CN104199028B - The microwave relevance imaging method of emission array is rotated based on radar - Google Patents

Abstract

The invention discloses a kind of microwave relevance imaging method rotating emission array based on radar, relate to radar information and obtain and processing technology field, the steps include: step 1, set radar and rotate transmitting antenna；Step 2, sets the test surface of radar, this test surface is divided into multiple probe unit；Step 3, asks for time delay；Step 4, utilizes time delay to ask for steering vector, obtains array manifold matrix；Step 5, sets echo-signal vector；Step 6, builds radiation field vector；Step 7, sets up the correlation form of the original echo vector under M the pulse that radar receives and radiation field vector；Step 8, solves the object function of target reflection factor vector at bound for objective function, obtains target reflection factor vector；Step 9, obtains the target reflection factor vector matrix reset, the i.e. imaging array of target.Randomness and spatial degrees of freedom when the present invention improves radiation field sky, it is achieved the high-resolution imaging to large scene target.

Description

The microwave relevance imaging method of emission array is rotated based on radar

Technical field

The invention belongs to radar information obtain and processing technology field, relate to microwave relevance imaging technology, particularly relate to a kind of base The microwave relevance imaging method of emission array is rotated in radar.

Technical background

Relevance imaging achieves in recent years and develops faster, and relevance imaging is otherwise varied with traditional radar imagery, association Imaging needs light source to participate in the process of imaging, and requires that light source to have the random of the statistical nature of hot light, i.e. time and space Fluctuation feature.In actual experimentation, the general method using counterfeit hot light to substitute true hot light studies relevance imaging, Martienssen et al. proposes the production method of counterfeit hot light, i.e. irradiates the clouded glass rotated with laser, and counterfeit hot light is by clouded glass In random distribution molecule modulation laser place produce, when the rotary speed of clouded glass meets some requirements, should The statistical nature of counterfeit hot light meets the time of hot light and the random fluctuation feature in space.In practice can be with random radiation time empty Replace counterfeit hot light because empty time random radiation field and counterfeit hot light be desirable that obedience random distribution, namely have the time and The random fluctuation feature in space.

The patent " microwave staring imaging correlation method " (application number 201110000698.3) of China Science & Technology University's application In disclose a kind of microwave staring imaging correlation method.Target-area object is irradiated by the method by random radiation field, Form radiation field distribution at body surface, be scattered field by multichannel or single channel and receive, to scattered field and random radiation Field is associated processing the imaging obtaining target-area object with inverting.The deficiency of the method is that the sampling number of requirement is the highest, Requirement to signal to noise ratio is the biggest.

In the patent " method of microwave staring imaging " (application number 201110000699.8) of China Science & Technology University's application Disclose a kind of based on time, empty bidimensional random radiation field and the microwave staring imaging method of association process.When the method is passed through, The association microwave staring imaging of empty bidimensional radiation field, can realize high-resolution microwave staring imaging.The deficiency of the method is radiation When field is empty, randomness and spatial degrees of freedom are the highest, thus it is few to recover pixel in causing same distance door, it is difficult to realize greatly The high-resolution imaging of scene objects.

Patent " microwave relevance imaging system based on thinned array and the formation method " (Shen of Xian Electronics Science and Technology University's application Please numbers 201310167360.6) in disclose a kind of microwave relevance imaging system based on thinned array and formation method, mainly The imaging effect when radar antenna does not has non-radial relative motion with target solving prior art is poor, the problem that resolution is low. When the deficiency of this system is radiation field sky, randomness and spatial degrees of freedom are relatively low, to large scene target target scene especially in flakes Quality reconstruction poor.

The process of random radiation field when electromagnetic signal radiative process in array element bore face to target area is exactly to be formed empty.By Target on test surface is sparse distribution, produced empty time bidimensional random radiation field be also sparse, i.e. radiation field Time empty, dependency is smaller, just has identical statistical property with the sensing matrix in compressed sensing.In compressed sensing Process in the middle of sensing matrix have a very important effect, therefore we can utilize compressed sensing processing sparse sampling letter Advantage on number Problems of Reconstruction, is applied to compressive sensing theory based on the microwave relevance imaging thunder of bidimensional random radiation field during sky In reaching.

Along with development and the progress in epoch of science and technology, longer-distance realization of goal high-resolution imaging is possibly realized, due to Spatial resolution is limited by antenna aperature, and traditional radar imagery is only applicable to closely imaging or to resolution Requiring under than some relatively low scenes, if to realize longer-distance high-resolution radar imaging, traditional radar is obvious Requirement can not be met.In microwave relevance imaging radar based on compressed sensing, the design of random radiation field is that high-resolution becomes As the key being capable of.The radiation field why microwave relevance imaging based on compressed sensing can form randomness bigger is divided Cloth, mainly employs transmitting signal randomness temporally and spatially.

Being the typical technology problem of conventional synthesis aperture radar to large scene imaging, the most sparse microwave imaging is urgently captured Difficult point.Existing radar microwave imaging technique, time empty, random radiation field degree of freedom is low, to large scene target imaging weak effect, Resolution is low.

Summary of the invention

Present invention aims to the deficiency of above-mentioned prior art, propose a kind of microwave rotating emission array based on radar Relevance imaging method, randomness and spatial degrees of freedom when improving radiation field sky, it is achieved the high-resolution imaging to large scene target.

For reaching above-mentioned purpose, the present invention is achieved by the following technical solutions.

A kind of microwave relevance imaging method rotating emission array based on radar, it is characterised in that comprise the following steps:

Step 1, it is the two-dimensional array with N number of array element that radar rotates emission array, and radar rotates the array element of emission array and divides Cloth is on a disc, and the receiver of radar is positioned at the center of circle of disc, and array element place disc walks around the axis in the center of circle with angular velocity ω rotates, and the axis in the described center of circle is perpendicular to disc；N is natural number；

Step 2, radar rotates emission array and launches the microwave signal of M pulse to test surface, and receives under M pulse Raw radar data Y；M is natural number；

Described test surface is divided into E × F probe unit, probe unit sum Q=E × F, and wherein, E represents horizontal Probe unit number, F represents longitudinal probing unit number, and E, F are respectively natural number, and Q > M, M represent that radar rotates Emission array launches umber of pulse；

Step 3, under m-th pulse, the n-th array element is expressed as s to q-th probe unit transmitting microwave signal_mn(t), thunder The echo-signal reaching receiver reception q-th probe unit is expressed as s_mn(t-τ_mnq), ask for launching microwave signal s_mn(t) with Echo-signal s_mn(t-τ_mnqTime delay τ between)_mnq, wherein, t express time, M=1,2 ..., M, n=1,2 ..., N, q=1,2 ..., Q, M represent that radar rotates emission array and launches umber of pulse, and N represents thunder Reaching the transmitting array number rotating emission array, Q represents probe unit sum；

Step 4, utilizes time delay τ_mnqAsk under m-th pulse N number of array element relative to the guiding of q-th probe unit Vector V_mq, V_mqDimension is N × 1；And then obtain under m-th pulse N number of array element relative to the array of Q probe unit Manifold matrix V_m, V_mDimension is N × Q；

Step 5, sets microwave signal s that under m-th pulse, the n-th array element is launched to q-th probe unit_mnT () is equal to connecing Echo-signal s of the q-th probe unit that receipts machine receives_mn(t-τ_mnq), i.e. s_mn(t-τ_mnq)=s_mn(t), then m-th pulse Under echo-signal vector:

s_m(t)=[s_m1(t),s_m2(t),...,s_mn(t),...,s_mN(t)]_1×N；M=1,2 ..., M, n=1,2 ..., N, q=1,2 ..., Q；

Step 6, utilizes the array manifold matrix V relative to Q probe unit of the N number of array element under m-th pulse_mAnd m-th Echo-signal vector s under pulse_mT (), builds the radiation field vector A under m-th pulse_m=s_m(t)·V_m, dimension is 1 × Q, And then obtain the radiation field matrix under M pulseA dimension is M × Q, wherein []^T Represent transposition；

