CN103353595A - Meter wave radar height measurement method based on array interpolation compression perception - Google Patents
Meter wave radar height measurement method based on array interpolation compression perception Download PDFInfo
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Abstract
The invention discloses a height measurement method based on an array interpolation compression perception. The height measurement method mainly aims at solving a low elevation height measurement problem under a multipath environment, and especially under low signal to noise ratio and less snapshot environments. The method comprises the following steps of extracting a target signal from a radar echo; acquiring a spatial-domain sparse signal through cancellation and signal reconstruction; using a wave beam formation method to obtain a rough measurement target angle; according to the rough measurement angle, acquiring the spatial domain and dividing the spatial domain; using the array interpolation to acquire a virtual array; according to a matrix transformation relation, acquiring an interpolation transformation matrix and carrying out prewhitening processing on the interpolation transformation matrix; using a whitening interpolation transformation matrix and an observation matrix to acquire an observation signal; using a whitening interpolation transformation matrix and observation signal iteration operation to acquire a target signal estimation value; extracting a target angle from the target signal estimation value so as to acquire a target height. By using the method of the invention, sampling points of the target signal and computation intensity are obviously reduced; sidelobes of a signal power spectrum and a space spectrum are effectively reduced; the method can be used in target tracking.
Description
Technical field
The invention belongs to the Radar Signal Processing Technology field, particularly compressed sensing and altitude measurement in VHF radar method can be used for target following.
Background technology
Radar circle generally believes both at home and abroad, and metre wave radar has anti-stealthy ability.Metre wave radar is because its wavelength is longer, and wave beam is wide, and particularly when measuring low angle target, wave beam is beaten ground, ground return multipath phenomenon strong, target is serious, causes the altitude measurement in VHF radar precision low, even complete failure.In the radar return signal except the radio wave refration effect that the unevenness of lower atmosphere layer causes, the multipath interference effect that also has mirror-reflection that ground, sea produce and diffuse scattering to cause.The multipath interference has a huge impact the low measurement of elevation precision of radar, and direct wave and multipath reflection ripple signal have strong correlation; The angle of target direct wave incident angle and multipath reflection ripple incident angle is very little, is usually located within the beam angle; The lobe division can cause the electrical level flash that receives signal, and the signal to noise ratio (S/N ratio) fluctuation is larger.Topographic relief is very large on the impact of measurement result during the low elevation angle, especially on the larger sea of sea condition or the land of complex area, ground (sea) face reflection clutter is stronger, and echo signal often is submerged in the clutter, and the non-stationary and spike of clutter can cause false-alarm probability to increase rapidly.Therefore under multi-path environment, be difficult to survey high, therefore the high problem of the survey of metre wave radar is the difficult problem of the not yet fine solution of radar circle always.
Survey a high difficult problem for solving preferably metric wave, the Major Technology of taking mainly contains: 1. increase a day linear content and particularly increase antenna in the aperture of height dimension, to reduce antenna at the beam angle of vertical dimension, improve angular resolution, for the higher elevation angle, make wave beam " not beat ground " and finish highly measurement; 2. suitably increase the antenna height of antenna, reduce wave beam and upwarp, be beneficial to detecting low-altitude objective.But for low target, " multipath " problem can't be avoided.
At present, mainly contain following three classes for the high method of the survey of metre wave radar:
(1) multifrequency lobe division altimetry.This method is utilized a plurality of frequency of operation time-division work, and its theory is feasible, but requires the bandwidth of operation of a plurality of frequencies wider, and system complex does not also have this utility system at present.
(2) the altitude measurement in VHF radar method that divides based on lobe.This method is utilized the phase relation of different antennae division lobe, determines that the elevation angle, target place is interval, carries out to received signal processing than the width of cloth and extracts the normalization error signal, obtains at last the height of target according to normalization error signal and elevation angle section scale-checking.Its mean square deviation at surface irregularity is no more than 1m, and signal to noise ratio (S/N ratio) reaches 16dB, and altimetry precision can reach 1% of distance.The paper that Chen Baixiao etc. delivered in " electronic letters, vol " in June, 2007 " based on the altitude measurement in VHF radar method of lobe division ".This is a kind of high method of low Elevation that only needs the metre wave radar of 3 antennas in vertical dimension.The method is only suitable in smooth position, and the flatness in position is had relatively high expectations, and altimetry precision also can only reach 1% of distance, is difficult to satisfy the higher actual operation requirements of some precision.
