CN101833095B - Star machine united SAR (Synthetic Aperture Radar) two-dimensional frequency domain imaging method based on airspace domain expansion - Google Patents

Abstract

The invention discloses a star machine united bistatic synthetic aperture radar two-dimensional frequency domain imaging method based on airspace domain expansion. By utilizing the characteristic that airspace expansion of distance history and second-order time domain of reference point distance history are approximate, a phase is expressed to a quadratic polynomial with respect to the slow time, and a stationary phase method is utilized to obtain a two-dimensional spectrum of a signal, good focus results can be obtained through azimuth and distance compression, and finally linear relationship of scattering point position is utilized to peel coordinates of the distance and the azimuth from a coupling term so as to obtain the correct coordinates. Therefore, the invention overcomes the complex process of two-dimensional spectrum calculation and target spatially variable compensation and realizes star machine united bistatic synthetic aperture radar imaging in larger scenes. The invention can be applied to the fields of synthetic aperture radar imaging, earth remote sensing, and the like.

Description

A kind of satellite machine combined SAR two-dimensional frequencies imaging method deployed based on spatial domain

Technical field：

The invention belongs to Radar Technology field, its more particularly to synthetic aperture radar (SAR) imaging technique culminant star machine united mode double-base synthetic aperture radar imaging method. 

Background technology：

Double-base synthetic aperture radar (Bistatic SAR) is a kind of new polarization sensitive synthetic aperture radar system being separately mounted to Receiver And Transmitter on different motion platforms.Satellite machine combined double-base synthetic aperture radar (Spaceborne-Airborne Bistatic SAR) is used as a kind of special pattern of double-base synthetic aperture radar, the mode of operation received using satellite launch, single (many) individual aircrafts, while biradical synthetic aperture radar advantage is inherited, also with following particular advantages： 

1. unique " remote hair is near to be received " pattern, both given full play to satellite station obtain it is high, look far, the advantage such as broad covered area, very high signal noise ratio (snr) of image is maintained again； 

2. reduction is to demand in terms of satellite power, data transmission capacity, disposal ability and cost； 

3. formulating observation program according to customer demand, implement the data acquisition modes more more flexible than distributed Spaceborne SAR System, reduce data acquisition cost； 

4. playing the characteristics of air maneuver is flexible, the Novel work pattern different from Traditional bandoleer, pack and scan pattern is built, is easy to high-resolution and wide swath SAR system to design and realizes. 

Therefore no matter spaceborne-airborne bistatic SAR suffers from more extensive development space, into the study hotspot in nearest double-base synthetic aperture radar field as the earth observation from space or reconnaissance means of new ideas in civilian or Military Application field. 

Usually, double-base synthetic aperture radar system is segmented into two classes：Move constant double-base synthetic aperture radar system and move and become double-base synthetic aperture radar system.Satellite machine combined double-base synthetic aperture radar becomes double-base synthetic aperture radar system as typical move, the geometrical relationship of transmitting/receiving system is changed over time, therefore the synthetic aperture radar image-forming method assumed based on LTI, such as, Range-doppler Method, wave-number domain method, it is impossible to meet the requirement of such double-base synthetic aperture radar imaging；Even if being imaged in addition, realizing shifting and becoming double-base synthetic aperture radar imaging point target, shifting change double-base synthetic aperture radar imaging distance still inevitably causes to move to become double-base synthetic aperture radar image fault to the nonorthogonality with orientation coordinate system.Become double-base synthetic aperture radar imaging method currently for moving, imaging method under particularly satellite machine combined pattern than relatively limited, in terms of effective time domain in addition to rear orientation projection's (BP) method and mutative scale inverse Fourier transform method few other methods.And influence of the mutative scale inverse Fourier transform method due to not accounting for spatial domain truncated error, so and be not suitable with large scene satellite machine combined double-base synthetic aperture radar imaging.See document " ShiJun；Xiaoling Zhang；Jianyu Yang；" Principle and Methods on Bistatic SARSignal Processing via Time Correlation ", Geoscience and Remote Sensing, IEEE Transactions, Volume 46, pp：3163-3178(2008)”. 

The advantage of frequency domain method is that arithmetic speed is fast, but imaging precision is not high, while the derivation of equation of echo 2-d spectrum is relative complex, and the LBF models proposed at present using German scholar Otmar Loffled is representatives. 

Phase in the Taylor expansion of point in phase bit of transmitter and receiver, is expressed as two quadratic term sums by phase by the LBF models that Loffled etc. is proposed, 2-d spectrum is obtained so as to calculate, and is introduced mutative scale Fourier transformation and obtained good focusing effect.But the frequency spectrum derivation of this method is excessively tediously long and complexity, and phase error is larger, and the calculating of the relevant coefficient of processing procedure is also quite cumbersome.See document " K.Natroshvili; O.Loffeld; H.Nies, A.Medrano Ortiz, and S.Knedlik; " Focusing of general bistaticSAR configuration data with 2-D inverse scaled FFT; " IEEE Trans.Geosci.Remote Sens., vol.44, no.10, pp.2718-2727, Oct.2006 "；And " R.Wang; O.Loffeld; Q.UI-Ann, H.Nies, A.Medrano-Ortiz; and S.Knedlik; " Analysis andextension of Loffeld ' s bistatic formula in spaceborne/airborne configuration, " inProc.EUSAR, Friedrichshafen; Germany, Jun.2008.CD-ROM. ". 

