CN102854506B - Dynamic baseline interference SAR (synthetic aperture radar) compensation method based on back-projection algorithm - Google Patents

Abstract

The invention discloses a phase compensation method for baseline oscillation of an interference SAR (synthetic aperture radar) based on back-projection algorithm. Due to the fact that a baseline changes along with motion of a platform, errors exist in Doppler phase compensation and coherent accumulation of an auxiliary antenna, which causes defocusing of SAR images of the auxiliary antenna. By multiplying a compensating factor to each direction in a synthetic aperture, the effect of a static baseline is achieved, the images are well focused during coherent accumulation, and interference phase images are equivalent to the interference phase images under a static baseline. Better measuring precision than traditional imaging methods is achieved by the method.

Description

A kind of moving base line interference SAR bias control method based on back-projection algorithm

Technical field

Present technique invention belongs to the Radar Technology field, and it has been particularly related to the synthetic aperture radar (SAR) technical field of imaging.

Background technology

Interference synthetic aperture radar (InSAR) be a kind of can after realize the important remote sensing technology of ground high resolving power, high-precision three-dimensional mapping, be one of effective sensor with the fastest developing speed in microwave remote sensor and.Interference synthetic aperture radar has application extremely widely in military affairs, the development of the national economy and scientific research.

Interference SAR is a kind of interfere measurement technique that grows up on the SAR basis, and it interferes processing by the echo data that a plurality of receiving antennas observations are obtained, and obtains ground elevation figure (DEM).Interference SAR has two kinds of mode of operations: repeat track is interfered and double antenna is interfered.Because the repeat track pattern has been brought time decorrelation and Doppler shift decorrelation, make and interfere the complex pattern correlativity greatly to reduce, thereby reduced the quality of interferogram.The double antenna list interference SAR system that navigated has higher measurement of higher degree precision, is widely used in topographic mapping etc., adopts the double antenna list pattern of navigating in the present invention.building stable baseline is the key that guarantees double antenna interference SAR system measurement of higher degree precision, yet the baseline shock at the interference SAR system duration of work is difficult to avoid, as document WANG Bingnan, ZHANG Fan, XIANG Maosheng, the baseline shock of mentioning in " Influence of baseline oscillations on SAR interferometric phase " brings kinematic error to the interference SAR echoed signal, not only affect auxiliary image imaging quality, the more important thing is and bring Interferometric phase error, reduce the interferogram quality, affect the interferometry precision.

When utilizing traditional rear orientation projection method (BP) to carry out imaging processing to interference SAR, because baseline shock causes main and auxiliary antenna movement track different, auxiliary image imaging Quality Down, the interferogram Quality Down, and due to baseline along with the orientation to constantly different and different, when utilizing baseline to carry out the inverting of InSAR elevation, cause baseline to select problem, so must address the above problem guarantee interference SAR system altimetry precision.

Summary of the invention

In order to solve under moving baseline (baseline shock) auxiliary image imaging Quality Down in the interference synthetic aperture radar imaging processing, the interferogram Quality Down, elevation inverting baseline such as chooses at the problem, the invention provides a kind of moving baseline interference synthetic aperture radar phase compensating method based on back-projection algorithm, adopt method of the present invention can obtain the measuring accuracy higher than traditional formation method.

Content of the present invention for convenience of description, at first make following term definition:

Definition 1, interference synthetic aperture radar (InSAR)

Interference synthetic aperture radar (InSAR) is a kind of interfere measurement technique that grows up on the SAR basis, and it obtains ground elevation figure by accepting the echo data that antennas observation obtains and interfere processing a plurality of.

Definition 2, interference synthetic aperture radar main antenna, auxiliary antenna:

The main antenna of interference synthetic aperture radar is the antenna that i.e. emission receives again, and auxiliary antenna is to receive only an antenna of not launching.

Definition 3, synthetic-aperture radar gauged distance compression method

Synthetic-aperture radar gauged distance compression method refers to utilize the synthetic-aperture radar emission parameter, adopts following formula generating reference signal, and adopts the distance of matched filtering technique Technologies Against Synthetic Aperture Radar to carry out the process of filtering to signal.

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

Wherein, f (t) is reference function, and B is the signal bandwidth of radar emission baseband signal, T _PBe the radar emission signal pulse width, t is independent variable, span from

Arrive See document " radar imagery technology " for details, protect polished grade and write, the Electronic Industry Press publishes.

Definition 4, mapping scene discretize scattering point

Continuous scene in mapping scene discretize scattering point refers to according to the systemic resolution of synthetic-aperture radar, mapping is with is separated into pixel one by one, and these pixels are exactly the scattering point of wanting imaging.

Definition 5, apart from history, range gate:

Apart from history refer to the dual-mode antenna phase center in the scene scattering point apart from sum.

Range gate refers to the position of echo data in whole echo data of respective distances history.

Definition 6, synthetic aperture and slow time

The synthetic aperture of interference synthetic aperture radar system refer to for the scattering point of mapping in scene from enter the radar beam range of exposures to leave the radar beam range of exposures during this period of time in, the length of passing by in the radar beam center.

The slow time of interference synthetic aperture radar system refers to that transmit-receive platform flies over a needed time of synthetic aperture, due to radar with certain repetition period T _rThe emission received pulse, the slow time can be expressed as the time variable t of a discretize _s=nT _r, n=1,2 ..., N, N are the discrete number of slow time in a synthetic aperture, T _rBe the repetition period.

Definition 7, the cosine law

For arbitrary triangle, any one side square equal two multiplicatrixs other both sides square and that deduct the cosine of these both sides and their angles, see wikipedia for details.

Definition 8, moving baseline

At the interference SAR system duration of work, the spacing between two antennas is baseline, due to the shake of platform, and pitching, some factors such as rolling cause baseline to change along with the difference in the platform motion moment, have formed moving baseline.

Definition 9, synthetic-aperture radar standard Singh interpolation method

Synthetic-aperture radar standard Singh interpolation method refers to for a bandlimited signal, in the situation that satisfy sampling thheorem, adopting convolution kernel is the function h (x) of sinc, and to be that window is long be W to the length of h (x).