(3) the array super-resolution is processed the high method of surveying.This method is that the super resolution technology in the Array Signal Processing is applied to differentiate direct-path signal and multipath signal.Comprise proper subspace algorithm and maximum likelihood algorithm.Wherein:
Proper subspace class algorithm, being applied to low Elevation must be in the face of the relevant problem of the caused direct wave of multipath transmisstion and multipath signal when high.But when signal source is fully relevant, the order of data covariance matrix will be 1, the existence of coherent source interpenetrates signal subspace and noise subspace, the steering vector and the incomplete quadrature of noise subspace that cause some coherent source, this meeting is so that a lot of classical proper subspace class Algorithm Performance descends even complete failure.
Maximum likelihood class algorithm idea is simple, superior performance, good performance is all arranged under high s/n ratio and low signal-to-noise ratio, it is a nonlinear multidimensional optimization problem that but likelihood function is found the solution, need to carry out the multidimensional grid search, calculated amount is along with the increase of target number is exponential increase, and implementation procedure is complicated.For example, the paper " the Beam Domain ML altitude measurement in VHF radar method of Array interpolation " that the people such as the paper that the people such as Zhao Guanghui delivered at " electronics and information journal " in February, 2009 " based on the low elevation angle of the pretreated metre wave radar of difference Processing Algorithm " and Hu Tiejun delivered at " electric wave science journal " in August, 2009, and the paper " research of metre wave radar maximum likelihood super-resolution height-finding technique " delivered in " radar science and technology " in September, 2011 of the people such as Yang Xueya.
In the said method, method 1 is difficult to realize; Method 2 is only applicable to smooth position, and low precision, can't practical requirement; Method 3 operands are large, require sample number many, hydraulic performance decline under multi-path environment, even lost efficacy.Therefore in processing the low high problem process of Elevation, the high method of existing various surveys is effective poor, no longer applicable.
Summary of the invention
The object of the invention is to the deficiency for above-mentioned prior art, propose a kind of altitude measurement in VHF radar method based on the Array interpolation compressed sensing, with further computation reduction, improve the angle measurement accuracy of direction of arrival DOA in the low signal-to-noise ratio situation.
For achieving the above object, technical thought of the present invention is:
By M array element is carried out Array interpolation, obtaining array element is P, P＞＞M, virtual array, thereby improve the dimension of array measurement signal, then the measurement signal of virtual array carried out compression sampling, obtain the target direction of arrival by sparse reconstruct at last.
The specific implementation step comprises as follows:
(1) from radar return, extracts echo signal, obtain the array manifold matrix V of true array, and this echo signal is carried out clutter the slake interference cancellation is processed, obtaining offseting rear echo signal x and spatial domain sparse signal S, the relation that offsets rear echo signal x and spatial domain sparse signal S is as follows:
x=ψS+n，
Wherein, ψ represents super complete redundant dictionary, and its length is c, and n represents white Gaussian noise;
(2) use digital beam forming method DBF that the echo signal x after offseting is carried out elevation angle bigness scale, obtain the bigness scale angle [alpha], and then obtain spatial domain, place, echo signal elevation angle Ο;
(3) described spatial domain Ο is divided into P part, P＞＞M, M represents array number, obtains spatial domain matrix Θ:
Θ=[α
l,α
l+Δα,…,α
r],
Wherein,
The left margin of expression Θ,
The right margin of expression Θ,
The expression half-power beam width, Δ α is step-length, Δ α=0.1 °;
(4) true array is carried out Array interpolation and process, obtain the array manifold matrix W of virtual array
IArray manifold matrix W according to virtual array
IWith the array manifold matrix W of true array, obtain interpolation transformation matrix B;
(5) interpolation transformation matrix B is carried out prewhitening and process, obtain albefaction interpolation transformation matrix T
