CN105487052B - Compressed sensing LASAR bare cloth linear array optimization methods based on low coherence - Google Patents
Compressed sensing LASAR bare cloth linear array optimization methods based on low coherence 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
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/88—Radar or analogous systems specially adapted for specific applications
- G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
- G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
- G01S13/904—SAR modes
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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
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
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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
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/88—Radar or analogous systems specially adapted for specific applications
- G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
- G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
-
- 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
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/88—Radar or analogous systems specially adapted for specific applications
- G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
- G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
- G01S13/9094—Theoretical aspects
Abstract
The invention discloses a kind of compressed sensing LASAR bare cloth linear array optimization methods based on low coherence, it is the reference frame that optimizes as compressed sensing LASAR Sparse arrays of coherence's characteristic of the calculation matrix by the use of in compressive sensing theory, minimum based on compressed sensing calculation matrix coherence in LASAR systems, by Fourier transformation iterative search method, realize the array element distribution optimization design of compression sensing LASAR bare cloth linear array antennas, it is more reasonable that Sparse array is optimized, and is conducive to improving the imaging performance of compressed sensing LASAR systems.Method proposed by the present invention is also applied for other bare cloth linear array antenna optimisation technique fields based on compressed sensing.
Description
Technical field：
This technology invention belongs to Radar Technology field, its more particularly to synthetic aperture radar (SAR) imaging technique and battle array
Array antenna design field.
Background technology：
Because with advantages such as round-the-clock, the observations of round-the-clock and large scene, synthetic aperture radar (SAR) has turned into current big
One important remote sensing technology of area mapping, in the fields such as mapping, Natural calamity monitoring and survey of natural resources hair
Wave increasing effect.Linear array SAR (LASAR) is the expansion of conventional two-dimensional SAR imaging technique target dimension spatial resolving powers
Exhibition, can obtain the three-dimensional radar imaging of observed object scene, can more subtly describe to observe the geometry of target in scene
And scattering signatures, compared with the target's feature-extraction and target identification ability that conventional two-dimensional SAR improves radar system, become in recent years
Come SAR imaging techniques hot research problem (refer to bibliography " the continuous scenes of Zhang Qingjuan, Li Daojing, Li Lie occasion it is sparse
Electronics and information journal, 2013, (5) are studied in array SAR side views three-dimensional imaging:1097-1102.”).LASAR imaging systems
General principle is, by the motion synthesis of linear array antenna virtual two-dimensional planar array one big, to obtain the two dimension in the battle array plane of face
High-resolution, obtains radar line of sight direction high-resolution, so as to realize three to observed object scene in conjunction with pulse compression technique
Dimension imaging.
The sparse reconstruct of compressed sensing breaches traditional Nyquist as a kind of signal processing theory newly proposed in recent years
Sampling thheorem is constrained, available (to refer to bibliography far below Nyquist sample rate Accurate Reconstruction original sparse signals
“D.L.Donoho.Compressed sensing.IEEE Transactions on Information Theory,2006,
52(4):1289-1306 "), there is huge application potential in terms of reduction radar system sample rate, raising image quality.
Because most of target number is all space sparse distribution in LASAR image scenes, therefore compressive sensing theory can be with LASAR systems
System is organically combined, and is generated the linear array three-dimensional SAR sparse imaging system based on compressed sensing, is realized the dilute of LASAR imaging systems
Dredge that signal is down-sampled and raising of three-dimensional imaging precision (refer to bibliography " S-J.Wei S, X-L.Zhang,
J.Shi.Linear array SAR imaging via compressed sensing,Progress In
Electromagnetics Research,2011,117(8):299-319.”)。
Linear array antenna is the key components of LASAR imaging systems, and the 3rd is provided for linear array three-dimensional SAR imaging systems
The imaging resolution capability of dimension.But, for single antenna in traditional SAR system, many array elements of LASAR system neutral array antennas
Also considerably increase hardware system realization difficulty and cost, cause excessive LASAR echo data amounts, data transfer, storage and
The problems such as difficult in imaging.In order to reduce the cost of LASAR hardware systems and data processing, generally using dilute in LASAR systems
Cloth linear array antenna realizes the collection of down-sampled echo data, but the array number of bare cloth linear array antenna is unsatisfactory for conventional radar systems
Nyquist sample rates, cause traditional SAR imaging methods precision and Quality Down.However, for compressed sensing imaging method, i.e.,
Make to use Sparse array antenna, the sparse imaging systems of LASAR still can ensure the precision and quality of imaging, realize high accuracy
D S AR imaging (refer to bibliography " such as Li Xueshi, Sun Guangcai, Xu Gang based on compressed sensing it is lower regard D S AR imaging
New method electronics and information journal, 2012,34 (5):1017-1023.”).Due to the array element number of LASAR bare cloth linear array antennas
The performance of compressed sensing imaging method is directly determined with distribution mode, distribution need to be carried out to the array element of bare cloth linear array antenna excellent
Change.But due to compressed sensing with traditional imaging theory in the presence of this qualitative difference, for the sparse imagings of the LASAR based on compressed sensing
System, traditional linear array antenna array element optimization method the array element of bare cloth linear array antenna can not optimize suitable for its system.
For the sparse imaging systems of LASAR based on compressed sensing, array number be not required to meet Nyquist sample rates and only with
Target sparse degree is relevant, if calculation matrix meets equidistant constraint property (RIP), bare cloth linear array antenna is that sparse target can be achieved
High-resolution imaging.However, it is a uncertainty that the RIP of compressed sensing calculation matrix, which is calculated, in linear array three-dimensional SAR system
Multinomial (NP) problem, measurement LASAR bare cloths linear array day is used as therefore, it is difficult to the RIP by the use of calculation matrix in compressive sensing theory
The index of line optimization (refers to bibliography " calculation matrix research Beijing Jiaotong University doctors of the Li little Bo based on compressed sensing
Paper, 2010. ").Compressive sensing theory is pointed out, if the coherence of calculation matrix is smaller to mean that compressed sensing algorithm is accurate
The probability for reconstructing target scattering coefficient is higher, therefore is difficult in calculation matrix RIP under calculated case, it is possible to use coherence's conduct
The array element distribution design for weighing bare cloth linear array antenna in the standard of LASAR Sparse array distribution optimizations, LASAR systems will be as far as possible
Make the coherence of compressed sensing calculation matrix in its system minimum.
The content of the invention：
The invention provides a kind of compressed sensing LASAR bare cloth linear array optimization methods based on low coherence, this method base
The minimum of compressed sensing calculation matrix coherence, by Fourier transformation iterative search method, is realized in LASAR systems
The array element distribution optimization design of compression sensing LASAR bare cloth linear array antennas, it is more reasonable that Sparse array is optimized, and is conducive to improving
The imaging performance of compressed sensing LASAR systems.Method proposed by the present invention is also applied for other bare cloth lines based on compressed sensing
Array antenna optimisation technique field.