The Air-Phase models that Liu's Zhe is proposed will regard an entirety as apart from history, in the case where ensureing that phase error is minimum, try to achieve the breaking up point of slow time, and obtain preferable 2-d spectrum analytical expression with this.But because time domain expansion can not use the spatial character between explicit expression scattering point, therefore, this method needs to correct by the space-variant for completing scattering point the step of a series of complex in imaging.See document " Zhe Liu; JianyuYang; Xiaoling Zhang; Yiming Pi.Study on Spaceborne/Airborne HybridBistatic SAR Image Formation in Frequency Domain.IEEE Geoscience andRemote Sensing Letters; 2008,5 (4)：578-582”. 

In summary, the time domain for history of adjusting the distance deploys not only so that the derivation of frequency spectrum becomes tediously long and complexity, and can not use the spatial character between explicit expression scattering point.And history of adjusting the distance can then be avoided using spatial domain expansion and be overcome disadvantages mentioned above.Therefore the present invention is based on apart from the expansion of the spatial domain of history, it is proposed that a kind of new two-dimensional frequency method suitable for satellite machine combined SAR. 

The content of the invention：

In order to overcome the problem of satellite machine combined double-base synthetic aperture radar lacks effectively simple frequency domain imaging method, the invention provides a kind of satellite machine combined double-base synthetic aperture radar two-dimensional frequency imaging method deployed based on spatial domain, the characteristics of this method and thinking is：Using approximate apart from the second order time domain of history in the spatial domain expansion of reference point and reference point apart from history, phase is expressed as a quadratic polynomial on the slow time, and obtains using Stationary phase method the 2-d spectrum of signal.Good focusing effect is obtained by azimuth-range compression.Finally using the linear relationship using scattering point position, the coordinate of distance and bearing is stripped out from coupling terms, correct coordinate is obtained.It is imaged so as to overcome the process that the 2-d spectrum of complexity is calculated and target space-variant is compensated, and realize compared with satellite machine combined double-base synthetic aperture radar under large scene. 

Present disclosure is described for convenience, makees following term definition first： 

Define 1, satellite machine combined double-base synthetic aperture radar (Spaceborne-Airborne Bistatic SAR)

Double-base synthetic aperture radar refers to the synthetic aperture radar that radar emission system and reception system are separately mounted on different motion platform, wherein, the platform for installing emission system is referred to as flat pad, and the platform for installing reception system is referred to as receiving platform. 

Satellite machine combined double-base synthetic aperture radar refers to that the flat pad and receiving platform of radar are respectively placed in the special pattern of the double-base synthetic aperture radar on satellite and aircraft. 

Define the description of 2, satellite machine combined double-base synthetic aperture radar system relevant parameter

Point vector to be observed

PRF represents pulse recurrence frequency； 

N-th of PRF moment position vector of flat pad

Represent flat pad initial time position vector；N-th of PRF moment position vector of receiving platform

Represent receiving platform initial time position vector. 

Flat pad is apart from historyReceiving platform is apart from history

Wherein | | represent modulo operator. 

Satellite machine combined double-base synthetic aperture radar system oblique distance history

It is the movement velocity size of transmitting and receiving platform relative target respectively； 

The beam position vector of flat pad radar

The initial beam pointing vector of flat pad radar

The beam position vector of receiving platform radar

The initial beam pointing vector of receiving platform radarSatellite machine combined double-base synthetic aperture radar system beam position vector

In order to record convenient order

Represent

In n=0 value. 

The angular velocity vector of flat pad radar

The initial angular velocity vector of flat pad radar

The angular velocity vector of receiving platform radar

The initial angular velocity vector of receiving platform radar

Satellite machine combined double-base synthetic aperture radar system angular velocity vector

In order to record convenient orderRepresent

In n=0 value. 

Other specification：T is fast (oblique distance) time；N is n-th of PRF moment, is also slow (orientation) time； Carrier wave wave number is represented,Represent apart from wave number, K '=K-K₀,

For orientation wave number；C is the light velocity, f₀For carrier frequency, f is the frequency corresponding to fast (oblique distance) time, f_aFor the Doppler frequency corresponding to slow (orientation) time. 

Define 3, shift variant mode double-base synthetic aperture radar

In a broad sense, shift variant mode double-base synthetic aperture radar refers to the platform polarization sensitive synthetic aperture radar system that relative position changes in data acquisition for installing emission system and reception system. 

But under actual conditions, the movement locus of flat pad and receiving platform always remains a constant speed linear motion.Therefore, " shift variant mode double-base synthetic aperture radar " refers to the movement locus of emission system platform and reception system platform, in data acquisition, the broad sense shift variant mode double-base synthetic aperture radar for the linear motion that always remains a constant speed defined in the present invention. 

Define 4 synthetic aperture radar gauged distance compression methods

Synthetic aperture radar gauged distance compression method refers to utilize synthetic aperture radar emission parameter, mainly included：Reference signal, and the process being filtered using matched filtering technique to the distance of synthetic aperture radar to signal are generated using below equation. 

