CN104181531B - A kind of three-dimensional relevance imaging method based on phased-array radar - Google Patents

Abstract

The invention discloses a kind of three-dimensional relevance imaging method based on phased-array radar, relate to radar imagery field, the steps include: step 1, divide Phased Array Radar Antenna front, linear FM signal launched by phased-array radar transmitter, and receive the echo-signal of target scattering point, the phase-shift value of target setting scattering point；Step 2, by the fundamental frequency echo-signal after distance pulse pressure by distance dividing elements；Step 3, builds the object function of the scattering coefficient vector of target scattering point；And under the conditions of sparse constraint, solve object function, obtain the scattering coefficient vector estimated value of the u target scattering point in unit；Step 4, is first formed two dimensional image by the scattering coefficient vector estimated value of the target scattering point in the u distance unit, then is obtained 3-D view by the two dimensional image of all distance unit according to the order arrangement of distance unit.Present invention achieves the high-resolution three-dimensional imaging to target.

Description

A kind of three-dimensional relevance imaging method based on phased-array radar

Technical field

The invention belongs to radar imaging technology field, particularly relate to a kind of three-dimensional relevance imaging method based on phased-array radar.

Background technology

Microwave radar has round-the-clock, round-the-clock, at a distance and the characteristic such as observation on a large scale, target scene can be carried out height Resolution imaging, obtains detection information, all plays the effect of key in civil and military field.Micro-as main two dimension Wave imaging method, develops synthetic aperture radar (SAR) imaging and ISAR (ISAR) fifties in last century rapidly Imaging is the array manifold utilizing relative motion between carrier platform and target to form synthesis in space, it is possible to obtain target away from Scatter distributions information in-Doppler's plane, i.e. two-dimensional radar image, but there is geometric distortion and lacked one-dimensional letter in image Breath, the measurement to target property causes the biggest obstacle.Therefore, high-resolution three-dimensional imaging is a weight in radar imagery field Want research direction.

Big antenna aperature is the direct way realizing high-resolution microwave radar imaging.According to wide-aperture implementation, three-dimensional Microwave imaging is broadly divided into two classes, and a class is based on integrated array, and another kind of is based on real aperture three-dimensional imaging.The former utilizes The scanning of single antenna or linear array forms two dimension synthetic aperture, it is thus achieved that span from the two-dimentional resolution capability of plane, in conjunction with away from Descriscent pulse compression technique obtains full objective distributed image, and this kind of method needs the motion of platform, and application scenario is limited, Data acquisition real-time is poor, and signal processing difficulty is higher；And the latter relies on the narrow beam of array antenna formation in space Being scanned obtaining 3-D view, its resolution depends on beam angle, and i.e. the real physical pore size size of antenna, obtain The resolution that secures satisfactory grades image, needs to increase array aperture, makes system complexity and cost all sharply increase, so should at great majority With in occasion, due to antenna volume and the restriction of cost, the method resolution is the highest.

Summary of the invention

It is an object of the invention to overcome the deficiency of above-mentioned prior art, propose a kind of three-dimensional based on phased-array radar and be associated to By simulations below, image space method, can be seen that this formation method can break through the side of conventional real array of apertures radar three-dimensional imaging The restriction of position resolving power, thus realize distance to, orientation to pitching to high-resolution three-dimensional imaging.

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

A kind of three-dimensional relevance imaging method based on phased-array radar, it is characterised in that comprise the following steps:

Step 1, is divided into M × N number of submatrix by Phased Array Radar Antenna front, and each submatrix has K × L array element, altogether Having M × N × K × L array element, array element is distributed by rectangular uniform, and phased-array radar transmitter will linearly be adjusted under q-th pulse Frequently signal s0_qIt is transmitted in image scene, and receives the echo-signal containing P target scattering point under q-th pulse, will row The array element of the row k l row in the submatrix of the m row n row being listed in phased-array radar front pth mesh under q-th pulse Phase-shift value at mark scattering point is set asQ=1,2 ..., the total number of Q, Q pulse, m=1,2,3 ..., M, M are sky Linear array face line number, n=1,2,3 ..., N, N are antenna array columns, l=1,2,3 ..., L, L are the columns of submatrix, K=1,2,3 ..., K, K are the line number of submatrix；

Step 2, removes carrier frequency f to the echo-signal containing P target scattering point under q-th pulse_c, obtain q-th Fundamental frequency echo-signal s1 containing P target scattering point under pulse_q, to fundamental frequency echo-signal s1_qCarry out distance pulse pressure, obtain Fundamental frequency echo-signal s2 after distance pulse pressure_q；Fundamental frequency echo-signal s2 after distance pulse pressure again_qIn to obtain the u distance single The echo-signal containing P target scattering point in unitU=1,2,3..., U, U represent the distance unit under each pulse Total number；

Step 3, utilizes the array element of row k l row in the submatrix that the m row n of phased-array radar front arranges in q-th pulse Under each target scattering point at phase-shift value obtain the Antenna gain pattern of P target scattering point under Q pulse and increase Benefit matrix F, F dimension Q × P；Recycling Antenna gain pattern gain matrix F build the u under Q pulse individual away from Echo-signal s containing P target scattering point in unit^u；Recycling F and Q arteries and veins of Antenna gain pattern gain matrix Echo-signal s containing P target scattering point in the u the distance unit swept away^uBuild P in the u distance unit The scattering coefficient vector σ of target scattering point^uObject function；And under the conditions of sparse constraint, solve object function obtain u The scattering coefficient vector estimated value of P target scattering point in individual distance unit