$h\left(x\right)=\sin c\left(x\right)=\frac{\sin \left(\mathrm{\πx}\right)}{\mathrm{\πx}}$

Carry out discrete signal g _d(i) interpolation obtains desired signal after interpolation

$g\left(x\right)=\underset{i}{\mathrm{\Σ}}{g}_d\left(i\right)\sin c(x-i)$

See document " radar imagery technology " for details, protect polished grade and write, the Electronic Industry Press publishes.

Definition 10, interference synthetic aperture radar rear orientation projection's formation method (BP)

Interference synthetic aperture radar rear orientation projection formation method (BP) is applied to traditional BP formation method in interference synthetic aperture radar.The method at first calculation method for scattering put corresponding synthetic aperture in the time distance of each antenna phase center historical, select the data of respective distance unit, the Doppler phase compensation of the column criterion of going forward side by side and coherent accumulation obtain the scattering coefficient of this point.The method process flow diagram is seen patent accompanying drawing.

Angle function in definition 11, MATLAB

Angle function in the MATLAB function library is the phase extraction function, sees document " the practical study course of MATLAB " for details, and Zheng Aqi etc. write, and the Electronic Industry Press publishes.

Definition 12, interferometric phase image

Respectively the echo data of two antennas carried out obtaining two width SAR images after imaging processing, calculate the phase differential of corresponding pixel points in two width images, form interferometric phase image.

The invention provides a kind of moving baseline interference synthetic aperture radar phase compensating method based on back-projection algorithm, it comprises following step:

Step 1, the moving baseline interference synthetic aperture radar imaging system parameter of initialization:

Be initialized to as systematic parameter and comprise: the platform speed vector, note is done , the main and auxiliary antenna initial position of platform vector, note is done

, the scene center position vector, note is done , in synthetic aperture time, roll shake angle, yaw angle are remembered respectively and are α (n)=[α ₁, α ₂..., α _N], α ' (n)=[α ' ₁, α ' ₂..., α ' _N], α ₁Roll shake angle degree during for n=1, α ₂Roll shake angle degree during for n=2, α _NRoll shake angle degree during for n=N, wherein, n is the orientation moment, the span of n is: n=1,2 ..., N, N are the discrete number of slow time in a synthetic aperture; The radar carrier frequency, note is K _rBase length, note is J; The signal bandwidth of radar emission baseband signal, note is B, the radar emission signal pulse width, note is T _p, the sample frequency of Radar Receiver System, note is f _cThe pulse repetition rate of radar system, note is PRF; Antenna length, note is D; The length of synthetic aperture of radar, note is L; The main and auxiliary antenna echo data of radar are remembered respectively and are done

Above-mentioned parameter is the canonical parameter of interference synthetic aperture radar system, wherein, and radar carrier frequency K _r, base length J, the signal bandwidth B of radar emission baseband signal, radar emission signal pulse width T _p, the sample frequency f of Radar Receiver System _c, antenna length D, the length of synthetic aperture L of radar determines in the pulse repetition rate PRF interference synthetic aperture radar design process of radar system; Wherein, platform speed vector , platform initial position vector

, the scene center position vector

, in synthetic aperture time, angle [alpha] (n)=[α is shaken to the moment in each orientation ₁, α ₂..., α _N], α ' (n)=[α ' ₁, α ' ₂..., α ' _N], n=1 wherein, 2 ..., N, the main and auxiliary antenna echo data of radar Determine in the design of interference synthetic aperture radar observation program.According to interference synthetic aperture radar system schema and interference synthetic aperture radar observation program, move being initialized to of baseline interference synthetic aperture radar fast imaging method needs and be known as systematic parameter.

Step 2, echo data Range compress:

Adopt traditional synthetic-aperture radar gauged distance compression method to the main and auxiliary antenna echo data of the synthetic-aperture radar in step 1

Carry out Range compress, obtain the main and auxiliary antenna data of synthetic aperture radar after Range compress, note is done

Step 3, the calculating roll angle bias control factor:

According to step 1 as can be known: roll shake angle in the synthetic aperture time, note is α (n)=[α ₁, α ₂..., α _N], wherein, n is the orientation moment, the span of n is: and n=1,2 ..., N, N are the discrete number of slow time in a synthetic aperture; α ₁Roll shake angle degree during for n=1, α ₂Roll shake angle degree during for n=2, α _NRoll shake angle degree during for n=N; To any one orientation moment n, according to the cosine law, have

$R_1(n,{\stackrel{\→}{P}}_{\mathrm{\ω}})=R_{11}(n,{\stackrel{\→}{P}}_{\mathrm{\ω}})-{2\mathrm{JR}}_1(n,{\stackrel{\→}{P}}_{\mathrm{\ω}})\sin ({\mathrm{\α}}_n/2)\cos (\mathrm{\θ}-{\mathrm{\α}}_n/2)---\left(1\right)$

Wherein

Be expressed as a scattering point in the image field scape,

Distance

The scattering point of the main antenna of expression roll angle shake in the imaging scene

Distance, The scattering point of the main antenna that expression does not have a roll angle shake in the imaging scene

Distance, J represents base length, α _nThe expression orientation is the roll shake angle degree of n constantly, and θ is the scene center incident angle, and n is the orientation moment, and the span of n is: n=1, and 2 ..., N, N are the discrete number of slow time in a synthetic aperture;

To any one orientation moment n, according to the cosine law, have

$R_2(n,{\stackrel{\→}{P}}_{\mathrm{\ω}})=R_{12}(n,{\stackrel{\→}{P}}_{\mathrm{\ω}})-{2\mathrm{JR}}_2(n,{\stackrel{\→}{P}}_{\mathrm{\ω}})\sin ({\mathrm{\α}}_n/2)\cos (\mathrm{\π}-\mathrm{\θ}+{\mathrm{\α}}_n/2)---\left(2\right)$

Wherein

Be expressed as a scattering point in the image field scape, Distance The scattering point of the auxiliary antenna that there is roll angle shake in expression in the imaging scene

Distance,

The scattering point of the auxiliary antenna that expression does not have a roll angle shake in the imaging scene

Distance, J represents base length, α _nThe expression orientation is the roll shake angle degree of n constantly, and θ is the scene center incident angle, and n is the orientation moment.

