CN106526530B - 2-L type array arrival direction estimation algorithm based on propagation operator - Google Patents
2-L type array arrival direction estimation algorithm based on propagation operator Download PDFInfo
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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
- 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 present invention relates to the technical fields that direction of arrival of signal is received using array antenna estimation, to solve the disadvantage that traditional propagator algorithm cannot construct a new propogator matrix using all bays.The propagation operator arrival direction estimation algorithm based on double parallel linear array is solved, the angle estimation Problem of Failure within the scope of the practical mobile communication pitch angle that pitch angle is 70 °~90 °.Improve the estimation performance at azimuth and pitch angle.The technical solution adopted by the present invention is that the 2-L type array arrival direction estimation algorithm based on propagation operator, steps are as follows: step 1: construction receipt signal matrix step 2: construction propogator matrix step 3: estimation spin matrix step 4: azimuth and pitching angular estimation.Present invention is mainly applied to the design and manufacture of unlimited detecting devices.
Description
Technical field
The present invention relates to the technical fields that direction of arrival of signal is received using array antenna estimation, more particularly to use 2-L
The estimating DOA forsingals method of type aerial array.
Background technique
Spacing wave arrival direction (Direction of Arrival, DOA) estimation is Estimation of Spatial Spectrum one and mainly grinds
Study carefully direction, is widely used in many fields such as radar, sonar, earthquake, communication.The basic problem of DOA estimation is exactly to determine together
When be in spatial position (the i.e. each signal sides that reach array reference array element of multiple interested signals in a certain region in space
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 rotation invariant technology
of Signal Parameter via Rotational Invitation Techniques).They belong to subspace class
Algorithm, wherein MUSIC algorithm is noise subspace class algorithm, and ESPRIT algorithm is signal subspace class algorithm, with MUSIC algorithm
Algorithm for representative includes characteristic vector method, rooting MUSIC method etc., includes least square by the algorithm of representative of ESPRIT algorithm
ESPRIT, total least square ESPRIT etc..The wherein central idea of MUSIC algorithm are as follows: using different characteristic value feature to
Orthogonality between amount divides the space into orthogonal subspace, then constructs array manifold spectral function using this orthogonality,
The coming to estimation of spacing wave electromagnetic wave can be realized by searching for its extreme value.
The high resolution algorithms such as traditional MUSIC algorithm and ESPRIT algorithm, although having good estimation performance,
Receipts signal covariance matrix progress Eigenvalues Decomposition is either docked due to needing to carry out spectrum peak search, is being applied to two-dimentional DOA
There is biggish calculation amount, especially when array element number is larger when estimation.Propagator algorithm solve signal subspace and
It only needs to carry out linear operation when noise subspace, therefore there is lower computation complexity.It is currently, there are a large amount of based on propagation
The arrival direction estimations algorithms such as the L-type array of operator, 2-L type array, double parallel linear array, three parallel linear arrays.But it is certain based on double
The practical mobile communication pitch angle that linear array and the propagator algorithm based on L-type array are 70 °~90 ° in pitch angle in parallel
There are angle estimation Problem of Failure in range, some use the arrival direction estimation algorithm of propagation operator simultaneously based on three parallel linear arrays
The design feature of aerial array is not made full use of, some arrival direction estimations using propagation operator based on 2-L type array are calculated
Method is utilized respectively two L-type submatrixs of array, individually estimates azimuth and the pitch angle of signal, and estimation performance is poor.Additionally
Some algorithms need to carry out time-consuming spectrum peak search.
