CN110244258A - For extending DOA matrix method in double parallel battle array two dimension direction finding - Google Patents
For extending DOA matrix method in double parallel battle array two dimension direction finding Download PDFInfo
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- CN110244258A CN110244258A CN201910504096.8A CN201910504096A CN110244258A CN 110244258 A CN110244258 A CN 110244258A CN 201910504096 A CN201910504096 A CN 201910504096A CN 110244258 A CN110244258 A CN 110244258A
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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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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
Abstract
The invention discloses for extending DOA matrix method in the two dimension direction finding of double parallel battle array, the autocorrelation matrix and cross-correlation matrix of the reception data of double parallel battle array has been fully utilized in this method, construct the DOA matrix of an extension, then pass through the feature decomposition to DOA matrix, sense vector sum sense element to be estimated can be directly obtained, and thus obtains the two-dimentional DOA angle estimation of signal to be estimated.Traditional DOA matrix method is compared, method proposed by the present invention because the autocorrelation matrix and cross-correlation matrix of the reception data of double parallel battle array has been fully utilized there is better DOA to estimate performance.Method proposed by the present invention does not need spatial spectrum search, has lower algorithm complexity, and obtained DOA estimation angle is able to achieve automatic matching.
Description
Technical field
The present invention relates to for extending DOA matrix method in the two dimension direction finding of double parallel battle array, and in particular to far-field signal source
Angle estimating method belongs to array signal processing technology.
Background technique
Traditional DOA matrix method constructs DOA matrix according to the property of covariance matrix.Pass through the feature to DOA matrix
It decomposes, sense vector sum sense element to be estimated can be directly obtained, and can thus estimate signal parameter, thus
Multinomial search is avoided completely, and operand is smaller, but the auto-correlation information since array received signal not being fully utilized
With cross-correlation information, so two dimension DOA angle estimation performance is lower.
Summary of the invention
The technical problems to be solved by the present invention are: provide for extending DOA matrix method in the two dimension direction finding of double parallel battle array,
The auto-correlation information and cross-correlation information of array received signal has been fully utilized, has constructed an extension DOA matrix, solves double flat
Arrival direction estimation problem under row battle array.
The present invention uses following technical scheme to solve above-mentioned technical problem:
For extending DOA matrix method in double parallel battle array two dimension direction finding, include the following steps:
Step 1, double parallel battle array, the uniform line temper that the double parallel battle array is parallel to each other by two are arranged on two-dimensional space
Array XaAnd YaIt constitutes, when there is K irrelevant narrowbands to be incident on double parallel battle array with carrier signal, solves linear sub-arrays Xa
And YaReceive the estimation of the autocorrelation matrix of signalWithLinear sub-arrays XaAnd YaReceive the cross-correlation matrix of signal
EstimationAnd linear sub-arrays YaAnd XaReceive the estimation of the cross-correlation matrix of signal
Step 2, according to the estimation of autocorrelation matrixWithAnd the estimation of cross-correlation matrixWithObtain square
Battle arrayWith
Step 3, according to the estimation of cross-correlation matrixWithAnd matrixWithDefine matrix R1And R2, and
Building extension DOA matrix
Step 4, to extension DOA matrix R ' carry out Eigenvalues Decomposition, obtain two-dimentional DOA's according to characteristic value and feature vector
Estimation.
As a preferred solution of the present invention, the estimation of autocorrelation matrix described in step 1WithAnd cross-correlation
The estimation of matrixWithIt is obtained by following formula:
Wherein, L is number of snapshots, and x (t) indicates t moment linear sub-arrays XaReception signal, y (t) indicate t moment it is linear
Subarray YaReception signal, ()HRepresenting matrix conjugate transposition.
As a preferred solution of the present invention, matrix described in step 2WithFormula it is as follows:
Wherein,WithIndicate autocorrelation matrix RxxAnd RyyEstimation, σ2For the variance of additive white Gaussian noise, IMFor
The unit matrix of M × M, M are linear sub-arrays XaOr YaNumber of sensors.
As a preferred solution of the present invention, the formula that DOA matrix R ' is extended described in step 3 is as follows:
Wherein, R1And R2It is matrix,WithIndicate cross-correlation matrix RxyAnd RyxEstimation,WithIt is
Matrix, ()+Representing matrix pseudoinverse.
