CN108872928A - The evaluation method of planar array angle based on four linear decompositions - Google Patents
The evaluation method of planar array angle based on four linear decompositions Download PDFInfo
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- G—PHYSICS
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- 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
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- G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
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Abstract
The invention discloses a kind of evaluation methods of planar array angle based on four linear decompositions, according to the array signal model construction non-uniform noise covariance matrix for receiving array element, and further construct the tetradic of non-uniform noise covariance matrix；Receiving direction matrix, direction of the launch matrix, target covariance matrix are initialized, receiving direction matrix, direction of the launch matrix, target covariance matrix are initialized as a unit matrix；Calculating is iterated to receiving direction matrix, direction of the launch matrix and target covariance matrix using alternating least-squares, until meeting the condition of convergence；The DOD and DOA of target are estimated by least square method；The evaluation method can effectively fight non-homogeneous white noise, and preferable estimation effect can be obtained under the conditions of small snap and big snap；The precision of its parameter Estimation is higher than ESPRIT algorithm and HOSVD algorithm, but complexity is lower than PARAFA C algorithm.
Description
Technical field
The present invention relates to a kind of Radar Signal Processing Technologies, more particularly to a kind of planar array based on four linear decompositions
The evaluation method of column angle.
Background technique
An important branch of the array signal processing as signal processing, essence are the sensings using spatial dispersion arrangement
The multidimensional information such as time domain and the airspace that device array and multichannel receive to obtain signal reach detection signal and extract its parameter
Purpose.It has been widely used in fields such as communication, radar, sonar, seismic prospecting and radio astronomies and rapidly develops,
There is very big application prospect.In recent years, multi-parameter inversion is carried out using array signal processing and obtained more and more concerns, especially
It is that space direction of arrival (direction of arrival, DOA) estimation has become one of hot issue of research.Two-dimensional parameter
The problem of estimation, is one and is bonded very much practical problem, and traditional DOA is typically estimated as referring in a plane to signal source
Azimuth estimated that belong to one-dimensional Parameter Estimation Problem, there are many limitations.In practical communication system, user is simultaneously
It is non-to be generally aligned in the same plane, it is therefore desirable to which that two-dimentional direction of arrival indicates.
Arrival direction estimation achieves extensive concern between past many decades.So far it has emerged and a large amount of outstanding has estimated
Calculating method, typical main representative have the classification of multiple spectral peak (multiple signal classification algorithm,
MUSIC) algorithm, parameter Estimation (the estimation of signal parameters via based on rotation invariant technology
Rotational invariance techniques, ESPRIT) algorithm, propagation operator (propogator method, PM)
Algorithm.Wherein, MUSIC algorithm is the orthogonal property using noise subspace and signal subspace, is estimated by spectrum peak search
DOA, computationally intensive, complexity is high；ESPRIT algorithm does not need to carry out spectrum peak search, but still needs singular value decomposition or spy
Value indicative is decomposed.Both the above method is all subspace of eigenvalue class algorithm, and for the battle array of face, Eigenvalues Decomposition operand is very
Greatly.And PM algorithm does not need Eigenvalues Decomposition, thus complexity is lower.Algorithm above is often carried out using matrix decomposition technology
Parameter Estimation often has ignored the intrinsic multidimensional structure of array data.Tensor resolution technology can effectively excavate number of arrays
According to internal multidimensional structure, thus more and more concerns are received in recent years.Typical tensor resolution technology mainly has high-order
Spatial decomposition (high-order singular value decomposition, HOSVD) algorithm and parallel factor
(parallel factor, PARAFAC) algorithm, wherein PARAFAC algorithm obtains parameter Estimation using the method for iteration, compares
HOSVD algorithm, estimated accuracy is often higher, and complexity is lower, thus is more suitable for large scale array signal processing.
However, above-mentioned algorithm is all assumed that and is carried out under the conditions of uniform white Gaussian noise, under the assumptions, noise
Covariance matrix and unit matrix are a linear relationships, therefore can be relatively easy to and separate signal and noise, but
It is that this hypothesis does not often conform to the actual conditions, in Practical Project, by array element gain-phase is inconsistent etc., factors are influenced, and noise is often
It is heterogeneous.In fact, white Gaussian noise can be considered as a kind of special case of non-uniform noise.Under the conditions of non-uniform noise,
Noise covariance matrix is a unknown diagonal matrix.At this point, signal and noise can not efficiently separate, estimate so as to cause angle
The decline for counting performance, especially under Low SNR, existing algorithm is possible to be distorted or even entirely ineffective, is unsuitable for
Engineering application.
