CN106526531A - Improved propagation operator two-dimensional DOA estimation algorithm based on three-dimensional antenna array - Google Patents
Improved propagation operator two-dimensional DOA estimation algorithm based on three-dimensional antenna array Download PDFInfo
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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
Abstract
The invention relates to the technical field of using an array antenna to estimate the arrival direction of a received signal. The problem of failed angle estimation in the actual mobile communication pitch angle range with pitch angle from 70 degrees to 90 degrees in conventional two-dimensional DOA estimation is solved, and pitch angle and azimuth matching is realized. According to the improved propagation operator two-dimensional DOA estimation method based on a three-dimensional antenna array, the antenna array is a three parallel linear array; a uniform linear array Y with N+1 array elements is on the y-axis; uniform linear arrays X and Z with N array elements and parallel to the y-axis are respectively in an xoy plane and a yoz plane; and the array element pitch of subarrays and the distance between subarrays Y and Z and subarrays Y and X are half of the wavelength of an incoming wave signal. The method comprises the steps that 1 a received signal matrix is constructed; 2 a propagation matrix is constructed; 3 a rotation matrix is estimated; and 4 the azimuth and the pitch angle are estimated. The method provided by the invention is mainly applied to the design and manufacture of wireless detection equipment.
Description
Technical field
The present invention relates to the technical field of the arrival direction of the signal for receiving is estimated using array antenna, more particularly to adopt
With the estimating DOA forsingals method of three-dimensional antenna array.
Background technology
It is that Estimation of Spatial Spectrum one is mainly ground that spacing wave arrival direction (Direction of Arrival, DOA) is estimated
Study carefully direction, be widely used in many fields such as radar, sonar, earthquake, communication.The basic problem that DOA estimates just is to determine together
When is in the locus of multiple signals interested in a certain region in space, and (i.e. each signal reaches the side of array reference array element
To angle, abbreviation direction of arrival).Classical super-resolution DOA algorithm for estimating has multiple signal classification algorithm (MUSIC, Multiple
Signal Classification) and Signal parameter estimation algorithm (ESPRIT, Estimation based on ESPRIT
of Signal Parameter via Rotational Invitation Techniques).They belong to subspace class
Algorithm, wherein MUSIC algorithms are noise subspace class algorithms, and ESPRIT algorithms are signal subspace class algorithms, with MUSIC algorithms
Algorithm to represent includes mensuration, rooting MUSIC methods of Characteristic Vectors etc., and the algorithm with ESPRIT algorithms as representative includes least square
ESPRIT, total least square ESPRIT etc..The central idea of wherein MUSIC algorithms is：Using different characteristic value feature to
Orthogonality between amount divides the space into orthogonal subspace, then constructs array manifold spectral function using this orthogonality,
Search for its extreme value and can just realize the coming to estimation of spacing wave electromagnetic wave.
The high resolution algorithm such as traditional MUSIC algorithms and ESPRIT algorithms, although with good estimation performance, but
Due to needing to carry out spectrum peak search or dock receipts signal covariance matrix carrying out Eigenvalues Decomposition, two-dimentional DOA is being applied to
There is larger amount of calculation, especially when array element number is larger during estimation.Propagator algorithm solve signal subspace and
Only need to carry out linear operation during noise subspace, therefore with relatively low computation complexity.At present, have substantial amounts of based on propagation
The arrival direction estimation algorithm of operator.But these algorithms have or need to carry out the pairing at azimuth and the angle of pitch or do not have
There are the construction featuress for making full use of array or in the actual mobile communication luffing angle scope internal memory that the angle of pitch is 70 °～90 °
In angle estimation Problem of Failure or remain a need for carrying out the limitation such as spectrum peak search.
The content of the invention
To overcome the deficiencies in the prior art, present invention seek to address that in traditional arrival direction estimation, being 70 ° in the angle of pitch
Angle estimation Problem of Failure in the range of～90 ° of actual mobile communication luffing angle, and the angle of pitch and azimuthal pairing
Problem.The technical solution used in the present invention is, based on the improvement propagation operator arrival direction estimation method of three-dimensional antenna array, day
Linear array is classified as three parallel linear arrays, wherein have the even linear array Y that an array element number is N+1 on the y axis, in xoy planes and yoz
There are even linear array X and Z that an array element number parallel with y-axis is N, the array element distance of submatrix, submatrix Y and son in plane respectively
Battle array Z and the distance between submatrix Y and submatrix X are the half of incoming wave signal wavelength；Comprise the following steps that：
Step 1：Construction receipt signal matrix.