As a preferred solution of the present invention, the detailed process of the step 4 are as follows:
DefinitionWithK is number of the irrelevant narrowband with carrier signal,
To extension DOA matrix R ' carry out Eigenvalues Decomposition, matrix A is obtainedEAnd Φ, and have R ' AE=AEΦ, then according to the feature in Φ
Value, obtains vkEstimated valueAnd then obtain DOA angle betakEstimation
By AEIt is divided into A and A Φ-1Two parts, after feature decomposition, this two-part estimation is respectivelyWithRecycling side
DOA angle estimation is carried out to direction matrix to the Vandermonde feature of matrix, to obtain DOA angle [alpha]kEstimation
Wherein, It serves as reasonsObtained uk1Estimated value,It serves as reasons
Obtained uk2Estimated value.
The invention adopts the above technical scheme compared with prior art, has following technical effect that
1, extension DOA matrix method proposed by the present invention, maintain traditional DOA matrix method can completely avoid it is multinomial
While operand smaller advantage, the auto-correlation information and cross-correlation letter of array received signal has been fully utilized in formula search
Breath constructs the DOA matrix of an extension, improves two-dimentional DOA angle estimation performance.
2, method proposed by the present invention does not need spatial spectrum search, has lower algorithm complexity.
3, the present invention is by the feature decomposition to DOA matrix, the angle DOA for obtaining the DOA angle of source signal, and obtaining
Degree is able to achieve automatic matching.
Detailed description of the invention
Fig. 1 is array structure topological diagram of the invention.
Fig. 2 is the emulation scatter diagram of the method for the present invention.
Fig. 3 is the angle RMSE performance comparison figure of the method for the present invention and tradition DOA matrix method under the conditions of different signal-to-noise ratio.
Fig. 4 is the angle RMSE performance comparison figure of the method for the present invention and tradition DOA matrix method under the conditions of different snaps.
Fig. 5 is angle RMSE performance comparison figure of the method for the present invention under various information source number under the conditions of different signal-to-noise ratio.
Specific embodiment
Embodiments of the present invention are described below in detail, the example of the embodiment is shown in the accompanying drawings.Below by
The embodiment being described with reference to the drawings is exemplary, and for explaining only the invention, and is not construed as limiting the claims.
Symbol indicates: using () in the present inventionTRepresenting matrix transposition, ()HRepresenting matrix conjugate transposition, () * indicate square
Battle array conjugation, capital X representing matrix, lowercase x () indicate vector, IMIt is expressed as the unit matrix of M × M,It indicates
Hadamard product, diag (v) indicate that the diagonal matrix constituted with element in v, E [] indicate it is expected Matrix Calculating, angle ()
Expression takes phase angle to operate.
One, data model
The two linear sub-arrays compositions being parallel to each other of signal receiving array as shown in Figure 1, two subarrays claim respectively
For XaAnd Ya.Each submatrix shows M sensor, and two adjacent sensors spacing in X direction and two submatrix column pitch are d.Assuming that
Space has K irrelevant narrowbands with carrier signal sk(t) (1≤k≤K) is incident on this array, and the angle with x-axis is αk, with
The angle of y-axis is βk.Submatrix XaAnd YaIt is respectively as follows: in the corresponding output signal of t moment
X (t)=As (t)+nx(t)
Y (t)=A Φ s (t)+ny(t)
Wherein, nx(t) and nyIt (t) is the additive white Gaussian noise vector of two submatrixs, it is mutually indepedent with signal s (t).He
Expression formula be respectively x (t)=[x1(t),…,xM(t)]T, y (t)=[y1 (t) ..., yM (t)]T, s (t)=[s1
(t),…,sK(t)]T, A=[a1,…,aK], and have
ak=[1, exp (j2 π dcos αk/λ),…,exp(j2π(M-1)dcosαk/λ)]T
Φ=diag [exp (j2 π dcos β1/λ),…,exp(j2πdcosβK/λ)]
Wherein, λ is wavelength.
Two, method derives
The autocorrelation matrix of the data x (t) received is Rxx, expression formula are as follows:
Rxx=E [x (t) xH(t)]=APAH+σ2IM
Wherein P=E [s (t) sHIt (t)] is the covariance matrix of signal source, σ2For the variance of additive white Gaussian noise.