Present disclosure is described for convenience, makees following term definition first：
Define 1, norm
If X is number fieldLinear Space,Complex field is represented, if it meets following property：| | X | | >=0, and | | X | |
=0 only X=0, | | aX | |=| a | | | X | |, a is arbitrary constant, | | X1+X2||≤||X1||+||X2| |, then | | X | | it is called X
Norm spatially, | | | | represent norm sign, wherein X1And X2For any two values of X spatially.For defining the N in 1
× 1 dimension discrete signal vector X=[x1,x2,…,xN]T, vectorial X LP norm expression formulas areWherein xi
For vectorial X i-th of element, | | represent absolute value sign, ∑ | | represent absolute value summation symbol, vectorial X L1 norms
Expression formula isVectorial X L2 norm expression formulas areVectorial X L0 norm expression formulas
ForAnd xi≠0.Refer to document " state's exoelectron and communication textbook series：Signals ＆ Systems (second edition) ",
Alan V.Oppenheim etc. are write, and Liu Shutang is translated, and Electronic Industry Press is published.
Define 2, nyquist sampling rate
In the transfer process for carrying out analog/digital signal, for bandwidth limit signal, when sample frequency is more than signal most
At high-frequency 2 times, data signal can intactly retain and recover the information in primary signal after sampling, and the sample rate is referred to as
Nyquist sampling rate.Sampling thheorem is also known as Nyquist's theorem (Nyquist theorems) or Shannon's theorems, refers to document " matrix
It is theoretical ", Huang Ting, which wishes, etc. writes, and Higher Education Publishing House publishes.
Define 3, full front's array antenna and bare cloth linear array antenna
When carrying out target acquisition using linear array antenna in radar system, if the distribution of linear array antenna array element, which is met, claims Nai Kuisi
During specific reason, then the linear array antenna is referred to as full front's array antenna, and the spacing between the adjacent array element of usual radar Zhong Man fronts battle array is
0.5 times of radar operation wavelength；If the distribution of linear array antenna array element is unsatisfactory for claiming Nyquist's theorem, the linear array antenna is referred to as
Bare cloth linear array antenna.
Define 4, compressed sensing
Higher-dimension primary signal mainly is carried out non-self-adapting linear projection to lower dimensional space to keep signal by compressed sensing
Structural information, then reconstruct by solving linear optimal solution the theory of primary signal, the theory mainly includes signal sparse table
Show, three aspects of sparseness measuring and sparse reconstruct.The basic thought of the sparse reconstructing method of compressed sensing is solution particular constraints bar
Optimal solution or near-optimal solution under part, main method have greedy tracing algorithm and convex relaxed algorithm etc..Detailed content refers to text
Offer " Donoho D L.Compressed sensing.IEEE Transactions on Information Theory,
2006,52(4):1289-1306.”。
Define the 5, coherence of compressed sensing calculation matrix
In perception theory, for some measuring system, the coherence of compressed sensing observing matrix is defined as：Wherein μ is the coherence factor of measuring system observing matrix, χiRepresent the i-th row of calculation matrix, χjTable
Show the jth row of calculation matrix,<·>Vectorial auto-correlation computation symbol is represented, | | it is the oeprator that takes absolute value, | | | |2For L2
Norm oeprator, max is function maximizing oeprator.
Define 6, linear array synthetic aperture radar (Linear Array SAR, abbreviation LASAR)
Linear array synthetic aperture radar be by linear array antenna be fixed on loading movement platform and with the platform direction of motion
With it is vertical, with reference to motion platform motion with synthesize two-dimensional planar array realize array plane tie up two-dimensional imaging, recycle radar
Wave beam is realized apart from one-dimensional image to echo delay, so as to realize a kind of synthetic aperture radar skill of observed object three-dimensional imaging
Art.
Define 7, linear array synthetic aperture radar cuts course made good
During online array synthetic-aperture radar observation, linear array synthetic aperture radar platform movement locus direction it is vertical and with
Course made good is cut in the parallel direction of linear array antenna array element arranged direction, referred to as linear array synthetic aperture radar.
Define 8, the linear array antenna observation space of linear array synthetic aperture radar
During online array synthetic-aperture radar observation, by cutting the two dimensional surface that course made good and earth's surface vertical direction are constituted,
The referred to as linear array antenna observation space of linear array synthetic aperture radar.
Define the excitation vector of sparse array element in 9, linear array antenna
Sparse array element excitation vector is the vector for characterizing sparse array element position distribution in linear array antenna in linear array antenna.
Assuming that the array element sum that can be disposed in linear array antenna is N, sparse array element excitation vector is β=[β1,…,βN], vectorial β dimension
For N, wherein β1Table is vector β the 1st element value, βNTable is vector β n-th element values, βkTable is vector k-th of element value of β,
The β when k-th of array element is chosen in linear array antennak=1, β when k-th of array element is not selected in linear array antennak=0.
Define the angular resolution of linear array antenna in 10, linear array synthetic aperture radar
The minimum angles that linear array antenna can be distinguished effectively in observation space in linear array synthetic aperture radar, referred to as linear array are synthesized
The angular resolution of linear array antenna in aperture radar system, angular resolution is relevant with radar operation wavelength and linear array antenna length, in detail
See document " double-base SAR is studied with linear array SAR principles and imaging technique ", Shi Jun, University of Electronic Science and Technology's thesis for the doctorate, 2012
Year.
A kind of compressed sensing LASAR bare cloth linear array optimization methods based on low coherence that the present invention is provided, it include with
Lower step：
Step 1, initialization LASAR systematic parameters：
Initialization LASAR systematic parameters include：Radar platform height, is denoted as H；Radar operating center frequency, is denoted as fc；Thunder
Up to carrier frequency wavelength, λ is denoted as；The signal bandwidth of radar emission baseband signal, is denoted as Br；Radar emission signal pulse width, is denoted as
TP；The chirp rate of radar emission signal, is denoted as fdr；Radar received wave door continues width, is denoted as To；Radar Receiver System is adopted
Sample frequency, is denoted as fs；The pulse recurrence frequency of radar emission system, is denoted as PRF；The pulse-recurrence time of radar system, it is designated as
PRI；Antenna is denoted as D in the effective aperture length of orientationa；Above-mentioned parameter is LASAR system standard parameters, wherein radar
Podium level H, radar center frequency fc, radar carrier frequency wavelength X, the signal bandwidth B of radar emission baseband signalr, radar emission letter
Number pulse width TP, radar emission signal chirp rate fdr, the lasting width T of radar received wave dooro, the sampling of Radar Receiver System
Frequency fs, the pulse recurrence frequency PRF of radar system, the pulse-recurrence time PRI of radar system, antenna is in the effective of orientation
Aperture length DaHad determined in LASAR system designs and observation process；According to LASAR imaging systems scheme and observation side
Case, the initialization systematic parameter that LASAR bare cloth linear array antennas optimization method needs is known.
