CN106526530A - Propagation operator-based 2-L type array two-dimensional DOA estimation algorithm - Google Patents
Propagation operator-based 2-L type array two-dimensional DOA estimation algorithm 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
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Abstract
The invention relates to the technical field of estimating the signal arrival direction by adopting an array antenna and overcomes the defect in the prior art that the conventional propagation operator-based algorithm cannot utilizes all antenna array elements, wherein a new propagation matrix is constructed. The algorithm solves the angle estimation invalidation problem during the actual mobile communication process with the range of pitch angles to be 70-90 degrees. In this way, the estimation performance for the azimuth angle and the pitch angle is improved. According to the technical scheme of the invention, the propagation operator-based 2-L type array two-dimensional DOA estimation algorithm comprises the steps of 1, constructing a received signal matrix; 2, constructing a propagation matrix; 3, estimating a rotation matrix; 4, estimating the azimuth angle and the pitch angle. The propagation operator-based 2-L type array two-dimensional DOA estimation algorithm is mainly used for the design and the manufacture of infinite detection equipment.
Description
Technical field
The present invention relates to adopt array antenna to estimate to receive the technical field of direction of arrival of signal, more particularly to adopt 2-L
The estimating DOA forsingals method of type aerial 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 for representing includes characteristic vector method, rooting MUSIC methods 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.It is currently, there are a large amount of based on propagation
The arrival direction estimation algorithms such as the L-type array of operator, 2-L type arrays, double parallel linear array, three parallel linear arrays.But some are based on double
Parallel linear array and the propagator algorithm based on L-type array are in the actual mobile communication luffing angle that the angle of pitch is 70 °～90 °
In the range of there is angle estimation Problem of Failure, some based on three parallel linear arrays using propagation operator arrival direction estimation algorithm simultaneously
The design feature of aerial array is not made full use of, some arrival direction estimations based on the employing propagation operator of 2-L type arrays are calculated
Method is utilized respectively two L-type submatrixs of array, individually estimates azimuth and the angle of pitch of signal, estimates poor-performing.Additionally
Some algorithms need to carry out time-consuming spectrum peak search.
The content of the invention
For overcoming the deficiencies in the prior art, present invention seek to address that traditional propagator algorithm can not utilize all antennas
The shortcoming of array element, constructs a new propogator matrix.The propagation operator arrival direction estimation algorithm based on double parallel linear array is solved,
Angle estimation Problem of Failure in the range of the actual mobile communication luffing angle that the angle of pitch is 70 °～90 °.Improve azimuth and
The estimation performance of the angle of pitch.The technical solution used in the present invention is that the 2-L type arrays arrival direction estimation based on propagation operator is calculated
Method, step are as follows：
Step 1：Construction receipt signal matrix
Using the array element positioned at the origin of coordinates 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(t)]TWith z (t)=[z1(t),z2(t),…,zN
(t)]T, wherein xi(t),yi(t),ziT () represents linear array X, Y, the signal that i-th array element on Z is received in t, N respectively
For submatrix array element number, T representing matrix transposition computings, new received signal vector w (t)=[x is constructedT(t),yT(t),zT(t)
]T, and haveWherein Ax,Ay,AzRespectively linear array X, the array manifold of Y, Z
Matrix, array manifold matrixes of the A for 2-L type arrays, incoming wave signals of the s (t) for array, n (t) they are noise component(s), then correspond to M fast
The receiving data matrix of bat 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 H representing matrixs take conjugate transposition computing, R1∈C3N×K, R2∈C3N×(3N-K), C is plural, then propogator matrix isDefine a new extension propogator matrixWherein IK×KFor the unit matrix of K ranks, K is
The number of incoming wave signal；
Step 3：Estimate spin matrix
By PcBy following form piecemeal,Wherein Px,Py,PzThe matrix of N × K is, matrix is definedWherein A1For the front K rows of A, Pz,1For PzFront N-1 rows, Pz,2For PzRear N-1 rows, to ΨzCarry out
Eigenvalues Decomposition, then its characteristic value beDiagonal components,For ΦzEstimate, eigenvectors matrixAs A1's
Estimate, wherein ΦzFor the corresponding spin matrix of submatrix Z, its form is Wherein diag represented a vectorial diagonalization, and d is array element distance, wavelength of the λ for incoming wave signal, θiRepresent
The angle of pitch of i-th signal, defines two new matrixesWherein Px,1For PxFront N-1 rows, Px,2
For PxRear N-1 rows, then haveWhereinFor ΦxEstimate, ΦxForm be For the azimuth of i-th signal of correspondence, two new matrixes are defined in the same mannerWherein Py,1For PyFront N-1 rows, Py,2For PyRear N-1 rows, then haveWherein
For ΦyEstimate, ΦyForm be
Step 4：Azimuth and pitching angular estimation
IfRespectivelyK-th diagonal components, then the estimate of azimuth and the angle of pitch
RespectivelyWherein angle represents and takes argument computing,
Atan is represented and is negated arctangent operation.