Step 7, the vectorization form of target setting reflection coefficient vector σ is [σ₁,σ₂,...,σ_q,...,σ_Q]^T, wherein []^TRepresent Transposition, σ_qThe target reflection factor of expression q-th probe unit, q=1,2 ..., Q；

Utilize under M the pulse that radar is received by the radiation field matrix A under M pulse and target reflection factor vector σ Original echo vector Y is written as form:

Y=A σ+w

Wherein, A represents the radiation field matrix of Q probe unit under M pulse, and w represents the dimension that the sets height as M × 1 This white noise vector；

Step 8, sets up the object function of target reflection factor vector σ, using Y=A σ+w as the constraint bar of object function Part, solves the object function of target reflection factor vector σ under bound for objective function, obtain target reflection factor to Amount σ, σ=[σ₁,σ₂,...,σ_q,...,σ_Q]^T=[σ₁,σ₂,...,σ_E,σ_E+1,σ_E+2,...,σ_2E,...,σ_(F-1)E+1,σ_(F-1)E+2,...,σ_Q]^T, Wherein []^TRepresenting transposition, Q=E × F, E represent horizontal detection unit number, and F represents longitudinal probing unit number；

Step 9, is arranged as E × F by target reflection factor vector σ by Q × 1 dimension and ties up matrix, obtains the target reflection system reset Matrix numberThe target reflection factor matrix resetThe i.e. imaging array of target.

The feature of technique scheme and further improvement is that:

(1) step 3 includes:

In rectangular coordinate system in space, the receiver setting radar is positioned at the center of circle initial point at rectangular coordinate system in space of disc Place, the coordinate of q-th probe unit is (x_q,y_q,z_q), the relation between the coordinate figure of q-th probe unit is:

z_q ²=r₀ ²-x_q ²-y_q ²

Set radar under m-th pulse and rotate the rotational time of emission array as △ t_m, the i.e. radar of rotational time rotates launches battle array Row never rotate to the time rotated, and the n-th array element is through rotational time △ t_mAfter coordinate beAt m Under individual pulse, the n-th array element is to distance r between q-th probe unit_mnqFor:

$\begin{array}{c}{r}_{mnq}=\sqrt{{({\tilde{x}}_{mn}-x_q)}^2+{({\tilde{y}}_{mn}-y_q)}^2+{(z_q-0)}^2}\\ =\sqrt{{({\tilde{x}}_{mn}-x_q)}^2+{({\tilde{y}}_{mn}-y_q)}^2+{r_0}^2-{x_q}^2-{y_q}^2}\\ =\sqrt{{r_0}^2+{\tilde{x}}_{mn}^2+{\tilde{y}}_{mn}^2-2x_q{\tilde{x}}_{mn}-2y_q{\tilde{y}}_{mn}}\end{array}$

Wherein, m=1,2 ..., M, n=1,2 ..., N, q=1,2 ..., Q, M represent that radar rotates emission array and launches umber of pulse, N represents that radar rotates the transmitting array number of emission array, and Q represents probe unit sum；

The test surface setting radar is in the initial point of rectangular coordinate system in space as the centre of sphere, radius as r₀Sphere on, set visit Spherical radius r at place, survey face₀At least above50 times, with the n-th array element through rotational time △ t_mAfter CoordinateFor variable, with Taylor series launch at point (0,0,0) place the n-th array element to q-th probe unit it Between distance r_mnq:

$\begin{array}{c}{r}_{mnq}=r_{mnq}{|}_{(0,0,0)}+{\tilde{x}}_{mn}\left(\frac{\∂r_{mnq}}{\∂{\tilde{x}}_{mn}}{|}_{(0,0,0)}\right)+{\tilde{y}}_{mn}\left(\frac{\∂r_{mnq}}{\∂{\tilde{y}}_{mn}}{|}_{(0,0,0)}\right)+O\\ \≈r_0-\frac{x_q{\tilde{x}}_{mn}+y_q{\tilde{y}}_{mn}}{r_0}\end{array}$

Wherein, r_mnq|_(0,0,0)Represent r_mnqIn the value at point (0,0,0) place,Represent r_mnqRightAsk after local derviation at point The value at (0,0,0) place,Represent r_mnqRightAsk the value at point (0,0,0) place, r after local derviation₀Spy for radar Survey face is in the radius of sphere, is also the initial point distance to each probe unit of rectangular coordinate system in space, and Ο represents that glug is bright Day type remainder；

Under m-th pulse, the n-th array element transmitting microwave signal is to q-th probe unit, receives echo-signal with receiver Time delay τ_mnqFor:

$\begin{array}{c}{\mathrm{\τ}}_{mnq}=t_{mnq}-t_0=\frac{r_{mnq}-r_0}{c}=-\frac{x_q{\tilde{x}}_{mn}+y_q{\tilde{y}}_{mn}}{{\mathrm{cr}}_0}\\ =-R_n\frac{\cos ({\mathrm{\ω\Δt}}_m+{\mathrm{\θ}}_n)x_q+\sin ({\mathrm{\ω\Δt}}_m+{\mathrm{\θ}}_n)y_q}{{\mathrm{cr}}_0}\end{array}$

Wherein, t_mnqRepresent n-th array element microwave signal propagation time to q-th probe unit, t₀Denotation coordination initial point arrives In the propagation time of q-th probe unit, c represents the light velocity, (x_q,y_q,z_q) represent q-th probe unit coordinate,Represent that the n-th array element is through rotational time △ t_mAfter coordinate, R_nRepresent that the n-th array element arrives zero Distance, △ t_mRepresent that under m-th pulse, radar rotates the rotational time of emission array, r₀Representation space rectangular coordinate system former Point is to the distance of each probe unit, and ω represents the angular velocity rotating emission array rotation, θ_nIt is the n-th element position and x-axis The angle in direction.

(2) step 4 includes:

Steering vector V_mqExpression formula be: V_mq=[V_m1q,V_m2q,...,V_mnq,...,V_mNq]^T, wherein, []^TRepresent transposition,

$\begin{array}{c}{V}_{mnq}=\exp (-j2{\mathrm{\πf}}_c{\mathrm{\τ}}_{mnq})\\ =\exp \left\{j2{\mathrm{\πf}}_c{R}_n\frac{\cos ({\mathrm{\ω\Δt}}_m+{\mathrm{\θ}}_n)x_q+\sin ({\mathrm{\ω\Δt}}_m+{\mathrm{\θ}}_n)y_q}{{\mathrm{cr}}_0}\right\}\end{array}$

Wherein, f_cRepresenting carrier frequency, c represents the light velocity, (x_q,y_q,z_q) represent q-th probe unit coordinate, R_nRepresent the N array element is to the distance of zero, △ t_mRepresent that under m-th pulse, radar rotates the rotational time of emission array, r₀Table Showing the initial point distance to each probe unit of rectangular coordinate system in space, ω represents the angular velocity rotating emission array rotation, θ_n It it is the angle of the n-th element position and x-axis direction；

Under m-th pulse, N number of array element is V relative to the array manifold matrix of Q probe unit_m, expression formula is:

$V_m={\left[\begin{array}{cccccc}{V}_{m11}& V_{m12}& \mathrm{...}& V_{m1q}& \mathrm{...}& V_{m1Q}\\ V_{m21}& V_{m22}& \mathrm{...}& V_{m2q}& \mathrm{...}& V_{m2Q}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ V_{mn1}& V_{mn1}& \mathrm{...}& V_{mnq}& \mathrm{...}& V_{mnQ}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ V_{mN1}& V_{mN2}& \mathrm{...}& V_{mNq}& \mathrm{...}& V_{mNQ}\end{array}\right]}_{N\×Q}$

Under M pulse, N number of array element is relative to the array manifold matrix V=[V of Q probe unit₁,V₂,...,V_m,...,V_M]^T。

(3) step 6 includes:

Radiation field vector A under m-th pulse_mExpression formula:

$A_m{\[s_{m1}\left(t\right),s_{m2}\left(t\right),\mathrm{...},s_{mn}\left(t\right),\mathrm{...},s_{mN}\left(t\right)\]}_{1\×N}\·{\left[\begin{array}{cccccc}{V}_{m11}& V_{m12}& \mathrm{...}& V_{m1q}& \mathrm{...}& V_{m1Q}\\ V_{m21}& V_{m22}& \mathrm{...}& V_{m2q}& \mathrm{...}& V_{m2Q}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ V_{mn1}& V_{mn1}& \mathrm{...}& V_{mnq}& \mathrm{...}& V_{mnQ}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ V_{mN1}& V_{mN2}& \mathrm{...}& V_{mNq}& \mathrm{...}& V_{mNQ}\end{array}\right]}_{N\×Q}$

Wherein, m=1,2 ... M, s_mnT () represents the microwave signal that under m-th pulse, the n-th array element is launched, V_mnqRepresent the Under m pulse, the n-th array element is multiplied relative to the steering vector of q-th probe unit, " " representing matrix；

Radiation field matrix A=[A under M pulse₁,A₂,…,A_m,…A_M]^T。

(4) step 8 includes:

The object function of target reflection factor vector σ and bound for objective function are following formula:

$\underset{\mathrm{\σ}}{min}\{Q-F_{{\mathrm{\α}}_j}\left(\mathrm{\σ}\right)\}$

Constraints Y=A σ+w

Wherein, Q represents probe unit sum,α_jExpression sets The fixed element variable in descending series, j=1,2 ..., J, J represent the element number in the descending series of setting, and σ is mesh Mark reflection coefficient vector, exp represents exponent arithmetic, σ_qRepresenting the target reflection factor of q-th probe unit, A represents M The radiation field matrix of Q probe unit under individual pulse.

(5) object function solving target reflection factor vector σ under bound for objective function specifically includes:

8a) target setting reflection coefficient vector initial value is σ₁=A^H(AA^H)^-1Y, wherein []^-1Representing matrix is inverted, A table Show the radiation field matrix of Q probe unit under M pulse；

Set descending series [α₁,α₂,...,α_j,...,α_J], wherein the relation between element meets α_j=η α_j-1, j=2 ..., J, η ∈ (0.5,1] it is constant, α₁=2max (σ₁), α_J<0.01；

8b) utilize jth element α in descending series_jStructure gradient vector

$\underset{j}{{\mathrm{\&Delta;\&sigma;}}_{k-1}}=\&lsqb;\underset{j}{{\mathrm{\&sigma;}}_{k-1,1}}\exp \left(\frac{-\underset{j}{{\mathrm{\&sigma;}}_{k-1,1}^2}}{2{{\mathrm{\&alpha;}}_j}^2}\right),\underset{j}{{\mathrm{\&sigma;}}_{k-1,2}}\exp \left(\frac{-\underset{j}{{\mathrm{\&sigma;}}_{k-1,2}^2}}{2{{\mathrm{\&alpha;}}_j}^2}\right),\mathrm{...},\underset{j}{{\mathrm{\&sigma;}}_{k-1,q}}\exp \left(\frac{-\underset{j}{{\mathrm{\&sigma;}}_{k-1,q}^2}}{2{{\mathrm{\&alpha;}}_j}^2}\right),\mathrm{...},\underset{j}{{\mathrm{\&sigma;}}_{k-1,Q}}\exp \left(\frac{-\underset{j}{{\mathrm{\&sigma;}}_{k-1,Q}^2}}{2{{\mathrm{\&alpha;}}_j}^2}\right)\&rsqb;$

, wherein exp represents exponent arithmetic,Represent and utilize jth element α_jThe target reflection factor vector kth obtained-1 time Iterative valueIn q-th element, q=1,2 ..., Q, Q represent probe unit sum；

8c) structure utilizes jth element α_jThe target reflection factor vector kth obtained time iterative valueWherein step factor μ=2；

By jth element α_jThe target reflection factor vector kth obtained time iterative valueConvert:Wherein, []^-1Representing matrix is inverted, and the vector on ← expression the right replaces the left side Vector, andWherein []^TRepresent transposition；

8d) make k from 1 to K, repeat step 8b) to step 8c), obtain jth element α_jUnder target reflection factor VectorWherein, the iterations that K sets, for positive integer；

8e) make j from 1 to J, repeat step 8b) to step 8d), obtain j-th element α_JUnder target reflection factor VectorBy j-th element α_JUnder target reflection factor vectorAs target reflection factor vector σ.

Compared with prior art, the present invention has prominent substantive distinguishing features and significantly progress.The present invention and existing method phase Ratio, has the advantage that

(1) the formation method restructural target numbers of the present invention improves more than 10 times than array element number, with existing based on The microwave relevance imaging system of thinned array is compared, and the reconfigurable target numbers of system is more, and imaging effect is more preferable, resolution Higher, the spatial degrees of freedom of random radiation field when effectively extending sky, can be used for the radar high-resolution imaging to large scene target.

(2) imaging system of the present invention can be at low signal-to-noise ratio, and the sparse target numbers of target scene exceedes the feelings of array element number Under condition, it is achieved break through the real-time process to target of the target imaging of more than 5 times Rayleigh diffraction-limited, beneficially radar.

Accompanying drawing explanation

The present invention will be further described with detailed description of the invention below in conjunction with the accompanying drawings.

Fig. 1 is that the present invention rotates the microwave relevance imaging method flow diagram of emission array based on radar；

Fig. 2 is that the present invention rotates the microwave relevance imaging system schematic of emission array based on radar；

Fig. 3 is the movement locus figure rotating emission array the n-th array element of the present invention；

Fig. 4 is the original distribution figure of 150 point targets；Abscissa represents lateral separation unit, and vertical coordinate represents fore-and-aft distance Unit, unit distance unit represents length 1.3m；

Fig. 5 is when launching array element number and being 15, ties the emulation of in Fig. 4 150 point targets with the formation method of the present invention Really；Abscissa represents lateral separation unit, and vertical coordinate represents fore-and-aft distance unit, and unit distance unit represents length 1.3m；

Fig. 6 is the original distribution figure of 150 targets in blocks；Abscissa represents lateral separation unit, vertical coordinate represent longitudinally away from From unit, unit distance unit represents length 1.3m；

Fig. 7 is when launching array element number and being 15, with the emulation in Fig. 6 150 targets in blocks of the formation method of the present invention Result；Abscissa represents lateral separation unit, and vertical coordinate represents fore-and-aft distance unit, and unit distance unit represents length 1.3m；

Fig. 8 is the original distribution figure of 90 point targets；Abscissa represents lateral separation unit, and vertical coordinate represents fore-and-aft distance list Unit, unit distance unit represents length 1.3m；

Fig. 9 be launch array element number be 25, signal to noise ratio is 10dB, in the case of breaking through 5 times of Rayleigh diffraction-limited, with The formation method of the invention simulation result in Fig. 8 90 point targets；Abscissa represents lateral separation unit, vertical coordinate generation Table fore-and-aft distance unit, unit distance unit represents length 1.3m；

Figure 10 is the original distribution figure of 90 targets in blocks；Abscissa represents lateral separation unit, vertical coordinate represent longitudinally away from From unit, unit distance unit represents length 1.3m；

Figure 11 be launch array element number be 25, signal to noise ratio is 10dB, in the case of breaking through 5 times of Rayleigh diffraction-limited, with The formation method of the invention simulation result in Figure 10 90 targets in blocks；Abscissa represents lateral separation unit, vertical coordinate Representing fore-and-aft distance unit, unit distance unit represents length 1.3m.

Detailed description of the invention

With reference to Fig. 1 and Fig. 2, illustrate that the present invention rotates the microwave relevance imaging method of emission array based on radar, can be used for revolving Forward and penetrate the structure of array antenna, it is achieved the raising of random radiation field randomness and the extension of degree of freedom time empty.