I
(6) the echo signal x after will offseting projects to albefaction interpolation transformation matrix T
I, obtain the measurement signal z of virtual array;
(7) with F * P dimension observing matrix φ measurement signal z is carried out compression sampling, F＜＜P, obtain the observation signal y that tie up F * 1;
(8) according to observation signal y and albefaction interpolation transformation matrix T
I, utilize greedy orthogonal matching pursuit method of following the trail of in the class algorithm, through type
Iteration is chosen a locally optimal solution and is progressively approached spatial domain sparse signal S, obtains the estimated value of spatial domain sparse signal S
Wherein, || ||
1Vectorial 1-norm is asked in expression, and s.t represents constraint condition, || ||
2Vectorial 2-norm is asked in expression, and ψ represents super complete redundant dictionary, and c represents the length of super complete redundant dictionary ψ, i=1, and 2 ..., c, β represent that noise criteria is poor;
(9) objective definition angular range 6=[θ
1, θ
2..., θ
i..., θ
c],
According to estimated value
Element and the one-to-one relationship of the element of θ, namely
With θ
iCorresponding one by one, obtain as a result θ of target angle measurement
d, d ∈ i:
Wherein, d represents estimated value
In non-vanishing element s
dSubscript;
(10) according to target angle measurement θ as a result
dTarget range R with known obtains object height by triangular transformation:
H=Rsin(θ
d)。
The present invention compared with prior art has following advantage:
1) the present invention is owing to adopting Array interpolation to process to echo signal, reduced the secondary lobe of power spectrum signal and spatial spectrum, Effective Raise the performance of altitude measurement in VHF radar method, under multi-path environment, especially the high problem of low Elevation under the less environment of low signal-to-noise ratio and fast umber of beats provides a kind of effective solution.
2) the present invention is owing to adopting observing matrix that measurement signal is carried out compression sampling to process, not only reduced operand, improved estimated accuracy, and can be when sample number be less the echo signal estimated result of gained more excellent than additive method.
Simulation result shows, the present invention can be directly used in the direction of arrival of coherent signal and estimate, and has higher angular resolution.
Description of drawings
Further specify advantage and the effect of the inventive method below in conjunction with accompanying drawing.
Fig. 1 is realization flow figure of the present invention;
Fig. 2 is that the present invention surveys the performance curve comparison diagram of high method when signal to noise ratio (S/N ratio) changes with existing two kinds;
Fig. 3 is that the present invention surveys the as a result comparison diagram that high method is estimated angle on target with existing two kinds;
Fig. 4 angle error that to be the present invention process measured data with existing a kind of method is comparison diagram as a result.
Embodiment
Describe content of the present invention and effect in detail below in conjunction with accompanying drawing.
With reference to Fig. 1, the present invention includes following steps:
Step 1: from radar return, extract echo signal, obtain the array manifold matrix W of true array.
Used array radar is a vertical even linear array of placing, and this even linear array is comprised of M array element, and array element is spaced apart d.
Suppose to have K far field narrow band signal to incide this even linear array, M〉K, the signal incident angle is α
i, i=1,2 ..., K, then array in the echo signal that t receives constantly is:
X(t)=Vs(t)+n(t)，
Wherein, X is the array element receive data of M * 1 dimension, and n is the white noise of M * 1 dimension, satisfies zero-mean, variance is σ
2Multiple Gaussian distribution, each array element output noise statistics is independent; S=[s
1, s
2..., s
i..., s
K]
TSignal phasor for K * 1 dimension; W is M * K dimension array manifold matrix:
W=[v(α
1),v(α
2),…，v(α
i),…，v(α
K)]，
Wherein,
Be the steering vector of i echo signal, subscript T represents transposition, and λ represents the radar signal wavelength.
Step 2: echo signal X (t) is carried out clutter the slake interference cancellation is processed, obtain offseting rear echo signal x; Adopt the space lattice division methods to re-construct and offset rear echo signal x, obtain spatial domain sparse signal S.