Step 4, first by the scattering coefficient vector estimated value of P target scattering point in the u distance unitForm two dimension Image Z_u, then the two dimensional image Z by U distance unit₁,Z₂,...Z_u...,Z_ULine up according to the order of distance unit and obtain 3-D view Z=[Z₁,Z₂,...Z_u...,Z_U]。

The feature of technique scheme and further improvement is that:

(1) step 1 includes following sub-step:

1a) Phased Array Radar Antenna front being divided into M × N number of submatrix, each submatrix has K × L array element, a total of M × N × K × L array element, array element divided by rectangular uniform, and the linear frequency modulation under q-th pulse is believed by phased-array radar transmitter NumberBe transmitted in image scene, and receive under q-th pulse containing P mesh The echo-signal of mark scattering point, in formulaBe distance to the fast time,For distance to window function, r be distance to frequency modulation rate, f_cIt is the carrier frequency of radar emission signal, t_q=qT_rIt is the slow time of q-th pulse, T_rIt is the pulse repetition period, q=1,2 ..., Q Representing pulse sequence number, Q represents total pulse number of radar emission；

1b) array element of the row k l row in the submatrix arranged by the m row n being arranged in phased-array radar front is in q-th pulse Under pth target scattering point at phase-shift valueIt is set as:

Wherein:

Δφ_x=γ d_xsinθ_pcosβ_p (2)

Δφ_y=γ d_ysinβ_p (3)

Δ φ in formula_xFor adjacent array element space quadrature in the X direction, Δ φ_yFor adjacent array element space phase in the Y direction Potential difference；d_xIt is the array element distance in X-direction, d_yBeing the array element distance in Y-direction, X-direction is antenna arrays of radar Horizontal direction, Y-direction is the vertical direction of antenna arrays of radar, and k is array element numbering in submatrix in X-direction, K=1,2,3..., K, l are array element numberings in submatrix in Y-direction, l=1, and 2,3..., L, m are the submatrixs at this array element place Numbering in the X direction, m=1,2,3..., M, n are the submatrix numberings in the Y direction at this array element place, N=1,2,3..., N, p=1,2,3..., P, P represent total number of target scattering point, θ in scene_pRepresent that pth target dissipates The azimuth of exit point, β_pRepresenting the angle of pitch of pth target scattering point, γ=2 π/λ is free space wave number, and λ is thunder Reach operation wavelength, Δ φ_m,n(t_q) it is the random phase shift of extra superposition between submatrix, and the most constant in each burst length, and pulse Between be all change at random, i.e. Δ φ_m,n(t_q) it is independent identically distributed a functional of a stochastic process and Δ φ_m,n(t_q)∈[-π,π]。

(2) step 2 includes following sub-step:

2a) echo-signal containing P target scattering point under q-th pulse is removed carrier frequency f by radar_c, obtain q-th Fundamental frequency echo-signal s1 of P target scattering point under pulse_q, it may be assumed that

${s1}_q=\underset{p=1}{\overset{P}{\mathrm{\Σ}}}{\mathrm{\σ}}_p{F}_q^p{a}_r(\hat{t}-\frac{{2R}_p}{c})\exp \left[\mathrm{j\πr}{(\hat{t}-\frac{{2R}_p}{c})}^2\right]\exp (-j\frac{4\mathrm{\π}}{\mathrm{\λ}}{R}_p)---\left(4\right)$

R in formula_pIt is the radar distance that arrives pth target scattering point, σ_pBeing the scattering coefficient of pth target scattering point, c is light Speed,Represent the Antenna gain pattern gain at pth the target scattering point under q-th pulse,Represent pth Individual target scattering point is relative to the time delay of radar；

2b) use matched filtering functionThe fundamental frequency of P target scattering point under q-th pulse is returned Ripple signal s1_qCarry out distance pulse pressure, obtain fundamental frequency echo-signal s2 after distance pulse pressure_q:

$\begin{array}{c}{s2}_q=\mathrm{IFFT}\left\{\mathrm{FFT}\right[{s1}_q\left]\mathrm{FFT}\right[s_r\left]\right\}\\ =\underset{p=1}{\overset{P}{\mathrm{\Σ}}}{\mathrm{\σ}}_p{F}_q^p\sin c\left[\mathrm{\Δ}{f}_r(\hat{t}-\frac{{2R}_p}{c})\right]\exp (-j\frac{4\mathrm{\π}}{\mathrm{\λ}}{R}_p)\end{array}---\left(5\right)$

Δ f in formula_rBandwidth for the frequency band of radar emission linear FM signal；

2c) by fundamental frequency echo-signal s2 after distance pulse pressure_qObtain after simplification under q-th pulse containing P target scattering point Echo-signalEcho-signal after simplifying be divided into U apart from unit, then under q-th pulse the The echo-signal of P target scattering point in u distance unitIt is expressed as:

$s_q^u=\underset{p=1}{\overset{P}{\mathrm{\Σ}}}{\mathrm{\σ}}_p^u{F}_q^p---\left(6\right)$

In formulaRepresent the scattering coefficient of the u pth target scattering point in unit, wherein u=1,2,3..., U, U Represent total number of distance unit under each pulse.