Summary of the invention
In order to overcome the deficiencies of the prior art, present invention seek to address that traditional propagator algorithm cannot utilize all antennas
The shortcomings that 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 within the scope of the practical mobile communication pitch angle that pitch angle is 70 °~90 °.Improve azimuth and
The estimation performance of pitch angle.The technical solution adopted by the present invention is that the 2-L type array arrival direction estimation based on propagation operator is calculated
Method, steps are as follows:
Step 1: construction receipt signal matrix
Using positioned at the array element of coordinate origin, as reference array element, linear array X, the signal vector that Y, Z are received is 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),zi(t) linear array X is respectively indicated, the signal that i-th of array element on Y, Z is received in t moment, N is
Submatrix array element number, T representing matrix transposition operation, constructs new received signal vector w (t)=[xT(t),yT(t),zT(t)]T,
And haveWherein Ax,Ay,AzRespectively linear array X, Y, the array manifold square of Z
Battle array, A are the array manifold matrix of 2-L type array, and s (t) is the incoming wave signal of array, and n (t) is noise component(s), then correspond to M snap
Reception data matrix be W=[w (1), w (2) ..., w (M)]；
Step 2: construction propogator matrix
Receive signal autocorrelation matrix beIt is pressed into following form piecemeal, R=[R1,
R2], wherein H representing matrix takes conjugate transposition operation, R1∈C3N×K, R2∈C3N×(3N-K), C is plural number, then propogator matrix isDefine a new extension propogator matrixWherein IK×KFor the unit matrix of K rank, K is
The number of incoming wave signal；
Step 3: estimation spin matrix
By PcBy following form piecemeal,Wherein Px,Py,PzIt is the matrix of N × K, defines matrixWherein A1For the preceding K row of A, Pz,1For PzPreceding N-1 row, Pz,2For PzRear N-1 row, to ΨzIt carries out special
Value indicative is decomposed, then its characteristic value isDiagonal components,For ΦzEstimated value, eigenvectors matrixAs A1Estimate
Evaluation, wherein ΦzFor the corresponding spin matrix of submatrix Z, form is
Wherein diag is indicated a vector diagonalization, and d is array element spacing, and λ is the wavelength of incoming wave signal, θiIndicate i-th of signal
Pitch angle defines two new matrixesWherein Px,1For PxPreceding N-1 row, Px,2For PxRear N-1
Row, then haveWhereinFor ΦxEstimated value, ΦxForm beFor the azimuth of corresponding i-th of signal,
Similarly define two new matrixesWherein Py,1For PyPreceding N-1 row, Py,2For PyRear N-1 row,
Then haveWhereinFor ΦyEstimated value, ΦyForm be
Step 4: azimuth and pitching angular estimation
IfRespectivelyK-th of diagonal components, then the estimated value at azimuth and pitch angle
RespectivelyWherein angle expression takes argument operation,
Atan expression negates arctangent operation.
The features of the present invention and beneficial effect are:
By one new propogator matrix of construction, the information of all array elements is utilized, it can be with lower computation complexity
Obtain preferable azimuth and pitching angular estimation performance；It can be realized the automatic matching at azimuth and pitching angular estimation；In pitching
It is not in direction ambiguity problem within the scope of the pitch angle for the practical mobile communication that angle is 70 °~90 °.
Detailed description of the invention:
Fig. 1 antenna array structure schematic diagram.
The orientation Fig. 2 angular estimation histogram.
Fig. 3 pitching angular estimation histogram.
Fig. 4 different angle combinational estimation combines mean square error figure.
The orientation Fig. 5 angular estimation mean square error is with signal-to-noise ratio situation of change.
Fig. 6 pitching angular estimation mean square error is with signal-to-noise ratio situation of change.
Specific embodiment
Existing DOA algorithm for estimating there are aiming at the problem that, the invention proposes a kind of 2-L type array based on propagation operator
Arrival direction estimation algorithm, it is characterised in that: the aerial array is 2-L type array, wherein having one respectively in x-axis, y-axis and z-axis
A array element number is the even linear array of N, uses X respectively, and Y, Z are indicated.Array element spacing is the half of incoming wave signal wavelength.
The technical solution adopted by the present invention: the 2-L type array arrival direction estimation algorithm based on propagation operator, including it is following
Step:
Step 1: construction receipt signal matrix.
Using positioned at the array element of coordinate origin, as reference array element, linear array X, the signal vector that Y, Z are received is 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)zi(t) linear array X is respectively indicated, the signal that i-th of array element on Y, Z is received in t moment.Structure
Make new received signal vector w (t)=[xT(t),yT(t),zT(t)]T, then the reception data matrix for corresponding to M snap is W=[w
(1),w(2),…,w(M)]。
Step 2: construction propogator matrix
Receive signal autocorrelation matrix beIt is pressed into following form piecemeal, R=[R1,
R2], wherein R1∈C3N×K, R2∈C3N×(3N-K).Then propogator matrixIt defines a new extension and propagates square
Battle arrayWherein IK×KFor the unit matrix of K rank, K is the number of incoming wave signal.