$\frac{R_{11}(n,{\stackrel{\→}{P}}_{\mathrm{\ω}})+R_{12}(n,{\stackrel{\→}{P}}_{\mathrm{\ω}})}{R_1(n,{\stackrel{\→}{P}}_{\mathrm{\ω}})+R_2\left(n,{\stackrel{\→}{P}}_{\mathrm{\ω}}\right)}\≈1---\left(3\right)$

According to formula (3), formula (1) is deducted formula (2) obtain the roll angle bias control factor

X(n)＝2Jsin(α _n/2)cos(θ-α _n/2)

Wherein n is the orientation moment, and J represents base length, α _nThe expression orientation is the roll shake angle degree of n constantly, and θ is the scene center incident angle.For first orientation to, obtaining the roll angle bias control factor is X (1), be X (2) for second orientation to obtaining the roll angle bias control factor, ..., ..., constantly obtaining the roll angle bias control factor for n orientation is X (n), constantly obtains roll angle bias control factor sequence for all orientation

N=1,2 ..., N, N are the discrete number of slow time in a synthetic aperture.

Step 4, the calculating crab angle bias control factor:

According to step 1, have in a scattering point synthetic aperture N orientation to, driftage shake angle degree sequence be α ' (n)=[α ' ₁, α ' ₂..., α ' _N], n=1 wherein, 2 ..., N, N are positive integer, N is the discrete number of slow time in a synthetic aperture: α ' ₁Driftage shake angle degree during for n=1, α ' ₂Driftage shake angle degree during for n=2 ... ..., α ' _NDriftage shake angle degree during for n=N.To any one orientation moment n, according to the cosine law, have

${\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="2012103321861100003DEST\_PATH\_IMAGE001.png"\; state="\{\{state\}\}">R</figure-callout>}}_1^{\&prime;}(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})=R_{11}^{\&prime;}(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})-2{\mathrm{JR}}_1^{\&prime;}(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})\sin ({\mathrm{\&alpha;}}_n^{\&prime;}/2)\sin ({\mathrm{\&alpha;}}_n^{\&prime;}/2)\sin \left(\mathrm{\&theta;}\right)---\left(4\right)$

Wherein Be expressed as a scattering point in the image field scape,

Distance

The scattering point of the main antenna of expression crab angle shake in the imaging scene

Distance,

The scattering point P ' of the main antenna that expression does not have a crab angle shake in the imaging scene _ωDistance, J represents base length, α ' _nThe expression orientation is the driftage shake angle degree of n constantly, and θ is the scene center incident angle, and n is the orientation moment.

To any one orientation moment n, according to the cosine law, have

$R_2^{\&prime;}(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})=R_{12}^{\&prime;}(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})+2{\mathrm{JR}}_2^{\&prime;}(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})\sin ({\mathrm{\&alpha;}}_n^{\&prime;}/2)\sin ({\mathrm{\&alpha;}}_n^{\&prime;}/2)\sin \left(\mathrm{\&theta;}\right)---\left(5\right)$

Wherein

Be expressed as a scattering point in the image field scape, Distance The scattering point of the auxiliary antenna of expression crab angle shake in the imaging scene

Distance,

The scattering point P ' of the auxiliary antenna that expression does not have a crab angle shake in the imaging scene _ωDistance, J represents base length, α ' _nThe expression orientation is the driftage shake angle degree of n constantly, and θ is the scene center incident angle, and n is the orientation moment.

$\frac{R_{11}^{\&prime;}(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})+R_{12}^{\&prime;}(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})}{{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="2012103321861100003DEST\_PATH\_IMAGE001.png"\; state="\{\{state\}\}">R</figure-callout>}}_1^{\&prime;}(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})+R_2^{\&prime;}(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})}\&ap;1---\left(6\right)$

According to formula (6), formula (4) is deducted formula (5) get the crab angle bias control factor

Y(n)＝2Jsin(α' _n/2)sin(α' _n/2)sin(θ)

Wherein n is the orientation moment, and J represents base length, α ' _nThe expression orientation is the crab angle shake angle degree of n constantly, and θ is the scene center incident angle.For first orientation to, obtaining the crab angle bias control factor is Y (1), be Y (2) for second orientation to obtaining the crab angle bias control factor, ..., ..., constantly obtaining the crab angle bias control factor for n orientation is Y (n), constantly obtains crab angle bias control factor sequence for all orientation

N=1,2 ..., N, N are the discrete number of slow time in a synthetic aperture.

Step 5, the main and auxiliary antenna distance history of calculating:

To a scattering point in the imaging scene

Choose orientation n constantly, obtain main antenna apart from history Wherein

The expression main antenna in the orientation constantly n to scattering point Distance;

To a scattering point in the imaging scene

Choose orientation n constantly, obtain auxiliary antenna distance history

Wherein

The expression main antenna in the orientation constantly n to scattering point

Distance,

Represent auxiliary antenna in the orientation constantly n to scattering point Distance;

Data interpolating, resampling after step 6, Range compress

According to the method that traditional standard Singh interpolation resamples, obtain the long W of being of a window ₀Sinc function $h\left(x\right)=\sin c\left(x\right)=\frac{\sin \left(\mathrm{\&pi;x}\right)}{\mathrm{\&pi;x}}.$

The n constantly in the orientation, according to the main antenna in step 5 apart from history and conventional interference synthetic-aperture radar rear orientation projection's formation method (BP), the main antenna echo data from step 2

Middle taking-up window is long is W ₀Data, adopting traditional standard Singh interpolation method is W to taking out rear length ₀Data carry out interpolation, the data after obtaining the main antenna interpolation and resampling Be the orientation moment.

At orientation moment n, according to the auxiliary antenna distance history in step 5 and conventional interference synthetic-aperture radar rear orientation projection's formation method (BP), the auxiliary antenna echo data from step 2

Middle taking-up window is long is W ₀Data, adopting traditional standard Singh interpolation method is W to taking out rear length ₀Data carry out interpolation, obtain the data after auxiliary antenna interpolation resamples

Be the orientation moment.