Belong to the radar signal conventional processing owing to the clutter of echo signal X (t) is processed the slake interference cancellation, and unnecessarily contact with main contents of the present invention, therefore be not described.
In order to show the sparse property in the spatial domain that offsets rear echo signal x, adopt space lattice to divide to process to offseting rear echo signal x, be about to space-180 °～180 ° and be divided into { α
1, α
2..., α
u..., α
U, α
uBe u angular interval, u=1,2 ..., U, U＞＞K;
Suppose each α
uAll with an echo signal s
uCorresponding, so just construct the spatial domain sparse signal that tie up a U * 1: S=[s
1, s
2..., s
u..., s
U]
T, will offset rear echo signal x and project to S, then in S, only have the element of K position of physical presence echo signal non-vanishing, the element of other U-K position is zero, obtains spatial domain sparse signal S:
S=(x-n)ψ
-1，
Wherein, subscript T represents transposition, and ψ is super complete redundant dictionary; X is consistent with the target information that S comprises, and different is, x be echo signal in the expression in array element territory, S is that echo signal is in the expression in spatial domain.
By following formula as can be known, offseting rear echo signal x also can write:
x=ΨS+n。
Step 3: use the echo signal x after digital beam forming method DBF offsets to carry out the angle bigness scale, obtain the bigness scale angle [alpha], and then obtain spatial domain, place, echo signal elevation angle Ο.
3a) utilize steering vector v (ξ)=[1, e
-j2 π sin (ξ)..., e
-j2 π (M-1) sin (ξ)]
T, the echo signal x after offseting is weighted summation, obtain the bigness scale angle [alpha]:
Wherein, arg max represents to seek the parameter with maximum cost function, and ξ represents the target search angular range, and-180 °≤ξ≤180 °, L represents fast umber of beats, and M represents element number of array, x (t
l) echo signal of expression after offseting, t
lThe expression sampling time, 1≤l≤L, subscript T represents transposition, subscript H represents conjugate transpose;
3b) utilize half-power beam width
Obtain the spatial domain Ο at angle on target place:
Wherein, λ represents the radar signal wavelength, and d represents array element distance.
Step 4: described spatial domain Ο is divided into P part, obtains spatial domain matrix Θ, P＞＞M, M represents array number:
Θ=[α
l,α
l+Δα，…，α
r]，
Wherein,
The left margin of expression Θ,
The right margin of expression Θ,
The expression half-power beam width, Δ α is step-length, Δ α=0.1 °.
Step 5: true array is carried out Array interpolation process, obtain the array manifold matrix W of virtual array
I
True array being carried out Array interpolation process, is to add Virtual array between the array element of true array, with the dimension of the array manifold matrix W that enlarges true array, obtains the M of virtual array * P dimension array manifold matrix W
I:
W
I=[v
I(α
l)，v
l(α
l+Δα)，…，v
I(α
j)，…，v
I(α
r)]，
Wherein,
The steering vector of j echo signal of expression virtual matrix, M represents element number of array, subscript T represents transposition, α
j∈ Θ, Θ=[α
l, α
l+ Δ α ..., α
r], Δ α is step-length, Δ α=0.1 °.
Step 6: according to the array manifold matrix W of virtual array
IWith the array manifold matrix W of true array, obtain interpolation transformation matrix B, minute following two kinds of situations are calculated:
In the situation that do not consider noise, according to the array manifold matrix W of virtual array
IAnd the fixed relationship between the array manifold matrix W of true array and the interpolation transformation matrix B: B
HW=W
I, and the steering vector of true array
Steering vector v with virtual array
I(α
j) and interpolation transformation matrix B between fixed relationship:
B=W
IW
H(WW
H)
-1，
Wherein,
The steering vector that represents true array,
The steering vector of expression virtual matrix, subscript H represents conjugate transpose,
Expression offsets the incident angle of front echo signal, α
j∈ Θ, Θ=[α
l, α
l+ Δ α ..., α
r], Δ α is step-length, Δ α=0.1 °;
In the situation that consider noise, it is the array manifold matrix W according to virtual array
IAnd the fixed relationship between the array manifold matrix W of true array and the interpolation transformation matrix B: B
H(W+N)=W
I+ N
I, and the steering vector of true array
Steering vector v with virtual array
I(α
j) and interpolation transformation matrix B between fixed relationship:
Wherein, N represents the noise matrix of true array, N
IThe noise matrix of expression virtual matrix, n represents the noise vector of N, n
IExpression N
INoise vector,
Be signal power,
Be noise power, I is unit matrix.