Summary of the invention
For these reasons, it is necessary to which providing one kind can reduce PARAFAC complexity under big snap background, and can disappear
The plane based on four linear decompositions of hardware computation except the influence under the conditions of non-uniform noise, and suitable for Practical Project
The evaluation method of array angle.
The present invention provides a kind of evaluation method of planar array angle based on four linear decompositions, described to be based on four linear points
The evaluation method of the planar array angle of solution includes the following steps：
S1, according to the array signal model construction non-uniform noise covariance matrix for receiving array element, and further construct non-
The tetradic of Uniform noise covariance matrix；
S2, receiving direction matrix, direction of the launch matrix, target covariance matrix are initialized, by receiving direction square
Battle array, direction of the launch matrix, target covariance matrix are initialized as a unit matrix；
S3, using alternating least-squares to receiving direction matrix, direction of the launch matrix and target covariance matrix into
Row iteration calculates, until meeting the condition of convergence；
S4, the DOD and DOA that target is estimated by least square method；
Wherein, the specific formula of the non-uniform noise covariance matrix is as follows：
Qest=Rest-diag{Rest}
In above formula, diag { } indicates diagonalization operation；Rest=XXH/L；L indicates number of snapshots；
Dm(Ay) indicate AyThe element of m row constitute a diagonal matrix in order.
The evaluation method of planar array angle of the present invention based on four linear decompositions utilizes the multidimensional of array signal
Structure according to the array signal model construction non-uniform noise covariance matrix of reception array element, and further constructs non-homogeneous make an uproar
The tetradic of sound covariance matrix；Receiving direction matrix, direction of the launch matrix, target covariance matrix are initialized,
Receiving direction matrix, direction of the launch matrix, target covariance matrix are initialized as a unit matrix；Utilize alternately minimum two
Multiplication is iterated calculating to receiving direction matrix, direction of the launch matrix and target covariance matrix, until meeting convergence item
Part；The DOD and DOA of target are estimated by least square method；Bistatic MIMO radar angle evaluation method of the present invention its
Compared with traditional algorithm, non-homogeneous white noise can be effectively fought, can be obtained preferably under the conditions of small snap and big snap
Estimation effect；It can also correctly estimate the azimuth information of target, and angle estimated by energy automatic matching；Its parameter Estimation
Precision is higher than ESPRIT algorithm and HOSVD algorithm, but complexity is lower than PARAFA C algorithm, and due to the covariance square of noise reduction
Battle array can inhibit the influence of non-homogeneous white noise, thus its performance can be better than the algorithm of its corresponding non-noise reduction, not have aperture with it
Loss, thus it has higher estimated accuracy.
Detailed description of the invention
Fig. 1 is planar array angle estimation schematic diagram；
Fig. 2 is scatter plot result of the evaluation method in SNR=-10dB；
Fig. 3 is the comparison result of the evaluation method from existing other algorithms RMSE performance under the conditions of different SNR；
Fig. 4 is the comparison result of the evaluation method from existing other algorithms RMSE performance under the conditions of different L.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments, right
The present invention is further elaborated, it should be understood that and the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.
The present invention provides a kind of evaluation method of planar array angle based on four linear decompositions, which is characterized in that described
The evaluation method of planar array angle based on four linear decompositions includes the following steps：
S1, according to the array signal model construction non-uniform noise covariance matrix for receiving array element, and further construct non-
The tetradic of Uniform noise covariance matrix；
S2, receiving direction matrix, direction of the launch matrix, target covariance matrix are initialized, by receiving direction square
Battle array, direction of the launch matrix, target covariance matrix are initialized as a unit matrix；
S3, using alternating least-squares to receiving direction matrix, direction of the launch matrix and target covariance matrix into
Row iteration calculates, until meeting the condition of convergence；
S4, the DOD and DOA that target is estimated by least square method.