The characteristics of of the invention and beneficial effect are：
By constructing a new propogator matrix, the information of all array elements is make use of, can be with relatively low computation complexity
Obtain preferable azimuth and pitching angular estimation performance；The automatic matching of azimuth and pitching angular estimation can be realized；In pitching
It in the range of the luffing angle of 70 °～90 ° of actual mobile communication is not in direction ambiguity problem that angle is.
Description of the drawings：
Fig. 1 antenna array structure schematic diagrames.
Fig. 2 orientation angular estimation histogram.
Fig. 3 pitching angular estimation histograms.
Fig. 4 difference angle combinations estimate joint mean square error figure.
Fig. 5 orientation angular estimation mean square error is with signal to noise ratio situation of change.
Fig. 6 pitching angular estimation mean square errors are with signal to noise ratio situation of change.
Specific embodiment
For the problem that existing DOA algorithm for estimating is present, the present invention proposes a kind of 2-L type arrays based on propagation operator
Arrival direction estimation algorithm, it is characterised in that：The aerial array is 2-L type arrays, has one wherein in x-axis, y-axis and z-axis respectively
Even linear array of the individual array element number for N, respectively with X, Y, Z are represented.Half of the array element distance for incoming wave signal wavelength.
The technical solution used in the present invention：Based on the 2-L type array arrival direction estimation algorithms of propagation operator, including following
Step：
Step 1：Construction receipt signal matrix.
Using the array element positioned at the origin of coordinates 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(t)]TWith z (t)=[z1(t),z2(t),…,zN
(t)]T, wherein xi(t),yi(t)ziT () represents linear array X, Y, the signal that i-th array element on Z is received in t respectively.Structure
Make new received signal vector w (t)=[xT(t),yT(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∈C3N×K, R2∈C3N×(3N-K).Then propogator matrixDefine a new extension and propagate square
Battle arrayWherein IK×KFor the unit matrix of K ranks, numbers of the K for incoming wave signal.
Step 3：Estimate spin matrix
By PcBy following form piecemeal,Wherein Px,Py,PzIt is the matrix of N × K.Define matrixWherein Pz,1For PzFront N-1 rows, Pz,2For PzRear N-1 rows.To ΨzEigenvalues Decomposition is carried out, then
Its characteristic value isDiagonal components,For ΦzEstimate, eigenvectors matrixAs A1Estimate, wherein
ΦzFor the array manifold matrix of submatrix Z.Define two new matrixesWherein Px,1For PxFront N-
1 row, Px,2For PxRear N-1 rows.Then haveWhereinFor ΦxEstimate, wherein ΦxFor the array manifold of submatrix X
Matrix.Two new matrixes are defined in the same mannerWherein Py,1For PyFront N-1 rows, Py,2For PyAfter
N-1 rows.Then haveWhereinFor ΦyEstimate, wherein ΦyFor the array manifold matrix of submatrix Y.
Step 4：Azimuth and pitching angular estimation
IfRespectivelyK-th diagonal components, then the estimate of azimuth and the angle of pitch
RespectivelyWherein angle represents and takes argument computing,
Atan is represented and is negated arctangent operation..
Below in conjunction with drawings and Examples, the present invention will be further described：
Construction 2-L type aerial arrays as shown in Figure 1.There is K arrowband unrelated signal to incide array in assuming space
On, the 2-d direction finding of wherein 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(t)]T, z (t)=[z1(t),z2(t),…,zN(t)]TCan be represented with formula (1).
Wherein nx(t),ny(t),nzT it is 0 that () is the average of N × 1 dimension, and variance is σ2Additive white Gaussian noise, and and s
T () is separate.For the array manifold matrix of submatrix X, wherein
For the array manifold matrix of submatrix Y, wherein For the array manifold matrix of submatrix Z, wherein
X (t), y (t), z (t) are combined as into new received signal vector w (t)=[xT(t),yT(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∈C3N×K, R2∈C3N×(3N-K).Then propogator matrix isDefine a new extension to propagate
Matrix
Step 3：Estimate spin matrix
By PcBy following form piecemeal,Wherein Px,Py,PzIt is the matrix of N × K dimensions.Define matrixWherein Pz,1For PzFront N-1 rows, Pz,2For PzRear N-1 rows.To ΨzEigenvalues Decomposition is carried out, then
Its characteristic value isDiagonal components,For ΦzEstimate, eigenvectors matrixAs A1Estimate.Φz's
Form isDiag is represented a vectorial diagonalization computing.
Define two new matrixesWherein Px,1For PxFront N-1 rows, Px,2For PxRear N-1 rows.Then
HaveWhereinFor ΦxEstimate, ΦxForm be Two new matrixes are defined in the same manner Wherein Py,1For PyFront N-1
OK, Py,2For PyRear N-1 rows.Then haveWhereinFor ΦyEstimate, ΦyForm be
Step 4：Azimuth and pitching angular estimation
IfRespectivelyK-th diagonal components, then the estimate of azimuth and the angle of pitch
RespectivelyWherein angle represents and takes argument computing,
Atan is represented and is negated arctangent operation.