Step 3: estimation spin matrix
By PcBy following form piecemeal,Wherein Px,Py,PzIt is the matrix of N × K.Define matrixWherein Pz,1For PzPreceding N-1 row, Pz,2For PzRear N-1 row.To ΨzEigenvalues Decomposition is carried out,
Then its characteristic value isDiagonal components,For ΦzEstimated value, eigenvectors matrixAs A1Estimated value,
Middle ΦzFor the array manifold matrix of submatrix Z.Define two new matrixesWherein Px,1For PxBefore
N-1 row, Px,2For PxRear N-1 row.Then haveWhereinFor ΦxEstimated value, wherein ΦxFor the array stream of submatrix X
Type matrix.Similarly define two new matrixesWherein Py,1For PyPreceding N-1 row, Py,2For Py's
N-1 row afterwards.Then haveWhereinFor ΦyEstimated value, wherein ΦyFor the array manifold matrix of submatrix Y.
Step 4: azimuth and pitching angular estimation
IfRespectivelyK-th of diagonal components, then the estimated value at azimuth and pitch angle
RespectivelyWherein angle expression takes argument operation,
Atan expression negates arctangent operation.
Below in conjunction with drawings and examples, the present invention will be further described:
Construct 2-L type aerial array as shown in Figure 1.Assuming that there is K narrowband unrelated signal to be incident on array in space
On, wherein the 2-d direction finding of k-th of signal is(k=1,2 ... K),And θkThe respectively orientation of incoming wave signal
Angle and pitch angle.
Step 1: construction receipt signal matrix.
Signal vector x (t)=[x that submatrix X, Y, Z are received in t moment1(t),x2(t),…,xN(t)]T, y (t)=[y1
(t),y2(t),…,yN(t)]T, z (t)=[z1(t),z2(t),…,zN(t)]TIt can be indicated with formula (1).
Wherein nx(t),ny(t),nz(t) mean value for being the dimension of N × 1 is 0, variance σ2Additive white Gaussian noise, and and s
(t) mutually indepedent.For the array manifold matrix of submatrix X, whereinFor submatrix Y
Array manifold matrix, wherein For the array manifold matrix of submatrix Z, wherein
By x (t), y (t), z (t) group is combined 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 beIt is pressed into following form piecemeal, R=[R1,
R2], wherein R1∈C3N×K, R2∈C3N×(3N-K).Then propogator matrix isA new extension is defined to propagate
Matrix
Step 3: estimation spin matrix
By PcBy following form piecemeal,Wherein Px,Py,PzIt is the matrix of N × K dimension.Define matrixWherein Pz,1For PzPreceding N-1 row, Pz,2For PzRear N-1 row.To ΨzEigenvalues Decomposition is carried out,
Then its characteristic value isDiagonal components,For ΦzEstimated value, eigenvectors matrixAs A1Estimated value.Φz
Form beDiag is indicated a vector diagonalization operation.It is fixed
Adopted two new matrixesWherein Px,1For PxPreceding N-1 row, Px,2For PxRear N-1 row.Then haveWhereinFor ΦxEstimated value, ΦxForm beSimilarly define two new matrixes Wherein Py,1For PyPreceding N-1 row, Py,2For PyRear N-1 row.Then haveWhereinFor ΦyEstimation
Value, ΦyForm be
Step 4: azimuth and pitching angular estimation
IfRespectivelyK-th of diagonal components, then the estimated value at azimuth and pitch angle
RespectivelyWherein angle expression takes argument operation,
Atan expression negates arctangent operation.
In conjunction with the embodiment in above-mentioned steps, it is as follows that simulating, verifying is carried out to effectiveness of the invention:
N=8 is taken in emulation, i.e. 2-L type array shares 22 array elements, and array pitch d=0.5 λ, wherein λ is signal wavelength,
Taking number of snapshots for each emulation experiment is 200, carries out M=500 Monte Carlo simulation.