Step 1, it is the two-dimensional array with N number of array element that radar rotates emission array, and radar rotates the array element of emission array and divides Cloth is on a disc, and the receiver of radar is positioned at the center of circle of disc, and array element place disc walks around the axis in the center of circle with angular velocity ω rotates, and the axis in the center of circle is perpendicular to disc.

As shown in Figure 2.Radar rotates emission array and is constituted by launching array element 1, and the radius of each array element is different, each array element Launching different microwave signals and form microwave radiation field in space non-coherent addition, test surface 2 is shone by this microwave radiation field Penetrate.The receiver of radar is constituted by receiving array element 3, for receiving the microwave radiation field original echo to producing after target illumination Data, random radiation field 4 when storage is radiated test surface 2 empty simultaneously, the raw radar data that receiver 3 receives and The radiation field 4 prestored is processed by signal processor 5, uses the inventive method to obtain the target image of super-resolution.

With reference to Fig. 3, rotate the movement locus of the n-th array element of emission array, set the n-th array element and rotate transmitting battle array at radar Coordinate when row do not rotate isIts coordinate figure is:Wherein, R_nFor N-th array element is to the distance of zero, θ_nIt is the angle of the n-th element position and x-axis direction, n=1,2 ..., N.

Radar rotates emission array and launches the microwave signal of M pulse to test surface, and array element number N < M is set in the Under m pulse, radar rotates the rotational time of emission array is △ t_m, the i.e. radar of rotational time rotates emission array and never revolves Go to the time rotated, the n-th array element is through rotational time △ t_mAfter coordinate beIts coordinate figure is:Wherein ω is to rotate the angular velocity of emission array rotation i.e. Array element place disc angular velocity omega, m=1,2 ..., M, n=1,2 ..., N.

Step 2, radar rotates emission array and launches the microwave signal of M pulse to test surface, and receives under M pulse Raw radar data Y；

Described test surface is divided into E × F probe unit, probe unit sum Q=E × F, and Q > M, wherein E table Showing horizontal detection unit number, F represents longitudinal probing unit number, and M represents that radar rotates emission array and launches umber of pulse.

Step 3, under m-th pulse, the n-th array element is expressed as s to q-th probe unit transmitting microwave signal_mn(t), thunder The echo-signal reaching receiver reception q-th probe unit is expressed as s_mn(t-τ_mnq), ask for launching microwave signal s_mn(t) with Echo-signal s_mn(t-τ_mnqTime delay τ between)_mnq, wherein, t express time, M=1,2 ..., M, n=1,2 ..., N, q=1,2 ..., Q, M represent that radar rotates emission array and launches umber of pulse, and N represents radar Rotating the transmitting array number of emission array, Q represents probe unit sum；.

The signal s that under m-th pulse, the n-th array element is launched to q-th probe unit_mnT () is microwave random coding signalN=1,2 ..., N, wherein B_mnT () is the amplitude that under m-th pulse, the n-th array element launches signal, ρ_mnLaunching the phase place of signal for the n-th array element under m-th pulse, phase place uses random coded, t express time.

In rectangular coordinate system in space, the receiver setting radar is positioned at the center of circle initial point at rectangular coordinate system in space of disc Place, the coordinate of q-th probe unit is (x_q,y_q,z_q), the relation between the coordinate figure of q-th probe unit is:

z_q ²=r₀ ²-x_q ²-y_q ²

Setting under m-th pulse, it is △ t that radar rotates the rotational time of emission array_m, the i.e. radar of rotational time rotates to be launched Array never rotated to the time rotated, and the n-th array element is through rotational time △ t_mAfter coordinate be? Under m pulse, the n-th array element is to distance r between q-th probe unit_mnqFor:

$\begin{array}{c}{r}_{mnq}=\sqrt{{({\tilde{x}}_{mn}-x_q)}^2+{({\tilde{y}}_{mn}-y_q)}^2+{(z_q-0)}^2}\\ =\sqrt{{({\tilde{x}}_{mn}-x_q)}^2+{({\tilde{y}}_{mn}-y_q)}^2+{r_0}^2-{x_q}^2-{y_q}^2}\\ =\sqrt{{r_0}^2+{\tilde{x}}_{mn}^2+{\tilde{y}}_{mn}^2-2x_q{\tilde{x}}_{mn}-2y_q{\tilde{y}}_{mn}}\end{array}$

The test surface setting radar is in the initial point of rectangular coordinate system in space as the centre of sphere, radius as r₀Sphere on, set visit The spherical radius at place, survey faceSpherical radius r at test surface place in the present invention₀At least above50 times, with the n-th array element through rotational time △ t_mAfter coordinateFor variable, with Thailand Strangle progression and launch the n-th array element at point (0,0,0) place to distance r between q-th probe unit_mnq:

$\begin{array}{c}{r}_{mnq}=r_{mnq}{|}_{(0,0,0)}+{\tilde{x}}_{mn}\left(\frac{\&part;r_{mnq}}{\&part;{\tilde{x}}_{mn}}{|}_{(0,0,0)}\right)+{\tilde{y}}_{mn}\left(\frac{\&part;r_{mnq}}{\&part;{\tilde{y}}_{mn}}{|}_{(0,0,0)}\right)+O\\ \&ap;r_0-\frac{x_q{\tilde{x}}_{mn}+y_q{\tilde{y}}_{mn}}{r_0}\end{array}$

Wherein, r_mnq|_(0,0,0)Represent r_mnqIn the value at point (0,0,0) place,Represent r_mnqRightAsk after local derviation at point The value at (0,0,0) place,Represent r_mnqRightAsk the value at point (0,0,0) place, r after local derviation₀Spy for radar Survey face is in the radius of sphere, is also the initial point distance to each probe unit of rectangular coordinate system in space, and Ο is Lagrange Type remainder；Under m-th pulse, the n-th array element transmitting microwave signal, to q-th probe unit, receives with receiver 3 Time delay τ of echo-signal_mnqFor:

$\begin{array}{c}{\mathrm{\&tau;}}_{mnq}=t_{mnq}-t_0=\frac{r_{mnq}-r_0}{c}=-\frac{x_q\widetilde{x_{mn}}+y_q{\tilde{y}}_{mn}}{{\mathrm{cr}}_0}\\ =-R_n\frac{\cos ({\mathrm{\&omega;\&Delta;t}}_m+{\mathrm{\&theta;}}_n)x_q+\sin ({\mathrm{\&omega;\&Delta;t}}_m+{\mathrm{\&theta;}}_n)y_q}{{\mathrm{cr}}_0}\end{array}$

Wherein, t_mnqRepresent n-th array element microwave signal propagation time to q-th probe unit, t₀Denotation coordination initial point arrives In the propagation time of q-th probe unit, c represents the light velocity, (x_q,y_q,z_q) represent q-th probe unit coordinate,Represent that the n-th array element is through rotational time △ t_mAfter coordinate, R_nBe the n-th array element to zero away from From, △ t_mRepresent that under m-th pulse, radar rotates the rotational time of emission array, r₀The initial point of representation space rectangular coordinate system To the distance of each probe unit, ω represents the angular velocity rotating emission array rotation, θ_nIt is the n-th element position and x-axis The angle in direction.

Step 4, utilizes time delay τ_mnqAsk under m-th pulse N number of array element relative to the guiding of q-th probe unit Vector V_mq, dimension is N × 1；And then obtain under m-th pulse N number of array element relative to the array manifold of Q probe unit Matrix V_m, dimension is N × Q.