With reference to the embodiment in above-mentioned steps, simulating, verifying is carried out to effectiveness of the invention as follows：
N=8, i.e. 2-L types array being taken in emulation and having 22 array elements, array pitch d=0.5 λ, wherein λ is signal wavelength,
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 that azimuth is estimated
Meter histogram and pitching angular estimation histogram.It can be seen that set forth herein algorithm can clearly differentiate the two
Incoming wave signal, without angle of arrival fuzzy problem.
Emulation experiment 2：Hypothesis has K=1 signal to incide aerial array, the side of signal to noise ratio snr=10dB, wherein signal
Parallactic angle and the angle of pitch are with 2 ° of step change between 10 °～80 °.Fig. 4 estimates joint mean square error for different angle combinations
Figure.
Emulation experiment 3：Hypothesis has K=2 constant power unrelated signal to incide aerial array, and wherein signal to noise ratio snr is in 5dB
With the step change of 5dB between～30dB, the azimuth of signal and the angle of pitch areFigure
5 and Fig. 6 are respectively the situation of change of azimuth and pitching angular estimation mean square error with signal to noise ratio.It can be seen that with
The increase of signal to noise ratio, azimuth and angle of pitch mean square error reduce.
Claims (1)
1. a kind of 2-L type array arrival direction estimation algorithms based on propagation operator, is characterized in that, step is as follows：
Step 1：Construction receipt signal matrix
Using the array element positioned at the origin of coordinates 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(t)]TWith z (t)=[z1(t),z2(t),…,zN(t)
]T, wherein xi(t),yi(t),ziT () represents linear array X respectively, Y, the signal that i-th array element on Z is received in t, and N is
Submatrix array element number, T representing matrix transposition computings construct new received signal vector w (t)=[xT(t),yT(t),zT(t)]T,
And haveWherein Ax,Ay,AzRespectively linear array X, the array manifold square of Y, Z
Battle array, array manifold matrixes of the A for 2-L type arrays, incoming wave signals of the s (t) for array, n (t) they are noise component(s), then correspond to M snaps
Receiving data matrix be 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 H representing matrixs take conjugate transposition computing, R1∈C3N×K, R2∈C3N×(3N-K), C is plural, then propogator matrix isDefine a new extension propogator matrixWherein IK×KFor the unit matrix of K ranks, K is
The number of incoming wave signal；
Step 3：Estimate spin matrix
By PcBy following form piecemeal,Wherein Px,Py,PzThe matrix of N × K is, matrix is definedWherein A1For the front K rows of A, Pz,1For PzFront N-1 rows, Pz,2For PzRear N-1 rows, to ΨzCarry out feature
Value is decomposed, then its characteristic value isDiagonal components,For ΦzEstimate, eigenvectors matrixAs A1Estimation
Value, wherein ΦzFor the corresponding spin matrix of submatrix Z, its form is
Wherein diag represented a vectorial diagonalization, and d is array element distance, wavelength of the λ for incoming wave signal, θiRepresent i-th signal
The angle of pitch, defines two new matrixes Wherein Px,1For PxFront N-1 rows, Px,2For PxRear N-1 rows,
Then haveWhereinFor ΦxEstimate, ΦxForm be For the azimuth of i-th signal of correspondence, two new matrixes are defined in the same manner
Wherein Py,1For PyFront N-1 rows, Py,2For PyRear N-1 rows, then haveWhereinFor ΦyEstimate, ΦyShape
Formula is
Step 4：Azimuth and pitching angular estimation
IfRespectivelyK-th diagonal components, then the estimate of azimuth and the angle of pitchRespectively
ForWherein angle represents and takes argument computing, atan tables
Show and negate arctangent operation.
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| CN107907854A (en) * | 2017-10-31 | 2018-04-13 | 大连大学 | DOA estimation new methods under impulse noise environment |
| CN108414967A (en) * | 2018-04-11 | 2018-08-17 | 华南理工大学 | Based on L gusts of underwater two-dimension Wave arrival direction estimating method and device of angle adjustable double |
| CN108535682A (en) * | 2018-06-15 | 2018-09-14 | 华南理工大学 | It is a kind of based on rotating non-homogeneous double L gusts of underwater two-dimension DOA estimation method and device |
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| CN111025225A (en) * | 2019-12-18 | 2020-04-17 | 南京航空航天大学 | Propagation operator-based direction of arrival estimation method suitable for co-prime linear array |
| CN111474534A (en) * | 2020-04-16 | 2020-07-31 | 电子科技大学 | Two-dimensional DOA estimation method based on symmetric parallel nested array |
| CN111474534B (en) * | 2020-04-16 | 2023-04-07 | 电子科技大学 | Two-dimensional DOA estimation method based on symmetric parallel nested 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 |
| CN111830458B (en) * | 2020-07-14 | 2022-03-29 | 电子科技大学 | Parallel linear array single-snapshot two-dimensional direction finding method |
| CN113325365A (en) * | 2021-05-18 | 2021-08-31 | 哈尔滨工程大学 | Quaternion-based coherent signal two-dimensional DOA estimation method |
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