(3) step 3 includes following sub-step:

3a) the array element of the row k l row in the submatrix that phased-array radar front m row n is arranged pth under q-th pulse Phase-shift value at individual target scattering pointExpression formula substitute into Antenna gain pattern gain function, thus obtain at q The Antenna gain pattern gain of pth the target scattering point under individual pulse

D in formula_xIt is the array element distance in X-direction, d_yBeing the array element distance in Y-direction, X-direction is antenna arrays of radar Horizontal direction, Y-direction is the vertical direction of antenna arrays of radar, p=1, and 2,3..., P, P represent target scattering in scene Total number of point, θ_pRepresent the azimuth of pth target scattering point, β_pRepresent the angle of pitch of pth target scattering point, k Being array element numbering in submatrix in X-direction, k=1,2,3..., K, γ=2 π/λ are free space wave numbers, and λ is radar work Making wavelength, l is array element numbering in submatrix in Y-direction, l=1, and 2,3..., L, m are that the submatrix at this array element place is in X side Numbering upwards, m=1,2,3..., M, n are the submatrix numberings in the Y direction at this array element place, n=1,2,3..., N, Δφ_m,n(t_q) be the random phase shift of extra superposition between submatrix, and every time the most constant in the burst length, and interpulse be all random change Change, i.e. Δ φ_m,n(t_q) it is independent identically distributed a functional of a stochastic process and Δ φ_m,n(t_q)∈[-π,π]；

And then obtain the Antenna gain pattern gain matrix F of P target scattering point under Q pulse, it may be assumed that

Echo vector s by P target scattering point in the u distance unit under Q pulse^uIt is expressed as: s^u=F σ^u； WhereinRepresent under Q pulse the echo of P target scattering point in the u distance unit to Amount,Represent the scattering coefficient vector of the u P target scattering point in unit；

3b) utilize the echo vector s of P target scattering point under Q pulse the u distance unit^uWith Q pulse Under P target constructing in the u distance unit of the Antenna gain pattern gain matrix F of P target scattering point scattered The scattering coefficient vector σ of exit point^uObject function J (σ^u):

$J\left({\mathrm{\σ}}^u\right)={\left|\right|s^u-F{\mathrm{\σ}}^u\left|\right|}_2^2+\mathrm{\μ}{\left|\right|{\mathrm{\σ}}^u\left|\right|}_1---\left(9\right)$

In formula | | | |₂It is L₂Norm operator, | | | |₁It is L₁Norm operator, μ is regularization parameter；

3c) construct the scattering coefficient vector σ of the u P target scattering point in unit^uObject function J (σ^u) Sparse constraint condition μ | | σ^u||₁Under equation be:

$\begin{array}{c}{\min \left|\right|s^u-F{\mathrm{\σ}}^u\left|\right|}_2^2+\mathrm{\μ}{\left|\right|{\mathrm{\σ}}^u\left|\right|}_1\\ s.t.\mathrm{\μ}{\left|\right|{\mathrm{\σ}}^u\left|\right|}_1\end{array}---\left(10\right)$

Ask in sparse constraint condition μ | | σ^u||₁Under equation obtain the scattering coefficient of P target scattering point in the u distance unit Vector estimated valueFor:

${\widehat{\mathrm{\σ}}}^u=\arg \min J\left({\mathrm{\σ}}^u\right)={[{\widehat{\mathrm{\σ}}}_1^u,{\widehat{\mathrm{\σ}}}_2^u,...{\widehat{\mathrm{\σ}}}_p^u...,{\widehat{\mathrm{\σ}}}_P^u]}^T---\left(11\right)$

In formula, argmin is minimum operation symbol,Represent the scattering system of the u P target scattering point in unit The estimated value of number vector,Represent the estimated value of the scattering coefficient of the u pth target scattering point in unit.

(4) step 4 includes following sub-step:

4a) set up with the orientation angles of target scattering point as abscissa, seat with the luffing angle of target scattering point as vertical coordinate Mark system, in a coordinate system, selects to place the scattering coefficient estimated value of pth the target scattering point in the u distance unit Point, the abscissa of this point is equal to orientation angles θ of pth target scattering point_p, the vertical coordinate of this point is equal to pth target The luffing angle β of scattering point_p；And then obtain the scattering coefficient estimated value of the u P target scattering point in unit The two dimensional image Z formed_u；

4b) make u travel through from 1 to U, repeat step 2, step 3 and step 4a), obtain U distance unit Two dimensional image Z₁,Z₂,...Z_u...,Z_U, by the two dimensional image Z of U distance unit₁,Z₂,...Z_u...,Z_UAccording to distance unit suitable Sequence is lined up, and finally gives the 3-D view Z=[Z of scene₁,Z₂,...Z_u...,Z_U]。

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 present invention uses two dimensional phased battle array radar, but compared with conventional scanning three-dimensional formation method, by phased array Array element carries out feeding back phase-shift value and forming space-time random radiation field in space, utilizes the pass of radiation profiles directional diagram and scatter echo Join sparse optimization process target scattering information is extracted, it is possible to break through the limit of real array of apertures theoretical resolution, it is achieved Distance to, orientation to pitching to high-resolution three-dimensional imaging, and have only to the sampling more less than scene unit number；

2, the present invention utilizes the pulse compression technique of linear FM signal in broadband, it is thus achieved that distance to high-resolution, in conjunction with Association process technology can realize three-dimensional imaging, more higher than existing chromatographic technique real-time；

3, the present invention is independent of radar carrier and the relative motion of target and the synthetic aperture that formed, can be according to application demand Adjust beam pointing-angle and range of exposures neatly, it is achieved the three-dimensional imaging under Duo Shijiao, thus application scenario is wider, both fits For motion platform, be also applied for static platform, and data acquisition and signal processing difficulty the most relatively low.