Steering vector V_mqExpression formula be: V_mq=[V_m1q,V_m2q,...,V_mnq,...,V_mNq]^T,

Wherein, []^TRepresent transposition,

$\begin{array}{c}{V}_{mnq}=\exp (-j2{\mathrm{\&pi;f}}_c{\mathrm{\&tau;}}_{mnq})\\ =\exp \left\{j2{\mathrm{\&pi;f}}_c{R}_n\frac{\cos ({\mathrm{\&omega;\&Delta;t}}_m+{\mathrm{\&theta;}}_n)x_q+\sin ({\mathrm{\&omega;\&Delta;t}}_m+{\mathrm{\&theta;}}_n)y_q}{{\mathrm{cr}}_0}\right\}\end{array}$

Wherein, f_cRepresenting carrier frequency, c represents the light velocity, (x_q,y_q,z_q) represent q-th probe unit coordinate, R_nRepresent the N array element is to the distance of zero, △ t_mUnder m-th pulse, radar rotates the rotational time of emission array, r₀Represent sky Between the initial point of rectangular coordinate system to the distance of each probe unit, ω represents and rotates the angular velocity that emission array rotates, θ_nIt is N element position and the angle in x-axis direction.

Under m-th pulse, N number of array element is V relative to the array manifold matrix of Q probe unit_m, then

$V_m={\left[\begin{array}{cccccc}{V}_{m11}& V_{m12}& \mathrm{...}& V_{m1q}& \mathrm{...}& V_{m1Q}\\ V_{m21}& V_{m22}& \mathrm{...}& V_{m2q}& \mathrm{...}& V_{m2Q}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ V_{mn1}& V_{mn1}& \mathrm{...}& V_{mnq}& \mathrm{...}& V_{mnQ}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ V_{mN1}& V_{mN2}& \mathrm{...}& V_{mNq}& \mathrm{...}& V_{mNQ}\end{array}\right]}_{N\&times;Q}$

Under M pulse, N number of array element is relative to the array manifold matrix V=[V of Q probe unit₁,V₂,...,V_m,...,V_M]^T。

Step 5, sets microwave signal s that under m-th pulse, the n-th array element is launched to q-th probe unit_mnT () is equal to connecing Echo-signal s of the q-th probe unit that receipts machine receives_mn(t-τ_mnq), i.e. s_mn(t-τ_mnq)=s_mn(t), then m-th pulse Under echo-signal vector s_m(t)=[s_m1(t),s_m2(t),...,s_mn(t),...,s_mN(t)]_1×N；

Step 6, utilizes the array manifold matrix V relative to Q probe unit of the N number of array element under m-th pulse_mAnd m-th Echo-signal vector s under pulse_mT (), builds the radiation field vector A under m-th pulse_m=s_m(t)·V_m, dimension is 1 × Q, And then obtain the radiation field matrix under M pulse

Radiation field vector A under m-th pulse_mExpression formula:

$A_m{\&lsqb;s_{m1}\left(t\right),s_{m2}\left(t\right),\mathrm{...},s_{mn}\left(t\right),\mathrm{...},s_{mN}\left(t\right)\&rsqb;}_{1\&times;N}\&CenterDot;{\left[\begin{array}{cccccc}{V}_{m11}& V_{m12}& \mathrm{...}& V_{m1q}& \mathrm{...}& V_{m1Q}\\ V_{m21}& V_{m22}& \mathrm{...}& V_{m2q}& \mathrm{...}& V_{m2Q}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ V_{mn1}& V_{mn1}& \mathrm{...}& V_{mnq}& \mathrm{...}& V_{mnQ}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ V_{mN1}& V_{mN2}& \mathrm{...}& V_{mNq}& \mathrm{...}& V_{mNQ}\end{array}\right]}_{N\&times;Q}$

Wherein, m=1,2 ... M, s_mnT () represents the microwave signal that under m-th pulse, the n-th array element is launched, V_mnqRepresent the Under m pulse, the n-th array element is multiplied relative to the steering vector of q-th probe unit, " " representing matrix.

Radiation field matrix A=[A under M pulse₁,A₂,…,A_m,…A_M]^T。

It should be noted that in prior art, if emission array does not rotates, the array manifold of N number of array element under each pulse Matrix is constant, set the array manifold matrix of N number of array element asThen

$\stackrel{\&OverBar;}{V}={\left[\begin{array}{cccccc}{V}_{11}& V_{12}& \mathrm{...}& V_{1q}& \mathrm{...}& V_{1Q}\\ V_{21}& V_{22}& \mathrm{...}& V_{2q}& \mathrm{...}& V_{2Q}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ V_{n1}& V_{n2}& \mathrm{...}& V_{nq}& \mathrm{...}& V_{nQ}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ V_{N1}& V_{N2}& \mathrm{...}& V_{Nq}& \mathrm{...}& V_{NQ}\end{array}\right]}_{N\&times;Q}$

Wherein, V_nq=exp (-j2 π f_cτ_nq), f_cRepresent carrier frequency, τ_nqRepresent that the n-th array element launches microwave signal to q-th The time delay of the echo-signal of probe unit reflection；

Because emission array does not rotates, then the n-th array element launches the echo-signal that microwave signal reflects to q-th probe unit Time delay τ_nqArray manifold matrix for array element N number of under constant, and then each pulseConstant.

I.e. radiation field matrixIt is represented by:

$\stackrel{\&OverBar;}{A}={\left[\begin{array}{cccccc}{s}_{11}\left(t\right)& s_{12}\left(t\right)& \mathrm{...}& s_{1n}\left(t\right)& \mathrm{...}& s_{1N}\left(t\right)\\ s_{21}\left(t\right)& s_{22}\left(t\right)& \mathrm{...}& s_{2n}\left(t\right)& \mathrm{...}& s_{2N}\left(t\right)\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ s_{m1}\left(t\right)& s_{m2}\left(t\right)& \mathrm{...}& s_{mn}\left(t\right)& \mathrm{...}& s_{mN}\left(t\right)\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ s_{M1}\left(t\right)& s_{M2}\left(t\right)& \mathrm{...}& s_{Mn}\left(t\right)& \mathrm{...}& s_{MN}\left(t\right)\end{array}\right]}_{M\&times;N}\&CenterDot;{\left[\begin{array}{cccccc}{V}_{11}& V_{12}& \mathrm{...}& V_{1q}& \mathrm{...}& V_{1Q}\\ V_{21}& V_{22}& \mathrm{...}& V_{2q}& \mathrm{...}& V_{2Q}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ V_{n1}& V_{n2}& \mathrm{...}& V_{nq}& \mathrm{...}& V_{nQ}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ V_{N1}& V_{N2}& \mathrm{...}& V_{Nq}& \mathrm{...}& V_{NQ}\end{array}\right]}_{N\&times;Q},$

Wherein, s_mnT () represents the microwave signal that under m-th pulse, the n-th array element is launched.

From the character of rank of matrix,The wherein order of R () representing matrix, by above Set, N < M < Q, it is known that radiation field matrixOrder be N to the maximum.

When emission array rotates, under each pulse, the array manifold matrix of N number of array element changes, thus causes every Radiation field vector under individual pulse changes, therefore, and the order of the radiation field matrix A under M pulse R (A)≤min (M, Q), the order of wherein M < Q, namely radiation field matrix A is M to the maximum.Therefore do not revolve when array When turning, radiation field rank of matrix is much smaller than radiation field rank of matrix during array rotation.Rotation is reflected from the angle of matrix knowledge During raising radiation field sky under Array Model, randomness and spatial degrees of freedom are reasonable.

Step 7, the vectorization form of target setting reflection coefficient vector σ is [σ₁,σ₂,...,σ_q,...,σ_Q]^T, σ_qRepresent q-th The target reflection factor of probe unit, q=1,2 ..., Q；

Utilize under M the pulse that radar is received by the radiation field matrix A under M pulse and target reflection factor vector σ Original echo vector Y is written as form:

Y=A σ+w

Wherein, A is the radiation field matrix of Q probe unit under M pulse, and w represents the dimension that the sets height as M × 1 This white noise vector.

The form of original echo vector Y given in step 7 reflects the Q under Y Yu M the pulse of original echo vector The association of the radiation field matrix A of individual probe unit.

