CN105445698B - High-accuracy time delay estimation method between a kind of bilinear battle array - Google Patents
High-accuracy time delay estimation method between a kind of bilinear battle 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
- G01S3/80—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 ultrasonic, sonic or infrasonic waves
- G01S3/802—Systems for determining direction or deviation from predetermined direction
- G01S3/808—Systems for determining direction or deviation from predetermined direction using transducers spaced apart and measuring phase or time difference between signals therefrom, i.e. path-difference systems
- G01S3/8083—Systems for determining direction or deviation from predetermined direction using transducers spaced apart and measuring phase or time difference between signals therefrom, i.e. path-difference systems determining direction of source
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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
- G01S3/46—Systems for determining direction or deviation from predetermined direction using antennas spaced apart and measuring phase or time difference between signals therefrom, i.e. path-difference systems
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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
- G01S3/78—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 electromagnetic waves other than radio waves
- G01S3/782—Systems for determining direction or deviation from predetermined direction
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Abstract
The present invention relates to high-accuracy time delay estimation method between a kind of bilinear battle array, every line array in bilinear battle array is divided into multiple overlapped submatrixs by this method, after the angle measurement result of multiple target is obtained using bilinear battle array, angle obtains multiple wave beams and exported where all submatrixs are pointed into some target.These wave beams are exported with progress processing and builds new covariance matrix and time sweep vector, the output along time dimension is obtained, search peak responds to estimate the time delay between bilinear battle array.This method in order to improve bilinear battle array between time delay measurement accuracy, eliminate azimuth ambiguity of the line array in angle measurement.
Description
Technical field
The invention belongs to array signal processing field, it is related to high-accuracy time delay estimation method between a kind of bilinear battle array.
Background technology
Single line array haves the shortcomings that azimuth ambiguity (Van Trees H L.Optimum array when carrying out angle measurement
processing:part 4 of detection,estimation,and modulation theory.Hoboken:John
Wiley&Sons Inc.,2002.).This shortcoming of single line array can be overcome using bilinear battle array, by estimating bilinear
Time delay between battle array is that can determine whether target bearing (the initial analysis acoustics of Li Qi tiger left-right ambiguity resolution performance for twin-line array
Journal, 2006；31(5):385-388. Li Qi tiger distinguish the time-delay estimation method and in fact of port and starboard target with two wires control system
Existing acoustic journals, 2006；31(6):485-487.).But, orientation of the existing method when overcoming angle measurement using bilinear battle array
When fuzzy, the time delay for being estimated using interpolation method between bilinear battle array (prolong by Li Qi tiger two wires control systems differentiation port and starboard target
When method of estimation and its realize acoustic journals, 2006；31(6):485-487.).Interpolation method is defeated to single line array beam in twin-line array
The correlation output sequences gone out carry out numerical value interpolation, and bilinear battle array time delay value is estimated according to correlation output sequences peak value after interpolation,
Its precision is unsatisfactory, is not highly desirable to eliminating azimuth ambiguity.
The content of the invention
The technical problem to be solved in the invention is：In order to improve bilinear battle array between time delay measurement accuracy, the present invention
Propose a kind of method for being handled using submatrix and carrying out high-precision time-delay estimation.This method divides every line array in bilinear battle array
For multiple overlapped submatrixs.After the angle measurement result of multiple target is obtained using bilinear battle array, all submatrixs are pointed to some
Angle where target obtains multiple wave beam outputs.These wave beams are exported with the new covariance matrix of progress processing structure and the time sweeps
Vector is retouched, the output along time dimension is obtained, search peak responds to estimate the time delay between bilinear battle array.