Step 7: interpolation transformation matrix B is carried out prewhitening process, obtain albefaction interpolation transformation matrix T
I
7a) to the autocorrelation matrix R of interpolation transformation matrix B
BCarry out Eigenvalues Decomposition:
R
B=B(B
HB)
-1B
H=QΣQ
H,
Wherein, Q represents orthogonal matrix, Q=B, and Σ represents diagonal matrix, Σ=(B
HB)
-1, subscript H represents conjugate transpose;
7b) according to orthogonal matrix Q and diagonal matrix Σ, obtain albefaction interpolation transformation matrix T by the prewhitening formula
I:
T
I=Σ
1/2Q
H=(B
HB)
-1/2B
H。
Step 8: the echo signal x after will offseting projects to albefaction interpolation transformation matrix T
I, obtain the P of virtual array * 1 dimension measurement signal: z=T
IX=T
Iψ S+T
IN, wherein, ψ represents super complete redundant dictionary, and n represents white noise, and S represents the spatial domain sparse signal.
Step 9: φ carries out compression sampling to measurement signal z with F * P dimension observing matrix, F＜＜P, namely dwindle the dimension of measurement signal z, obtain the observation signal y of F * 1 dimension:
y=φz=φT
Iψs+φT
In。
Step 10: according to observation signal y and albefaction interpolation transformation matrix T
I, utilize greedy orthogonal matching pursuit method of following the trail of in the class algorithm, through type
Iteration is chosen a locally optimal solution and is progressively approached spatial domain sparse signal S, obtains the estimated value of spatial domain sparse signal S
Wherein, || ||
1Vectorial 1-norm is asked in expression, and s.t represents constraint condition, || ||
2Vectorial 2-norm is asked in expression, and ψ represents super complete redundant dictionary, and c represents the length of super complete redundant dictionary ψ, i=1, and 2 ..., c, β represent that noise criteria is poor.
Step 11: objective definition angular range, theta=[θ
1, θ
2..., θ
i..., θ
c],
According to estimated value
Element and the one-to-one relationship of the element of θ, namely
With θ
iCorresponding one by one, obtain as a result θ of target angle measurement
d, d ∈ i:
Wherein, d represents estimated value
In non-vanishing element s
dSubscript.
Step 12: according to target angle measurement θ as a result
dTarget range R with known obtains object height by triangular transformation:
H=Rsin(θ
d)。
Advantage of the present invention and effect further specify by following Calculation Simulation and measured data result:
1. simulated conditions
In the simulation process, for equidistantly structuring the formation of vertically arranged 20 horizonally-polarized arraies unit's composition, the high 20m of radar frame, ground reflection coefficent is-0.95, carrier frequency is 300MHz, only considers the mirror-reflection on ground, 9 Virtual arrays of interpolation between per two array elements, total array number of the interpolation battle array that obtains is 191, and the observing matrix dimension is 20.
2. emulation content
Emulation one: select single static target, distance at target and reference antenna is 200km, the through angle of target is 2 °, the multipath reflection angle is-2.01 °, the array element signal to noise ratio (S/N ratio) is changed to 30dB from-10dB, fast umber of beats is under 10 the condition, to carry out angle measurement accuracy emulation to hanging down elevation angle target respectively with existing front-rear space smooth multiple signal classification method, alternating projection maximum likelihood method and the present invention.Simulation result as shown in Figure 2.Wherein:
Transverse axis represents signal to noise ratio (S/N ratio) variation from-10 decibels to 20 decibels, and the longitudinal axis represents angle error;
SS-MUSIC represents the angle error of front-rear space smooth multiple signal classification method when signal to noise ratio (S/N ratio) changes according to transverse axis,
APML represents the angle error of alternating projection maximum likelihood method when signal to noise ratio (S/N ratio) changes according to transverse axis,
IA-CS represents the angle error of the present invention when signal to noise ratio (S/N ratio) changes according to transverse axis.