$f\left(t\right)=\exp (j\·\mathrm{\π}\·\frac{B}{T_p}\·t^2),t\∈[-\frac{T_p}{2},\frac{T_p}{2}]---\left(1\right)$

Wherein, f (t) is reference function, and B is the signal bandwidth of radar emission baseband signal, T_PFor radar emission signal pulse width, t is fast (oblique distance) time, span from

Arrive

Refer to document " radar imaging technology ", protect it is polished etc. write, Electronic Industry Press is published.The data obtained after Range compress are referred to as apart from numeric field data in this specification. 

Define 5 synthetic aperture radar scene spaces

Synthetic aperture radar scene space refers to the set of all scene objects points to be observed in realistic space.There are different expressions under different spaces coordinate system, once but coordinate system establishment its expression later is unique.Generally imaging takes earth axes, i.e. distance to-orientation-highly to coordinate system for convenience. 

Define 6 synthetic aperture radar image-forming spaces

Synthetic aperture radar image-forming space refers to the two dimensional surface space that synthetic aperture radar image-forming method projects to the scattering point in scene space, the space is determined that the imaging space of typical case's synthetic aperture radar includes distance to-orientation projector space at present by the mutually orthogonal coordinate base of two in synthetic aperture radar image-forming space.In the present invention imaging space M is represented with following mathematical relationship： 

Wherein

With

Represent to constitute imaging space M mutually orthogonal coordinate base, represent respectively distance to and orientation. 

For the point to be observed vector in imaging space, u, v represents the distance and bearing coordinate of the point respectively, and represents real number. 

Define 7 synthetic aperture radar image-forming scene reference points

Synthetic aperture radar image-forming scene reference point refers to some scattering point in synthetic aperture radar image-forming space, is used as the reference for analyzing and handling other scattering points in scene. 

8 satellite machine combined double-base synthetic aperture radars are defined apart from the spatial domain of history to deploy

Satellite machine combined double-base synthetic aperture radar apart from history refer to scattering point to be observed in any time scene space to satellite platform and aircraft platform distance and.Synthetic aperture radar refers to the process of three directions apart from history along scene space doing polynary Taylor expansion (multi-variables Taylor ' stheorem) apart from the spatial domain expansion of history.Error more than wherein ignored second order and second order is referred to as spatial domain truncated error.See document " Shi Jun；Xiaoling Zhang；Jianyu Yang；" Principle and Methods on BistaticSAR Signal Processing via Time Correlation ", Geoscience and Remote Sensing, IEEE Transactions, Volume 46, pp：3163-3178(2008)” 

$R(n;{\stackrel{\‾}{P}}_{\mathrm{\ω}})\≈R(n;\stackrel{\‾}{0})+[\stackrel{\‾}{\mathrm{\α}}\left(n\right)+\stackrel{\‾}{\mathrm{\β}}\left(n\right)\·n]\·{\stackrel{\‾}{P}}_{\mathrm{\ω}}---\left(3\right)$

Wherein, related symbol, which is explained, sees definition 2, it should be noted that here： 

$\stackrel{\‾}{\mathrm{\α}}\left(n\right)\≈\stackrel{\‾}{\mathrm{\α}}-[({\stackrel{\‾}{\mathrm{\α}}}_r\·{\stackrel{\‾}{\mathrm{\β}}}_r){\stackrel{\‾}{\mathrm{\α}}}_r+({\stackrel{\‾}{\mathrm{\α}}}_t\·{\stackrel{\‾}{\mathrm{\β}}}_t){\stackrel{\‾}{\mathrm{\α}}}_t]n---\left(4\right)$

$\stackrel{\‾}{\mathrm{\β}}\left(n\right)\≈\stackrel{\‾}{\mathrm{\β}}---\left(5\right)$

9 satellite machine combined double-base synthetic aperture radar reference points are defined apart from history time domain to deploy

Satellite machine combined double-base synthetic aperture radar apart from history refer to reference point in any time scene space to satellite platform and aircraft platform apart from history and, be designated as

Satellite machine combined double-base synthetic aperture radar apart from the time domain expansion of history refers to the process of that Taylor expansion (Taylor ' s theorem) will be done along the slow time apart from history

$R(n;\stackrel{\‾}{0})\≈A+B\·n+\frac{1}{2}D\·n^2---\left(6\right)$

Wherein： 

$A=\left|{\stackrel{\‾}{P}}_R\left(0\right)\right|+\left|{\stackrel{\‾}{P}}_T\left(0\right)\right|---\left(7\right)$

$B={\stackrel{\‾}{\mathrm{\α}}}_t\·{\stackrel{\‾}{V}}_t+{\stackrel{\‾}{\mathrm{\α}}}_r\·{\stackrel{\‾}{V}}_r---\left(8\right)$