It should be noted that because test surface is divided into the probe unit of E × F, then the target reflection system of Q probe unit Matrix number σ ' is expressed as:

${\mathrm{\&sigma;}}^{\&prime;}={\left[\begin{array}{cccccc}{\mathrm{\&sigma;}}_{11}& {\mathrm{\&sigma;}}_{12}& \mathrm{...}& {\mathrm{\&sigma;}}_{1f}& \mathrm{...}& {\mathrm{\&sigma;}}_{1F}\\ {\mathrm{\&sigma;}}_{21}& {\mathrm{\&sigma;}}_{22}& \mathrm{...}& {\mathrm{\&sigma;}}_{2f}& \mathrm{...}& {\mathrm{\&sigma;}}_{2F}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ {\mathrm{\&sigma;}}_{e1}& {\mathrm{\&sigma;}}_{e2}& \mathrm{...}& {\mathrm{\&sigma;}}_{ef}& \mathrm{...}& {\mathrm{\&sigma;}}_{eF}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ {\mathrm{\&sigma;}}_{E1}& {\mathrm{\&sigma;}}_{E2}& \mathrm{...}& {\mathrm{\&sigma;}}_{Ef}& \mathrm{...}& {\mathrm{\&sigma;}}_{EF}\end{array}\right]}_{E\&times;F}$

Wherein, σ_efRepresent the target reflection factor of e row f row probe unit.

By target reflection factor matrix σ ' vectorization process obtain target reflection factor vector σ, the dimension of σ is Q × 1, σ=[σ₁,σ₂,...,σ_q,...,σ_Q]^T, wherein, []^TRepresent transposition, σ_qRepresent the target reflection factor of q-th probe unit.

In same probe unit, think that target reflection factor and radiation field are identical, if there is no mesh on some probe unit Target words are just set to zero target reflection factor.

Step 8, sets up the object function of target reflection factor vector σ, using Y=A σ+w as the constraint bar of object function Part, solves the object function of target reflection factor vector σ under bound for objective function, obtain target reflection factor to Amount σ.

The object function of target reflection factor vector σ and bound for objective function are following formula:

$\underset{\mathrm{\&sigma;}}{min}\{Q-F_{{\mathrm{\&alpha;}}_j}\left(\mathrm{\&sigma;}\right)\}$

Constraints Y=A σ+w

Wherein, Q is probe unit sum,α_jIt is to set Element variable in descending series, j=1,2 ..., the element number in the descending series that J, J set, σ is target reflection system Number vector, σ_qBeing the target reflection factor of q-th probe unit, A is the radiation of Q probe unit under M pulse Field matrix.

The object function of target reflection factor vector σ is solved under constraints Y=A σ+wOf equal value Make in solving under constraints Y=A σ+wMaximum target reflection factor vector σ.

The object function of target reflection factor vector σ is solved, concrete steps under bound for objective function:

8a) target setting reflection coefficient vector initial value is σ₁=A^H(AA^H)^-1Y, the Q under wherein A is M pulse The radiation field matrix of probe unit, sets descending series [α₁,α₂,...,α_j,...,α_J], wherein the relation between element meets α_j=η α_j-1, j=2 ..., and J, η ∈ (0.5,1] it is constant, α₁=2max (σ₁), α_J<0.01；

8b) utilize jth element α in descending series_jStructure gradient vector Wherein exp represents exponent arithmetic,Represent and utilize jth element α_jThe target reflection factor vector kth obtained-1 time Iterative valueIn q-th element, q=1,2 ..., Q, Q represent probe unit sum,Represent the local derviation found a function；

8c) structure utilizes jth element α_jThe target reflection factor vector kth obtained time iterative valueWherein step factor μ=2；

By jth element α_jThe target reflection factor vector kth obtained time iterative valueConvert:The vector on ← expression the right replaces the vector on the left side, and

8d) make k from 1 to K, repeat step 8b) to step 8c), obtain jth element α_jUnder target reflection factor VectorWherein, the iterations that K sets, for positive integer K ∈ [3,20]；

8e) make j from 1 to J, repeat step 8b) to step 8d), obtain j-th element α_JUnder target reflection factor VectorBy j-th element α_JUnder target reflection factor vectorAs target reflection factor vector σ.

Step 9, by target reflection factor vectorIt is arranged as E × F by Q × 1 dimension and ties up matrix, Obtain the target reflection factor matrix resetThe target reflection factor matrix resetThe i.e. imaging array of target.

It is exemplary above by the embodiment being described with reference to the drawings, is only used for explaining the present invention, and can not be construed to this The restriction of invention.

Below in conjunction with emulation experiment, the effect of the present invention is described further.

1. simulated conditions

Consider that rotating each array element of emission array launches microwave random coding signal, array aperture D=4m, launches umber of pulse M=400, carrier frequency f_c=3GHz, carrier wavelength lambda=c/f_c=0.1m, wherein c is the light velocity, array rotation angle speed Degree is 12 revs/min, distance r between zero and probe unit₀=1km, Rayleigh diffraction-limited α=r₀λ/D=25m, In this experiment, resolution cell size is 1.3m × 1.3m, i.e. breaches more than 5 times Rayleigh diffraction-limited.Receiver employing single antenna, Single channel model, receives array element and is positioned at zero.

2. emulation content

Under described simulated conditions, test as follows:

Experiment one, rotating emission array array number is 15, and target scene is 150 point targets, and the most every 15 are connected in one Play composition string bar target, totally 10 row.In Fig. 4 150 point targets are emulated by the formation method using the present invention Imaging, simulation result is as shown in Figure 5.

When simulation result from Fig. 5 is it can be seen that 150 point targets are reconstructed by 15 array elements, imaging effect is fine, Target image is apparent from, and therefore uses the formation method of the present invention that system restructural target numbers can be made to improve than array element number 10 times, time i.e. empty, random radiation field achieves the extension of 10 times of degree of freedom.

Experiment two, rotating emission array array number is 15, and target scene is 150 targets in blocks, and totally 15 row 10 arrange.Adopt With the formation method of the present invention, in Fig. 6 150 targets in blocks being carried out simulation imaging, simulation result is as shown in Figure 7.

When simulation result from Fig. 7 is it can be seen that 150 targets in blocks are reconstructed by 15 array elements, imaging effect is preferable, Target image is more visible, therefore when target numbers be array element number 10 times, uses the formation method of the present invention in flakes The recovery effects of target is the most fine.

The simulation result of experiment one and experiment two shows, in the case of breaking through 5 times of Rayleigh diffraction-limited, uses the imaging of the present invention Method can make system restructural target numbers improve 10 times than array element number, it is achieved that the high-resolution to large scene target Imaging.

Experiment three, rotating emission array array number is 25, and system signal noise ratio is 10dB, and target scene is 90 point targets, The most every 9 connect together composition string bar target, totally 10 row.Use the formation method of the present invention in Fig. 8 90 Point target carries out simulation imaging, and simulation result is as shown in Figure 9.

Simulation result from Fig. 9, it can be seen that be 10dB in signal to noise ratio, breaks through 5 times of Rayleigh diffraction-limited, the sparse mesh of scene In the case of mark number exceedes array element number, when using the formation method of the present invention to be reconstructed target, imaging effect is preferable, Target image is apparent from.

Experiment four, rotating emission array array number is 25, and system signal noise ratio is 10dB, and target scene is 90 targets in blocks, Totally 9 row 10 arrange, and use the formation method of the present invention that in Figure 10 90 targets in blocks are carried out simulation imaging, simulation result As shown in figure 11.

Simulation result from Figure 11, it can be seen that be 10dB in signal to noise ratio, breaks through 5 times of Rayleigh diffraction-limited, and scene is sparse In the case of target numbers exceedes array element number, when using the formation method of the present invention to be reconstructed target in blocks, imaging is imitated Preferably, target image is more visible for fruit,

The simulation result of experiment three and experiment four shows, the formation method utilizing the present invention can be at low signal-to-noise ratio, and target field In the case of the sparse target numbers of scape exceedes array element number, it is achieved break through the target imaging of more than 5 times Rayleigh diffraction-limited.