For first orientation moment, obtain the main antenna data after interpolation resamples

Auxiliary antenna data

For second orientation moment, obtain the main antenna data after interpolation resamples

Auxiliary antenna data

For n the orientation moment, obtain the main antenna data after interpolation resamples

Auxiliary antenna data

For all slow time, obtain the main antenna data sequence C after interpolation resamples _1n, n=1,2 ..., N, auxiliary antenna data sequence C _2n, n=1,2 ..., N, N are the discrete number of slow time in a synthetic aperture.

After step 7, main antenna interpolation resample, data are sued for peace along slow time coherence:

The phase compensating factor of main antenna and auxiliary antenna is K (n), and the computing formula of K (n) is:

Wherein

For main antenna corresponding apart from history, n=1,2 ..., N, N are the discrete number of slow time in a synthetic aperture, f _cBe the radar sampling frequency, c is the light velocity.

At orientation moment n, with the data after in step 6, resulting interpolation resamples Multiply each other with the phase compensating factor K (n) of main antenna, obtain the data after phase compensation For first orientation constantly, being compensated rear data is

For second orientation constantly, being compensated rear data is

For N orientation constantly, being compensated rear data is

Finally obtain data sequence A after the compensation constantly of all orientation _1n, n=1,2 ..., N, N are the discrete number of slow time in a synthetic aperture, for a scattering point

Data addition after the phase compensation constantly of all orientation is obtained a scattering point

The main antenna imaging data: A ₁₁+ A ₁₂+ ...+A _1n+ ...+A _1N

After step 8, auxiliary antenna interpolation resample, data are sued for peace along slow time coherence:

The phase compensating factor of main antenna and auxiliary antenna is K (n), and the computing formula of K (n) is: Wherein

For main antenna corresponding apart from history, n=1,2 ..., N, N are the discrete number of slow time in a synthetic aperture, f _cBe the radar sampling frequency, c is light velocity P ₁

At orientation moment n, with the data after in step 6, resulting interpolation resamples

The bias control factor that obtains with phase compensating factor K (n), step 3,4

Multiply each other, obtain the data after phase compensation

For first orientation constantly, being compensated rear data is For second orientation constantly, being compensated rear data is

For N orientation constantly, being compensated rear data is Finally obtain data sequence A after the compensation constantly of all orientation _2n, n=1,2 ..., N, N are the discrete number of slow time in a synthetic aperture, for a scattering point

Data addition after the phase compensation constantly of all orientation is obtained a scattering point

Auxiliary antenna imaging data: A ₂₁+ A ₂₂+ ...+A _2n+ ...+A _2N

Step 9, whole scene imaging

To each scattering point in the imaging scene, repeating step 5 obtains the main and auxiliary antenna imaging data of all scattering points in the imaging scene to step 8, namely obtains main antenna single width SAR image and the auxiliary antenna single width SAR image of whole imaging scene.

With main antenna imaging data and auxiliary antenna imaging data conjugate multiplication, get phase place according to traditional MATLAB function angle method, obtain interferometric phase image.

Step 5 is moving baseline interference synthetic aperture radar bias control method based on back-projection algorithm to the imaging process of step 9, and its method block scheme is seen accompanying drawing 1.

Principle of the present invention: along with the platform motion changes, have error due to baseline when auxiliary antenna is carried out Doppler phase compensation and coherent accumulation, can cause defocusing of auxiliary antenna SAR image like this.We to multiply by a compensating factor, make its equivalence for the motionless situation of baseline by each orientation in Technologies Against Synthetic Aperture, just can well make the figure image focu like this when carrying out coherent accumulation.Finally the equivalence of our interferometric phase image is the interferometric phase image of baseline under motionless.Essence of the present invention be for baseline in actual interference synthetic aperture radar imaging along with the orientation to the time Variation Features, adopt a kind of BP imaging technique based on phase compensation, the most moving base line interference SAR equivalence is the interference SAR imaging processing under motionless baseline case, has well solved the problem of moving baseline interference synthetic aperture radar imaging.

Innovative point of the present invention is the auxiliary image imaging Quality Down that causes for baseline shock in actual conditions, interferometric phase Quality Down and elevation inverting baseline such as choose at the problem, a kind of moving base line interference SAR bias control method based on BP is proposed, moving base line interference SAR is converted into interference SAR imaging problem under motionless baseline, thereby has well solved the interference SAR imaging problem that baseline shock brings.

The invention has the advantages that and solve the auxiliary image quality decrease that the traditional BP formation method occurs when moving base line interference SAR is carried out imaging, interferometric phase Quality Down and elevation inverting baseline On The Choice, for real flight conditions, can obtain the measuring accuracy higher than traditional formation method by the BP imaging after bias control.The present invention is applied to the fields such as synthetic aperture radar image-forming.

Description of drawings

Fig. 1 is the moving base line interference SAR bias control algorithm flow chart based on BP provided by the invention

Wherein, phase compensating factor can be calculated by step 5 in instructions, and the bias control factor can be calculated by step 3 in instructions, the synthetic-aperture radar gauged distance compression method that Range compress is described for definition 3.Interpolation/resampling and coherent accumulation are the standard method of two-dimentional rear orientation projection formation method, and K (n) is the main antenna phase compensating factor in step 7,

Be the roll angle bias control factor in step 3,

Be the crab angle bias control factor in step 4.

Fig. 2 is the moving baseline interference synthetic aperture radar flight geometric relationship figure that the specific embodiment of the invention adopts.

Wherein, O is true origin, X, and Y, Z represents system coordinates,

Be a scattering point in three-dimensional mapping scene,

The platform speed vector, at orientation moment n-1, R1-APC (n-1) expression main antenna n-1 antenna phase center constantly, the auxiliary antenna n-1 of R2-APC (n-1) expression antenna phase center constantly,

Expression main antenna n-1 is constantly apart from scattering point

Distance,

Represent that auxiliary antenna n-1 is constantly apart from scattering point

Distance; At orientation moment n, R1-APC (n) expression main antenna n antenna phase center constantly, the auxiliary antenna n of R2-APC (n) expression antenna phase center constantly,

Expression main antenna n is constantly apart from scattering point

Distance,

Represent that auxiliary antenna n is constantly apart from scattering point

Distance; At orientation moment n+1, R1-APC (n+1) expression main antenna n+1 antenna phase center constantly, the auxiliary antenna n+1 of R2-APC (n+1) expression antenna phase center constantly, Expression main antenna n+1 is constantly apart from scattering point

Distance,

Represent that auxiliary antenna n+1 is constantly apart from scattering point Distance.