Step 2, the parameter for initializing LASAR bare cloth linear array antennas：
The parameter of initialization LASAR bare cloth linear array antennas includes：The array element sum of full front array antenna is designated as NA；Full front
The spacing of adjacent array element, is designated as d in array antenna, and d value is the half of system carrier frequency wavelength in LASAR systems, isWherein λ be step 1 in initialize obtained radar carrier frequency wavelength；The array length of full front array antenna, is designated as L, and
And L value is L=(NA-1)d；Array element sum in bare cloth linear array antenna, is designated as NS, and NS＜ NA；Bare cloth linear array antenna
Array element is that the subset of full front's array antenna array element, i.e. bare cloth linear array antenna array element are N from full front's array antennaASelected in individual array element
Take NSIndividual array element composition；1st position of the array element in flight path-elevation plane is cut in full front array antenna, is designated as p1；Full front
The 2nd position of the array element in flight path-elevation plane is cut, is designated as p in array antenna2；N in full front array antennaAIndividual array element is being cut
Position in flight path-elevation plane, is designated asPosition of n-th of the array element in flight path-elevation plane is cut in full front array antenna
Put, be designated as pn, wherein subscript n is the sequence number of n-th of array element in full front array antenna, and n is natural number, n=1,2 ..., NA, and
And pn=[(n-1) d, H]T, wherein H be step 1 in initialize obtain radar platform height；All battle arrays in full front array antenna
Location sets of the member in flight path-elevation plane is cut, are denoted as P, wherein set P is a 2 × NAThe matrix of dimension, and
Step 3, initialization LASAR linear array antenna observation space parameters：
Linear array SAR linear array antenna observation space parameters are initialized, including：With the 1st element position of full front's array antenna
For reference array element, the interval size of observation angle of the linear array antenna in flight path-elevation plane is cut is designated as θ0；LASAR linear array antennas
Observation angle in flight path-elevation plane is cut is always interval, is designated asLASAR linear array antennas are cutting flight path-height
The total interval discretization cell sum of observation angle, is designated as M in plane；Reference array element using full front's array antenna as the center of circle,
By LASAR linear array antennas, the total interval of observation angle is evenly dividing into equal-sized angle-unit in flight path-elevation plane is cut
Lattice, and each corresponding angle value of angle-unit lattice is less than LASAR linear array antennas and cutting the angular resolution of course made good；
Using formulaM=1,2 ..., M, calculating are obtained in LASAR observation angles interval m-th
Position of the cell on ground level, is designated as qm, m=1,2 ..., M, wherein m represent in LASAR observation angles interval m-th jiao
Cell is spent, m is natural number, and m=1,2 ..., M；H is initializes obtained radar platform highly in step 1, the upper right corner
Symbol T represents transposition oeprator.
Step 4, the relevant parameter for initializing LASAR bare cloth linear array antenna optimization methods：
The relevant parameter of initialization LASAR bare cloth linear array antenna optimization methods includes：The maximum of algorithm iteration estimation procedure
Iterations, is denoted as MaxIter；K is designated as the kth time iteration of iterative estimation procedure, and k is natural number, and k initial values are set to k=
0, and k span is k=0,1,2 ..., MaxIter；Correlation coefficient threshold in iterative algorithm, is designated as T；Iteration is calculated
Stopping criterion for iteration threshold value in method, is designated as ε；The excitation vector of LASAR bare cloth linear array antenna array elements, is designated as in kth time iteration
β(k), k=0,1,2 ..., MaxIter, wherein β(k)It is a NATie up the vector of size, NAIt is expiring of obtaining of initialization in step 2
The array element sum of front's array antenna；Randomly generate a NAThe vector of dimension, it is only 1 or 0 to be designated as in α, wherein α each element value,
And the element number that value is 1 is NS, NSTo initialize the array element sum of obtained bare cloth linear array antenna in step 2；By vectorial α
It is assigned to the excitation vector β of LASAR bare cloths linear array antenna array element in all iterative process(k), k=0,1,2 ..., MaxIter make
For bare cloth linear array antenna array element excitation vector β(k)Initial value；Excitation vector β in kth time iteration(k)Middle element value is 1 element
The sequence number set of position composition, is designated as Ω(k), k=0,1,2 ..., MaxIter, wherein sequence number set omega(k)For a NS
Tie up the vector of size；Sequence number set omega(k)In element value be in kth time iteration bare cloth linear array excitation array element in full front battle array
Corresponding array element sequence number in antenna；
Step 5, using iterative algorithm carry out LASAR bare cloth linear array optimization designs, the iterative algorithm mainly include step 5.1
To step 5.5, specific steps are realized as follows：
Step 5.1, the position that LASAR bare cloths linear array antenna encourages array element is calculated in kth time iteration
In kth time iterative process, if during iterations k=0, according to set omega(0)In element, full front battle array day
Corresponding array element is chosen in line, the location sets that LASAR bare cloths linear array in the 0th iteration encourages array element is obtained, is designated as S(0), its
Middle Ω(0)Excitation vector β in the 0th time obtained iteration is initialized for step 4(0)Middle element value constitutes for 1 element position
Sequence number set, β(0)For the excitation vector of LASAR bare cloth linear array antenna array elements in the 0th iteration；S(0)It is expressed as location sets P
Middle selection meets element numbers for Ω(0)Element value composition location sets, S(0)For a 2 × NSThe matrix of dimension, wherein P are
Each array element in obtained full front's array antenna is initialized in step 2 and is cutting the location sets of course made good；Order matrix S(0)Column vector
Constituting expression-form isWhereinFor matrix S(0)The 1st row and physical significance be the 0th time repeatedly
1st excitation element position in bare cloth linear array antenna in generation,For matrix S(0)The 2nd row and physical significance is the 0th iteration
2nd excitation element position in middle bare cloth linear array antenna,For matrix S(0)NSArrange and physical significance is in the 0th iteration
N in bare cloth linear array antennaSIndividual excitation element position；Matrix S(0)L row be designated asAnd physical significance is in the 0th iteration
L-th of excitation element position in bare cloth linear array antenna, l is natural number, and l span is l=1,2 ..., NS, NSFor step
The bare cloth linear array antenna array element sum that rapid 2 initialization is obtained；
In algorithm kth time iteration, if during iterations k ＞ 0, array element serial number set is chosen in full front's array antenna
Ω(k-1)Array element corresponding to middle element, obtains the element position set that LASAR bare cloths linear array in kth time iteration encourages array element,
It is designated as S(k), wherein Ω(k-1)For the excitation vector β obtained in -1 iteration of iterative algorithm kth(k-1)Middle element value is 1 element institute
The sequence number set constituted in position, β(k-1)For the excitation vector of LASAR bare cloth linear array antenna array elements in -1 iteration of kth；S(k)Table
It is shown as choosing in location sets P and meets element numbers for Ω(k)Element value composition location sets, S(k)For a 2 × NSDimension
Matrix；Define matrix S(k)Column vector groups be into expression-formWhereinFor matrix S(k)
The 1st row and physical significance is the 1st excitation element position in bare cloth linear array antenna in kth time iteration,For matrix S(k)'s
2nd row and physical significance are the 2nd excitation element position in bare cloth linear array antenna in kth time iteration,For matrix S(k)NS
Arrange and physical significance is N in bare cloth linear array antenna in kth time iterationSIndividual excitation element position, matrix S(k)L row be designated asAnd physical significance is l-th of excitation element position in bare cloth linear array antenna in kth time iteration, l is natural number, and l=1,
2,…,NS。
Coefficient correlation in step 5.2, calculating LASAR linear array antenna observation spaces between different units lattice