The technical scheme is that：High-accuracy time delay estimation method between a kind of bilinear battle array, comprises the following steps：
Step one：By bilinear battle array to target carry out angle measurement, carry out Wave beam forming, obtain wave beam output quantity, including with
Lower sub-step：
Sub-step one：Bilinear battle array is made up of line array 1 and line array 2.Line array 1 and line array 2 are array element spacing
For d M member uniform straight line arrays, both are parallel to each other and apart from for d0；Bilinear battle array receives P (P=1,2,3 ...) individual target institute
The signal of transmitting, and form angle in bilinear battle array；Bilinear battle array carries out multiple target angle measurement, obtains the angle measurement knot of multiple target
Fruit and spatial spectrum b (θ), wherein θ be scanning angle, span is -180 ° to 180 °；P-th of target is right on spatial spectrum
The peak response angle, θ answeredp(p=1,2,3 ... P), now due to the influence of azimuth ambiguity, it is difficult to directly sentence from angle measurement result
Disconnected target comes from larboard or starboard；
Sub-step two：Line array 1 and line array 2 are respectively divided into N number of overlapped submatrix, i.e., two line arrays have
2N submatrix；The array element of each submatrix is M0(M0≤M)；In each M members line array, the array number that adjacent submatrix overlaps
N0, it is represented by：
Wherein,Represent to take the smallest positive integral more than or equal to wherein numerical value, f is the center frequency of handled signal subspace band
Rate, fDFor Array Design frequency corresponding with array element spacing d, f is expressed asD=c/ (2d), wherein c are signal velocity；
2N submatrix is pointed into P target corresponding peak response angle, θ on spatial spectrump(p=1,2,3 ...) is carried out
Wave beam forming, obtains 2N wave beam output vector；The wave beam output vector of n-th of submatrix is in line array 1Line array
The wave beam output vector of n-th of submatrix is in 2
Step 3：Including following sub-step：
Sub-step one：Wave beam output vector in step 2, asks N number of cross-spectrum output of two line arrays, and formula is
Wherein Rn(θp) n-th of cross-spectrum being obtained by line array 1 and line array 2；
Wherein []HConjugate transposition is sought in representative, and L is expressed as the fast umber of beats of wave beam output；Represent in N number of cross-spectrum
Preceding k (k=1,2 ..., N) individual quadrature.
Sub-step two：Covariance matrix R (θ are built to the N number of cross-spectrum output obtainedp)
Sub-step three：Design the weighing vector changed in time dimension, a (Δ t)：
Wherein, Δ t is time delay, and its span is Δ t ∈ [- d0/c,d0/c]；F is handled signal subspace band
Centre frequency.
Step 4：By the R (θ obtained in step 3p), a (Δ t) substitute into time delay estimation formulas in, obtain p-th of target
(correspond to θ on spatial spectrump) corresponding bilinear battle array time delay, judge that target is to come from larboard or starboard according to the time delay,
Eliminate azimuth ambiguity.
Invention effect
The technical effects of the invention are that：The general principle and embodiment of the present invention have passed through Computerized Numerical Simulation
Checking, its result shows：The method of division submatrix processing proposed by the invention can accurately estimate between bilinear battle array when
Prolong, azimuth ambiguity of the line array in angle measurement can be eliminated.
Brief description of the drawings
Coordinate system figure of Fig. 1 bilinears battle array when carrying out angle measurement；
The flow chart of key step in Fig. 2 present invention；
In Fig. 3 present invention the flow chart that submatrix carries out time delay estimation is divided using bilinear battle array；
The multiple target angle measurement result figure of bilinear battle array in Fig. 4 embodiments；
The time delay estimated result figure obtained in Fig. 5 embodiments using the inventive method.
Embodiment
With reference to specific implementation example, technical solution of the present invention is further illustrated.
Using bilinear battle array (being made up of line array 1 and line array 2, both of which is M members uniform straight line array and is parallel to each other)
Multiple target angle measurement is carried out, every line array is divided into N number of overlapped submatrix, 2 line arrays can obtain 2 groups of common 2N sons
Battle array.The angle measurement result of multiple target is obtained using bilinear battle array, this 2 groups common 2N submatrixs are pointed to the angle measurement knot corresponding to certain target
Really, 2N wave beam output vector is obtained.Conjugation is asked to n-th (n=1,2 ..., N) individual sub- array beam output vector in line array 1
Transposition, while being multiplied using n-th of submatrix wave beam output vector in line array 2 with the conjugate transposition result, obtains n-th of cross-spectrum
2N submatrix obtains N number of cross-spectrum altogether.
By preceding k (k=1,2 ..., N) individual quadrature in N number of cross-spectrum, by result of product divided by the conjugation of the 1st cross-spectrum, such as
This obtains N number of output altogether.Covariance matrix is built using N number of output, while the weighing vector that design changes in time dimension, is obtained
Obtain the output response in different delay value.The corresponding time delay value of search peak response, that is, obtain the time delay between bilinear battle array
Value.
The angle measurement result using method in the present invention is given by Computerized Numerical Simulation, institute of the present invention is demonstrated with this
Extracting method can obtain the bilinear battle array time delay estimation result of degree of precision.