Fig. 3 is the moving baseline interference synthetic aperture radar system parameter table that the invention embodiment adopts.

Embodiment

The present invention mainly adopts the method for emulation experiment to verify, institute in steps, conclusion all on VC++, MATLAB7.0 checking correct.Concrete implementation step is as follows:

Step 1, the moving baseline interference synthetic aperture radar imaging system parameter of initialization:

Be initialized to as systematic parameter and comprise: platform speed vector [0 150 0], speed unit is m/s, the main and auxiliary antenna initial position of platform vector [0 0 6000], [10 0 6000], scene center position vector [8,000 0 0], unit is m, and in the synthetic aperture time, each orientation to moment roll, driftage and pitching shake angle is Unit is degree, radar carrier frequency 10GHz, base length 10m, the signal bandwidth 150MHz of radar emission baseband signal, radar emission signal pulse width 1us, the sample frequency 300MHz of Radar Receiver System, the pulse repetition rate 500Hz of radar system, antenna length 2m, the length of synthetic aperture 150m of radar.

Step 2, echo data Range compress:

Adopt traditional synthetic-aperture radar gauged distance compression method to the main and auxiliary antenna echo data of the synthetic-aperture radar in step 1

Carry out Range compress, obtain the main and auxiliary antenna data of synthetic aperture radar after Range compress, note is done

Step 3, the calculating roll angle bias control factor:

Defining a scattering point synthetic aperture interior orientation moment number is 500, and roll shake angle degree sequence is α (n)=[α ₁, α ₂..., α ₅₀₀], n=1 wherein, 2 ..., 500, α ₁Roll shake angle degree during for n=1, α ₂Roll shake angle degree during for n=2, α ₅₀₀Roll shake angle degree during for n=500 to any one orientation moment n, according to the cosine law, has

$R_1(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})=R_{11}(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})-{2\mathrm{JR}}_1(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})\sin ({\mathrm{\&alpha;}}_n/2)\cos (\mathrm{\&theta;}-{\mathrm{\&alpha;}}_n/2)---\left(1\right)$

Wherein

Be expressed as a scattering point in the image field scape,

Distance

The scattering point of the main antenna of expression roll angle shake in the imaging scene Distance,

The scattering point of the main antenna that expression does not have a roll angle shake in the imaging scene

Distance, J represents base length, α _nThe expression orientation is the roll shake angle degree of n constantly, and θ is the scene center incident angle, and n is the orientation moment.

To any one orientation moment n, according to the cosine law, have

$R_2(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})=R_{12}(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})-{2\mathrm{JR}}_2(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})\sin ({\mathrm{\&alpha;}}_n/2)\cos (\mathrm{\&pi;}-\mathrm{\&theta;}+{\mathrm{\&alpha;}}_n/2)---\left(2\right)$

Wherein

Be expressed as a scattering point in the image field scape,

Distance

The scattering point of the auxiliary antenna of expression roll angle shake in the imaging scene Distance,

The scattering point of the auxiliary antenna that expression does not have a roll angle shake in the imaging scene

Distance, J represents base length, α _nThe expression orientation is the roll shake angle degree of n constantly, and θ is the scene center incident angle, and n is the orientation moment.

According to formula (3), formula (1) is deducted formula (2) get the roll angle bias control factor

X(n)＝2Jsin(α _n/2)cos(θ-α _n/2)

Wherein n is the orientation moment, and J represents base length, α _nThe expression orientation is the roll shake angle degree of n constantly, and θ is the scene center incident angle.For first orientation to, obtaining the roll angle bias control factor is X (1), be X (2) for second orientation to obtaining the roll angle bias control factor, constantly obtaining the roll angle bias control factor for n orientation is X (n), constantly obtains roll angle bias control sequence for all orientation N=1,2 ..., 500.

Step 4, the calculating crab angle bias control factor:

Define have in a scattering point synthetic aperture 500 orientation to, driftage shake angle degree sequence be α ' (n)=[α ' ₁, α ' ₂..., α ' ₅₀₀], n=1 wherein, 2 ..., 500, α ' ₁Driftage shake angle degree during for n=1, α ' ₂Driftage shake angle degree during for n=2, α ' ₅₀₀Driftage shake angle degree during for n=5.To any one orientation moment n, according to the cosine law, have

${\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="2012103321861100003DEST\_PATH\_IMAGE001.png"\; state="\{\{state\}\}">R</figure-callout>}}_1^{\&prime;}(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})=R_{11}^{\&prime;}(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})-2{\mathrm{<figure-callout\; id="1"\; label="JR"\; filenames="2012103321861100003DEST\_PATH\_IMAGE001.png"\; state="\{\{state\}\}">JR</figure-callout>}}_1^{\&prime;}(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})\sin ({\mathrm{\&alpha;}}_n^{\&prime;}/2)\sin ({\mathrm{\&alpha;}}_n^{\&prime;}/2)\sin \left(\mathrm{\&theta;}\right)---\left(4\right)$

Wherein

Be expressed as a scattering point in the image field scape,

Distance

The scattering point of the main antenna of expression crab angle shake in the imaging scene

Distance,

The scattering point of the main antenna that expression does not have a crab angle shake in the imaging scene

Distance, J represents base length, α ' _nThe expression orientation is the driftage shake angle degree of n constantly, and θ is the scene center incident angle, and n is the orientation moment.

To any one orientation moment n, according to the cosine law, have

$R_2^{\&prime;}(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})=R_{12}^{\&prime;}(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})+{2\mathrm{JR}}_2^{\&prime;}(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})\sin ({\mathrm{\&alpha;}}_n^{\&prime;}/2)\sin ({\mathrm{\&alpha;}}_n^{\&prime;}/2)\sin \left(\mathrm{\&theta;}\right)---\left(5\right)$

Wherein

Be expressed as a scattering point in the image field scape, Distance

The scattering point of the auxiliary antenna of expression crab angle shake in the imaging scene

Distance,

The scattering point of the auxiliary antenna that expression does not have a crab angle shake in the imaging scene

Distance, J represents base length, α ' _nThe expression orientation is the driftage shake angle degree of n constantly, and θ is the scene center incident angle, and n is the orientation moment.