In algorithm kth time iteration, any two different units lattice in course made good observation angle interval, sequence are cut to LASAR
Number it is designated as i and j respectively, i and j are natural number, and i and j span is respectively i=1,2 ..., M and j=1,2 ...,
M and i ≠ j, wherein M be step 3 in initialize obtained LASAR linear array antennas observation angle in flight path-elevation plane is cut
Total interval discretization cell sum；M-th of unit in the LASAR observation angles interval obtained using being initialized in step 3
Position of the lattice on ground levelM=1,2 ..., M, obtain the corresponding m=i of sequence number i values
Individual unit cuts course made good position, is designated as qi, and qiValue beObtain sequence number j values corresponding
The m=j unit cuts course made good position, is designated as qj, and qjValue be
Using formulaL=1,2 ..., NS, i=1,2 ..., M, calculating obtains algorithm kth and changes
The oblique distance of interval i-th of the cell of LASAR observation angles l-th of excitation array element into bare cloth linear array antenna, is designated as R in generation(k)
(l, i), whereinThe location sets S obtained for step 5.1(k)L row, | | | |2Represent the L2 norm operators of vector
Number；Using formulaL=1,2 ..., NS, j=1,2 ..., M are calculated and obtained in k iteration
The oblique distance of j-th of the cell in LASAR observation angles interval, l-th of excitation array element into bare cloth linear array antenna, is designated as R(k)(l,j)；
Using calculation formula Δ R(k)(l, i, j)=R(k)(l,j)-R(k)(l, i), calculating obtains LASAR observation angles area in kth iteration
Between i-th and j-th of cell l-th of the excitation array element into bare cloth linear array antenna oblique distance it is poor, be designated as Δ R(k)(l,i,j)；
Using formulaI=1,2 ..., M, j=1,2 ..., M
And i ≠ j, calculate and obtain interval i-th of LASAR observation angles in kth iteration and j-th of cell in Sparse array antenna conditions
Under coefficient correlation, be designated as ρ(k)(i, j), wherein NSThe array element sum in obtained bare cloth linear array antenna is initialized for step 2,It is element l values from 1 to NSIn the range of function summation symbol, exp () is the exponent arithmetic symbol that natural constant e is bottom,
| | for the oeprator that takes absolute value, 1i represents imaginary symbols, K0For radar system wave number andπ is pi, and λ is
The radar carrier frequency wavelength that step 1 initialization is obtained；
Using formula g=| j-i |, i=1,2 ..., M, j=1,2 ..., M, i ≠ j is calculated and is obtained LASAR observation angles area
Between i-th and j-th cell the poor absolute value of sequence number, be designated as g, natural number g span is g=1,2 ..., M-1；Will
Meet the correlation coefficient ρ of g values corresponding all i-th and j-th of cell under Sparse array antenna conditions(k)(i, j) is asked
Be averaged, obtain coefficient correlation result and be designated asG=1,2 ..., M-1；Will be allAccording to subscript sequence number from it is small to
Big sequence composition of vector, obtains the coefficient correlation in LASAR linear array antenna observation spaces between different units lattice in kth time iteration
Vector, is designated asWhereinIt is expressed as corresponding element value during g=1 It is expressed as g
Corresponding element value when=2 It is expressed as corresponding element value during g=M-1
Step 5.3, the value using threshold value constraint coefficient correlation vector
In kth time iteration, if vector X(k)In g-th of elementValue be less than threshold value T, then keep the element
Value it is constant, if vector X(k)In g-th of element valueValue be more than threshold value T, then elementValue be set to threshold value T, obtain
Coefficient correlation vector after to threshold value constraint, is designated as Y(k), wherein X(k)The coefficient correlation vector obtained for step 5.2, T is step
Obtained iterative algorithm correlation coefficient threshold is initialized in rapid 4.
Step 5.4, the excitation vector for estimating LASAR bare cloth linear array antenna array elements
In kth time iteration, using expression Z(k)=| IFFT (Y(k)) | calculating obtains the vector after inverse Fourier transform,
It is designated as Z(k), wherein Y(k)Coefficient correlation after the threshold value constraint obtained for kth in step 5.3 time iteration is vectorial, and IFFT () is
Inverse Fourier transform oeprator, | | for the oeprator that takes absolute value；By vector Z(k)In before NSThe value of individual maximum element is put
For 1, the value of other positions element is set to 0, and obtained vector is designated as C(k), wherein NSThe bare cloth linear array antenna obtained for step 2
Array element sum；Using β(k)=C(k)Obtain the excitation vector of LASAR bare cloth linear array antenna array elements in kth time iteration.
Step 5.5, iterative criterion
IfAnd k ＜ MaxIter, then k value be updated to k+1, perform step 5.1 to step 5.5,
Otherwise termination algorithm iteration, the β that kth time iteration is obtained this moment(k)As the excitation of LASAR bare cloths linear array antenna array element finally to
Amount, whereinThe function maximizing symbol in i and j excursions is expressed as, k represents the kth in iterative estimation procedure
Iterations, MaxIter is to initialize the maximum iteration of obtained algorithm reconstruction processing, ρ in step 4(k)(i, j) is step
Coefficient correlation in rapid 5.2 obtained kth time iteration LASAR linear array antenna observation spaces between different units lattice, ε is step 4
The middle stopping criterion for iteration threshold value initialized in obtained iterative algorithm.
Step 6, obtain final bare cloth linear array antenna array element optimum results：
The LASAR bare cloth linear array antenna array element excitation vectors β finally given using alternative manner step 5.5(k), according to step
Rapid 5.1 obtain the location sets S that LASAR bare cloths linear array encourages array element(k)；LASAR bare cloths linear array is encouraged to the location sets of array element
S(k)Bare cloth linear array antenna array element is assigned, the final array element optimum results of LASAR Sparse array antennas are obtained.
The innovative point of the present invention is to utilize in compressive sensing theory coherence's characteristic of calculation matrix, and there is provided a kind of base
In the compressed sensing LASAR bare cloth linear array optimization methods of low coherence, this method is based on compressed sensing measurement square in LASAR systems
The minimum of battle array coherence, by Fourier transformation iterative search method, realizes compression sensing LASAR bare cloth linear array antennas
Array element distribution optimization is designed.
The advantage of the invention is that coherence's characteristic by the use of calculation matrix in compressive sensing theory is used as compressed sensing
The reference frame of LASAR Sparse arrays optimization, it is more reasonable that Sparse array is optimized, and is conducive to improving compressed sensing LASAR systems
The imaging performance of system.Method proposed by the present invention is also applied for other bare cloth linear array antenna optimisation technique necks based on compressed sensing
Domain.
Brief description of the drawings：
Fig. 1 is the compressed sensing LASAR bare cloth linear array optimization method processing streams provided by the present invention based on low coherence
Journey schematic diagram.
Fig. 2 is the system emulation parameter list that the specific embodiment of the invention is used.
Embodiment
The main method for using emulation experiment of the invention is verified that all steps and conclusion are all soft in MATLABR2012b
Verified on part correct.Specific implementation step is as follows：
Step 1, initialization LASAR systematic parameters：
Initialization LASAR systematic parameters include：Radar platform height H=1000m；Radar operating center frequency fc=35 ×
109Hz；Radar carrier frequency wavelength X=0.00857m；The signal bandwidth B of radar emission baseband signalr=1.5 × 108Hz；Radar is sent out
Penetrate signal pulse width TP=5 × 10-6s；The chirp rate f of radar emission signaldr=3 × 1013Hz/s；Radar received wave door
Continue width To=6 × 10-4s；The sample frequency f of Radar Receiver Systems=3 × 108Hz；The pulse of radar emission system is repeated
Frequency PRF=600Hz；Pulse-recurrence time PRI=1 × 10 of radar system-3s；Effective aperture length of the antenna in orientation
Da=1.06m；Above-mentioned parameter is LASAR system standard parameters, is had determined in LASAR system designs and observation process；
The initialization systematic parameter needed according to LASAR imaging systems scheme and observation program, LASAR bare cloth linear array antennas optimization method
It is known.