Specifically, N and M respectively indicate the array element in the direction x and y as shown in Figure 1, the two-way array has N × M array element
Number.Array element spacing is λ/2, and λ indicates transmitting signal wavelength.Assuming that having K incoherent members, kth (1≤k≤K) in array far field
The orientation in a gust of source isWhereinAzimuth for target with respect to array element, θkPitch angle for target relative to array element,
Then the wave path-difference between i-th of space array element and reference array element 0 is
Face battle array is generally in the face x-y, so ziGenerally 0, (xi,yi) be i-th of array element coordinate.Assuming that N number of in x-axis
The direction matrix for receiving array element is Ax, the direction matrix of M reception array element is A in y-axisy, then the direction of submatrix 1 as shown in Figure 1
Matrix Ax, and the direction matrix of submatrix 2 must consider the offset along y-axis, each array element relative to reference array element wave path-difference just
Wave path-difference equal to the array element of submatrix 1 addsSo the direction matrix that can obtain each subarray is respectively
Wherein, Dm(Ay) indicate AyThe element of m row constitute a diagonal matrix in order.AxAnd AyRespectively as expressed
Shown in formula (3) and expression formula (4).
In above formulaIndicate N number of reception in x-axis
The steering vector of array element,Indicate M reception battle array in y-axis
The steering vector of member.Then array output can be write as
Wherein,For information source matrix,Indicate non-uniform noise matrix.According to expression formula 6, direction square
Battle array can also be expressed as⊙ indicates Khatri-Rao product.It is defined as follows covariance matrix:
E { } and { } in above formulaHRespectively indicate mathematic expectaion and conjugate transposition.Assuming that N to S be it is non-relevant, according to table
It is obtained up to formula (5) and expression formula (7)
R=E { XXH}=APAH+ Q expression formula (8)
In engineering, signal covariance matrix can estimate R by the data of L snapest=XXH/ L, L indicate number of snapshots.
Consider information source be it is non-relevant, then
Wherein pkIndicate the power of k-th of signal.When noise is non-homogeneous white noise, noise covariance matrix is
Wherein, qiIndicate the noise function of i-th of array element.Enable atFor t (t=1,2 ..., the MN) row of A.It is sent out by analysis
It is existing, matrix A PAHT-th of diagonal element beI.e. it is a constant.By such as
The covariance matrix of lower simplification can effectively inhibit non-uniform noise, and signal characteristic is unaffected, then the non-homogeneous of simplification is made an uproar
Sound covariance matrix is
Qest=Rest-diag{Rest}=APAH- λ I expression formula (11)
In above formula, diag { } indicates diagonalization operation, and I is a unit matrix.
Expression formula (11) can also be expressed as a tetradic
In formula,Respectively Ax, AyConjugation, expression formula (12) defines four linear models, and R is also referred to as
Symmetrical multimode expanded form.It can also be expressed as the form of four linear decompositions
Wherein,For a diagonal tensor, symmetrical multimode expands into P, in order to estimate K target
DOA needs to estimate direction matrix AxAnd Ay, covariance tensorIt can be by calculating an optimal approximationCome
It realizes, i.e.,
||·||FIndicate Frobenius norm.The core of ALS (alternating least squares) is to make one
Matrix changes and other matrixes immobilize, and then converts Linear least squares minimization problem for tensor optimization problem.According to expression
Formula (14), willIt is launched into available four matrixes of n (n=1,2,3,4) mould：
In formula,It indicatesMould-n expanded form [10].Expression formula (15) can be addressed further under into following joint
Optimization problem：
Utilize A known to criterion of least squaresx, Ay,Least-squares estimation be respectively
Wherein A1,A2,A3,A4Respectively represent the A in least-squares estimationx,Ay,According to expression formula (8), P can
It is acquired by following expression
It then can directly acquire the least-squares estimation of P
ALS algorithm obtains the estimation of matrix by the method for iteration, and core assumes that in all matrixes for constituting tensor
Only one is unknown, and its complementary submatrix is thought it is known that obtaining the estimation of the matrix using criterion of least squares.For example, fixed P,
Ay,A is sought by criterion of least squaresx；Fixed P, Ax,Seek Ay；Then P, A are fixedx,Ay,It asks
Fixed P, Ax,Ay,EstimationFinally assume Ax,Ay, It is fixed, update P.ALS algorithm steps be repeated alternatively until calculation
Method convergence, i.e. the number of iterations reach a threshold value, orOr | εnew-εold|/εold≤10-10, εnewAnd εold
Respectively indicate the residual error of last iteration and current iteration.