According to formula (6), formula (4) is deducted formula (5) get the crab angle bias control factor

Y(n)＝2Jsin(α' _n/2)sin(α' _n/2)sin(θ)

Wherein n is the orientation moment, and J represents base length, α ' _nThe expression orientation is the crab angle shake angle degree of n constantly, and θ is the scene center incident angle.For first orientation to, obtaining the crab angle bias control factor is Y (1), be Y (2) for second orientation to obtaining the crab angle bias control factor, constantly obtaining the crab angle bias control factor for n orientation is Y (n), constantly obtains crab angle bias control sequence for all orientation N=1,2 ..., 500.

Step 5, the main and auxiliary antenna distance history of calculating:

To a scattering point in the imaging scene

Choose orientation n constantly, obtain main antenna apart from history

Wherein

The expression main antenna in the orientation constantly n to scattering point

Distance;

To a scattering point in the imaging scene

Choose orientation n constantly, obtain auxiliary antenna distance history Wherein The expression main antenna in the orientation constantly n to scattering point

Distance,

Represent auxiliary antenna in the orientation constantly n to scattering point

Distance;

Data interpolating, resampling after step 6, Range compress

The requirement that resamples according to traditional standard Singh interpolation obtains the long W of being of a window ₀Sinc function $h\left(x\right)=\sin c\left(x\right)=\frac{\sin \left(\mathrm{\&pi;x}\right)}{\mathrm{\&pi;x}}.$

The n constantly in the orientation, according to the main antenna in step 5 apart from history and define traditional back-projection algorithm in 10, the main antenna echo data from step 2 Middle taking-up window is long is W ₀Data, adopt traditional standard Singh interpolation method to length W ₀Carry out interpolation for the data after taking out, obtain the data after the main antenna interpolation resamples

N is the orientation moment.

The n constantly in the orientation is according to the auxiliary antenna distance history in step 5 and define traditional back-projection algorithm in 10, the auxiliary antenna echo data from step 2 Middle taking-up window is long is W ₀Data, adopt traditional standard Singh interpolation method to length W ₀Carry out interpolation for the data after taking out, obtain the data after auxiliary antenna interpolation resamples

N is the orientation moment.

For first orientation moment, obtain the main antenna data after interpolation resamples

Auxiliary antenna data

For second orientation moment, obtain the main antenna data after interpolation resamples

Auxiliary antenna data

For n the orientation moment, obtain the main antenna data after interpolation resamples

Auxiliary antenna data For all slow time, obtain the main antenna data sequence C after interpolation resamples _1n, n=1,2 ..., 500, auxiliary antenna data sequence C _1n, n=1,2 ..., 500.

After step 7, main antenna interpolation resample, data are sued for peace along slow time coherence:

The phase compensating factor of main antenna and auxiliary antenna is K (n), and the computing formula of K (n) is:

Wherein

For main antenna corresponding apart from history, n=1,2 ..., 500, f _cBe the radar sampling frequency, c is the light velocity.

At orientation moment n, with the data after in step 6, resulting interpolation resamples Multiply each other with phase compensating factor K (n), obtain the data after phase compensation

For first orientation constantly, being compensated rear data is For second orientation constantly, being compensated rear data is

For n orientation constantly, being compensated rear data is Finally obtain data sequence A after the compensation constantly of all orientation _1n, n=1,2 ..., 500, the data addition after the phase compensation constantly of all orientation obtains a scattering point

The main antenna imaging data.

After step 8, auxiliary antenna interpolation resample, data are sued for peace along slow time coherence:

The phase compensating factor of main antenna and auxiliary antenna is K (n), and the computing formula of K (n) is: Wherein

For main antenna corresponding apart from history, n=1,2 ..., 500, f _cBe the radar sampling frequency, c is the light velocity.

At orientation moment n, with the data after in step 6, resulting interpolation resamples

The bias control factor that obtains with phase compensating factor K (n), step 3,4

Multiply each other, obtain the data after phase compensation

For first orientation constantly, being compensated rear data is

For second orientation constantly, being compensated rear data is

For n orientation constantly, being compensated rear data is

Finally obtain data sequence A after the compensation constantly of all orientation _2n, n=1,2 ..., 500, the data addition after the phase compensation constantly of all orientation obtains a scattering point Auxiliary antenna imaging data.

Step 9, whole scene imaging

To each scattering point in the imaging scene, repeating step 5 obtains the main and auxiliary antenna imaging data of all scattering points in the imaging scene to step 8, namely gets main antenna single width SAR image and the auxiliary antenna single width SAR image of whole imaging scene.With main antenna imaging results and auxiliary antenna imaging results conjugate multiplication, get phase place according to the MATLAB function angle in definition 12, finally obtain interferometric phase image.

Can find out by the specific embodiment of the invention, moving base line interference SAR bias control method based on back-projection algorithm provided by the present invention can well solve the bad problem of auxiliary figure image focu, and will move base line interference SAR imaging equivalence for the interference SAR imaging under motionless baseline, only need to come the inverting elevation with an identical equivalent baseline like this in follow-up elevation inverting, and not need to come the inverting elevation with a plurality of baselines.