Accompanying drawing explanation

Fig. 1 is the solution of the present invention flow chart；

Fig. 2 is the radar work coordinate system figure that the present invention sets up；The scene center point taken in the drawings in scene plane is coordinate zero Point O, X-axis is the horizontal direction of scene plane, and Y-axis is the vertical direction of scene plane, and radar normal direction is as Z axis；

Fig. 3 is the bay arrangement schematic diagram that the present invention uses；First array element taking the lower left corner in the drawings is co-ordinate zero point O, X-direction is the horizontal direction of antenna arrays of radar, and Y-direction is the vertical direction of antenna arrays of radar, is perpendicular to radar The normal direction of antenna array is as Z-direction；

Fig. 4 is simulated point target profile of the present invention；In figure X-axis be radar relative target orientation to, Y-axis is radar phase To the pitching of target to, Z axis be radar relative target distance to；

Fig. 5 is the two-dimensional antenna radiation directivity gain diagram that the present invention produces；In figure, abscissa represents orientation angles, vertical coordinate Represent luffing angle；

Fig. 6 is the three-dimensional relevance imaging result figure of 625 echoes of the present invention；In figure X-axis be radar relative target orientation to, Y-axis be radar relative target pitching to, Z axis be radar relative target distance to；

Fig. 7 is the three-dimensional relevance imaging result figure of 80 echoes of the present invention.In figure X-axis be radar relative target orientation to, Y-axis be radar relative target pitching to, Z axis be radar relative target distance to.

Detailed description of the invention

With reference to present invention protocol procedures figure as shown in Figure 1, a kind of based on phased-array radar the three-dimensional association of the present invention is described Formation method.It is embodied as step as follows:

Step 1, is divided into M × N number of submatrix by Phased Array Radar Antenna front, and each submatrix has K × L array element, altogether Having M × N × K × L array element, array element is distributed by rectangular uniform, and phased-array radar transmitter will linearly be adjusted under q-th pulse Frequently signal s0_qIt is transmitted in image scene, and receives the echo-signal containing P target scattering point under q-th pulse, will row The array element of the row k l row in the submatrix of the m row n row being listed in phased-array radar front pth mesh under q-th pulse Phase-shift value at mark scattering point is set as

1a) as shown in Figure 3, Phased Array Radar Antenna front being divided into M × N number of submatrix, each submatrix has K × L Array element, a total of M × N × K × L array element, array element is divided by rectangular uniform.Phased-array radar transmitter is by under q-th pulse Linear FM signalIt is transmitted in image scene, and receives q-th pulse Under the echo-signal containing P target scattering point, in formulaBe distance to the fast time,For distance to window function, r it is Distance is to frequency modulation rate, f_cIt is the carrier frequency of radar emission signal, t_q=qT_rIt is the slow time of q-th pulse, T_rIt is that pulse repeats Cycle, q=1,2 ..., Q represents pulse sequence number, and Q represents total pulse number of radar emission.

1b) array element of the row k l row in the submatrix arranged by the m row n being arranged in phased-array radar front is in q-th pulse Under pth target scattering point at phase-shift valueIt is set as:

Wherein:

Δφ_x=γ d_xsinθ_pcosβ_p (2)

Δφ_y=γ d_ysinβ_p (3)

Δ φ in formula_xFor adjacent array element space quadrature in the X direction, Δ φ_yFor adjacent array element space phase in the Y direction Potential difference；d_xIt is the array element distance in X-direction, d_yIt it is the array element distance in Y-direction.X-direction is antenna arrays of radar Horizontal direction, Y-direction is the vertical direction of antenna arrays of radar.P=1,2,3..., P, P represent target scattering point in scene Total number.θ_pRepresent the azimuth of pth target scattering point, β_pRepresenting the angle of pitch of pth target scattering point, k is Array element is the numbering in X-direction in submatrix, k=1, and 2,3..., K, γ=2 π/λ is free space wave number, and λ is radar work Wavelength, l is array element numbering in submatrix in Y-direction, l=1,2,3..., L.M is that the submatrix at this array element place is in X-direction On numbering, m=1,2,3..., M, n are the submatrix numberings in the Y direction at this array element place, n=1,2,3..., N, Δφ_m,n(t_q) be the random phase shift of extra superposition between submatrix, and every time the most constant in the burst length, and interpulse be all random change Change, i.e. Δ φ_m,n(t_q) it is independent identically distributed a functional of a stochastic process and Δ φ_m,n(t_q)∈[-π,π]。

Linear FM signal is transmitted in image scene by phased-array radar transmitter, and the scene center point taken in scene plane is Co-ordinate zero point O, and using radar normal direction as Z axis, in scene plane, set up XOY axle, the radar work of foundation is sat Mark system is as in figure 2 it is shown, as a example by some a in scene plane, a spot projection to X-axis is b point, then phased-array radar and the company of b point Line is exactly azimuth angle theta with the angle of Z axis, the angle of the line of phased-array radar and the line of a point and phased-array radar and b point It it is exactly pitching angle beta.