The technical scheme that present invention solution Problems Existing is used can be divided into following steps：
Using bilinear battle array (being made up of line array 1 and line array 2, both of which is M members uniform straight line array and is parallel to each other)
Multiple target angle measurement is carried out, the angle measurement result of multiple target is obtained using bilinear battle array, now there is port and starboard ambiguity in angle measurement result.
Every line array is divided into N number of overlapped submatrix, 2 line arrays can obtain 2 groups of common 2N submatrixs.Some target is carried out
When eliminating azimuth ambiguity, angle carries out Wave beam forming where this 2 groups of submatrixs are pointed into the target, and 2N wave beam output is obtained altogether.
Conjugate transposition is asked to the individual sub- array beam output vectors of n-th (n=1,2 ..., N) in line array 1, while using directly
N-th of submatrix wave beam output vector is multiplied with the conjugate transposition in linear array 2, obtains n-th of cross-spectrum output.2N submatrix is obtained altogether
N number of cross-spectrum output.By preceding k (k=1,2 ..., N) individual quadrature in N number of cross-spectrum, by being total to for result of product divided by the 1st cross-spectrum
Yoke, so obtains N number of phase difference factor altogether.Covariance matrix is built using this N number of phase difference factor, while design is with double straight
The weighing vector of linear array time delay value changes.
Utilize step 2) in covariance matrix and weighing vector, obtain different delay value on response output.Search for peak
It is worth the time delay value where response, that is, obtains delay inequality of certain echo signal between bilinear battle array.Certain is judged according to the delay inequality
Target is to come from larboard or starboard, reaches the purpose for eliminating azimuth ambiguity.
Each step to the present invention elaborates below：
Step 1) correlation theory and particular content it is as follows：
Angle measurement is carried out using bilinear battle array.If the distance between bilinear battle array is d0, every line array is that array element spacing is d
M member uniform straight line arrays (ULA:Uniform linear array), as shown in Figure 1.Bilinear battle array receives P, far field target spoke
The signal with certain bandwidth penetrated, and using the sampled signal in the method processing bilinear battle array of molecule tape handling.For letter
Change analysis, hereafter by taking the sampled signal in certain subband as an example, provide specific process step.The processing side of signal on other subbands
Formula refers to the process step of the subband.
It is located in the subband, the spatial spectrum obtained using double ULA progress angle measurements is b (θ), and wherein θ is scanning angle, is taken
Value scope is -180 ° to 180 °.As shown in figure 1, and θpWhen corresponding direction vector and the coincidence of y-axis positive direction, θ is 0 °；With θ p
When corresponding direction vector and the coincidence of y-axis negative direction, θ is 180 ° and -180 °；Direction vector corresponding with θ p and x-axis positive direction
θ is 90 ° during coincidence, and θ is -90 ° when direction vector corresponding with θ p and the coincidence of x-axis negative direction.In spatial spectrum b (θ), with pth
The corresponding peak response of (p=1,2 ..., P) individual target is in θ=θpPlace.Due to there is port and starboard ambiguity, according to spatial spectrum result
It can not directly judge that the target is located at θpIn angle.
Two M members ULA are carried out with Subarray partition respectively, each ULA is divided into N number of overlapped sub- ULA, per height
ULA element number of array is M0(M0≤M).In each M members ULA, the array number that adjacent sub- ULA overlaps, N0 is represented by：
Wherein,Represent to take the smallest positive integral more than or equal to wherein numerical value, f is the center frequency of handled signal subspace band
Rate, fD=c/ (2d) is Array Design frequency corresponding with array element spacing d, and c is signal velocity.
Two M members ULA mark off 2N sub- ULA altogether.By the sub- ULA of this 2N point to P target on spatial spectrum it is corresponding
Peak response angle, θp(p=1,2 ..., P) carries out Wave beam forming, then 2N sub- ULA obtain 2N wave beam output vector altogether.It is right
For 1st ULA, n-th (n=1,2 ..., N) individual sub- ULA wave beam output complex vector is therebetweenUse discretization table
Up to when, it is that 1 × L ties up plural row vector, and wherein L represents the fast umber of beats of wave beam output.Correspondingly, n-th of son in the 2nd ULA
ULA wave beam exports complex vectorIt also ties up plural row vector for 1 × L.