Ax,Ay, P can be by random initializtion, however to will lead to algorithm the convergence speed slow for this initialization.In the present invention
In patent, the initial value of direction matrix can be obtained by PM algorithm, be restrained with accelerating algorithm.Due to Ax, AyRespectively and
It is conjugation, therefore only needs to update A using criterion of least squares in ALS algorithmx, Ay, P.
Theorem 1 hereinafter gives the condition of evaluation method parameter Estimation uniqueness of the present invention.
Theorem 1：For four linear models in the present invention, it is assumed thatK- order be respectively
WithIf it meets
So for A estimated by ALS1, A2, A3And A4, other than arranging fuzzy and scale and obscuring, parameter Estimation is unique
's.
The ambiguity of the parameter Estimation of four linear decompositions can be expressed as the form of following split-matrix
Wherein ∏ is permutation matrix, N1, N2, N3, N4Respectively indicate corresponding error of fitting matrix, Δ1, Δ2, Δ3, Δ4For
Four diagonal matrix, diagonal element respectively indicates corresponding scale factor, and it meets Δ1Δ2Δ3Δ4=IK.Pay attention to A1,
A2Phase be still linear, at this point, still can use LS method estimation DOA.Using the method for LS to k-th target
The method that DOA is fitted is
Wherein, Phase () indicates to ask plural phase,WithRespectively indicate A1, A2Kth column.Thus c is obtained1,
c2LS solution be
ObviouslySecond elementRespectivelyWithEstimated value.Cause
This can find out θkWithEstimated value be
For uniform rectangular array arrival direction estimation method under non-uniform noise background proposed by the present invention, portion has been carried out
Fractional value emulation experiment.Assume that K=3 information source is in far field in emulation, two dimension DOA is respectively WithInformation source matrix is Gaussian matrix.In emulation experiment in X-axis array element
N=6 is counted, the number M=8 of array number in Y-axis, both for uniform linear array, array element spacing is transmitting signal half-wavelength.
Non-uniform noise covariance matrix diagonal element is by randn function is randomly generated in MATLAB sequence.Letter in emulation
It makes an uproar and is defined as than (signal-to-noise ratio, SNR)
Attached drawing 2 is that the present invention proposes calculation in SNR=-10dB, number of snapshots L=100, the scatterplot of deflection and elevation estimate
Figure.By attached drawing 2 it is found that evaluation method of the present invention can correctly estimate the azimuth information of target, and energy automatic matching is estimated
The angle of meter.
It is evaluation method more of the present invention compared with the estimated accuracy of algorithm, 500 Monte Carlos is carried out to algorithm
The precision of emulation, angle estimation carries out performance evaluation with root-mean-square error (Root Mean Squared Error, RMSE),
Middle RMSE is defined as
In formulaWithRespectively obtained in i-th Monte Carlo simulation to θkWithEstimation.To further illustrate
Algorithm of the invention (is labeled as by algorithm performance with ESPRIT algorithm (being labeled as ESPRIT), the direct Tensor Method of noise reduction
HOSVD), the performance of the covariance Tensor Method (being labeled as HOSVD-2) of noise reduction and PARAFAC algorithm (being labeled as PARAFAC)
It compares, wherein prefix noise reduction indicates to carry out parameter Estimation using the covariance matrix of noise reduction.
Attached drawing 3 gives evaluation method of the present invention (labeled as proposed) compared with algorithm in different SNR conditions
Lower performance comparison result, wherein L=500.By simulation result it is found that with signal-to-noise ratio increase, all algorithms estimation essence
Degree is promoted.Due to the influence of non-uniform noise, when noise is relatively low, the performance of HOSVD and PARAFAC can all have
Declined.Since the covariance matrix of noise reduction can inhibit the influence of non-homogeneous white noise, thus its performance can be corresponding better than its
The algorithm of non-noise reduction.Simultaneously as when final angle is estimated it is of the present invention be LS fitting method, thus it does not have
Aperture loss, thus it has higher estimated accuracy.