Step 2, removes carrier frequency f to the echo-signal containing P target scattering point under q-th pulse_c, obtain q-th arteries and veins Fundamental frequency echo-signal s1 of P the target scattering point swept away_q, to fundamental frequency echo-signal s1_qCarry out distance pulse pressure, obtain distance Fundamental frequency echo-signal s2 after pulse pressure_q；Fundamental frequency echo-signal s2 after distance pulse pressure again_qIn obtain the u distance unit in The echo-signal containing P target scattering point

2a) echo-signal containing P target scattering point under q-th pulse is removed carrier frequency f by radar_c, obtain q-th Fundamental frequency echo-signal s1 of P target scattering point under pulse_q, it may be assumed that

${s1}_q=\underset{p=1}{\overset{P}{\mathrm{\Σ}}}{\mathrm{\σ}}_p{F}_q^p{a}_r(\hat{t}-\frac{{2R}_p}{c})\exp \left[\mathrm{j\πr}{(\hat{t}-\frac{{2R}_p}{c})}^2\right]\exp (-j\frac{4\mathrm{\π}}{\mathrm{\λ}}{R}_p)---\left(4\right)$

R in formula_pIt is the radar distance that arrives pth target scattering point, σ_pBeing the scattering coefficient of pth target scattering point, c is the light velocity,Represent the Antenna gain pattern gain at pth the target scattering point under q-th pulse,Represent pth mesh Mark scattering point is relative to the time delay of radar.

2b) use matched filtering functionThe fundamental frequency of P target scattering point under q-th pulse is returned Ripple signal s1_qCarry out distance pulse pressure, obtain fundamental frequency echo-signal s2 after distance pulse pressure_q。

$\begin{array}{c}{s2}_q=\mathrm{IFFT}\left\{\mathrm{FFT}\right[{s1}_q\left]\mathrm{FFT}\right[s_r\left]\right\}\\ =\underset{p=1}{\overset{P}{\mathrm{\Σ}}}{\mathrm{\σ}}_p{F}_q^p\sin c\left[\mathrm{\Δ}{f}_r(\hat{t}-\frac{{2R}_p}{c})\right]\exp (-j\frac{4\mathrm{\π}}{\mathrm{\λ}}{R}_p)\end{array}---\left(5\right)$

Δ f in formula_rBandwidth for the frequency band of radar emission linear FM signal.

Due to fundamental frequency echo-signal s2 containing P target scattering point under the q-th pulse after distance pulse pressure_qIn amplitude itemDistance to some scattering function, only with the signal bandwidth Δ f of radar system_rRelevant, and to fixing Scattering point be all constant；And phase termIt also it is constant term for fixing scattering point.This is to three-dimensional Relevance imaging does not affect, therefore can ignore these two.

2c) by fundamental frequency echo-signal s2 after distance pulse pressure_qReturning of P target scattering point under q-th pulse is obtained after simplification Ripple signalEcho-signal after simplifying is divided into U distance unit, then u under q-th pulse The echo-signal containing P target scattering point in individual distance unitIt is expressed as:

$s_q^u=\underset{p=1}{\overset{P}{\mathrm{\Σ}}}{\mathrm{\σ}}_p^u{F}_q^p---\left(6\right)$

In formulaRepresent the scattering coefficient of the u pth target scattering point in unit.Wherein u=1,2,3..., U, U table Show total number of the distance unit of division.

Step 3, utilizes the array element of row k l row in the submatrix that the m row n of phased-array radar front arranges in q-th pulse Under each target scattering point at phase-shift value obtain the Antenna gain pattern of P target scattering point under Q pulse and increase Benefit matrix F；Recycling Antenna gain pattern gain matrix F build the u under Q pulse in unit containing P Echo-signal s of individual target scattering point^u；U under recycling F and Q pulse of Antenna gain pattern gain matrix individual away from Echo-signal s containing P target scattering point in unit^uBuild dissipating of P target scattering point in the u distance unit Penetrate coefficient vector σ^uObject function；And under the conditions of sparse constraint, solve object function obtain in the u distance unit The scattering coefficient vector estimated value of P target scattering point

3a) the array element of the row k l row in the submatrix that phased-array radar front m row n is arranged pth under q-th pulse Phase-shift value at individual target scattering pointExpression formula substitute into Antenna gain pattern gain function, thus obtain at q The Antenna gain pattern gain of pth the target scattering point under individual pulse

And then obtain the Antenna gain pattern gain matrix F of P target scattering point under Q pulse, it may be assumed that

Echo vector s by P target scattering point in the u distance unit under Q pulse^uIt is expressed as: s^u=F σ^u。 WhereinRepresent under Q pulse the echo of P target scattering point in the u distance unit to Amount,Represent the scattering coefficient vector of the u P target scattering point in unit.