Step 2, the parameter for initializing LASAR bare cloth linear array antennas：
The parameter of initialization LASAR bare cloth linear array antennas includes：The array element sum N of full front array antennaA=1000；Man Zhen
The spacing d of adjacent array element is the half of LASAR system carrier frequency wavelength in linear array antenna, i.e.,Wherein λ is
Obtained radar carrier frequency wavelength X=0.00857m is initialized in step 1；The array length L values of full front array antenna are L=
(NA-1)d；Array element sum N in bare cloth linear array antennaS=500；Bare cloth linear array antenna array element is the son of full front's array antenna array element
Collection, i.e. bare cloth linear array antenna array element are that 500 array element compositions are chosen from full 1000 array elements of front's array antenna；Full front's battle array day
The 1st position of the array element in flight path-elevation plane is cut is p in line1=[0, H]T, wherein H is that initialization is obtained in step 1
Radar platform height H=1000m；The 2nd position of the array element in flight path-elevation plane is cut is p in full front array antenna2=
[d,H]T；N in full front array antennaAPosition of the individual array element in flight path-elevation plane is cut isThe in full front's array antenna
N array element is set to p cutting flight path-elevation plane middle positionn, wherein subscript n is the sequence number of n-th of array element in full front array antenna, n
For natural number, n=1,2 ..., NA, NA=1000, and pn=[(n-1) d, H]T；All array elements are being cut in full front array antenna
Location sets P in flight path-elevation plane, wherein set P is a 2 × NAThe matrix of dimension, and
Step 3, initialization LASAR linear array antenna observation space parameters：
LASAR linear array antenna observation space parameters are initialized, including：Using the 1st element position of full front's array antenna as
Reference array element, the interval size θ of observation angle of the linear array antenna in flight path-elevation plane is cut0=10 °；LASAR linear array antennas exist
The observation angle cut in flight path-elevation plane is total interval for [- 5 °, 5 °]；LASAR linear array antennas are in flight path-elevation plane is cut
Total interval discretization cell sum M=1000 of observation angle；Reference array element using full front's array antenna, will as the center of circle
LASAR linear array antennas total interval of observation angle in flight path-elevation plane is cut is evenly dividing into equal-sized angle-unit lattice；
Using formulaCalculating obtain LASAR observation angles it is interval in m-th of cell in Horizon
Position q on facem, wherein m represent LASAR observation angles it is interval in m-th of angle-unit lattice, m is natural number, m=1,2 ...,
M；H be step 1 in initialize obtained radar platform height H=1000m, upper right corner symbol T representing matrix transposition oeprators.
Step 4, the relevant parameter for initializing LASAR bare cloth linear array antenna optimization methods：
The relevant parameter of initialization LASAR bare cloth linear array antenna optimization methods includes：The maximum of algorithm iteration estimation procedure
Iterations MaxIter=100；K is the kth time iteration of iterative estimation procedure, and k is natural number, and k initial values are set to k=0, k
Span is k=0,1,2 ..., MaxIter；Correlation coefficient threshold T=0.3 in iterative algorithm；Iteration in iterative algorithm
End condition threshold value is ε=0.1；The excitation vector β of LASAR bare cloth linear array antenna array elements in kth time iteration(k), k=0,1,
2 ..., MaxIter, MaxIter=100, β(k)It is a NATie up the vector of size；Randomly generate a NAThe vectorial α of dimension, wherein
Each element value is only 1 or 0 in α, and the element number that value is 1 is NS, wherein, NAObtained full front is initialized for step 2
Array element sum N in array antennaA=1000, NSArray element sum N in obtained bare cloth linear array antenna is initialized for step 2S=500；Will
Vectorial α is assigned to the excitation vector β of LASAR bare cloths linear array antenna array element in all iterative process(k), k=0,1,2 ...,
MaxIter, MaxIter=100, are used as bare cloth linear array antenna array element excitation vector β(k)Initial value；Encouraged in kth time iteration
Vectorial β(k)Middle element value is combined into Ω for the sequence number collection of 1 element position composition(k), k=0,1,2 ..., MaxIter,
MaxIter=100, sequence number set omega(k)For a NSTie up the vector of size, sequence number set omega(k)In element value be kth time
Bare cloth linear array encourages array element corresponding array element sequence number in full front's array antenna in iteration.
Step 5, using iterative algorithm carry out LASAR bare cloth linear array optimization designs, the iterative algorithm mainly include step 5.1
To step 5.5, specific steps are realized as follows：
Step 5.1, the position that LASAR bare cloths linear array antenna encourages array element is calculated in kth time iteration
In kth time iterative process, if during iterations k=0, according to set omega(0)In element, full front battle array day
Corresponding array element is chosen in line, the location sets S that LASAR bare cloths linear array in the 0th iteration encourages array element is obtained(0)；S(0)Represent
It is Ω for selection meets element numbers in location sets P(0)Element value composition location sets, S(0)It is a 2 × NSDimension
Matrix；Matrix S(0)Column vector groups be into expression-formWhereinFor matrix S(0)The 1st row
And physical significance is the 1st excitation element position in bare cloth linear array antenna in the 0th iteration,For matrix S(0)The 2nd row and
Physical significance is the 2nd excitation element position in bare cloth linear array antenna in the 0th iteration,For matrix S(0)NSRow and thing
It is N in bare cloth linear array antenna in the 0th iteration to manage meaningSIndividual excitation element position；Matrix S(0)L row be designated asAnd thing
It is l-th of excitation element position in bare cloth linear array antenna in the 0th iteration to manage meaning, and l is natural number, and l span
For l=1,2 ..., NS, wherein k=0,1,2 ..., MaxIter, MaxIter=100, Ω(0)Obtain the is initialized for step 4
Excitation vector β in 0 iteration(0)Middle element value is the sequence number set of 1 element position composition, β(0)For the 0th time in step 4
The excitation vector of LASAR bare cloths linear array antenna array element in iteration, P is each in obtained full front's array antenna to be initialized in step 2
Array element is cutting the location sets of course made good, NSObtained bare cloth linear array antenna array element sum N is initialized for step 2S=500；
In algorithm kth time iteration, if during iterations k ＞ 0, array element serial number set is chosen in full front's array antenna
Ω(k-1)Array element corresponding to middle element, obtains the element position set S that bare cloth linear array in kth time iteration encourages array element(k), k
=0,1,2 ..., MaxIter, MaxIter=100；S(k)It is to choose in location sets P to meet element numbers for Ω(k)Element
It is worth the location sets of composition, S(k)It is a 2 × NSThe matrix of dimension；Matrix S(k)Column vector groups be into expression-formK=0,1,2 ..., MaxIter, MaxIter=100,For matrix S(k)The 1st row and thing
It is the 1st excitation element position in bare cloth linear array antenna in kth time iteration to manage meaning,For matrix S(k)The 2nd row and physics
Meaning is the 2nd excitation element position in bare cloth linear array antenna in kth time iteration,For matrix S(k)NSRow and physics meaning
Justice is N in bare cloth linear array antenna in kth time iterationSIndividual excitation element position, matrix S(k)L row be designated asAnd physics is anticipated
Justice is l-th of excitation element position in bare cloth linear array antenna in kth time iteration, and l is natural number, l=1,2 ..., NS, wherein
MaxIter is the maximum iteration MaxIter=100, Ω of algorithm iteration estimation procedure in step 4(k-1)For iteration in step 4
The excitation vector β obtained in -1 iteration of algorithm kth(k-1)Middle element value is the sequence number set that 1 element position is constituted,
β(k-1)For the excitation vector of LASAR bare cloth linear array antenna array elements in -1 iteration of kth in step 4.