Step 2) correlation theory and particular content it is as follows：
To in the 1st ULA n-th (n=1,2 ..., N) individual sub- array beam output vectorConjugate transposition is sought, is obtainedWherein []HConjugate transposition is sought in representative.Use the wave beam output vector of n-th of sub- ULA in the 2nd ULA
WithIt is multiplied, obtains n-th of cross-spectrum, Rn(θp), its expression formula is：
2N wave beam output on 2N sub- ULA is handled according to formula (2), N number of cross-spectrum is obtained altogether.To N number of cross-spectrum
In preceding k (k=1,2 ..., N) individual quadrature, by result of product divided by the conjugation [R of the 1st cross-spectrum1(θp)]*(wherein []*Represent
Seek conjugation) obtain k-th of value, Xk(θp), its expression formula is：
Wherein,Represent and first k value be multiplied, | | representative takes absolute value.N number of cross-spectrum is handled according to formula (3), is obtained altogether
Obtain N number of output.
The N number of output obtained using formula (3) builds covariance matrix, R (θp)：
Design the weighing vector changed in time dimension, a (Δ t)：
Wherein, Δ t is time delay, and its span is Δ t ∈ [- d0/c,d0/c]。
Step 3) correlation theory and particular content it is as follows：
Utilize step 2) in build covariance matrix and weighing vector obtain different delay under estimated result.According to
Time delay between conventional method estimation bilinear battle array, then the output on time dimension, (Δ t), is represented by b：
B (Δ t)=[a (Δ t)]HR(θp)a(Δt) (6)
Estimate the time delay between bilinear battle array, the then output on time dimension, b (Δs according to Capon beam-forming schemes
T), it is represented by：
Wherein, []-1Represent to matrix inversion.
Estimate the time delay between bilinear battle array according to MUSIC methods, include p-th of target due to main in wave beam output
Component of signal, therefore can directly assume number of targets be 1, then the output on time dimension, (Δ t), is represented by b：
Wherein, Unoise(θp) it is to R (θp) decomposed after the small characteristic values of N-1 corresponding characteristic vectors constituted
Eigenmatrix, corresponding feature decomposition expression formula is as follows：
R(θp)=U (θp)Γ(θp)UH(θp) (9)
Wherein U (θp) and Γ (θp) it is respectively R (θp) eigenvectors matrix and eigenvalue matrix.
According to formula (6), formula (7) and formula (8), it can obtain corresponding with p-th of target (corresponding to θ p on spatial spectrum)
Bilinear battle array time delay.It is that can determine whether that certain target is to come from larboard or starboard according to the time delay, is finally reached elimination azimuth ambiguity
Purpose.
The key step flow of the present invention is as shown in Fig. 2 carry out flow such as Fig. 3 of bilinear battle array time delay estimation using submatrix
It is shown.
By taking typical submarine target angle measurement as an example, the embodiment of the present invention is provided.
If the line array in bilinear battle array is 36 yuan of ULA, array element spacing is d=1.5 meters, the spacing between bilinear battle array
For d0=1.5 meters.2 targets are located on -60 ° and 150 ° respectively, radiate 200Hz to 800Hz broadband signal.Molecule is brought into
Row angle measurement, extracts centre frequency and carries out time delay estimation for 500Hz subband (with a width of 10Hz).In 500Hz subbands, if each
The PSNR power signal-to-noise ratio received in array element is set to 10dB.Each 36 yuan of ULA are marked off into 8 sub- ULA, submatrix is 29 yuan of ULA.
Angle measurement result using bilinear battle array is as shown in Figure 4, although can see peak response at -60 ° and 30 ° respectively, but
It is due to the presence of ambiguity of space angle, target is also possible to respectively from -120 ° and 150 °.
According to Fig. 2 and Fig. 3 flow, the result for carrying out time delay estimation using institute's extracting method of the present invention is as shown in Figure 4.Group
When array beam points to -60 °, the result of corresponding time delay estimation is as shown in figure 4, now conventional Time Delay Estimation Method, Capon time delays are estimated
The time delay estimated result that meter method and the MUSIC experiments estimation technique are obtained is 0.4986 millisecond, close to 0.5 millisecond of actual value.