3b) utilize the echo vector s of P target scattering point under Q pulse the u distance unit^uWith Q pulse Under P target constructing in the u distance unit of the Antenna gain pattern gain matrix F of P target scattering point scattered The scattering coefficient vector σ of exit point^uObject function J (σ^u):

$J\left({\mathrm{\σ}}^u\right)={\left|\right|s^u-F{\mathrm{\σ}}^u\left|\right|}_2^2+\mathrm{\μ}{\left|\right|{\mathrm{\σ}}^u\left|\right|}_1---\left(9\right)$

In formula | | | |₂It is L₂Norm operator, | | | |₁It is L₁Norm operator, μ is regularization parameter；

In the prior art, the echo vector s to P target scattering point in the u distance unit under Q pulse^uEnter Row first-order linear association process, i.e. solves equation s^u=F σ^uObtain the scattering of the u P target scattering point in unit Coefficient vector σ^u, it is intended that obtain σ^uUnique solution, but owing to the number of array element is limited, under Q obtained pulse The Antenna gain pattern gain matrix F of P target scattering point be unable to reach completely random, i.e. the coefficient matrix F of equation Non-full rank, so non trivial solution is not unique, therefore have employed the sparse characteristic of three-dimensional scenic, in solution procedure in the present invention Add sparse constraint condition μ | | σ^u||₁Seek the scattering coefficient vector σ of the u P target scattering point in unit^u's Sparse solution, i.e. can get σ^uUnique solution.

3c) construct the scattering coefficient vector σ of the u P target scattering point in unit^uObject function J (σ^u) Sparse constraint condition μ | | σ^u||₁Under equation be:

$\begin{array}{c}{\min \left|\right|s^u-F{\mathrm{\σ}}^u\left|\right|}_2^2+\mathrm{\μ}{\left|\right|{\mathrm{\σ}}^u\left|\right|}_1\\ s.t.\mathrm{\μ}{\left|\right|{\mathrm{\σ}}^u\left|\right|}_1\end{array}---\left(10\right)$

Solve formula (10) and i.e. can get the scattering coefficient vector estimated value of P target scattering point in the u distance unitFor:

${\widehat{\mathrm{\σ}}}^u=\arg \min J\left({\mathrm{\σ}}^u\right)={[{\widehat{\mathrm{\σ}}}_1^u,{\widehat{\mathrm{\σ}}}_2^u,...{\widehat{\mathrm{\σ}}}_p^u...,{\widehat{\mathrm{\σ}}}_P^u]}^T---\left(11\right)$

In formula, argmin is minimum operation symbol,Represent the scattering system of the u P target scattering point in unit The estimated value of number vector.Represent the estimated value of the scattering coefficient of the u pth target scattering point in unit.

The present invention realizes 3c) process can utilize matching pursuit algorithm.The concrete steps of matching pursuit algorithm refer to J.A. IEEE paper " the Signal recovery from random that Tropp and A.C.Gilbert delivers in December, 2007 measurements via orthogonal matching pursuit”。

Step 4, first by the scattering coefficient vector estimated value of P target scattering point in the u distance unitForm two dimension Image Z_u, then the two dimensional image Z by U distance unit₁,Z₂,...Z_u...,Z_ULine up according to the order of distance unit and obtain 3-D view Z=[Z₁,Z₂,...Z_u...,Z_U]。

4a) set up with the orientation angles of target scattering point as abscissa, seat with the luffing angle of target scattering point as vertical coordinate Mark system, in a coordinate system, selects to place the scattering coefficient estimated value of pth the target scattering point in the u distance unit Point, the abscissa of this point is equal to orientation angles θ of pth target scattering point_p, the vertical coordinate of this point is equal to pth target The luffing angle β of scattering point_p；And then obtain the scattering coefficient estimated value of the u P target scattering point in unit The two dimensional image Z formed_u；

4b) make u travel through from 1 to U, repeat step 2, step 3 and step 4a), obtain U distance unit Two dimensional image Z₁,Z₂,...Z_u...,Z_U, by the two dimensional image Z of U distance unit₁,Z₂,...Z_u...,Z_UAccording to distance unit suitable Sequence is lined up, and finally gives the 3-D view Z=[Z of scene₁,Z₂,...Z_u...,Z_U]。

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

1. simulated conditions

This emulation uses the geometric model shown in Fig. 2 to carry out simulating, verifying, and making zero is the scene center in scene plane Point, radar phase center at scene center point 1Km, i.e. R=1000m；The distribution of target scattering point as shown in Figure 4, Imaging region is divided into the rectangular mesh of 25*25*25 (pitching of distance * orientation *).Assume two dimensional surface phased-array radar battle array Unit is distributed by rectangular uniform, total array element 40*40=1600, array element distance d in the X direction_x=0.004m, at Y Array element distance d on direction_y=0.004m.Then antenna bearingt is to aperture D_x=0.004*40=0.16m, antenna pitching is to hole Footpath D_y=0.004*40=0.16m；The carrier frequency f of radar emission signal_c=35GHz, bandwidth B=100MHz, sampling frequency Rate F_s=200MHz.

2. emulation content and result

Make Phased Array Radar Antenna front carry out feeding back phase-shift value according to conventional sweep pattern, then can form narrow beam spoke in space Penetrating directional diagram, the width of wave beam determines the resolution of conventional sweep three-dimensional imaging；Phased Array Radar Antenna front is divided into 5*5 Individual submatrix, each submatrix is made up of 8*8 array element, feeds back phase-shift value, the two-dimensional antenna of formation according to of the present invention carrying out Radiation directivity gain diagram is as shown in Figure 5, it can be seen that the wavefront planar radiation that two-dimensional antenna radiation directivity gain diagram represents Field intensity presents the form of random fluctuation so that the width phase of the radiation signal that the different scattering points in same wavefront plane are subject to There is the coding form of independent random, thus possess space can distinguishing characteristic.