Using the array element positioned at zero as reference array element, linear array X, Y, the signal vector that Z is received are respectively x (t)
=[x1(t),x2(t),…,xN(t)]T, y (t)=[y1(t),y2(t),…,yN+1(t)]TWith z (t)=[z1(t),z2(t),…,
zN(t)]T, wherein xi(t),yi(t),ziT () is respectively submatrix X, the signal that i-th array element of Y, Z is received in t, construction
New received signal vector w (t)=[yT(t),xT(t),zT(t)]T, then the receiving data matrix for corresponding to M snaps is W=[w
(1),w(2),…,w(M)]；
Step 2：Construction propogator matrix
Receive signal autocorrelation matrix bePressed following form piecemeal, R=[R1,
R2], wherein R1∈C(3N+1)×K, R2∈C(3N+1)×(3N+1-K), then propogator matrixDefinition extension propogator matrixWherein IK×KFor K rank unit matrixs, H represents conjugate transpose；
Step 3：Estimate spin matrix
By PcBy following form piecemeal,Wherein Py∈C(N+1)×K,Px∈CN×K,Pz∈CN×K, C is multiple
Number, defines matrix Ψx=P1 +Px, wherein P1For PyFront N rows, to ΨxEigenvalues Decomposition is carried out, then its eigenvalue is's
Diagonal components,For ΦxEstimated value, eigenvectors matrixAs A1Estimated value, wherein ΦxFor correspondence submatrix X
Spin matrix, A1For the front K rows of the array manifold matrix of submatrix Y；Define two new matrixesWherein P2For PyRear N rows, P3For PxFront N-1 rows, P4For PxRear N-1 rows, then haveWhereinFor ΦyEstimated value, ΦyFor the spin matrix of correspondence submatrix Y；
In the same manner, define matrix Ψz=P1 +Pz, to ΨzEigenvalues Decomposition is carried out, then its eigenvalue isDiagonal point
Amount,For ΦzEstimated value, wherein ΦzTo correspond to the spin matrix of submatrix Z, eigenvectors matrix isAs A1Estimation
Value.Define two matrixesWherein P5For PzFront N-1 rows, P6For PzRear N-1 rows, then haveWhereinFor ΦyEstimated value；
Step 4：Azimuth and pitching angular estimation
Respectively willWithAccording to element argument order from big to small on their diagonal, its diagonal entry is entered
Row is rearranged, and obtains new matrixWithAnd haveWherein Π1And Π2It is K
The permutation matrix of × K, orderIfRespectively's
K-th diagonal components, the then estimated value of azimuth and the angle of pitchRespectively Wherein angle is represented and is taken argument computing, and atan is represented and negated arctangent operation.
The characteristics of of the invention and beneficial effect are：
As the present invention is using improvement propagation operator two-dimensional estimation algorithm based on three-dimensional antenna array, it is thus possible to compared with
Low computation complexity obtains preferable azimuth and pitching angular estimation performance；Can realize azimuth and pitching angular estimation from
Dynamic pairing；Be not in direction ambiguity problem in the range of the luffing angle of the actual mobile communication that the angle of pitch is 70 °～90 °.
Because there is no overlap array element in the array that the present invention is adopted, so received signal vector w (t) of present invention construction=
[yT(t),xT(t),zT(t)]TIn there is no redundant data, reduce computation complexity.
The present invention is directed to three parallel linear arrays, it is proposed that a kind of straightforward procedure of the marriage problem between solution spin matrix.
Description of the drawings：
Fig. 1 three-dimensional antenna array structural representations.
Fig. 2 orientation angular estimation rectangular histogram.
Fig. 3 pitching angular estimation rectangular histograms.
Fig. 4 difference angle combinations estimate joint mean square error figure.
Specific embodiment
For the problem that existing DOA algorithm for estimating is present, the present invention proposes a kind of improvement based on three-dimensional antenna array
Propagation operator arrival direction estimation algorithm, the aerial array are three parallel linear arrays, wherein there is an array element number to be N+1 on the y axis
Even linear array Y, with the even linear array X for having an array element number parallel with y-axis to be N in yoz planes respectively in the xoy planes
And Z, the array element distance of submatrix, submatrix Y and submatrix Z and the distance between submatrix Y and submatrix X are the one of incoming wave signal wavelength
Half.