Coefficient correlation in step 5.2, calculating LASAR linear array antenna observation spaces between different units lattice
In algorithm kth time iteration, any two different units lattice in course made good observation angle interval, sequence are cut to LASAR
Number it is designated as i and j respectively, i and j are natural number, and i and j span is respectively i=1,2 ..., M and j=1,2 ...,
M and i ≠ j, wherein M are total interval discrete of LASAR linear array antennas observation angle in flight path-elevation plane is cut in step 3
Change cell sum M=1000；M-th of cell is on ground in the LASAR observation angles interval obtained using being initialized in step 3
Position in planeM=1,2 ..., M, M=1000, obtain the corresponding m of sequence number i values
=i unit cuts course made good position qi, and qiValue beI=1,2 ..., M, obtain sequence
Number corresponding the m=j unit of j values cuts course made good position qj, and qjValue beJ=
1,2 ..., M, wherein H be step 1 in initialize obtained radar platform height H=1000m, θ0Cut for step 3 linear array antenna
The interval size θ of observation angle in flight path-elevation plane0=10 °, upper right corner symbol T representing matrix transposition oeprators；
Using formulaK=0,1,2 ..., MaxIter, l=1,2 ..., NS, i=1,2 ...,
M, calculating obtains i-th of the cell in LASAR observation angles interval, l-th of excitation into bare cloth linear array antenna in algorithm kth iteration
The oblique distance R of array element(k)(l, i), wherein MaxIter are the maximum iteration MaxIter of algorithm iteration estimation procedure in step 4
=100, NSObtained bare cloth linear array antenna array element sum N is initialized for step 2S=500, M obtain for initialization in step 3
Total interval discretization cell sum M=1000 of LASAR linear array antennas observation angle in flight path-elevation plane is cut,For
The location sets S that step 5.1 is obtained(k)L row, | | | |2Represent the L2 norm oeprators of vector；Using formulaL=1,2 ..., NS, j=1,2 ..., M are calculated and obtained to LASAR observation angles area in k iteration
Between j-th of cell into bare cloth linear array antenna l-th excitation array element oblique distance R(k)(l,j)；Using formula Δ R(k)(l,i,j)
=R(k)(l,j)-R(k)(l, i), calculating obtains in kth iteration interval i-th of LASAR observation angles and j-th of cell to dilute
The poor Δ R of the oblique distance of l-th of excitation array element in cloth linear array antenna(k)(l, i, j), k=0,1,2 ..., MaxIter, l=1,2 ...,
NS, i=1,2 ..., M, j=1,2 ..., M, MaxIter=100, NS=500, M=1000；
Using formulaK=0,1,2 ..., MaxIter, i=
1,2 ..., M, j=1,2 ..., M and i ≠ j, calculating obtain i-th and j-th of unit of LASAR observation angles interval in kth iteration
Correlation coefficient ρ of the lattice under Sparse array antenna conditions(k)(i, j),It is element l values from 1 to NSIn the range of function summation symbol
Number, exp () is the exponent arithmetic symbol that natural constant e is bottom, | | for the oeprator that takes absolute value, 1i represents that imaginary number is accorded with
Number, K0For radar system wave number andπ is that pi=3.1415, λ is the radar carrier frequency that step 1 initialization is obtained
Wavelength X=0.00857m；
Using formula g=| j-i |, i=1,2 ..., M, j=1,2 ..., M, i ≠ j, M=1000, calculating obtain LASAR sights
The poor absolute value g, natural number g of sequence number of interval i-th and j-th cell of measuring angle span is g=1,2 ..., M-1；
The correlation coefficient ρ of g values corresponding all i-th and j-th of cell under Sparse array antenna conditions will be met(k)(i,j)
Summation is averaged, and obtains coefficient correlation resultG=1,2 ..., M-1；Will be allAccording to subscript sequence number from small to large
Sort composition of vector, obtain coefficient correlation in kth time iteration in LASAR linear array antenna observation spaces between different units lattice to
AmountWhereinIt is expressed as corresponding element value during g=1 When being expressed as g=2
Corresponding element value It is expressed as corresponding element value during g=M-1K=0,1,2 ..., MaxIter,
MaxIter=100.
Step 5.3, the value using threshold value constraint coefficient correlation vector
In kth time iteration, if vector X(k)In g-th of elementValue be less than threshold value T, then keep the element
Value it is constant, if vector X(k)In g-th of element valueValue be more than threshold value T, then elementValue be set to threshold value T, obtain
Coefficient correlation vector Y after to threshold value constraint(k), wherein X(k)LASAR linear array antennas in the kth time iteration obtained for step 5.2
Coefficient correlation vector in observation space between different units lattice, k=0,1,2 ..., MaxIter, wherein MaxIter are step 4
The maximum iteration MaxIter=100 of middle algorithm iteration estimation procedure, T are to initialize obtained iterative algorithm phase in step 4
Close coefficient threshold T=0.3.
Step 5.4, the excitation vector for estimating LASAR bare cloth linear array antenna array elements
In kth time iteration, using expression Z(k)=| IFFT (Y(k)) | calculating obtains the vector Z after inverse Fourier transform(k), by vector Z(k)In before NSThe value of individual maximum element is set to 1, and the value of other positions element is set to 0, obtains vectorial C(k), adopt
Use β(k)=C(k)Obtain the excitation vector of LASAR bare cloth linear array antenna array elements in kth time iteration, k=0,1,2 ..., MaxIter；
Wherein Y(k)Coefficient correlation vector after the threshold value constraint obtained for kth in step 5.3 time iteration, MaxIter is calculation in step 4
The maximum iteration of method iterative estimation procedure is MaxIter=100, and IFFT () is inverse Fourier transform oeprator, |
| for take absolute value oeprator, NSThe array element sum N of the bare cloth linear array antenna obtained for step 2S=500.
Step 5.5, iterative criterion
IfAnd k ＜ MaxIter, then k value be updated to k+1, perform step 5.1 to step 5.5,
Otherwise termination algorithm iteration, the β that kth time iteration is obtained this moment(k)As the excitation of LASAR bare cloths linear array antenna array element finally to
Amount, whereinThe function maximizing symbol in i and j excursions is expressed as, k represents the kth in iterative estimation procedure
Iterations, k=0,1,2 ..., MaxIter, MaxIter is the greatest iteration of the algorithm iteration estimation procedure obtained in step 4
Number of times MaxIter=100, ρ(k)(i, j) is difference in the kth time iteration LASAR linear array antenna observation spaces that step 5.2 is obtained
Coefficient correlation between cell, ε be initialize in step 4 stopping criterion for iteration threshold epsilon in obtained iterative algorithm=
0.1。
Step 6, obtain final bare cloth linear array antenna array element optimum results：
The LASAR bare cloth linear array antenna array element excitation vectors β finally given using alternative manner step 5.5(k), according to step
Rapid 5.1 obtain the location sets S that LASAR bare cloths linear array encourages array element(k), LASAR bare cloths linear array is encouraged to the location sets of array element
S(k)Bare cloth linear array antenna array element is assigned, the final array element optimization position of LASAR Sparse array antennas is obtained.