Claims (1)

1. moving baseline interference synthetic aperture radar phase compensating method based on back-projection algorithm is characterized in that it comprises following step:

Step 1, the moving baseline interference synthetic aperture radar imaging system parameter of initialization:

Be initialized to as systematic parameter and comprise: the platform speed vector, note is done , the main and auxiliary antenna initial position of platform vector, note is done

The scene center position vector, note is done

, in synthetic aperture time, roll shake angle, yaw angle are remembered respectively and are α (n)=[α ₁, α ₂..., α _N], α ' (n)=[α ' ₁, α ' ₂..., α ' _N], α ₁Roll shake angle degree during for n=1, α ₂Roll shake angle degree during for n=2, α _NRoll shake angle degree during for n=N, wherein, n is the orientation moment, the span of n is: n=1,2 ..., N, N are the discrete number of slow time in a synthetic aperture; The radar carrier frequency, note is K _rBase length, note is J; The signal bandwidth of radar emission baseband signal, note is B, the radar emission signal pulse width, note is T _p, the sample frequency of Radar Receiver System, note is f _cThe pulse repetition rate of radar system, note is PRF; Antenna length, note is D; The length of synthetic aperture of radar, note is L; The main and auxiliary antenna echo data of radar are remembered respectively and are done

Above-mentioned parameter is the canonical parameter of interference synthetic aperture radar system, wherein, and radar carrier frequency K _r, base length J, the signal bandwidth B of radar emission baseband signal, radar emission signal pulse width T _p, the sample frequency f of Radar Receiver System _c, antenna length D, the length of synthetic aperture L of radar determines in the pulse repetition rate PRF interference synthetic aperture radar design process of radar system; Wherein, platform speed vector

, platform initial position vector

, the scene center position vector

, in synthetic aperture time, angle [alpha] (n)=[α is shaken to the moment in each orientation ₁, α ₂..., α _N], α ' (n)=[α ' ₁, α ' ₂..., α ' _N], n=1 wherein, 2 ..., N, the main and auxiliary antenna echo data of radar

Determine in the design of interference synthetic aperture radar observation program; According to interference synthetic aperture radar system schema and interference synthetic aperture radar observation program, move being initialized to of baseline interference synthetic aperture radar fast imaging method needs and be known as systematic parameter;

Step 2, echo data Range compress:

Adopt traditional synthetic-aperture radar gauged distance compression method to the main and auxiliary antenna echo data of the synthetic-aperture radar in step 1 Carry out Range compress, obtain the main and auxiliary antenna data of synthetic aperture radar after Range compress, note is done

Step 3, the calculating roll angle bias control factor:

According to step 1 as can be known: roll shake angle in the synthetic aperture time, note is α (n)=[α ₁, α ₂..., α _N], wherein, n is the orientation moment, the span of n is: and n=1,2 ..., N, N are the discrete number of slow time in a synthetic aperture; α ₁Roll shake angle degree during for n=1, α ₂Roll shake angle degree during for n=2, α _NRoll shake angle degree during for n=N; To any one orientation moment n, according to the cosine law, have

$R_1(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})=R_{11}(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})-{2\mathrm{JR}}_1(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})\sin ({\mathrm{\&alpha;}}_n/2)\cos (\mathrm{\&theta;}-{\mathrm{\&alpha;}}_n/2)---\left(1\right)$

Wherein

Be expressed as a scattering point in the image field scape,

Distance The scattering point of the main antenna of expression roll angle shake in the imaging scene

Distance,

The scattering point of the main antenna that expression does not have a roll angle shake in the imaging scene Distance, J represents base length, α _nThe expression orientation is the roll shake angle degree of n constantly, and θ is the scene center incident angle, and n is the orientation moment, and the span of n is: n=1, and 2 ..., N, N are the discrete number of slow time in a synthetic aperture;

To any one orientation moment n, according to the cosine law, have

$R_2(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})=R_{12}(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})-{2\mathrm{JR}}_2(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})\sin ({\mathrm{\&alpha;}}_n/2)\cos (\mathrm{\&pi;}-\mathrm{\&theta;}+{\mathrm{\&alpha;}}_n/2)---\left(2\right)$

Wherein

Be expressed as a scattering point in the image field scape,

Distance

The scattering point of the auxiliary antenna that there is roll angle shake in expression in the imaging scene

Distance,

The scattering point of the auxiliary antenna that expression does not have a roll angle shake in the imaging scene

Distance, J represents base length, α _nThe expression orientation is the roll shake angle degree of n constantly, and θ is the scene center incident angle, and n is the orientation moment;

$\frac{R_{11}(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})+R_{12}(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})}{R_1(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})+R_2(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})}\&ap;1---\left(3\right)$

According to formula (3), formula (1) is deducted formula (2) obtain the roll angle bias control factor

X(n)＝2Jsin(α _n/2)cos(θ-α _n/2)

Wherein n is the orientation moment, and J represents base length, α _nThe expression orientation is the roll shake angle degree of n constantly, and θ is the scene center incident angle; For first orientation to, obtaining the roll angle bias control factor is X (1), be X (2) for second orientation to obtaining the roll angle bias control factor, ..., ..., constantly obtaining the roll angle bias control factor for n orientation is X (n), constantly obtains roll angle bias control factor sequence for all orientation

, n=1,2 ..., N, N are the discrete number of slow time in a synthetic aperture;

Step 4, the calculating crab angle bias control factor:

According to step 1, have in a scattering point synthetic aperture N orientation to, driftage shake angle degree sequence be α ' (n)=[α ' ₁, α ' ₂..., α ' _N], n=1 wherein, 2 ..., N, N are positive integer, N is the discrete number of slow time in a synthetic aperture; α ' ₁Driftage shake angle degree during for n=1, α ' ₂Driftage shake angle degree during for n=2 ... ..., α ' _NDriftage shake angle degree during for n=N; To any one orientation moment n, according to the cosine law, have

$R_1^{\&prime;}(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})=R_{11}^{\&prime;}(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})-2{\mathrm{JR}}_1^{\&prime;}(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})\sin ({\mathrm{\&alpha;}}_n^{\&prime;}/2)\sin ({\mathrm{\&alpha;}}_n^{\&prime;}/2)\sin \left(\mathrm{\&theta;}\right)---\left(4\right)$

Wherein Be expressed as a scattering point in the image field scape,

Distance

The scattering point of the main antenna of expression crab angle shake in the imaging scene

Distance,

The scattering point of the main antenna that expression does not have a crab angle shake in the imaging scene

Distance, J represents base length, α ' _nThe expression orientation is the driftage shake angle degree of n constantly, and θ is the scene center incident angle, and n is the orientation moment;

To any one orientation moment n, according to the cosine law, have

$R_2^{\&prime;}(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})=R_{12}^{\&prime;}(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})+2{\mathrm{JR}}_2^{\&prime;}(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})\sin ({\mathrm{\&alpha;}}_n^{\&prime;}/2)\sin ({\mathrm{\&alpha;}}_n^{\&prime;}/2)\sin \left(\mathrm{\&theta;}\right)---\left(5\right)$