Emulation experiment 1: assuming that there is K=2 constant power unrelated signal to be incident on aerial array, wherein Signal to Noise Ratio (SNR)=
15dB, the azimuth of signal and pitch angle areFig. 2 and Fig. 3 shows that azimuth is estimated
Count histogram and pitching angular estimation histogram.It can be seen from the figure that algorithm proposed in this paper can clearly differentiate the two
Incoming wave signal, without direction ambiguity problem.
Emulation experiment 2: assuming that there is K=1 signal to be incident on aerial array, Signal to Noise Ratio (SNR)=10dB, the wherein side of signal
Parallactic angle and pitch angle are between 10 °~80 ° with 2 ° of step change.Fig. 4 is that different angle combinational estimation combines mean square error
Figure.
Emulation experiment 3: assuming that there is K=2 constant power unrelated signal to be incident on aerial array, wherein Signal to Noise Ratio (SNR) exists
With the step change of 5dB between 5dB~30dB, the azimuth of signal and pitch angle are
Fig. 5 and Fig. 6 is respectively the situation of change of azimuth and pitching angular estimation mean square error with signal-to-noise ratio.It can be seen from the figure that with
The increase of signal-to-noise ratio, azimuth and pitch angle mean square error reduce.
Claims (1)
1. a kind of 2-L type array arrival direction estimation algorithm based on propagation operator, characterized in that steps are as follows:
Step 1: construction receipt signal matrix
Using positioned at the array element of coordinate origin, as reference array element, linear array X, the signal vector that Y, Z are received is 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,
Middle xi(t),yi(t),zi(t) linear array X is respectively indicated, the signal that i-th of array element on Y, Z is received in t moment, N is submatrix battle array
First number, T representing matrix transposition operation, constructs new received signal vector w (t)=[xT(t),yT(t),zT(t)]T, and haveWherein Ax,Ay,AzRespectively linear array X, Y, the array manifold matrix of Z, A are
The array manifold matrix of 2-L type array, s (t) are the incoming wave signal of array, and n (t) is noise component(s), then correspond to the reception of M snap
Data matrix is W=[w (1), w (2) ..., w (M)]；
Step 2: construction propogator matrix
Receive signal autocorrelation matrix beIt is pressed into following form piecemeal, R=[R1,R2],
Middle H representing matrix takes conjugate transposition operation, R1∈C3N×K, R2∈C3N×(3N-K), C is plural number, then propogator matrix isDefine a new extension propogator matrixWherein IK×KFor the unit matrix of K rank, K is
The number of incoming wave signal；
Step 3: estimation spin matrix
By PcBy following form piecemeal,Wherein Px,Py,PzIt is the matrix of N × K, defines matrixWherein A1For the preceding K row of A, Pz,1For PzPreceding N-1 row, Pz,2For PzRear N-1 row, to ΨzIt carries out
Eigenvalues Decomposition, then its characteristic value beDiagonal components,For ΦzEstimated value, eigenvectors matrixAs A1
Estimated value, wherein ΦzFor the corresponding spin matrix of submatrix Z, form isWherein diag indicates that d is array element by a vector diagonalization
Spacing, λ are the wavelength of incoming wave signal, θiIt indicates the pitch angle of i-th of signal, defines two new matrixes Wherein Px,1For PxPreceding N-1 row, Px,2For PxRear N-1 row, then haveWhereinFor ΦxEstimation
Value, ΦxForm be For corresponding i-th of letter
Number azimuth, similarly define two new matrixesWherein Py,1For PyPreceding N-1 row, Py,2For
PyRear N-1 row, then haveWhereinFor ΦyEstimated value, ΦyForm be
Step 4: azimuth and pitching angular estimation
IfRespectivelyK-th of diagonal components, then the estimated value at azimuth and pitch angleRespectively
ForWherein angle expression takes argument operation, atan table
Show and negates arctangent operation, k=1,2 ... K.
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| 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 |
| CN110018438B (en) * | 2019-04-23 | 2020-09-25 | 北京邮电大学 | Direction-of-arrival estimation method and device |
| CN111131116A (en) * | 2019-12-12 | 2020-05-08 | 国网江苏省电力有限公司信息通信分公司 | Frequency offset estimation method and system |
| 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 |
| 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 |
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