Attached drawing 4 gives evaluation method of the present invention (labeled as proposed) and compared with algorithm in different L conditions
Lower performance comparison result, wherein SNR=0dB.By simulation result it is found that with number of snapshots increase, the estimation of all algorithms
Precision is promoted.But influenced by aperture loss or non-uniform noise, ESPRIT algorithm, HOSVD algorithm and
PARAFAC algorithm can bring the decline of estimation performance.And evaluation method of the present invention can effectively fight non-homogeneous white noise
Sound can obtain preferable estimation effect under the conditions of small snap and big snap.
The evaluation method of planar array angle of the present invention based on four linear decompositions utilizes the multidimensional of array signal
Structure according to the array signal model construction non-uniform noise covariance matrix of reception array element, and further constructs non-homogeneous make an uproar
The tetradic of sound covariance matrix；Receiving direction matrix, direction of the launch matrix, target covariance matrix are initialized,
Receiving direction matrix, direction of the launch matrix, target covariance matrix are initialized as a unit matrix；Utilize alternately minimum two
Multiplication is iterated calculating to receiving direction matrix, direction of the launch matrix and target covariance matrix, until meeting convergence item
Part；The DOD and DOA of target are estimated by least square method；Bistatic MIMO radar angle evaluation method of the present invention its
Compared with traditional algorithm, non-homogeneous white noise can be effectively fought, can be obtained preferably under the conditions of small snap and big snap
Estimation effect；It can also correctly estimate the azimuth information of target, and angle estimated by energy automatic matching；Its parameter Estimation
Precision is higher than ESPRIT algorithm and HOSVD algorithm, but complexity is lower than PARAFAC algorithm, and due to the covariance matrix of noise reduction
It can inhibit the influence of non-homogeneous white noise, thus its performance can be better than the algorithm of its corresponding non-noise reduction, not have aperture damage with it
It loses, thus it has higher estimated accuracy.
The foregoing is merely presently preferred embodiments of the present invention, is not intended to limit the invention, it is all in spirit of the invention and
Within principle, any modification, equivalent replacement, improvement and so on be should all be included in the protection scope of the present invention.
Claims (5)
1. a kind of evaluation method of the planar array angle based on four linear decompositions, which is characterized in that described to be based on four linear points
The evaluation method of the planar array angle of solution includes the following steps：
S1, according to the array signal model construction non-uniform noise covariance matrix for receiving array element, and further construct non-homogeneous
The tetradic of noise covariance matrix；
S2, receiving direction matrix, direction of the launch matrix, target covariance matrix are initialized, by receiving direction matrix, hair
Penetrate direction matrix, target covariance matrix is initialized as a unit matrix；
S3, it is changed using alternating least-squares to receiving direction matrix, direction of the launch matrix and target covariance matrix
In generation, calculates, until meeting the condition of convergence；
S4, the DOD and DOA that target is estimated by least square method；
Wherein, the specific formula of the non-uniform noise covariance matrix is as follows：
Qest=Rest-diag{Rest}
In above formula, diag { } indicates diagonalization operation；Rest=XXH/L；L indicates number of snapshots；
Dm(Ay) indicate AyThe element of m row constitute a diagonal matrix in order.
2. the evaluation method of the planar array angle based on four linear decompositions according to claim 1, which is characterized in that described
Alternating least-squares by random matrix respectively to receiving direction matrix, direction of the launch matrix and target covariance matrix into
Row initialization.
3. the evaluation method of the planar array angle based on four linear decompositions according to claim 1, which is characterized in that described
The tetradic model of covariance matrix is as follows：
In above formula,For the tetradic of covariance matrix,For a diagonal tensor, symmetrical multimode expansion
For P；AxFor direction of the launch matrix；AyFor receiving direction matrix,Respectively matrix Ax, AyConjugation.
4. the evaluation method of the planar array angle based on four linear decompositions according to claim 3, which is characterized in that step
It is changed using alternating least-squares to receiving direction matrix, direction of the launch matrix and target covariance matrix described in S3
The specific formula that generation calculates is as follows：
5. the evaluation method of the planar array angle based on four linear decompositions according to claim 4, which is characterized in that step
By the DOD and DOA of least square method estimation target, the specific method is as follows described in S4：
It is respectively to the fitting of DOD and DOA using LS method
In above formula, Phase () indicates to ask plural phase,WithRespectively indicate A1, A2Kth column, thus obtain c1,
c2LS solution be
ObviouslySecond elementRespectivelyWithEstimated value, therefore can ask
θ outkWithEstimated value be
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