Claims (1)
1. a kind of compressed sensing LASAR bare cloth linear array optimization methods based on low coherence, it is characterized in that it comprises the following steps：
Step 1, initialization LASAR systematic parameters：
Initialization LASAR systematic parameters include：Radar platform height, is denoted as H；Radar operating center frequency, is denoted as fc；Radar is carried
Frequency wavelength, is denoted as λ；The signal bandwidth of radar emission baseband signal, is denoted as Br；Radar emission signal pulse width, is denoted as TP；Thunder
Up to the chirp rate of transmission signal, f is denoted asdr；Radar received wave door continues width, is denoted as To；The sampling frequency of Radar Receiver System
Rate, is denoted as fs；The pulse recurrence frequency of radar emission system, is denoted as PRF；The pulse-recurrence time of radar system, it is designated as PRI；
Antenna is denoted as D in the effective aperture length of orientationa；Above-mentioned parameter is LASAR system standard parameters, wherein radar platform
Height H, radar center frequency fc, radar carrier frequency wavelength X, the signal bandwidth B of radar emission baseband signalr, radar emission signal arteries and veins
Rush width TP, radar emission signal chirp rate fdr, the lasting width T of radar received wave dooro, the sample frequency of Radar Receiver System
fs, the pulse recurrence frequency PRF of radar system, the pulse-recurrence time PRI of radar system, antenna is in the effective aperture of orientation
Length DaHad determined in LASAR system designs and observation process；According to LASAR imaging systems scheme and observation program,
The initialization systematic parameter that LASAR bare cloth linear array antennas optimization method needs is known；
Step 2, the parameter for initializing LASAR bare cloth linear array antennas：
The parameter of initialization LASAR bare cloth linear array antennas includes：The array element sum of full front array antenna is designated as NA；Full front's battle array day
The spacing of adjacent array element, is designated as d in line, and d value is the half of system carrier frequency wavelength in LASAR systems, is
Wherein λ be step 1 in initialize obtained radar carrier frequency wavelength；The array length of full front's array antenna, be designated as L, and L takes
It is worth for L=(NA-1)d；Array element sum in bare cloth linear array antenna, is designated as NS, and NS＜ NA；Bare cloth linear array antenna array element is full
The subset of front's array antenna array element, i.e. bare cloth linear array antenna array element are the N from full front's array antennaAN is chosen in individual array elementSIndividual battle array
Member composition；1st position of the array element in flight path-elevation plane is cut in full front array antenna, is designated as p1；In full front array antenna
2nd position of the array element in flight path-elevation plane is cut, is designated as p2；N in full front array antennaAIndividual array element is cutting flight path-height
The position spent in plane, is designated asPosition of n-th of the array element in flight path-elevation plane is cut in full front array antenna, is designated as
pn, wherein subscript n is the sequence number of n-th of array element in full front array antenna, and n is natural number, n=1,2 ..., NA, and pn=[(n-
1)d,H]T, wherein H be step 1 in initialize obtain radar platform height；In full front's array antenna all array elements cut flight path-
Location sets in elevation plane, are denoted as P, wherein set P is a 2 × NAThe matrix of dimension, and
Step 3, initialization LASAR linear array antenna observation space parameters：
Linear array SAR linear array antenna observation space parameters are initialized, including：Using the 1st element position of full front's array antenna as ginseng
Array element is examined, the interval size of observation angle of the linear array antenna in flight path-elevation plane is cut is designated as θ0；LASAR linear array antennas are being cut
Observation angle in flight path-elevation plane is always interval, is designated asLASAR linear array antennas are cutting flight path-elevation plane
The total interval discretization cell sum of middle observation angle, is designated as M；Reference array element using full front's array antenna, will as the center of circle
LASAR linear array antennas total interval of observation angle in flight path-elevation plane is cut is evenly dividing into equal-sized angle-unit lattice,
And each corresponding angle value of angle-unit lattice is less than LASAR linear array antennas and is cutting the angular resolution of course made good；Adopt
Use formulaM=1,2 ..., M, calculating obtain m-th of list in LASAR observation angles interval
Position of first lattice on ground level, is designated as qm, m=1,2 ..., M, wherein m represent m-th of angle in LASAR observation angles interval
Cell, m is natural number, and m=1,2 ..., M；H is initializes obtained radar platform height in step 1, the upper right corner is accorded with
Number T represents transposition oeprator；
Step 4, the relevant parameter for initializing LASAR bare cloth linear array antenna optimization methods：
The relevant parameter of initialization LASAR bare cloth linear array antenna optimization methods includes：The greatest iteration of algorithm iteration estimation procedure
Number of times, is denoted as MaxIter；K is designated as the kth time iteration of iterative estimation procedure, and k is natural number, and k initial values are set to k=0, and
And k span is k=0,1,2 ..., MaxIter；Correlation coefficient threshold in iterative algorithm, is designated as T；In iterative algorithm
Stopping criterion for iteration threshold value, be designated as ε；The excitation vector of LASAR bare cloth linear array antenna array elements, is designated as β in kth time iteration(k), k
=0,1,2 ..., MaxIter, wherein β(k)It is a NATie up the vector of size, NAIt is that obtained full front battle array is initialized in step 2
The array element sum of antenna；Randomly generate a NAThe vector of dimension, it is only 1 or 0 to be designated as in α, wherein α each element value, and is worth
It is N for 1 element numberS, NSTo initialize the array element sum of obtained bare cloth linear array antenna in step 2；Vectorial α is assigned to
The excitation vector β of LASAR bare cloths linear array antenna array element in all iterative process(k), k=0,1,2 ..., MaxIter are used as bare cloth
Linear array antenna array element excitation vector β(k)Initial value；Excitation vector β in kth time iteration(k)Middle element value is in place for 1 element institute
The sequence number set of composition is put, Ω is designated as(k), k=0,1,2 ..., MaxIter, wherein sequence number set omega(k)For a NSTie up size
Vector；Sequence number set omega(k)In element value be in kth time iteration bare cloth linear array encourage array element in full front's array antenna
Corresponding array element sequence number；
Step 5, LASAR bare cloth linear array optimization designs are carried out using iterative algorithm, the iterative algorithm mainly includes step 5.1 to step
Rapid 5.5, specific steps are realized as follows：
Step 5.1, the position that LASAR bare cloths linear array antenna encourages array element is calculated in kth time iteration
In kth time iterative process, if during iterations k=0, according to set omega(0)In element, in full front's array antenna
Corresponding array element is chosen, the location sets that LASAR bare cloths linear array in the 0th iteration encourages array element is obtained, is designated as S(0), wherein
Ω(0)Excitation vector β in the 0th time obtained iteration is initialized for step 4(0)Middle element value is 1 element position composition
Sequence number set, β(0)For the excitation vector of LASAR bare cloth linear array antenna array elements in the 0th iteration；S(0)It is expressed as in location sets P
Selection meets element numbers for Ω(0)Element value composition location sets, S(0)For a 2 × NSThe matrix of dimension, wherein P are step
Each array element in obtained full front's array antenna is initialized in rapid 2 and is cutting the location sets of course made good；Order matrix S(0)Column vector groups
It is into expression-formWhereinFor matrix S(0)The 1st row and physical significance is the 0th iteration
1st excitation element position in middle bare cloth linear array antenna,For matrix S(0)The 2nd row and during physical significance is the 0th iteration