The technical solution used in the present invention：Based on the improvement propagation operator arrival direction estimation method of three-dimensional antenna array, wrap
Include following steps：
Step 1：Construction receipt signal matrix.
Using the array element positioned at zero as reference array element, linear array X, Y, the signal vector that Z is received are respectively x (t)
=[x1(t),x2(t),…,xN(t)]T, y (t)=[y1(t),y2(t),…,yN+1(t)]TWith z (t)=[z1(t),z2(t),…,
zN(t)]T.New received signal vector w (t)=[y of constructionT(t),xT(t),zT(t)]T, then correspond to the receiving data square of M snaps
Battle array is W=[w (1), w (2) ..., w (M)].
Step 2：Construction propogator matrix
Receive signal autocorrelation matrix bePressed following form piecemeal, R=[R1,
R2], wherein R1∈C(3N+1)×K, R2∈C(3N+1)×(3N+1-K).Then propogator matrixDefinition extension propogator matrix
Step 3：Estimate spin matrix
By PcBy following form piecemeal,Wherein Py∈C(N+1)×K,Px∈CN×K,Pz∈CN×K.Define square
Battle array Ψx=P1 +Px, wherein P1For PyFront N rows.To ΨxEigenvalues Decomposition is carried out, then its eigenvalue isDiagonal point
Amount,For ΦxEstimated value, eigenvectors matrixAs A1Estimated value.Define two new matrixes Wherein P2For PyRear N rows, P3For PxFront N-1 rows, P4For PxRear N-1 rows.Then haveWhereinFor ΦyEstimated value.
Matrix Ψ is defined in the same mannerz=P1 +Pz, to ΨzEigenvalues Decomposition is carried out, then its eigenvalue isDiagonal point
Amount,For ΦzEstimated value, eigenvectors matrix isAs A1Estimated value.Define two matrixesWherein P5For PzFront N-1 rows, P6For PzRear N-1 rows.Then haveWhereinFor ΦyEstimated value.
Step 4：Azimuth and pitching angular estimation
Respectively willWithAccording to element argument order from big to small on their diagonal, its diagonal entry is entered
Row is rearranged, and obtains new matrixWithAnd haveWherein Π1And Π2
For the permutation matrix of K × K.OrderIfRespectivelyK-th diagonal components, then the estimated value of azimuth and the angle of pitchRespectively Wherein angle is represented and is taken argument computing, and atan is represented and negated arctangent operation.
Below in conjunction with drawings and Examples, the present invention will be further described：
Construction three-dimensional antenna array as shown in Figure 1.There is K arrowband unrelated signal to incide array in assuming space
On, wherein the 2-d direction finding of k-th signal is(k=1,2 ... K),And θkThe respectively orientation of incoming wave signal
Angle and the angle of pitch.
Step 1：Construction receipt signal matrix.
Submatrix X, signal vector x (t) that Y, Z are received in t=[x1(t),x2(t),…,xN(t)]T, y (t)=[y1
(t),y2(t),…,yN+1(t)]T, z (t)=[z1(t),z2(t),…,zN(t)]TCan be represented with formula (1).
Wherein nx(t)∈CN×1,ny(t)∈C(N+1)×1,nz(t)∈CN×1It is that average is 0, variance is σ2Additive white gaussian
Noise, and it is separate with s (t), and s (t) is incoming wave signal.For submatrix Y
Array manifold matrix, AyFor AxFront N rows,Φx,ΦzBe comprising
The diagonal matrix of the K × K of azimuth and pitching angle information, and with following expression-form,
X (t), y (t), z (t) are combined as into new received signal vector w (t)=[yT(t),xT(t),zT(t)]T。
Then W=fast for M [w (1), w (2) ..., w (M)].
Step 2：Construction propogator matrix
Receive signal autocorrelation matrix bePressed following form piecemeal, R=[R1,
R2], wherein R1∈C(3N+1)×K, R2∈C(3N+1)×(3N+1-K).Then propogator matrixDefinition extension propogator matrix
Step 3：Estimate spin matrix
By PcBy following form piecemeal,Wherein Py∈C(N+1)×K,Px∈CN×K,Pz∈CN×K.Define square
Battle array Ψx=P1 +Px, wherein P1For PyFront N rows.To ΨxEigenvalues Decomposition is carried out, then its eigenvalue isDiagonal point
Amount,For ΦxEstimated value, eigenvectors matrix isAs A1Estimated value.Define two new matrixes Wherein P2For PyRear N rows, P3For PxFront N-1 rows, P4For PxRear N-1 rows.Then have
For ΦyEstimated value, wherein
Matrix Ψ is defined in the same mannerz=P1 +Pz, to ΨzEigenvalues Decomposition is carried out, then its eigenvalue isDiagonal point
Amount,For ΦzEstimated value, eigenvectors matrixAs A1Estimated value.Define two matrixes Wherein P5For PzFront N-1 rows, P6For PzRear N-1 rows.Then haveWhereinFor ΦyEstimation
Value.