The theoretical resolution of the real aperture three-dimensional imaging of prior art is determined by bandwidth and antenna aperature, imitates according to the numeral be given True parameter, range resolution ρ_r=C/2B=1.5m, distance is to differentiating point target；But azimuth resolution ρ_a=λ R/D_x=53.57m, pitching is to resolution ρ_p=λ R/D_y=53.57m；Orientation is to pitching to resolution significantly Space interval beyond point target 10m so that the scattering point on center reference distance face cannot be differentiated.

Based on phased-array radar the three-dimensional relevance imaging method using the present invention to propose, in conjunction with sparse optimized algorithm, obtains mesh The analogous diagram of mark scattering point, is to utilize 625 subpulses that the scattering point of scene is carried out three-dimensional imaging checking as shown in Figure 6, away from Descriscent resolution ρ_r=C/2B=1.5m, azimuth resolution ρ_a=D_x/ 2=0.08m；Pitching is to resolution ρ_p=D_y/ 2=0.08m；Not only scattering point is told effectively, and obtains the height of the scattering point of radar illumination scene Differentiating 3-D view, demonstrate the high-resolution three-dimensional imaging effect of the present invention, and scattering point location estimation is accurate, secondary lobe is relatively low, And scattering point cannot be gone out in district by the conventional real aperture imaging method of prior art；Give as shown in Figure 7 and only utilize 80 arteries and veins The three-dimensional relevance imaging of punching is as a result, it is possible to find out that the present invention, in the case of the pulse number deficiency of sampling, still can obtain Preferably imaging results, can be substantially reduced the requirement of data acquisition storage and real time signal processing.Having the strongest engineering should By value.

Claims (4)

1. a three-dimensional relevance imaging method based on phased-array radar, it is characterised in that comprise the following steps:

Step 1, is divided into M × N number of submatrix by Phased Array Radar Antenna front, and each submatrix has K × L array element, a total of M × N × K × L array element, and array element is distributed by rectangular uniform, phased-array radar transmitter under q-th pulse by linear FM signal s0_qIt is transmitted in image scene, and receiving the echo-signal containing P target scattering point under q-th pulse, the phase-shift value at the array element of the row k l row in the submatrix arrange the m row n being arranged in phased-array radar front pth target scattering point under q-th pulse is set asQ=1,2 ..., the total number of Q, Q pulse, m=1,2,3 ..., M, M are antenna array line number, n=1,2,3 ..., N, N are antenna array columns, l=1,2,3 ..., L, L are the columns of submatrix, k=1,2,3 ..., K, K are the line number of submatrix；

Step 2,

2a) echo-signal containing P target scattering point under q-th pulse is removed carrier frequency f by radar_c, obtain fundamental frequency echo-signal s1 of P target scattering point under q-th pulse_q, it may be assumed that

R in formula_pIt is the radar distance that arrives pth target scattering point, σ_pBeing the scattering coefficient of pth target scattering point, c is the light velocity,Represent the Antenna gain pattern gain at pth the target scattering point under q-th pulse,Represent the time delay relative to radar of pth the target scattering point；

2b) use matched filtering functionFundamental frequency echo-signal s1 to P target scattering point under q-th pulse_qCarry out distance pulse pressure, obtain fundamental frequency echo-signal s2 after distance pulse pressure_q:

Δ f in formula_rBandwidth for the frequency band of radar emission linear FM signal；

2c) by fundamental frequency echo-signal s2 after distance pulse pressure_qThe echo-signal containing P target scattering point under q-th pulse is obtained after simplificationEcho-signal after simplifying is divided into U distance unit, the then echo-signal of P target scattering point in the u distance unit under q-th pulseIt is expressed as:

In formulaRepresenting the scattering coefficient of the u pth target scattering point in unit, wherein u=1,2,3..., U, U represent total number of the distance unit under each pulse；

Step 3, the phase-shift value at the array element of the row of row k l in the submatrix that the m row n of phased-array radar front the arranges each target scattering point under q-th pulse is utilized to obtain Antenna gain pattern gain matrix F, the F dimension Q × P of P target scattering point under Q pulse；Recycling Antenna gain pattern gain matrix F builds echo-signal s containing P target scattering point in the u distance unit under Q pulse^u；Echo-signal s containing P target scattering point in the u distance unit under recycling F and Q pulse of Antenna gain pattern gain matrix^uBuild the scattering coefficient vector σ of the u P target scattering point in unit^uObject function；And under the conditions of sparse constraint, solve object function obtain the scattering coefficient vector estimated value of P target scattering point in the u distance unit

Step 4, first by the scattering coefficient vector estimated value of P target scattering point in the u distance unitForm two dimensional image Z_u, then the two dimensional image Z by U distance unit₁,Z₂,...Z_u...,Z_ULine up according to the order of distance unit and obtain 3-D view Z=[Z₁,Z₂,...Z_u...,Z_U]。

A kind of three-dimensional relevance imaging method based on phased-array radar the most according to claim 1, it is characterised in that step 1 includes following sub-step:

1a) Phased Array Radar Antenna front being divided into M × N number of submatrix, each submatrix has K × L array element, a total of M × N × K × L array element, and array element is divided by rectangular uniform, and phased-array radar transmitter is by the linear FM signal under q-th pulseIt is transmitted in image scene, and receives the echo-signal containing P target scattering point under q-th pulse, in formulaBe distance to the fast time,For distance to window function, r is that distance is to frequency modulation rate, f_cIt is the carrier frequency of radar emission signal, t_q=qT_rIt is the slow time of q-th pulse, T_rIt is the pulse repetition period, q=1,2 ..., Q represents pulse sequence number, and Q represents total pulse number of radar emission；