$D=-\frac{{\left({\stackrel{\‾}{\mathrm{\α}}}_t{\stackrel{\‾}{V}}_t\right)}^2}{\left|{\stackrel{\‾}{P}}_T\left(0\right)\right|}+{\stackrel{\‾}{\mathrm{\β}}}_t{\stackrel{\‾}{V}}_t-\frac{{\left({\stackrel{\‾}{\mathrm{\α}}}_r{\stackrel{\‾}{V}}_r\right)}^2}{\left|{\stackrel{\‾}{P}}_R\left(0\right)\right|}+{\stackrel{\‾}{\mathrm{\β}}}_r{\stackrel{\‾}{V}}_r---\left(9\right)$

A represents initial distance history；B represents velocity equivalent；D represents equivalent acceleration.Other related symbols are shown in definition 2； 

10 satellite machine combined double-base synthetic aperture radars are defined apart from history approximate expression

Satellite machine combined double-base synthetic aperture radar refers to scattering point to be observed in any time scene space to the approximate representation process apart from history of satellite platform and aircraft platform apart from history.Combine the expression formula of formula (3) and (6)： 

$R(n;{\stackrel{\‾}{P}}_{\mathrm{\ω}})\≈A_{\mathrm{mod}}+B_{\mathrm{mod}}\·n+\frac{D}{2}\·n^2---\left(10\right)$

Wherein：A_mod=A+ α, B_mod=B+ β,

α=u α_u+vα_v, β=u β_u+vβ_v；Symbol " " represents to seek the inner product of vector

Define the 2-d spectrum of 11 satellite machine combined double-base synthetic aperture radar system impulses response

According to the characteristics of satellite machine combined double-base synthetic aperture radar system, the 2-d spectrum H (K, Ka) for defining the response of satellite machine combined double-base synthetic aperture radar system impulse is

$H(K,\mathrm{Ka})=\exp (j\·(K^{\′}(A_{\mathrm{mod}}-\frac{{B_{\mathrm{mod}}}^2}{2D})+\frac{\mathrm{Ka}\·C\·B_{\mathrm{mod}}}{D}-\frac{{\mathrm{Ka}}^2\·C^2}{2K^{\′}\·D}))---\left(11\right)$

Wherein related symbol, which is shown in, defines 2 and definition 10； 

Define 12 principles in phase bit

Principle in phase bit is to the frequency spectrum analysis method with big Timed automata signal.Referring specifically to document " Pi Yiming, Yang Jianyu, synthetic aperture radar image-forming principle, publishing house of University of Electronic Science and Technology, in March, 2007, p22-p24. "

A kind of satellite machine combined SAR two-dimensional frequencies imaging method deployed based on spatial domain that the present invention is provided, it includes following steps： 

Step 1: the initialization of synthetic aperture radar image-forming space and imaging system parameters； 

Synthetic aperture radar image-forming space is determined by the mutually orthogonal coordinate base of two in synthetic aperture radar image-forming space, and unit vector ground level in parallel with flat pad (i.e. satellite) velocity attitude is defined as first coordinate base in synthetic aperture radar image-forming space, i.e.,

Be defined in ground level, and with first coordinate base in synthetic aperture radar image-forming space

Vertical unit vector is denoted as second coordinate base in synthetic aperture radar image-forming space

Initialization imaging system parameters include：Flat pad velocity, i.e. satellite are denoted as with respect to ground speed vector

Receiving platform velocity, i.e. aircraft velocity vector are denoted as

Flat pad initial position vector, is denoted as

Receiving platform initial position vector, is denoted as

The wave number of radar emission electromagnetic wave, is denoted as K₀, the signal bandwidth of radar emission baseband signal is denoted as B, and radar emission signal pulse width is denoted as T_P, radar received wave door continues width, is denoted as T_o, the sample frequency of Radar Receiver System is denoted as f_s, the pulse recurrence frequency of radar system is denoted as PRF.Flat pad initial position vector

Receiving platform initial position vectorWherein x_T y_T z_TAnd x_R y_R z_RThe 3 d space coordinate of flat pad and receiving platform is represented respectively.Using formula

Obtain the position vector at n-th of PRF moment of flat pad

Using formula

Obtain the position vector at n-th of PRF moment of flat pad

N=1 ..., N_sRepresent n-th of PRF moment, N_sFor the sampling number of orientation. 

Launch the initial pointing vector of wave beam of radar, be denoted as

Receive the initial pointing vector of wave beam of radar

Represent that the initial beam of radar is pointed to and vector.The initial angular velocity vector of flat pad radarThe initial angular velocity vector of receiving platform radar

Satellite machine combined double-base synthetic aperture radar system initial angular velocity and vector

And utilize formula

Parameter is tried to achieve respectively：A, B, D.Wherein：A represents initial distance history；B represents velocity equivalent；D represents equivalent acceleration； 

Symbol " | | " represent modulus computing. 

According to satellite machine combined double-base synthetic aperture radar system schema and satellite machine combined double-base synthetic aperture radar observation program, the initialization imaging system parameters that satellite machine combined double-base synthetic aperture radar imaging method needs are known.Its geometry is as shown in Figure 1. 

Step 2: satellite machine combined double-base synthetic aperture radar initial data carries out Range compress. 

The satellite machine combined double-base synthetic aperture radar echo data that receiver is received is denoted as by we

The satellite machine combined double-base synthetic aperture radar echo data received is compressed using synthetic aperture radar gauged distance compression method, the satellite machine combined double-base synthetic aperture radar data after Range compress is obtained, is denoted as

N represents n-th of PRF moment, r be apart from independent variable,

Represent point target vector to be observed. 