The autocorrelation matrix of the data y (t) received is Ryy, expression formula are as follows:
Ryy=E [y (t) yH(t)]=A Φ P ΦHAH+σ2IM
=AP Φ ΦHAH+σ2IM
=APAH+σ2IM
Consider the independence of noise itself, and independently of signal, it is assumed that the cross-correlation matrix of y (t) and x (t) is Ryx, then:
Ryx=E [y (t) xH(t)]=A Φ PAH
It can similarly obtain, the cross-correlation matrix of x (t) and y (t) are as follows:
Rxy=E [x (t) yH(t)]=A Φ-1PAH
To RxxIt carries out Eigenvalues Decomposition (EVD), enables ε1,…,εKFor matrix RxxK big characteristic values, in the vacation of white noise
It sets, can be averaged to obtain noise variance σ by a small characteristic value of M-K2Estimation.It then, can by removing the influence of noise
To obtain:
Cxx=APAH=Rxx-σ2IM
It can similarly obtain
Cyy=APAH=Ryy-σ2IM
Definition
Definition
Therefore
R1=AEPAH
R2=AEΦPAH
According to the thought of DOA matrix method, the DOA matrix that can be defined as follows
Wherein
If A and P full rank, Φ is without identical diagonal element, then the K nonzero eigenvalue of DOA matrix R ' is equal in Φ K
Diagonal element, and these are worth corresponding feature vector and are equal to corresponding sense vector, it may be assumed that
R′AE=AEΦ
DefinitionWithTo DOA matrix R ', feature decomposition is carried out, so that it may
To matrix AEAnd Φ.According to the characteristic value in Φ, available vkEstimated valueAnd then obtain DOA angle betakEstimation:
According to AEDefinition, we are classified as A and A Φ-1Two parts, after feature decomposition, this two-part estimation difference
ForWith
It estimatesWithAfterwards, ifA certain column ai, the Vandermonde feature of utilization orientation matrix is to direction square
Battle array carries out DOA angle estimation.First to direction vector aiNormalization, makes its first term 1.Take angle (ai), estimate between its array
Phase difference, finally estimate its DOA angle using least square method.Because of ai=[1, exp (j2 π dcos αi/λ),…,exp
(j2π(M-1)dcosαi/λ)]T, it is possible to it obtains:
T=angle (ai)
=[0,2 π dcos αk/λ,…,2(M-1)πdcosαk/λ]T
Least square fitting is Bc=T, wherein c1=[c01,uk1]T, and have
It obtains
WhereinIt is exactly cos αk1Estimation, then it is availableEstimation:
Similarly, we can be fromIt obtainsTherefore DOA angle [alpha]kEstimation:
The method of the present invention step:
[1] autocorrelation matrix and the estimation of cross-correlation matrix of data x (t) and the y (t) received are asked
[2] influence of noise is removed to autocorrelation matrix, obtainedWith
[3] R is defined1And R2And construct extension DOA matrix
[4] to R ' carry out Eigenvalues Decomposition, the estimation of two-dimentional DOA is obtained according to characteristic value and feature vector.
Three, method analysis and emulation
Analysis of complexity is carried out to DOA angle estimating method of the invention, obtains the complexity of auto-correlation and cross-correlation matrix
Degree is O { 4LM2, wherein L indicates to receive signal number of snapshots；It calculatesComplexity be O { 5M3}；It calculatesAnswer
Miscellaneous degree is O { 4M3}；Complexity to R ' carry out feature decomposition is O { 8M3}.The total complexity of the algorithm asked is O { 4LM2+17M3}。
Auto-correlation information and the cross-correlation information of array received data has been fully utilized to construct one in method of the invention
The DOA matrix of a extension, and traditional DOA matrix method, be not fully utilized array received data auto-correlation information and mutually
Information is closed, therefore method of the invention has higher DOA angle estimation performance than traditional DOA matrix method.
Simulation result:
Assuming that three narrow band signal (α of space far-field1,β150 ° of)=(, 55 °), (α2,β260 ° of)=(, 65 °) and (α3,β3)
=(70 °, 75 °) are incident on array shown in Fig. 1, irrelevant between signal.The present invention uses 1000 Monte Carlo simulations
Performance is estimated to assess DOA, and it is as follows to define root-mean-square error (RMSE) expression formula:
WhereinWithIndicate k-th of information source parameter estimation result, α in n-th Monte Carlo simulationkAnd βkIt indicates
The parameter true value of k-th of information source.
Fig. 2 gives the scatter diagram of the extension DOA matrix method of double parallel battle array, and simulation parameter is L=500 and SNR=
20dB.This it appears that the two-dimentional DOA of information source from figure.
Fig. 3 gives traditional DOA matrix algorithm of double parallel battle array under the same conditions and extension DOA matrix algorithm with noise
Than (SNR) variation angle estimation performance and with CRB (Cramér-Rao lower bound) performance comparison curve graph.Simulation parameter is set as double
The array number M=8, number of snapshots L=500 of parallel battle array neutron array 1 and submatrix 2.From figure 3, it can be seen that extension DOA matrix method,
Angle estimation performance with higher.