To sum up, this simulating, verifying correctness of the present invention, realizability and reliability.

Claims (5)

1. the microwave relevance imaging method rotating emission array based on radar, it is characterised in that comprise the following steps:

Step 1, it is the two-dimensional array with N number of array element that radar rotates emission array, and radar rotates the array element of emission array and divides Cloth is on a disc, and the receiver of radar is positioned at the center of circle of disc, and array element place disc walks around the axis in the center of circle with angular velocity ω rotates, and the axis in the described center of circle is perpendicular to disc；N is natural number；

Step 2, radar rotates emission array and launches the microwave signal of M pulse to test surface, and receives under M pulse Raw radar data Y；M is natural number；

Described test surface is divided into E × F probe unit, probe unit sum Q=E × F, and wherein, E represents horizontal Probe unit number, F represents longitudinal probing unit number, and E, F are respectively natural number, and Q > M, M represent that radar rotates Emission array launches umber of pulse；

Step 3, under m-th pulse, the n-th array element is expressed as s to q-th probe unit transmitting microwave signal_mn(t), thunder The echo-signal reaching receiver reception q-th probe unit is expressed as s_mn(t-τ_mnq), ask for launching microwave signal s_mn(t) with Echo-signal s_mn(t-τ_mnqTime delay τ between)_mnq, wherein, t express time, M=1,2 ..., M, n=1,2 ..., N, q=1,2 ..., Q, M represent that radar rotates emission array and launches umber of pulse, and N represents thunder Reaching the transmitting array number rotating emission array, Q represents probe unit sum；

Specifically, in rectangular coordinate system in space, the receiver setting radar is positioned at the center of circle of disc at rectangular coordinate system in space Initial point at, the coordinate of q-th probe unit is (x_q,y_q,z_q), the relation between the coordinate figure of q-th probe unit is:

z_q ²=r₀ ²-x_q ²-y_q ²

Set radar under m-th pulse and rotate the rotational time of emission array as △ t_m, the i.e. radar of rotational time rotates launches battle array Row never rotate to the time rotated, and the n-th array element is through rotational time △ t_mAfter coordinate beAt m Under individual pulse, the n-th array element is to distance r between q-th probe unit_mnqFor:

$\begin{array}{c}{r}_{mnq}=\sqrt{{({\tilde{x}}_{mn}-x_q)}^2+{({\tilde{y}}_{mn}-y_q)}^2+{(z_q-0)}^2}\\ =\sqrt{{({\tilde{x}}_{mn}-x_q)}^2+{({\tilde{y}}_{mn}-y_q)}^2+{r_0}^2-{x_q}^2-{y_q}^2}\\ =\sqrt{{r_0}^2+{\tilde{x}}_{mn}^2+{\tilde{y}}_{mn}^2-2x_q{\tilde{x}}_{mn}-2y_q{\tilde{y}}_{mn}}\end{array}$

Wherein, m=1,2 ..., M, n=1,2 ..., N, q=1,2 ..., Q, M represent that radar rotates emission array and launches umber of pulse, N represents that radar rotates the transmitting array number of emission array, and Q represents probe unit sum；

The test surface setting radar is in the initial point of rectangular coordinate system in space as the centre of sphere, radius as r₀Sphere on, set visit Spherical radius r at place, survey face₀At least above50 times, with the n-th array element through rotational time △ t_mAfter CoordinateFor variable, with Taylor series launch at point (0,0,0) place the n-th array element to q-th probe unit it Between distance r_mnq:

$\begin{array}{c}{r}_{mnq}=r_{mnq}{|}_{(0,0,0)}+{\tilde{x}}_{mn}\left(\frac{\&part;r_{mnq}}{\&part;{\tilde{x}}_{mn}}{|}_{(0,0,0)}\right)+{\tilde{y}}_{mn}\left(\frac{\&part;r_{mnq}}{\&part;{\tilde{y}}_{mn}}{|}_{(0,0,0)}\right)+O\\ \&ap;r_0-\frac{x_q{\tilde{x}}_{mn}+y_q{\tilde{y}}_{mn}}{r_0}\end{array}$

Wherein, r_mnq|_(0,0,0)Represent r_mnqIn the value at point (0,0,0) place,Represent r_mnqRightAsk after local derviation at point The value at (0,0,0) place,Represent r_mnqRightAsk the value at point (0,0,0) place, r after local derviation₀Spy for radar Survey face is in the radius of sphere, is also the initial point distance to each probe unit of rectangular coordinate system in space, and Ο represents that glug is bright Day type remainder；

Under m-th pulse, the n-th array element transmitting microwave signal is to q-th probe unit, receives echo-signal with receiver Time delay τ_mnqFor:

$\begin{array}{c}{\mathrm{\&tau;}}_{mnq}=t_{mnq}-t_0=\frac{r_{mnq}-r_0}{c}=-\frac{x_q{\tilde{x}}_{mn}+y_q{\tilde{y}}_{mn}}{{\mathrm{cr}}_0}\\ =-R_n\frac{\cos ({\mathrm{\&omega;\&Delta;t}}_m+{\mathrm{\&theta;}}_n)x_q+\sin ({\mathrm{\&omega;\&Delta;t}}_m+{\mathrm{\&theta;}}_n)y_q}{{\mathrm{cr}}_0}\end{array}$

Wherein, t_mnqRepresent n-th array element microwave signal propagation time to q-th probe unit, t₀Denotation coordination initial point arrives In the propagation time of q-th probe unit, c represents the light velocity, (x_q,y_q,z_q) represent q-th probe unit coordinate,Represent that the n-th array element is through rotational time △ t_mAfter coordinate, R_nRepresent that the n-th array element arrives zero Distance, △ t_mRepresent that under m-th pulse, radar rotates the rotational time of emission array, r₀Representation space rectangular coordinate system former Point is to the distance of each probe unit, and ω represents the angular velocity rotating emission array rotation, θ_nIt is the n-th element position and x-axis The angle in direction；

Step 4, utilizes time delay τ_mnqAsk under m-th pulse N number of array element relative to the guiding of q-th probe unit Vector V_mq, V_mqDimension is N × 1；And then obtain under m-th pulse N number of array element relative to the array of Q probe unit Manifold matrix V_m, V_mDimension is N × Q；

Step 5, sets microwave signal s that under m-th pulse, the n-th array element is launched to q-th probe unit_mnT () is equal to connecing Echo-signal s of the q-th probe unit that receipts machine receives_mn(t-τ_mnq), i.e. s_mn(t-τ_mnq)=s_mn(t), then m-th pulse Under echo-signal vector:

s_m(t)=[s_m1(t),s_m2(t),...,s_mn(t),...,s_mN(t)]_1×N；M=1,2 ..., M, n=1,2 ..., N, q=1,2 ..., Q；

Step 6, utilizes the array manifold matrix V relative to Q probe unit of the N number of array element under m-th pulse_mAnd m-th Echo-signal vector s under pulse_mT (), builds the radiation field vector A under m-th pulse_m=s_m(t)·V_m, dimension is 1 × Q, And then obtain the radiation field matrix under M pulseA dimension is M × Q, wherein []^T Represent transposition；

Step 7, the vectorization form of target setting reflection coefficient vector σ is [σ₁,σ₂,...,σ_q,...,σ_Q]^T, wherein []^TRepresent Transposition, σ_qThe target reflection factor of expression q-th probe unit, q=1,2 ..., Q；

Utilize under M the pulse that radar is received by the radiation field matrix A under M pulse and target reflection factor vector σ Original echo vector Y is written as form:

Y=A σ+w

Wherein, A represents the radiation field matrix of Q probe unit under M pulse, and w represents the dimension that the sets height as M × 1 This white noise vector；

Step 8, sets up the object function of target reflection factor vector σ, using Y=A σ+w as the constraint bar of object function Part, solves the object function of target reflection factor vector σ under bound for objective function, obtain target reflection factor to Amount σ, σ=[σ₁,σ₂,...,σ_q,...,σ_Q]^T=[σ₁,σ₂,...,σ_E,σ_E+1,σ_E+2,...,σ_2E,...,σ_(F-1)E+1,σ_(F-1)E+2,...,σ_Q]^T, Wherein []^TRepresenting transposition, Q=E × F, E represent horizontal detection unit number, and F represents longitudinal probing unit number；

Step 9, is arranged as E × F by target reflection factor vector σ by Q × 1 dimension and ties up matrix, obtains the target reflection system reset Matrix numberThe target reflection factor matrix resetThe i.e. imaging array of target.