Step 3: satellite machine combined double-base synthetic aperture radar initial data carries out two-dimensional Fourier transform

The echo data stored in the matrix form after the satellite machine combined double-base synthetic aperture radar Range compress that step 2 is obtained

Fourier transformation is done respectively along row and column, the two-dimensional frequency data of satellite machine combined double-base synthetic aperture radar echo-signal is obtained, is designated as

Step 4: satellite machine combined double-base synthetic aperture radar direction reference function is compensated

The two-dimensional frequency data for the satellite machine combined double-base synthetic aperture radar echo-signal that step 3 is obtained

With orientation reference function

It is multiplied, obtains the two-dimensional frequency data of the satellite machine combined double-base synthetic aperture radar echo-signal after orientation compensation

Wherein

Carrier wave wave number is represented,

Represent apart from wave number, K '=K-K₀,

For orientation wave number；C is the light velocity, f₀For carrier frequency, f is the frequency corresponding to fast (oblique distance) time, f_aFor the Doppler frequency corresponding to slow (orientation) time, D represents equivalent acceleration. 

Step 5: satellite machine combined double-base synthetic aperture radar nonlinear phase is compensated

The two-dimensional frequency data of satellite machine combined double-base synthetic aperture radar echo-signal after the orientation obtained in step 4 is compensated

Inverse Fourier transform (IFFT) is done along the row (i.e. orientation) of data, frequency of distance-orientation time numeric field data of satellite machine combined double-base synthetic aperture radar echo-signal is obtained： 

With reference to the relevant parameter initialized in step one, to dataIn the i-th row data be multiplied by respectivelyConjugation.Wherein

Represent the value of i-th of slow time, i=1...N_s, N_sFor azimuth sample point, PRF is pulse recurrence frequency.Obtain

By obtained data

Fourier transformation, and multiplication by constants phase are done along row

Then obtain the data on scattering point coordinate linear phase to be observed

$s_6(K,\mathrm{Ka};{\stackrel{\‾}{P}}_{\mathrm{\ω}})={\mathrm{FFT}}_{\mathrm{az}}\left(s_5(K,r_{\mathrm{az}};{\stackrel{\‾}{P}}_{\mathrm{\ω}})\right)\·\exp (-j\·\mathrm{Ka}\left(\frac{B\·C}{D}\right))---\left(12\right)$

Wherein

Carrier wave wave number is represented,

Represent apart from wave number, K '=K-K₀,

For orientation wave number；C is the light velocity, f₀For carrier frequency, f is the frequency corresponding to fast (oblique distance) time, f_aFor the Doppler frequency corresponding to slow (orientation) time, A represents initial distance history；B represents velocity equivalent；D represents equivalent acceleration； 

Symbol " | | " represent modulus computing. 

Step 6: satellite machine combined double-base synthetic aperture radar is decoupling

It will cause to move change double-base synthetic aperture radar image fault to the nonorthogonality with orientation coordinate system due to moving change double-base synthetic aperture radar imaging distance.Therefore need respectively to be stripped out the coupling terms in phase and orientation phase, i.e., it is decoupling. 

By the data on scattering point coordinate linear phase to be observed obtained in step 5

Inverse Fourier transform is done along row (i.e. distance to), distance-Doppler numeric field data is obtained

With reference to the related initiation parameter in step one, by data

In the i-th i row data be multiplied by the decoupling function in orientation respectively

Wherein

Represent the value of the i-th i fast time, ii=1...N_r, N_rFor distance sample；f_sFor the sample frequency of Radar Receiver System.Obtain orientation it is decoupling after data

By data of the obtained orientation after decouplingInverse Fourier transform is done along row, frequency of distance-orientation time numeric field data is obtained

To data

In jth j rows data be multiplied by respectively apart from decoupling function

Wherein

Represent the value of the slow time of jth j, jj=1...N_s, N_sFor azimuth sample point, PRF is pulse recurrence frequency,

For constant coefficient.The data after distance decoupling are obtained, and inverse Fourier transform is done along row to it, final imaging results are obtained

Wherein

Carrier wave wave number is represented,

Represent apart from wave number, K '=K-K₀,

For orientation wave number；C is the light velocity, f₀For carrier frequency, f is the frequency corresponding to fast (oblique distance) time, f_aFor the Doppler frequency corresponding to slow (orientation) time, A represents initial distance history；B represents velocity equivalent；D represents equivalent acceleration； 

Symbol " | | " represent modulus computing. 

It is pointed out that there may be the satellite machine combined double-base synthetic aperture radar scene orientation reference function s in the relation being conjugated each other, step of the present invention due to the signal of different synthetic aperture radar transmitting_refSymbol in the phase of (K ', Ka), and the phase Ψ (K) that uses in satellite machine combined double-base synthetic aperture radar nonlinear phase compensates and be decoupling_cmp, Ψ^*(Ka)_cmpAnd Θ^*(K)_cmpSymbol should according to actual synthetic aperture radar launch signal phase function sign modification. 