Step 4：Azimuth and pitching angular estimation
Respectively willWithAccording to element argument order from big to small on their diagonal, its diagonal entry is entered
Row is rearranged, and obtains new matrixWithAnd haveWherein Π1And Π2It is K
The permutation matrix of × K.OrderIfRespectively
K-th diagonal components, then the estimated value of azimuth and the angle of pitchRespectively Wherein angle is represented and is taken argument computing, and atan is represented and negated arctangent operation.
With reference to the embodiment in above-mentioned steps, simulating, verifying is carried out to effectiveness of the invention as follows：
The parallel linear array of N=5, i.e., three is taken in emulation and has 16 array elements, array pitch d=0.5 λ, wherein λ is signal wave
It is long, it is 200 for each emulation experiment takes fast umber of beats, carries out M=500 Monte Carlo simulation.
Emulation experiment 1：Hypothesis has K=2 constant power unrelated signal to incide aerial array, wherein signal to noise ratio snr=
15dB, the azimuth of signal and the angle of pitch areFig. 2 and Fig. 3 show azimuth
Estimate rectangular histogram and pitching angular estimation rectangular histogram.It can be seen that set forth herein algorithm clearly can differentiate this two
Individual incoming wave signal.
Emulation experiment 2：Hypothesis has K=1 signal to incide aerial array, the side of signal to noise ratio snr=15dB, wherein signal
Parallactic angle and the angle of pitch are with 5 ° of step change between 10 °～80 °.Fig. 4 estimates joint mean square error for different angle combinations
Figure.
Claims (1)
1. a kind of improvement propagation operator arrival direction estimation method based on three-dimensional antenna array, is characterized in that, aerial array is three
Parallel linear array, wherein have the even linear array Y that an array element number is N+1 on the y axis, in xoy planes and in yoz planes respectively
There are even linear array X and Z that an array element number parallel with y-axis is N, the array element distance of submatrix, submatrix Y and submatrix Z and son
Battle array the distance between Y and submatrix X are the half of incoming wave signal wavelength；Comprise the following steps that：
Step 1：Construction receipt signal matrix.
Using the array element positioned at zero as reference array element, linear array X, Y, the signal vector that Z is received are respectively x (t)=[x1
(t),x2(t),…,xN(t)]T, y (t)=[y1(t),y2(t),…,yN+1(t)]TWith z (t)=[z1(t),z2(t),…,zN
(t)]T, wherein xi(t),yi(t),ziT () is respectively submatrix X, the signal that i-th array element of Y, Z is received in t, construction
New received signal vector w (t)=[yT(t),xT(t),zT(t)]T, then the receiving data matrix for corresponding to M snaps is W=[w
(1),w(2),…,w(M)]；
Step 2：Construction propogator matrix
Receive signal autocorrelation matrix bePressed following form piecemeal, R=[R1,R2], its
Middle R1∈C(3N+1)×K, R2∈C(3N+1)×(3N+1-K), then propogator matrixDefinition extension propogator matrixWherein IK×KFor K rank unit matrixs, H represents conjugate transpose；
Step 3：Estimate spin matrix
By PcBy following form piecemeal,Wherein Py∈C(N+1)×K,Px∈CN×K,Pz∈CN×K, C is plural number, fixed
Adopted matrixWherein P1For PyFront N rows, to ΨxEigenvalues Decomposition is carried out, then its eigenvalue isDiagonal
Component,For ΦxEstimated value, eigenvectors matrixAs A1Estimated value, wherein ΦxFor the spin moment of correspondence submatrix X
Battle array, A1For the front K rows of the array manifold matrix of submatrix Y；Define two new matrixesWherein
P2For PyRear N rows, P3For PxFront N-1 rows, P4For PxRear N-1 rows, then haveWhereinFor ΦyEstimation
Value, ΦyFor the spin matrix of correspondence submatrix Y；
In the same manner, define matrix Ψz=P1 +Pz, to ΨzEigenvalues Decomposition is carried out, then its eigenvalue isDiagonal components,
For ΦzEstimated value, wherein ΦzTo correspond to the spin matrix of submatrix Z, eigenvectors matrix isAs A1Estimated value.It is fixed
Adopted two matrixesWherein P5For PzFront N-1 rows, P6For PzRear N-1 rows, then haveWhereinFor ΦyEstimated value；
Step 4：Azimuth and pitching angular estimation
Respectively willWithAccording to element argument order from big to small on their diagonal, its diagonal entry is entered
Row is rearranged, and obtains new matrixWithAnd haveWherein Π1And Π2It is
The permutation matrix of K × K, orderIfRespectively
K-th diagonal components, then the estimated value of azimuth and the angle of pitchRespectively Wherein angle is represented and is taken argument computing, and atan is represented and negated arctangent operation.