1b) the phase-shift value at the array element of the row k l row in the submatrix that the m row n being arranged in phased-array radar front is arranged pth target scattering point under q-th pulseIt is set as:

Wherein:

Δφ_x=γ d_x sinθ_p cosβ_p (2)

Δφ_y=γ d_y sinβ_p (3)

Δ φ in formula_xFor adjacent array element space quadrature in the X direction, Δ φ_yFor adjacent array element space quadrature in the Y direction；d_xIt is the array element distance in X-direction, d_yBeing the array element distance in Y-direction, X-direction is the horizontal direction of antenna arrays of radar, and Y-direction is the vertical direction of antenna arrays of radar, k is array element numbering in submatrix in X-direction, k=1,2,3..., K, l are array element numberings in submatrix in Y-direction, l=1,2,3..., L, m are the submatrix numberings in the X direction at this array element place, m=1,2,3..., M, n is the submatrix numbering in the Y direction at this array element place, n=1,2,3..., N, p=1,2,3..., P, P represents total number of target scattering point, θ in scene_pRepresent the azimuth of pth target scattering point, β_pRepresenting the angle of pitch of pth target scattering point, γ=2 π/λ is free space wave number, and λ is radar operation wavelength, Δ φ_m,n(t_q) be the random phase shift of extra superposition between submatrix, and every time the most constant in the burst length, and interpulse be all change at random, i.e. Δ φ_m,n(t_q) it is independent identically distributed a functional of a stochastic process and Δ φ_m,n(t_q)∈[-π,π]。

A kind of three-dimensional relevance imaging method based on phased-array radar the most according to claim 2, it is characterised in that step 3 includes following sub-step:

3a) the phase-shift value at the array element of the row k l row in the submatrix that phased-array radar front m row n is arranged pth target scattering point under q-th pulseExpression formula substitute into Antenna gain pattern gain function, thus obtain the Antenna gain pattern gain of pth the target scattering point under q-th pulse

D in formula_xIt is the array element distance in X-direction, d_yBeing the array element distance in Y-direction, X-direction is the horizontal direction of antenna arrays of radar, and Y-direction is the vertical direction of antenna arrays of radar, p=1, and 2,3..., P, P represent total number of target scattering point, θ in scene_pRepresent the azimuth of pth target scattering point, β_pRepresenting the angle of pitch of pth target scattering point, k is array element numbering in submatrix in X-direction, k=1,2,3..., K, γ=2 π/λ is free space wave number, and λ is radar operation wavelength, l is array element numbering in submatrix in Y-direction, l=1,2,3..., L, m are the submatrix numberings in the X direction at this array element place, m=1,2,3..., M, n are the submatrix numberings in the Y direction at this array element place, n=1,2,3..., N, Δ φ_m,n(t_q) be the random phase shift of extra superposition between submatrix, and every time the most constant in the burst length, and interpulse be all change at random, i.e. Δ φ_m,n(t_q) it is independent identically distributed a functional of a stochastic process and Δ φ_m,n(t_q)∈[-π,π]；

And then obtain the Antenna gain pattern gain matrix F of P target scattering point under Q pulse, it may be assumed that

Echo vector s by P target scattering point in the u distance unit under Q pulse^uIt is expressed as: s^u=F σ^u；WhereinThe echo vector of P the target scattering point represented under Q pulse in the u distance unit,Represent the scattering coefficient vector of the u P target scattering point in unit；

3b) utilize the echo vector s of P target scattering point under Q pulse the u distance unit^uWith the scattering coefficient vector σ that the Antenna gain pattern gain matrix F of P target scattering point under Q pulse constructs the u P target scattering point in unit^uObject function J (σ^u):

In formula | | | |₂It is L₂Norm operator, | | | |₁It is L₁Norm operator, μ is regularization parameter；

3c) construct the scattering coefficient vector σ of the u P target scattering point in unit^uObject function J (σ^u) in sparse constraint condition μ | | σ^u||₁Under equation be:

Ask in sparse constraint condition μ | | σ^u||₁Under equation obtain the scattering coefficient vector estimated value of P target scattering point in the u distance unitFor:

In formula, argmin is minimum operation symbol,Represent the estimated value of the scattering coefficient vector of the u P target scattering point in unit,Represent the estimated value of the scattering coefficient of the u pth target scattering point in unit.

A kind of three-dimensional relevance imaging method based on phased-array radar the most according to claim 1, it is characterised in that step 4 includes following sub-step:

4a) set up with the orientation angles of target scattering point as abscissa, coordinate system with the luffing angle of target scattering point as vertical coordinate, in a coordinate system, select to place the scattering coefficient estimated value of the u pth target scattering point in unitPoint, the abscissa of this point is equal to orientation angles θ of pth target scattering point_p, the vertical coordinate of this point is equal to the luffing angle β of pth target scattering point_p；And then obtain the scattering coefficient estimated value of the u P target scattering point in unitThe two dimensional image Z formed_u；

4b) make u travel through from 1 to U, repeat step 2, step 3 and step 4a), obtain the two dimensional image Z of U distance unit₁,Z₂,...Z_u...,Z_U, by the two dimensional image Z of U distance unit₁,Z₂,...Z_u...,Z_ULine up according to the order of distance unit, finally give the 3-D view Z=[Z of scene₁,Z₂,...Z_u...,Z_U]。