The essence and innovative point of the present invention is the space-variant in azimuth for satellite machine combined double-base synthetic aperture radar system：I.e. its range migration curve is with the time and apart from the characteristics of changing simultaneously.Using approximate apart from the second order time domain of history in the spatial domain expansion of reference point and reference point apart from history, phase is expressed as a quadratic polynomial on the slow time, and obtains using Stationary phase method the 2-d spectrum of signal.Good focusing effect is obtained by azimuth-range compression.Finally using the linear relationship using scattering point position, the coordinate of distance and bearing is stripped out from coupling terms, correct coordinate is obtained.It is imaged so as to overcome the process that the 2-d spectrum of complexity is calculated and target space-variant is compensated, and realize compared with satellite machine combined double-base synthetic aperture radar under large scene.Present invention could apply to synthetic aperture radar image-forming, the field such as earth remote sensing. 

Brief description of the drawings：

Fig. 1 is the satellite machine combined double-base synthetic aperture radar flight geometrical relationship figure that the specific embodiment of the invention is used. 

WhereinWith

The respectively initial position in a coordinate system of flat pad and receiving platform；X therein_T, y_T, z_TAnd x_R, y_R, z_RThe respectively three-dimensional coordinate of flat pad and receiving platform in a coordinate system； Represent the tested point vector in scene； 

With

Represent the unit vector of scene coordinate axle. 

With

Represent that flat pad and receiving platform radar beam point to unit vector respectively； With

The velocity of transmitter and receiver is represented respectively. 

Fig. 2 is the satellite machine combined double-base synthetic aperture radar system parameter table that invention embodiment is used. 

Fig. 3 is the schematic process flow diagram of method provided by the present invention. 

Fig. 4 is the 9 point target satellite machine combined double-base synthetic aperture radar imaging results that the method provided by the present invention is obtained. 

The stain of 9 square profiles is the satellite machine combined double-base synthetic aperture radar imaging results of the scattering point for 9 square profiles being arranged on ground in figure.This 9 points are represented with letter A, B, C, D, E, F, G, H, I respectively in figure.It can be seen that the method that the present invention is provided can be very good to realize satellite machine combined double-base synthetic aperture radar point target imaging. 

It can be seen that the method that the present invention is provided can be very good to realize satellite machine combined double-base synthetic aperture radar Area Objects imaging. 

Embodiment

The main method for using emulation experiment of the invention is verified that all steps, conclusion are verified correctly all on MATLAB7.0.Specific implementation step is as follows： 

Step 1: producing the emulation data of satellite machine combined double-base synthetic aperture radar using Computer Simulation, the systematic parameter needed for emulation is as shown in Figure 3.And define synthetic aperture radar image-forming space and initialization imaging system parameters； 

Selection is parallel with satellite platform velocity attitude and unit vector in ground level as synthetic aperture radar image-forming space first coordinate base

Second coordinate base in synthetic aperture radar image-forming space is selected in addition

Satellite is initialized with respect to ground speed vector

Receiving platform velocity, i.e. aircraft velocity vector

Flat pad initial position vector

Receiving platform initial position vector

Using formula

Obtain the position vector at n-th of PRF moment of flat pad

Using formulaObtain the position vector at n-th of PRF moment of flat pad

Launch the initial pointing vector of wave beam of radar,The initial pointing vector of wave beam of radar is received,

The initial pointing vector of satellite machine combined double-base synthetic aperture radar system wave beamThe initial angular velocity vector of flat pad radar

The initial angular velocity vector of receiving platform radar

Satellite machine combined double-base synthetic aperture radar system initial angular velocity vector

And utilize formula

Try to achieve parameter：A=524110, B=30.6587, D=96.1151, α_u=-0.8185, α_v=-0.0480,

β_u=-0.0015, β_v=-0.022. 

The systematic parameter for being used to initialize satellite machine combined double-base synthetic aperture radar imaging method that this tests selection is consistent with the parameter provided in table one. 

Step 2: satellite machine combined double-base synthetic aperture radar initial data is compressed. 

By the synthetic aperture radar distance received to echo-signal, write as matrix form according to the pulse repetition period, be denoted as

Row matrix represents the PRF moment, and rectangular array represents echo delay time；The satellite machine combined double-base synthetic aperture radar initial data received is compressed using synthetic aperture radar gauged distance compression method, the satellite machine combined double-base synthetic aperture radar after Range compress is obtained apart from numeric field data, is denoted as

Step 3: satellite machine combined double-base synthetic aperture radar initial data carries out two-dimensional Fourier transform

The echo data stored in the matrix form after the satellite machine combined double-base synthetic aperture radar Range compress obtained to step 2N is along row_r=2000 points of Fourier transformation, N is further along row_s=1200 Fourier transformations, obtain the two-dimensional frequency data of satellite machine combined double-base synthetic aperture radar echo-signal, are designated as

Step 4: satellite machine combined double-base synthetic aperture radar direction reference function is compensated

Using the parameter in step one, a N is generated_s×N_rMatrix, as orientation reference function

Wherein

For N_sPoint vector,

For N_rPoint vector.The two-dimensional frequency data for the satellite machine combined double-base synthetic aperture radar echo-signal that step 3 is obtained