As can be drawn from Figure 2, for the angle measurement of low elevation angle target, existing front-rear space smooth multiple signal classification method, alternating projection maximum likelihood method angle error are bigger than normal, and angle error of the present invention is minimum.
Emulation two: select single target, at object height 12000m, radially fly to 650km from 50km, the array element distance half-wavelength, signal to noise ratio (S/N ratio) 10dB, fast umber of beats 10 under the condition that the Monte Carlo experiment number of times is 100 times, carries out emulation on the different elevations angle to the impact of algorithm estimated accuracy respectively with existing front-rear space smooth multiple signal classification method, alternating projection maximum likelihood method and the present invention.Simulation result as shown in Figure 3.Wherein:
Fig. 3 (a) is the elevation angle of the distance of existing front-rear space smooth multiple signal class methods in target and position when changing according to transverse axis;
Fig. 3 (b) is the elevation angle of the distance of existing alternating projection maximum likelihood method in target and position when changing according to transverse axis;
Elevation angle when Fig. 3 (c) changes according to transverse axis for the distance of the present invention in target and position.
Transverse axis among Fig. 3 represents that the distance in target and position changes from 0 km to 650 km, and the longitudinal axis represents the elevation angle.
As can be drawn from Figure 3, for the angle measurement of low elevation angle target, existing front-rear space smooth multiple signal classification method, alternating projection maximum likelihood method angle error are bigger than normal, and angle error of the present invention is minimum.
3. to the angle measurement result of certain surveillance radar measured data
With the present invention and existing front-rear space smooth multiple signal classification method this surveillance radar measured data is carried out angle measurement and process, angle error as shown in Figure 4.Wherein:
Transverse axis represents the distance in target and position, the angle error the when longitudinal axis represents that distance changes with transverse axis;
SS-MUSIC represents the angle error of front-rear space smooth multiple signal classification method;
IA-CS represents angle error of the present invention.
As can be drawn from Figure 4, existing front-rear space smooth multiple signal classification method angle error is bigger than normal, and angle error of the present invention is less than normal.
Claims (4)
1. high method of the survey based on the Array interpolation compressed sensing may further comprise the steps:
(1) from radar return, extracts echo signal, obtain the array manifold matrix W of true array, and this echo signal is carried out clutter the slake interference cancellation is processed, obtaining offseting rear echo signal x and spatial domain sparse signal S, the relation that offsets rear echo signal x and spatial domain sparse signal S is as follows:
x=ψS+n，
Wherein, ψ represents super complete redundant dictionary, and its length is c, and n represents white Gaussian noise;
(2) use digital beam forming method DBF that the echo signal x after offseting is carried out elevation angle bigness scale, obtain the bigness scale angle [alpha], and then obtain spatial domain, place, echo signal elevation angle Ο;
(3) described spatial domain Ο is divided into P part, P＞＞M, M represents array number, obtains spatial domain matrix Θ:
Θ=[α
l,α
l+Δα,…,α
r],
Wherein,
The left margin of expression Θ,
The right margin of expression Θ,
The expression half-power beam width, Δ α is step-length, Δ α=0.1 °;
(4) true array is carried out Array interpolation and process, obtain the array manifold matrix W of virtual array
IArray manifold matrix W according to virtual array
IWith the array manifold matrix W of true array, obtain interpolation transformation matrix B;
(5) interpolation transformation matrix B is carried out prewhitening and process, obtain albefaction interpolation transformation matrix T
I
(6) the echo signal x after will offseting projects to albefaction interpolation transformation matrix T
I, obtain the measurement signal z of virtual array;
(7) with F * P dimension observing matrix φ measurement signal z is carried out compression sampling, F＜＜P, obtain the observation signal y that tie up F * 1;