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| CN107918108A (en) * | 2017-11-14 | 2018-04-17 | 重庆邮电大学 | A kind of uniform circular array 2-d direction finding method for quick estimating |
| CN108020812A (en) * | 2017-11-28 | 2018-05-11 | 天津大学 | Arrival direction estimation method based on special three parallel linear array structures |
| CN108320739A (en) * | 2017-12-22 | 2018-07-24 | 景晖 | According to location information assistant voice instruction identification method and device |
| CN108761383A (en) * | 2018-04-13 | 2018-11-06 | 中国人民解放军陆军工程大学 | A kind of time delay based on two-dimensional matrix beam and angle combined estimation method |
| CN108919174A (en) * | 2018-05-28 | 2018-11-30 | 北京交通大学 | The short-wave radio direction-finding system and method for irregular antenna array structure |
| CN109001678A (en) * | 2017-06-06 | 2018-12-14 | 中国科学技术大学 | A kind of thunder detection and localization method based on three-dimensional microphone array |
| CN109696652A (en) * | 2019-01-29 | 2019-04-30 | 西安电子科技大学 | A kind of arrival direction estimation method and device thereof, equipment, storage medium |
| CN109782218A (en) * | 2019-02-01 | 2019-05-21 | 中国空间技术研究院 | A kind of non-circular signal DOA estimation method of relevant distribution based on double parallel antenna array |
| CN111830458A (en) * | 2020-07-14 | 2020-10-27 | 电子科技大学 | Parallel linear array single-snapshot two-dimensional direction finding method |
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| CN109001678A (en) * | 2017-06-06 | 2018-12-14 | 中国科学技术大学 | A kind of thunder detection and localization method based on three-dimensional microphone array |
| CN107918108A (en) * | 2017-11-14 | 2018-04-17 | 重庆邮电大学 | A kind of uniform circular array 2-d direction finding method for quick estimating |
| CN108020812A (en) * | 2017-11-28 | 2018-05-11 | 天津大学 | Arrival direction estimation method based on special three parallel linear array structures |
| CN108020812B (en) * | 2017-11-28 | 2021-11-26 | 天津大学 | Two-dimensional DOA estimation method based on special three-parallel line array structure |
| CN108320739A (en) * | 2017-12-22 | 2018-07-24 | 景晖 | According to location information assistant voice instruction identification method and device |
| CN108761383A (en) * | 2018-04-13 | 2018-11-06 | 中国人民解放军陆军工程大学 | A kind of time delay based on two-dimensional matrix beam and angle combined estimation method |
| CN108919174A (en) * | 2018-05-28 | 2018-11-30 | 北京交通大学 | The short-wave radio direction-finding system and method for irregular antenna array structure |
| CN109696652A (en) * | 2019-01-29 | 2019-04-30 | 西安电子科技大学 | A kind of arrival direction estimation method and device thereof, equipment, storage medium |
| CN109696652B (en) * | 2019-01-29 | 2020-07-31 | 西安电子科技大学 | Two-dimensional DOA estimation method and device, equipment and storage medium thereof |
| CN109782218A (en) * | 2019-02-01 | 2019-05-21 | 中国空间技术研究院 | A kind of non-circular signal DOA estimation method of relevant distribution based on double parallel antenna array |
| CN111830458A (en) * | 2020-07-14 | 2020-10-27 | 电子科技大学 | Parallel linear array single-snapshot two-dimensional direction finding method |
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