A kind of microwave relevance imaging method rotating emission array based on radar the most according to claim 1, its feature Being, step 4 includes:

Steering vector V_mqExpression formula be: V_mq=[V_m1q,V_m2q,...,V_mnq,...,V_mNq]^T, wherein, []^TRepresent transposition,

$\begin{array}{c}{V}_{mnq}=\exp (-j2{\mathrm{\&pi;f}}_c{\mathrm{\&tau;}}_{mnq})\\ =\exp \left\{j2{\mathrm{\&pi;f}}_c{R}_n\frac{cos({\mathrm{\&omega;\&Delta;t}}_m+{\mathrm{\&theta;}}_n)x_q+sin({\mathrm{\&omega;\&Delta;t}}_m+{\mathrm{\&theta;}}_n)y_q}{{\mathrm{cr}}_0}\right\}\end{array}$

Wherein, f_cRepresenting carrier frequency, c represents the light velocity, (x_q,y_q,z_q) represent q-th probe unit coordinate, R_nRepresent the N array element is to the distance of zero, △ t_mRepresent that under m-th pulse, radar rotates the rotational time of emission array, r₀Table Showing the initial point distance to each probe unit of rectangular coordinate system in space, ω represents the angular velocity rotating emission array rotation, θ_n It it is the angle of the n-th element position and x-axis direction；

Under m-th pulse, N number of array element is V relative to the array manifold matrix of Q probe unit_m, expression formula is:

$V_m={\left[\begin{array}{cccccc}{V}_{m11}& V_{m12}& \mathrm{...}& V_{m1q}& \mathrm{...}& V_{m1Q}\\ V_{m21}& V_{m22}& \mathrm{...}& V_{m2q}& \mathrm{...}& V_{m2Q}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ V_{mn1}& V_{mn1}& \mathrm{...}& V_{mnq}& \mathrm{...}& V_{mnQ}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ V_{mN1}& V_{mN2}& \mathrm{...}& V_{mNq}& \mathrm{...}& V_{mNQ}\end{array}\right]}_{N\&times;Q}$

Under M pulse, N number of array element is relative to the array manifold matrix V=[V of Q probe unit₁,V₂,...,V_m,...,V_M]^T。

A kind of microwave relevance imaging method rotating emission array based on radar the most according to claim 2, its feature Being, step 6 includes:

Radiation field vector A under m-th pulse_mExpression formula:

$A_m={\&lsqb;s_{m1}\left(t\right),s_{m2}\left(t\right),\mathrm{...},s_{mn}\left(t\right),\mathrm{...},s_{mN}\left(t\right)\&rsqb;}_{1\&times;N}\&CenterDot;{\left[\begin{array}{cccccc}{V}_{m11}& V_{m12}& \mathrm{...}& V_{m1q}& \mathrm{...}& V_{m1Q}\\ V_{m21}& V_{m22}& \mathrm{...}& V_{m2q}& \mathrm{...}& V_{m2Q}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ V_{mn1}& V_{mn1}& \mathrm{...}& V_{mnq}& \mathrm{...}& V_{mnQ}\\ .& .& & .& & .\\ .& .& & .& & .\\ .& .& & .& & .\\ V_{mN1}& V_{mN2}& \mathrm{...}& V_{mNq}& \mathrm{...}& V_{mNQ}\end{array}\right]}_{N\&times;Q}$

Wherein, m=1,2 ... M, s_mnT () represents the microwave signal that under m-th pulse, the n-th array element is launched, V_mnqRepresent the Under m pulse, the n-th array element is multiplied relative to the steering vector of q-th probe unit, " " representing matrix；

Radiation field matrix A=[A under M pulse₁,A₂,…,A_m,…A_M]^T。

A kind of microwave relevance imaging method rotating emission array based on radar the most according to claim 1, its feature Being, step 8 includes:

The object function of target reflection factor vector σ and bound for objective function are following formula:

$\underset{\mathrm{\&sigma;}}{min}\{Q-F_{{\mathrm{\&alpha;}}_j}\left(\mathrm{\&sigma;}\right)\}$

Constraints Y=A σ+w

Wherein, Q represents probe unit sum,α_jExpression sets The fixed element variable in descending series, j=1,2 ..., J, J represent the element number in the descending series of setting, and σ is mesh Mark reflection coefficient vector, exp represents exponent arithmetic, σ_qRepresenting the target reflection factor of q-th probe unit, A represents M The radiation field matrix of Q probe unit under individual pulse.

A kind of microwave relevance imaging method rotating emission array based on radar the most according to claim 4, its feature Being, the object function solving target reflection factor vector σ under bound for objective function specifically includes:

8a) target setting reflection coefficient vector initial value is σ₁=A^H(AA^H)^-1Y, wherein []^-1Representing matrix is inverted, A table Show the radiation field matrix of Q probe unit under M pulse；

Set descending series [α₁,α₂,...,α_j,...,α_J], wherein the relation between element meets α_j=η α_j-1, j=2 ..., J, η ∈ (0.5,1] it is constant, α₁=2max (σ₁), α_J<0.01；

8b) utilize jth element α in descending series_jStructure gradient vector

$\underset{j}{{\mathrm{\&Delta;\&sigma;}}_{k-1}}=\&lsqb;\underset{j}{{\mathrm{\&sigma;}}_{k-1,1}}\exp \left(\frac{-\underset{j}{{\mathrm{\&sigma;}}_{k-1,1}^2}}{2{{\mathrm{\&alpha;}}_j}^2}\right),\underset{j}{{\mathrm{\&sigma;}}_{k-1,2}}\exp \left(\frac{-\underset{j}{{\mathrm{\&sigma;}}_{k-1,2}^2}}{2{{\mathrm{\&alpha;}}_j}^2}\right),\mathrm{...},\underset{j}{{\mathrm{\&sigma;}}_{k-1,q}}\exp \left(\frac{-\underset{j}{{\mathrm{\&sigma;}}_{k-1,q}^2}}{2{{\mathrm{\&alpha;}}_j}^2}\right),\mathrm{...},\underset{j}{{\mathrm{\&sigma;}}_{k-1,Q}}\exp \left(\frac{-\underset{j}{{\mathrm{\&sigma;}}_{k-1,Q}^2}}{2{{\mathrm{\&alpha;}}_j}^2}\right)\&rsqb;$ , wherein exp represents exponent arithmetic,Represent and utilize jth element α_jThe target reflection factor vector kth obtained-1 time Iterative valueIn q-th element, q=1,2 ..., Q, Q represent probe unit sum；

8c) structure utilizes jth element α_jThe target reflection factor vector kth obtained time iterative value Wherein step factor μ=2；

By jth element α_jThe target reflection factor vector kth obtained time iterative valueConvert:Wherein, []^-1Representing matrix is inverted, and the vector on ← expression the right replaces the left side Vector, andWherein []^TRepresent transposition；

8d) make k from 1 to K, repeat step 8b) to step 8c), obtain jth element α_jUnder target reflection factor VectorWherein, the iterations that K sets, for positive integer；

8e) make j from 1 to J, repeat step 8b) to step 8d), obtain j-th element α_JUnder target reflection factor VectorBy j-th element α_JUnder target reflection factor vectorAs target reflection factor vector σ.