With orientation reference function s_ref(K ', Ka) is multiplied, and obtains the two-dimensional frequency data of the satellite machine combined double-base synthetic aperture radar echo-signal after orientation compensation

Step 5: satellite machine combined double-base synthetic aperture radar nonlinear phase is compensated

The two-dimensional frequency data of satellite machine combined double-base synthetic aperture radar echo-signal after the orientation obtained in step 4 is compensated

N is along the row of data_s=1200 inverse Fourier transforms (IFFT), obtain frequency of distance-orientation time numeric field data of satellite machine combined double-base synthetic aperture radar echo-signal： 

● with reference to the related initiation parameter in step one, and operate following steps： 

1) to data

In the i-th=1 row data be multiplied by vector

Conjugation.Wherein

Represent the value of i-th of slow time, i=1, N_sFor orientation sampled point, PRF is pulse recurrence frequency. 

2) obtain

The 1st row data, take i=2, and repeat 1), until i gets N_sUntill, then we obtain

Whole N_sCapable data. 

By obtained data

N is along row_s=1200 point FFT, and phase is multiplied by its each column data

Then obtain the data on scattering point coordinate linear phase to be observed

Step 6: satellite machine combined double-base synthetic aperture radar is decoupling

By the data on scattering point coordinate linear phase to be observed obtained in step 5

N is along row_r=2000 point IFFT, obtain distance-Doppler numeric field data

● with reference to the related initiation parameter in step one, and operate following steps

1) by data

In the i-th i=1 row data be multiplied by N_s=1200 points of vectors

Wherein

Represent the value of the i-th i fast time, ii=1, N_rFor distance sample, f_sFor radar system sample frequency； 

2) the decoupling rear data in orientation are obtained

The 1st row.Ii=2 is taken, and is repeated 1), until ii gets N_rUntill, then we obtain

Whole N_rCapable data. 

By data of the obtained orientation after decoupling

First N is along row_r=2000 points of FFT, then it is N along row_s=1200 point IFFT, obtain frequency of distance-orientation time numeric field data

● with reference to the related initiation parameter in step one, and operate following steps

1) by data

In jth j=1 row data be multiplied by

Conjugation.Wherein

Represent the value of the slow time of jth j, jj=1, N_sFor azimuth sample point, PRF is pulse recurrence frequency, constant coefficient

2) data after distance decoupling are obtained

The 1st row, take jj=2, and repeat 1), until jj gets N_sUntill.Then we obtain

Whole N_sCapable data. 

3) it is right

N is along row_r=2000 point IFFT, obtain final imaging results

By the specific embodiment of the invention it can be seen that, it is effective that the present invention overcomes satellite machine combined double-base synthetic aperture radar to lack, the problem of frequency domain imaging method of simplicity, the invention provides a kind of satellite machine combined double-base synthetic aperture radar two-dimensional frequency imaging method deployed based on spatial domain, the characteristics of this method and thinking is：Using approximate apart from the second order time domain of history in the spatial domain expansion of reference point and reference point apart from history, phase is expressed as a quadratic polynomial on the slow time, and utilization principle in phase bit obtains the 2-d spectrum of signal.Good focusing effect is obtained by azimuth-range compression.Finally using the linear relationship using scattering point position, the coordinate of distance and bearing is stripped out from coupling terms, correct coordinate is obtained.It is imaged so as to overcome the process that the 2-d spectrum of complexity is calculated and target space-variant is compensated, and realize compared with satellite machine combined double-base synthetic aperture radar under large scene. 

Claims (1)

1. a kind of satellite machine combined SAR two-dimensional frequencies imaging method deployed based on spatial domain, it is characterized in that it comprises the following steps：

Step 1: the initialization of synthetic aperture radar image-forming space and imaging system parameters；

Synthetic aperture radar image-forming space is determined by the mutually orthogonal coordinate base of two in synthetic aperture radar image-forming space, and unit vector ground level in parallel with the velocity attitude of flat pad satellite is defined as first coordinate base in synthetic aperture radar image-forming space, i.e.,

Be defined in ground level, and with first coordinate base in synthetic aperture radar image-forming space

Vertical unit vector is denoted as second coordinate base in synthetic aperture radar image-forming space

Initialization imaging system parameters include：Flat pad velocity, i.e. satellite are denoted as with respect to ground speed vector

Receiving platform velocity, i.e. aircraft velocity vector are denoted as

Flat pad initial position vector, is denoted asReceiving platform initial position vector, is denoted as

The wave number of radar emission electromagnetic wave, is denoted as K₀, the signal bandwidth of radar emission baseband signal is denoted as B, and radar emission signal pulse width is denoted as T_P, radar received wave door continues width, is denoted as T_o, the sample frequency of Radar Receiver System is denoted as f_s, the pulse recurrence frequency of radar system is denoted as PRF；Flat pad initial position vectorReceiving platform initial position vector

Wherein x_T y_T z_TAnd x_R y_R z_RThe 3 d space coordinate of flat pad and receiving platform is represented respectively；Using formula

Obtain the position vector at n-th of PRF moment of flat padUsing formula

Obtain the position vector at n-th of PRF moment of flat pad

N=1 ..., N_sRepresent n-th of PRF moment, N_sFor the sampling number of orientation；