Fig. 4 is given under the conditions of identical signal-to-noise ratio, the traditional DOA matrix algorithm and extension DOA matrix algorithm of double parallel battle array
The performance chart that changes with snap of angle estimation performance, signal-to-noise ratio is set as SNR=10dB.Figure 4, it is seen that
With the increase of number of snapshots, the angle estimation performance for extending DOA matrix method is substantially better than traditional DOA matrix method.
Fig. 5 gives under the same conditions, when information source number changes, extends the angle estimation performance of DOA matrix method with letter
It makes an uproar than the curve graph of (SNR) variation.From fig. 5, it can be seen that increasing with information source number, extends the angle estimation of DOA matrix method
Performance is decreased obviously.
The above examples only illustrate the technical idea of the present invention, and this does not limit the scope of protection of the present invention, all
According to the technical idea provided by the invention, any changes made on the basis of the technical scheme each falls within the scope of the present invention
Within.
Claims (5)
1. for extending DOA matrix method in the two dimension direction finding of double parallel battle array, which comprises the steps of:
Step 1, double parallel battle array, the homogenous linear subarray that the double parallel battle array is parallel to each other by two are arranged on two-dimensional space
XaAnd YaIt constitutes, when there is K irrelevant narrowbands to be incident on double parallel battle array with carrier signal, solves linear sub-arrays XaAnd Ya
Receive the estimation of the autocorrelation matrix of signalWithLinear sub-arrays XaAnd YaReceive the estimation of the cross-correlation matrix of signalAnd linear sub-arrays YaAnd XaReceive the estimation of the cross-correlation matrix of signal
Step 2, according to the estimation of autocorrelation matrixWithAnd the estimation of cross-correlation matrixWithObtain matrixWith
Step 3, according to the estimation of cross-correlation matrixWithAnd matrixWithDefine matrix R1And R2, and construct expansion
Open up DOA matrix
Step 4, to extension DOA matrix R ' carry out Eigenvalues Decomposition, estimating for two-dimentional DOA is obtained according to characteristic value and feature vector
Meter.
2. according to claim 1 for extending DOA matrix method in the two dimension direction finding of double parallel battle array, which is characterized in that step 1
The estimation of the autocorrelation matrixWithAnd the estimation of cross-correlation matrixWithIt is obtained by following formula:
Wherein, L is number of snapshots, and x (t) indicates t moment linear sub-arrays XaReception signal, y (t) indicate t moment linear sub-arrays
YaReception signal, ()HRepresenting matrix conjugate transposition.
3. according to claim 1 for extending DOA matrix method in the two dimension direction finding of double parallel battle array, which is characterized in that step 2
The matrixWithFormula it is as follows:
Wherein,WithIndicate autocorrelation matrix RxxAnd RyyEstimation, σ2For the variance of additive white Gaussian noise, IMFor M × M
Unit matrix, M be linear sub-arrays XaOr YaNumber of sensors.
4. according to claim 1 for extending DOA matrix method in the two dimension direction finding of double parallel battle array, which is characterized in that step 3
The formula of the extension DOA matrix R ' is as follows:
Wherein, R1And R2It is matrix,WithIndicate cross-correlation matrix RxyAnd RyxEstimation,WithIt is matrix,
(·)+Representing matrix pseudoinverse.
5. according to claim 1 for extending DOA matrix method in the two dimension direction finding of double parallel battle array, which is characterized in that described
The detailed process of step 4 are as follows:
DefinitionWithK=1,2 ..., K, K is number of the irrelevant narrowband with carrier signal, to expansion
DOA matrix R ' carry out Eigenvalues Decomposition is opened up, matrix A is obtainedEAnd Φ, and have R ' AE=AEΦ is obtained then according to the characteristic value in Φ
To vkEstimated valueAnd then obtain DOA angle betakEstimation
By AEIt is divided into A and A Φ-1Two parts, after feature decomposition, this two-part estimation is respectivelyWithRecycle direction square
The Vandermonde feature of battle array carries out DOA angle estimation to direction matrix, to obtain DOA angle [alpha]kEstimation
Wherein, It serves as reasonsObtained uk1Estimated value,It serves as reasonsIt obtains
uk2Estimated value.
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| CN111175692A (en) * | 2020-01-17 | 2020-05-19 | 西北工业大学 | Discrete sparse Bayesian DOA estimation method based on layered synthesis Lasso prior model |
| CN111337872A (en) * | 2020-02-21 | 2020-06-26 | 南京航空航天大学 | Generalized DOA matrix method for coherent information source direction finding |
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