2nd excitation element position in bare cloth linear array antenna,For matrix S(0)NSArrange and physical significance is dilute in the 0th iteration
N in cloth linear array antennaSIndividual excitation element position；Matrix S(0)L row be designated asAnd physical significance is dilute in the 0th iteration
L-th of excitation element position in cloth linear array antenna, l is natural number, and l span is l=1,2 ..., NS, NSFor step
The bare cloth linear array antenna array element sum that 2 initialization are obtained；
In algorithm kth time iteration, if during iterations k ＞ 0, array element serial number set omega is chosen in full front's array antenna(k-1)
Array element corresponding to middle element, obtains the element position set that LASAR bare cloths linear array in kth time iteration encourages array element, is designated as S(k), wherein Ω(k-1)For the excitation vector β obtained in -1 iteration of iterative algorithm kth(k-1)Middle element value is 1 element position
The sequence number set of composition, β(k-1)For the excitation vector of LASAR bare cloth linear array antenna array elements in -1 iteration of kth；S(k)It is expressed as position
Put to choose in set P and meet element numbers for Ω(k)Element value composition location sets, S(k)For a 2 × NSThe matrix of dimension；
Define matrix S(k)Column vector groups be into expression-formWhereinFor matrix S(k)The 1st row
And physical significance is the 1st excitation element position in bare cloth linear array antenna in kth time iteration,For matrix S(k)The 2nd row and
Physical significance is the 2nd excitation element position in bare cloth linear array antenna in kth time iteration,For matrix S(k)NSRow and thing
It is N in bare cloth linear array antenna in kth time iteration to manage meaningSIndividual excitation element position, matrix S(k)L row be designated asAnd thing
It is l-th of excitation element position in bare cloth linear array antenna in kth time iteration to manage meaning, and l is natural number, and l=1,2 ...,
NS；
Coefficient correlation in step 5.2, calculating LASAR linear array antenna observation spaces between different units lattice
In algorithm kth time iteration, any two different units lattice in course made good observation angle interval, sequence number point are cut to LASAR
I and j are not designated as, and i and j are natural number, and i and j span is respectively i=1,2 ..., M and j=1, and 2 ..., M is simultaneously
And i ≠ j, wherein M be step 3 in initialize obtained LASAR linear array antennas total area of observation angle in flight path-elevation plane is cut
Between discretization cell sum；M-th of cell exists in the LASAR observation angles interval obtained using being initialized in step 3
Position on ground levelM=1,2 ..., M, obtain the corresponding the m=i list of sequence number i values
Member cuts course made good position, is designated as qi, and qiValue beObtain the corresponding m of sequence number j values
=j unit cuts course made good position, is designated as qj, and qjValue be
Using formulaL=1,2 ..., NS, i=1,2 ..., M are calculated and obtained in algorithm kth iteration
The oblique distance of i-th of the cell in LASAR observation angles interval, l-th of excitation array element into bare cloth linear array antenna, is designated as R(k)(l, i),
WhereinThe location sets S obtained for step 5.1(k)L row, | | | |2Represent the L2 norm oeprators of vector；Using
FormulaL=1,2 ..., NS, j=1,2 ..., M are calculated and obtained to LASAR observation angles in k iteration
The oblique distance of interval j-th of cell l-th of excitation array element into bare cloth linear array antenna, is designated as R(k)(l,j)；Using formula Δ R(k)
(l, i, j)=R(k)(l,j)-R(k)(l, i), which is calculated, obtains i-th and j-th of unit of LASAR observation angles interval in kth iteration
The oblique distance of lattice l-th of excitation array element into bare cloth linear array antenna is poor, is designated as Δ R(k)(l,i,j)；
Using formulaI=1,2 ..., M, j=1,2 ..., M and i ≠
J, calculating obtains interval i-th of LASAR observation angles in kth iteration and j-th of cell under Sparse array antenna conditions
Coefficient correlation, is designated as ρ(k)(i, j), wherein NSThe array element sum in obtained bare cloth linear array antenna is initialized for step 2,For
Element l values are from 1 to NSIn the range of function summation symbol, exp () is the exponent arithmetic symbol that natural constant e is bottom, | |
For the oeprator that takes absolute value, 1i represents imaginary symbols, K0For radar system wave number andπ is pi, and λ is step
The radar carrier frequency wavelength that 1 initialization is obtained；
Using formula g=| j-i |, i=1,2 ..., M, j=1,2 ..., M, i ≠ j is calculated and is obtained LASAR observation angles interval i-th
The individual sequence number difference absolute value with j-th of cell, is designated as g, natural number g span is g=1,2 ..., M-1；G will be met
The correlation coefficient ρ of value corresponding all i-th and j-th of cell under Sparse array antenna conditions(k)(i, j) summation takes
It is average, obtain coefficient correlation result and be designated asG=1,2 ..., M-1；Will be allArranged from small to large according to subscript sequence number
Sequence composition of vector, obtain coefficient correlation in kth time iteration in LASAR linear array antenna observation spaces between different units lattice to
Amount, is designated asWhereinIt is expressed as corresponding element value during g=1 It is expressed as g=
Corresponding element value when 2 It is expressed as corresponding element value during g=M-1
Step 5.3, the value using threshold value constraint coefficient correlation vector
In kth time iteration, if vector X(k)In g-th of elementValue be less than threshold value T, then keep the elementValue
It is constant, if vector X(k)In g-th of element valueValue be more than threshold value T, then elementValue be set to threshold value T, obtain threshold
Coefficient correlation vector after value constraint, is designated as Y(k), wherein X(k)The coefficient correlation vector obtained for step 5.2, T is in step 4
Initialize obtained iterative algorithm correlation coefficient threshold；
Step 5.4, the excitation vector for estimating LASAR bare cloth linear array antenna array elements
In kth time iteration, using expression Z(k)=| IFFT (Y(k)) | calculating obtains the vector after inverse Fourier transform, is designated as
Z(k), wherein Y(k)Coefficient correlation vector after the threshold value constraint obtained for kth in step 5.3 time iteration, IFFT () is inverse Fu
In leaf transformation oeprator, | | to take absolute value oeprator；By vector Z(k)In before NSThe value of individual maximum element is set to 1,
The value of other positions element is set to 0, and obtained vector is designated as C(k), wherein NSThe array element of the bare cloth linear array antenna obtained for step 2
Sum；Using β(k)=C(k)Obtain the excitation vector of LASAR bare cloth linear array antenna array elements in kth time iteration；
Step 5.5, iterative criterion
IfAnd k ＜ MaxIter, then k value be updated to k+1, perform step 5.1 to step 5.5, otherwise
Termination algorithm iteration, the β that kth time iteration is obtained this moment(k)The as final excitation vector of LASAR bare cloths linear array antenna array element, its
InThe function maximizing symbol in i and j excursions is expressed as, k represents the kth iteration time in iterative estimation procedure
Number, MaxIter is to initialize the maximum iteration of obtained algorithm reconstruction processing, ρ in step 4(k)(i, j) obtains for step 5.2
To kth time iteration LASAR linear array antenna observation spaces in coefficient correlation between different units lattice, ε is to initialize in step 4
Stopping criterion for iteration threshold value in obtained iterative algorithm；
Step 6, obtain final bare cloth linear array antenna array element optimum results：
The LASAR bare cloth linear array antenna array element excitation vectors β finally given using alternative manner step 5.5(k), according to step 5.1
Obtain the location sets S that LASAR bare cloths linear array encourages array element(k)；LASAR bare cloths linear array is encouraged to the location sets S of array element(k)Assign
Bare cloth linear array antenna array element is given, the final array element optimum results of LASAR Sparse array antennas are obtained.
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