Launch the initial pointing vector of wave beam of radar, be denoted as

Receive the initial pointing vector of wave beam of radar

Represent that the initial beam of radar is pointed to and vector；The initial angular velocity vector of flat pad radar

The initial angular velocity vector of receiving platform radarSatellite machine combined double-base synthetic aperture radar system initial angular velocity and vector

And utilize formula

Parameter is tried to achieve respectively：A, B, D；Wherein：A represents initial distance history；B represents velocity equivalent；D represents equivalent acceleration； 

Symbol " | | " represent modulus computing；

According to satellite machine combined double-base synthetic aperture radar system schema and satellite machine combined double-base synthetic aperture radar observation program, the initialization imaging system parameters that satellite machine combined double-base synthetic aperture radar imaging method needs are known；

Step 2: satellite machine combined double-base synthetic aperture radar initial data carries out Range compress；

The satellite machine combined double-base synthetic aperture radar echo data that receiver is received is denoted as by we

The satellite machine combined double-base synthetic aperture radar echo data received is compressed using synthetic aperture radar gauged distance compression method, the satellite machine combined double-base synthetic aperture radar data after Range compress is obtained, is denoted as

N represents n-th of PRF moment, r be apart from independent variable,

Represent point target vector to be observed；

Step 3: satellite machine combined double-base synthetic aperture radar initial data carries out two-dimensional Fourier transform

The echo data stored in the matrix form after the satellite machine combined double-base synthetic aperture radar Range compress that step 2 is obtained

Fourier transformation is done respectively along row and column, the two-dimensional frequency data of satellite machine combined double-base synthetic aperture radar echo-signal is obtained, is designated as

Step 4: satellite machine combined double-base synthetic aperture radar direction reference function is compensated

The two-dimensional frequency data for the satellite machine combined double-base synthetic aperture radar echo-signal that step 3 is obtained

With orientation reference function

It is multiplied, obtains the two-dimensional frequency data of the satellite machine combined double-base synthetic aperture radar echo-signal after orientation compensation

WhereinCarrier wave wave number is represented,

Represent apart from wave number, K '=K-K₀,

For orientation wave number；C is the light velocity, f₀For carrier frequency, f is the frequency corresponding to the fast time, f_aFor the Doppler frequency corresponding to the slow time, D represents equivalent acceleration；

Step 5: satellite machine combined double-base synthetic aperture radar nonlinear phase is compensated

The two-dimensional frequency data of satellite machine combined double-base synthetic aperture radar echo-signal after the orientation obtained in step 4 is compensated

It is that orientation is inverse Fourier transform IFFT along the row of data, obtains frequency of distance-orientation time numeric field data of satellite machine combined double-base synthetic aperture radar echo-signal：

With reference to the relevant parameter initialized in step one, to data

In the i-th row data be multiplied by respectively

Conjugation；Wherein

Represent the value of i-th of slow time, i=1...N_s, N_sFor azimuth sample point, PRF is pulse recurrence frequency；Obtain

By obtained data

Fourier transformation, and multiplication by constants phase are done along rowThen obtain the data on scattering point coordinate linear phase to be observed

Wherein

Carrier wave wave number is represented,

Represent apart from wave number, K '=K-K₀,

For orientation wave number；C is the light velocity, f₀For carrier frequency, f is the frequency corresponding to the fast time, and fa is the Doppler frequency corresponding to the slow time, and A represents initial distance history；B represents velocity equivalent；D represents equivalent acceleration； 

Symbol " | | " represent modulus computing；

Step 6: satellite machine combined double-base synthetic aperture radar is decoupling

It will cause to move change double-base synthetic aperture radar image fault to the nonorthogonality with orientation coordinate system due to moving change double-base synthetic aperture radar imaging distance；Therefore need respectively to be stripped out the coupling terms in phase and orientation phase, i.e., it is decoupling；

By the data on scattering point coordinate linear phase to be observed obtained in step 5

Along row be distance to inverse Fourier transform is done, obtain distance-Doppler numeric field dataWith reference to the related initiation parameter in step one, by data

In the i-th i row data be multiplied by the decoupling function in orientation respectivelyWherein

Represent the value of the i-th i fast time, ii=1...N_r, N_rFor distance sample；f_sFor the sample frequency of Radar Receiver System；Obtain orientation it is decoupling after data

By data of the obtained orientation after decoupling

Inverse Fourier transform is done along row, frequency of distance-orientation time numeric field data is obtained

To data

In jth j rows data be multiplied by respectively apart from decoupling function

Wherein

Represent the value of the slow time of jth j, jj=1...N_s, N_sFor azimuth sample point, PRF is pulse recurrence frequency,

For constant coefficient；The data after distance decoupling are obtained, and inverse Fourier transform is done along row to it, final imaging results are obtained

Wherein

Carrier wave wave number is represented,

Represent apart from wave number, K '=K-K₀,For orientation wave number；C is the light velocity, f₀For carrier frequency, f is the frequency corresponding to the fast time, f_aFor the Doppler frequency corresponding to the slow time, A represents initial distance history；B represents velocity equivalent；D represents equivalent acceleration； 

Symbol " | | " represent modulus computing. 

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