(8) according to observation signal y and albefaction interpolation transformation matrix T
I, utilize greedy orthogonal matching pursuit method of following the trail of in the class algorithm, through type
Iteration is chosen a locally optimal solution and is progressively approached spatial domain sparse signal S, obtains the estimated value of spatial domain sparse signal S
Wherein, || ||
1Vectorial 1-norm is asked in expression, and s.t represents constraint condition, || ||
2Vectorial 2-norm is asked in expression, and ψ represents super complete redundant dictionary, and c represents the length of super complete redundant dictionary ψ, i=1, and 2 ..., c, β represent that noise criteria is poor;
(9) objective definition angular range, theta=[θ
1, θ
2..., θ
i..., θ
c],
According to estimated value
Element and the one-to-one relationship of the element of θ, namely
With θ
iCorresponding one by one, obtain as a result θ of target angle measurement
d, d ∈ i:
Wherein, d represents estimated value
In non-vanishing element s
dSubscript;
(10) according to target angle measurement θ as a result
dTarget range R with known obtains object height by triangular transformation:
H=Rsin(θ
d)。
2. the high method of the survey of Array interpolation compressed sensing according to claim 1, use digital beam forming method DBF that the echo signal x after offseting is carried out the angle bigness scale in the wherein said step (2), obtain the bigness scale angle [alpha], and then obtain spatial domain, place, echo signal elevation angle Ο, carry out as follows:
2a) utilize steering vector v (ξ)=[1, e
-j2 π sin (ξ)..., e
-j2 π (M-1) sin (ξ)]
T, x is weighted summation, obtain the bigness scale angle [alpha]:
Wherein, arg max represents to seek the parameter with maximum cost function, and ξ represents the target search angular range, and-180 °≤ξ≤180 °, L represents fast umber of beats, and M represents element number of array, x (t
l) echo signal of expression after offseting, t
lThe expression sampling time, 1≤l≤L, subscript T represents transposition, subscript H represents conjugate transpose;
2b) utilize half-power beam width
Obtain the spatial domain Ο at angle on target place:
Wherein, λ represents the radar signal wavelength, and d represents array element distance.
3. the high method of the survey of Array interpolation compressed sensing according to claim 1, wherein step (4) is described carries out the Array interpolation processing to true array, between the array element of true array, to add Virtual array, with the dimension of the array manifold matrix W that enlarges true array, obtain the M of virtual array * P dimension array manifold matrix W
I:
W
I=[v
I(α
l),v
I(α
l+Δα),…,v
I(α
j),…,v
I(α
r)]，
Wherein,
The steering vector of j echo signal of expression virtual matrix, M represents element number of array, subscript T represents transposition, α
j∈ Θ, Θ=[α
l, α
l+ Δ α ..., α
r], Δ α is step-length, Δ α=0.1 °.
4. the high method of the survey of Array interpolation compressed sensing according to claim 1, the wherein described array manifold matrix W according to virtual array of step (4)
IWith the array manifold matrix W of true array, obtain interpolation transformation matrix B, minute following two kinds of situations are calculated:
In the situation that do not consider noise, according to the array manifold matrix W of virtual array
IAnd the fixed relationship between the array manifold matrix W of true array and the interpolation transformation matrix B: B
HW=W
I, and the steering vector of true array
Steering vector v with virtual array
I(α
j) and interpolation transformation matrix B between fixed relationship:
B=W
IW
H(WW
H)
-1
Wherein,
The steering vector that represents true array,
In the situation that consider noise, it is the array manifold matrix W according to virtual array
IAnd the fixed relationship between the array manifold matrix W of true array and the interpolation transformation matrix B: B
H(W+N)=W
I+ N
I, and the steering vector of true array
Steering vector v with virtual array
I(α
j) and interpolation transformation matrix B between fixed relationship:
Draw interpolation transformation matrix B:
Wherein, N represents the noise matrix of true array, N
IThe noise matrix of expression virtual matrix, n represents the noise vector of N, n
IExpression N
INoise vector,
Be signal power,
Be noise power, I is unit matrix.
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