk)＝exp[j(m-1)uk]，k＝1,2,…,K，m＝1,2,…,M，
Figure FDA0003293889130000013
uk＝2πdcos(θk)/λ；s[n]Is a signal vector of ε [ n ]]Is a noise vector;
step (2) dimension compression is carried out based on singular value decomposition:
performing singular value decomposition on Y, and performing dimensionality compression on Y to obtain Y
Figure FDA0003293889130000014
VsRepresenting a matrix formed by right singular vectors corresponding to K maximum singular values of Y;
step (3) establishing an optimization problem based on the nulling constraint:
the optimization problem is represented as:
Figure FDA0003293889130000015
wherein | · | purple sweet2Expressing 2 norm, vectorization of Zz ═ vec (z), vec (·) denotes stacking vectorization of the matrix by columns, IKWhich represents an identity matrix of order K,
Figure FDA0003293889130000016
denotes the Kronecker product, the mutual coupling matrix C ═ Toeplitz ([1, C)T,0,...,0]) The mutual coupling vector c ═ c1,c2,...,cP′]TP' represents an estimated value of the mutual coupling, an auxiliary parameter
Figure FDA0003293889130000017
ηkA vector of M (K-1) to Mk elements, K being 1,2T,γT,hT]T(ii) a Multi-block shooting matrix
Figure FDA0003293889130000018
To construct the operators of the Toeplitz matrix,
Figure FDA0003293889130000019
is eta, is the ith row and the jth column element ofnI-j + K +1 th element of (M-K), i-1, 2, …, (M-K), j-1, 2, …, (K +1), a nulling filter
Figure FDA00032938891300000110
Omega is a constant vector; s.t. represents a constraint, (.)H、(·)TRespectively representing conjugate transposition and transposition;
and (4) solving an optimization problem of the nulling constraint by adopting an iterative method:
first of all, initializing
Figure FDA0003293889130000021
Wherein c is0＝0P′，0P′Zero vector representing P' × 1, initial value γ of γ0And an initial value h of h0Obtaining by assuming no mutual coupling of the arrays and performing TLS-ESTTRIT-like method on Z; then iterative computation is carried out, and upsilon is obtained in the process of q +1 iterationq+1＝υq+ Δ upsilon, q ≧ 0, wherein
Figure FDA0003293889130000022
And (3) for a result obtained by the q-th iteration calculation, wherein the Delta upsilon is a search vector and is obtained by solving the following linear quadratic optimization problem:
Figure FDA0003293889130000023
wherein, f vector
Figure FDA0003293889130000024
Cross coupling matrix obtained by q iteration
Figure FDA0003293889130000025
g vector
Figure FDA0003293889130000026
f vector Jacobian matrix
Figure FDA0003293889130000027
g vector Jacobian matrix
Figure FDA0003293889130000028
Multi-block Q matrix
Figure FDA0003293889130000029
Namely, it is
Figure FDA00032938891300000210
Is gammaqThe M (k-1) th to Mk th elements of (b),
Figure FDA00032938891300000211
[·].,1:P′representing the first P' column of the matrix constituting a new matrix, Toeplitz matrix
Figure FDA00032938891300000212
Hankel matrix
Figure FDA00032938891300000213
Figure FDA00032938891300000214
Is composed of
Figure FDA00032938891300000215
1, and so on;
Figure FDA00032938891300000216
to construct another operator of the Toeplitz matrix,
Figure FDA00032938891300000217
ith action of
Figure FDA00032938891300000218
Gamma is an inverse angle identity matrix;
step (5) DOA and mutual coupling estimation:
after iterative convergence, a convergence solution is obtained
Figure FDA00032938891300000219
Figure FDA00032938891300000220
Is an estimate of the mutual coupling vector,
Figure FDA00032938891300000221
is an estimate of the value of y,
Figure FDA00032938891300000222
is an estimate of the value of h,
Figure FDA00032938891300000223
will be provided with
Figure FDA00032938891300000224
Bringing in
Figure FDA00032938891300000225
Obtaining a polynomial, solving K roots of the polynomial to obtain x1,x2,...,xKThen DOA is estimated as
Figure FDA00032938891300000226
Wherein, the angle (·) takes a plurality of amplitude main values; according to
Figure FDA0003293889130000031
Obtaining an estimated cross-coupling matrix
Figure FDA0003293889130000032
2. The joint estimation method of DOA and mutual coupling based on nulling constraints as recited in claim 1, wherein: the value of ω in step (3) is the initial value of h in the iterative calculation of step (4), that is, ω is h0。
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CN114624665A (en) * 2022-03-24 2022-06-14 电子科技大学 Mutual coupling error DOA self-correction method based on dynamic parameter iterative optimization

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114624665A (en) * 2022-03-24 2022-06-14 电子科技大学 Mutual coupling error DOA self-correction method based on dynamic parameter iterative optimization
CN114624665B (en) * 2022-03-24 2023-11-07 电子科技大学 Mutual coupling error DOA self-correction method based on dynamic parameter iterative optimization

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