Because the time delay value of estimation is positive number, it can be determined that it is first to reach line array 1 to go out signal, rear to reach line array 2, it is known that the target
Positioned at -60 °.When group array beam points to 30 °, the result of corresponding time delay estimation is as shown in Figure 4.Now conventional time delay estimation
The time delay estimated result that method, Capon Time Delay Estimation Methods and the MUSIC experiments estimation technique are obtained is -0.8679 millisecond, close to very
- 0.8660 millisecond of real value.Because the time delay value of estimation is negative, it can be determined that it is first to reach line array 2 to go out signal, rear to reach
Line array 1, it is known that the target is located at 150 °.
It can be seen from embodiment, the method proposed by the present invention to bilinear battle array progress Subarray partition and estimation time delay can
To obtain the time delay estimated result being closer to actual value, and orientation mould when can eliminate according to the time delay estimated result angle measurement
Paste.
Claims (1)
1. high-accuracy time delay estimation method between a kind of bilinear battle array, it is characterised in that comprise the following steps：
Step one：Angle measurement is carried out to target by bilinear battle array, Wave beam forming is carried out, wave beam output quantity, including following son is obtained
Step：
Sub-step one：Bilinear battle array is made up of line array 1 and line array 2；Line array 1 and line array 2 are that array element spacing is d
M member uniform straight line arrays, both are parallel to each other and apart from for d0；Bilinear battle array receives the signal that P target is launched, and double straight
Angle, wherein P=1,2,3 ... are formed in linear array；Bilinear battle array carries out multiple target angle measurement, obtains the angle measurement result of multiple target
And spatial spectrum b (θ), wherein θ are scanning angle, span is -180 ° to 180 °；P-th of target correspondence on spatial spectrum
Peak response angle, θp, p=1,2,3 ... P, now due to the influence of azimuth ambiguity, it is difficult to directly judge from angle measurement result
Target comes from larboard or starboard；
Sub-step two：Line array 1 and line array 2 are respectively divided into N number of overlapped submatrix, i.e., two line arrays have 2N
Submatrix；The array element of each submatrix is M0, and M0≤M；In each M members line array, the array number N that adjacent submatrix overlaps0,
It is represented by：
Wherein,Represent to take the smallest positive integral more than or equal to wherein numerical value, f is the centre frequency of handled signal subspace band, fD
For Array Design frequency corresponding with array element spacing d, f is expressed asD=c/ (2d), wherein c are signal velocity；
2N submatrix is pointed into P target corresponding peak response angle, θ on spatial spectrumpWave beam forming is carried out, 2N ripple is obtained
Beam output vector, wherein p=1,2,3 ...；The wave beam output vector of n-th of submatrix is in line array 1Line array 2
In the wave beam output vector of n-th of submatrix be
Step 3：Including following sub-step：
Sub-step one：Wave beam output vector in step 2, asks N number of cross-spectrum output of two line arrays, and formula is
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</msub>
<mo>)</mo>
</mtd>
</mtr>
</mtable>
</mfenced>
<msup>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msub>
<mi>X</mi>
<mn>1</mn>
</msub>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mi>p</mi>
</msub>
<mo>)</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>X</mi>
<mi>k</mi>
</msub>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mi>p</mi>
</msub>
<mo>)</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>X</mi>
<mi>N</mi>
</msub>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mi>p</mi>
</msub>
<mo>)</mo>
</mtd>
</mtr>
</mtable>
</mfenced>
<mi>H</mi>
</msup>
</mrow>
Sub-step three：Design the weighing vector changed in time dimension, a (Δ t)：
<mrow>
<mi>a</mi>
<mrow>
<mo>(</mo>
<mi>&Delta;</mi>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mi>j</mi>
<mn>2</mn>
<mi>&pi;</mi>
<mi>f</mi>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>N</mi>
<mo>-</mo>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<mi>&Delta;</mi>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
Wherein, Δ t is time delay, and its span is Δ t ∈ [- d0/c,d0/c]；F is the center of handled signal subspace band
Frequency；
Step 4：By the R (θ obtained in step 3p), a (Δ t) substitute into time delay estimation formulas in, obtain p-th of target, in space
Correspond to θ in spectrump, corresponding bilinear battle array time delay judges that target is to come from larboard or starboard, elimination orientation according to the time delay
It is fuzzy.
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| 基于稀疏阵列技术的ＭIＭＯ声呐低运算量二维成像;潘浩 等;《西北工业大学学报》;20140831;第32卷(第4期);第586-592页 * |
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