Wherein

Be expressed as a scattering point in the image field scape,

Distance

The scattering point of the auxiliary antenna of expression crab angle shake in the imaging scene

Distance,

The scattering point of the auxiliary antenna that expression does not have a crab angle shake in the imaging scene

Distance, J represents base length, α ' _nThe expression orientation is the driftage shake angle degree of n constantly, and θ is the scene center incident angle, and n is the orientation moment;

$\frac{R_{11}^{\&prime;}(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})+R_{12}^{\&prime;}(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})}{R_1^{\&prime;}(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})+R_2^{\&prime;}(n,{\stackrel{\&RightArrow;}{P}}_{\mathrm{\&omega;}})}\&ap;1---\left(6\right)$

According to formula (6), formula (4) is deducted formula (5) get the crab angle bias control factor

Y(n)＝2Jsin(α' _n/2)sin(α' _n/2)sin(θ)

Wherein n is the orientation moment, and J represents base length, α ' _nThe expression orientation is the crab angle shake angle degree of n constantly, and θ is the scene center incident angle; For first orientation to, obtaining the crab angle bias control factor is Y (1), be Y (2) for second orientation to obtaining the crab angle bias control factor, ..., ..., constantly obtaining the crab angle bias control factor for n orientation is Y (n), constantly obtains crab angle bias control factor sequence for all orientation

, n=1,2 ..., N, N are the discrete number of slow time in a synthetic aperture;

Step 5, the main and auxiliary antenna distance history of calculating:

To a scattering point in the imaging scene

, choose orientation n constantly, obtain main antenna apart from history

Wherein

The expression main antenna in the orientation constantly n to scattering point

Distance;

To a scattering point in the imaging scene

Choose orientation n constantly, obtain auxiliary antenna distance history

Wherein

The expression main antenna in the orientation constantly n to scattering point

Distance,

Represent auxiliary antenna in the orientation constantly n to scattering point Distance;

Data interpolating, resampling after step 6, Range compress

According to the method that traditional standard Singh interpolation resamples, obtain the long W of being of a window ₀Sinc function $h\left(x\right)=\sin c\left(x\right)=\frac{\sin \left(\mathrm{\&pi;x}\right)}{\mathrm{\&pi;x}};$

The n constantly in the orientation, according to the main antenna in step 5 apart from history and conventional interference synthetic-aperture radar rear orientation projection's formation method (BP), the main antenna echo data from step 2 Middle taking-up window is long is W ₀Data, adopting traditional standard Singh interpolation method is W to taking out rear length ₀Data carry out interpolation, the data after obtaining the main antenna interpolation and resampling

, n is the orientation moment;

At orientation moment n, according to the auxiliary antenna distance history in step 5 and conventional interference synthetic-aperture radar rear orientation projection's formation method (BP), the auxiliary antenna echo data from step 2

Middle taking-up window is long is W ₀Data, adopting traditional standard Singh interpolation method is W to taking out rear length ₀Data carry out interpolation, obtain the data after auxiliary antenna interpolation resamples

N is the orientation moment;

For first orientation moment, obtain the main antenna data after interpolation resamples Auxiliary antenna data

For second orientation moment, obtain the main antenna data after interpolation resamples

Auxiliary antenna data

For n the orientation moment, obtain the main antenna data after interpolation resamples

Auxiliary antenna data

For all slow time, obtain the main antenna data sequence C after interpolation resamples _1n, n=1,2 ..., N, auxiliary antenna data sequence C _2n, n=1,2 ..., N, N are the discrete number of slow time in a synthetic aperture;

After step 7, main antenna interpolation resample, data are sued for peace along slow time coherence:

The phase compensating factor of main antenna and auxiliary antenna is K (n), and the computing formula of K (n) is:

Wherein

For main antenna corresponding apart from history, n=1,2 ..., N, N are the discrete number of slow time in a synthetic aperture, f _cBe the radar sampling frequency, c is the light velocity;

At orientation moment n, with the data after in step 6, resulting interpolation resamples

Multiply each other with the phase compensating factor K (n) of main antenna, obtain the data after phase compensation

For first orientation constantly, being compensated rear data is

For second orientation constantly, being compensated rear data is

For N orientation constantly, being compensated rear data is

Finally obtain data sequence A after the compensation constantly of all orientation _1n, n=1,2 ..., N, N are the discrete number of slow time in a synthetic aperture, for a scattering point

Data addition after the phase compensation constantly of all orientation is obtained a scattering point

The main antenna imaging data: A ₁₁+ A ₁₂+ ...+A _1n+ ...+A _1N

After step 8, auxiliary antenna interpolation resample, data are sued for peace along slow time coherence:

The phase compensating factor of main antenna and auxiliary antenna is K (n), and the computing formula of K (n) is:

, wherein For main antenna corresponding apart from history, n=1,2 ..., N, N are the discrete number of slow time in a synthetic aperture, f _cBe the radar sampling frequency, c is light velocity P ₁

At orientation moment n, with the data after in step 6, resulting interpolation resamples

The bias control factor that obtains with phase compensating factor K (n), step 3,4

Multiply each other, obtain the data after phase compensation For first orientation constantly, being compensated rear data is

For second orientation constantly, being compensated rear data is

For N orientation constantly, being compensated rear data is

Finally obtain data sequence A after the compensation constantly of all orientation _2n, n=1,2 ..., N, N are the discrete number of slow time in a synthetic aperture, for a scattering point

Data addition after the phase compensation constantly of all orientation is obtained a scattering point

Auxiliary antenna imaging data: A ₂₁+ A ₂₂+ ...+A _2n+ ...+A _2N

Step 9, whole scene imaging

To each scattering point in the imaging scene, repeating step 5 obtains the main and auxiliary antenna imaging data of all scattering points in the imaging scene to step 8, namely obtains main antenna single width SAR image and the auxiliary antenna single width SAR image of whole imaging scene;

With main antenna imaging data and auxiliary antenna imaging data conjugate multiplication, get phase place according to traditional MATLAB function angle method, obtain interferometric phase image.

Images