CN104007440B - One accelerated decomposition rear orientation projection spot beam SAR formation method - Google Patents

Abstract

The invention belongs to synthetic aperture radar image-forming technical field, particularly a kind of accelerated decomposition rear orientation projection spot beam SAR formation method. This accelerated decomposition rear orientation projection spot beam SAR formation method comprises the following steps: utilize platform motion to form synthetic aperture, set up polar coordinate system (r, θ), and full aperture is divided into N taking aperture center as initial point₀Individual isometric sub-aperture; Make α=sin θ, by u (r corresponding to sub-aperture_p, θ) and the impulse response function of locating pixel is expressed as I^(u)(α)＝I^(u)(r_p, α); Define two-dimentional wave number variable; Draw u two-dimentional wave-number spectrum corresponding to sub-aperture; For each two-dimentional wave-number spectrum corresponding apart from wave number, to each two-dimentional wave-number spectrum corresponding to sub-aperture spliced, draw each one dimension wave-number spectrum corresponding apart from wave number along orientation; Then by each apart from one dimension wave-number spectrum corresponding to wave number along distance to splicing, draw full aperture two dimension wave-number spectrum; Described full aperture two dimension wave-number spectrum is carried out to two-dimensional Fourier transform, draw total space resolution image under polar coordinate system.

Description

One accelerated decomposition rear orientation projection spot beam SAR formation method

Technical field

The invention belongs to synthetic aperture radar (SAR) technical field of imaging, particularly a kind of accelerated decomposition rear orientation projectionSpot beam SAR formation method, can be used for airborne or Space-borne SAR Imaging processing platform, is applicable to non-linear flight path, largeThe complicated imaging occasions such as stravismus.

Background technology

Time domain rear orientation projection (Back-Projection, BP) method is by the integration along oblique distance course (being called BP integration)Being embodied as the continuous accumulation of each pixel energy on picture grid, is a kind of accurate Spotlight SAR Imaging imaging algorithm. Time domain rear orientation projectionMethod has solved the coupled problem of distance and bearing ideally, is applicable to the complicated one-tenth such as large coherent accumulation angle or non-linear flight pathThe image reconstruction that picture how much is lower, and there is not geometric distortion in image after focusing. But the computing of time domain rear orientation projection method is negativeLoad has limited its application in large data scale imaging occasion.

In order to improve the efficiency of time domain rear orientation projection method, some quick rear orientation projection methods are suggested in succession, wherein withFast decoupled rear orientation projection (FastFactorizedBP, FFBP) method is the most representative. Fast decoupled rear orientation projection methodBP integration on full aperture is divided into substep, the subsection integral on sub-aperture, and decompose and Recursive Fusion in aperture. Wherein, holeButterfly computation structure has been set up in footpath decomposition, is the rapid precondition of fast decoupled rear orientation projection method; Recursive Fusion is realizedImage resolution ratio formation from low to high, be to rebuild the important channel of two-dimentional full resolution image. Based on above thinking, fastDecompose rear orientation projection's method and greatly reduced the computational burden that BP integration brings, obtained the computing effect that approaches frequency domain algorithmRate. The starting stage and processing stage, fast decoupled rear orientation projection method is set up local pole taking each sub-aperture center as initial pointCoordinate system. For certain point target in imaging scene, this is corresponding different distance and angular domain under different coordinate systemsCoordinate. Therefore the subimage that, different pore size is corresponding need to be set up corresponding coordinate and be tied to the mapping of new coordinate system in the time mergingRelation, and this process is the two-dimensional process process of a dependence distance and angular domain interpolation in essence. But, two dimension (pointwise) interpolationRealize image co-registration and can cause two subject matters: 1) interpolation operation is inevitably introduced error, and this error is along with passingReturn the carrying out of fusion constantly to accumulate and to amplify, finally cause the loss of picture quality; 2) after two-dimensional interpolation is fast decoupledTo part very consuming time in projecting method. The aperture number of dividing when the starting stage is when less, the accumulation of image Recursive FusionInterpolation error is less, and picture quality improves thereupon, but corresponding operation efficiency reduces; And the aperture number of dividing when the starting stageWhen more, the number of times of image Recursive Fusion increases, and the interpolation error of accumulation is larger, and picture quality decreases.

Summary of the invention

The object of the invention is to propose a kind of accelerated decomposition rear orientation projection spot beam SAR formation method, this addsSpeed is decomposed rear orientation projection's spot beam SAR formation method for accelerating the quick method (AcceleratedFast of rear orientation projectionBP, AFBP), referred to as AFBP method. Due to without two-dimensional interpolation and Recursive Fusion, AFBP method has been avoided the long-pending of interpolation errorTire out and amplify, accurately retaining the original form of wave-number spectrum. Therefore, AFBP method has higher than fast decoupled rear orientation projection methodOperation efficiency and more desirable focusing performance. The present invention is achieved in that

Framework configuration and processing links to existing fast decoupled rear orientation projection method are analyzed, and find out computing in algorithmThe part that complexity is high; AFBP method is carried out excellent to the high part of computational complexity in existing fast decoupled rear orientation projection methodChange and improve, accelerating efficiency of algorithm. Concrete steps are as follows:

For realizing above-mentioned technical purpose, the present invention adopts following technical scheme to be achieved.

One accelerated decomposition rear orientation projection spot beam SAR formation method comprises the following steps:

S1: utilize the synthetic aperture radar on motion platform to receive echo-signal, echo-signal is carried out to matched filtering,Go out range pulse compressed signal, described motion platform is aircraft or satellite;

S2: set up polar coordinate system taking synthetic aperture center O as initial point, in described polar coordinate system, coordinate is (r_p, θ)Point is expressed as (r_p, θ) and locate pixel, full aperture is divided into N₀Individual sub-aperture equal in length, N₀For being greater than 1 natural number, orderα=sin θ; By u (r corresponding to sub-aperture_p, θ) and the impulse response function of locating pixel is expressed as I^(u)(r_p, α), u get 1 toN₀; Make I^(u)(α)＝I^(u)(r_p,α)；

S3: definition is apart from wave number variable K_rWith angular wave number variable K_α; By to I^(u)(α) carry out inverse Fourier transform, drawU two-dimentional wave-number spectrum H corresponding to sub-aperture^(u)(K_r,K_α); In two-dimentional wave-number spectrum corresponding to all sub-apertures, for eachThe two-dimentional wave-number spectrum corresponding apart from wave number, along orientation to each two-dimentional wave-number spectrum corresponding to sub-aperture spliced, draws everyThe individual one dimension wave-number spectrum corresponding apart from wave number; Then by each apart from one dimension wave-number spectrum corresponding to wave number along distance to spellingConnect, draw full aperture two dimension wave-number spectrum; Described full aperture two dimension wave-number spectrum is carried out to two-dimensional Fourier transform, draw polar coordinate systemLower total space resolution image.

Feature of the present invention and further improvement are:

In step S1, motion platform in the time flying at a constant speed, to form length be L synthetic aperture, described synthetic apertureCenter is expressed as O; In the process of motion platform flight, synthetic aperture radar outwards transmits, and receives echo-signal,Go out the echo-signal after demodulation;

In step S1, show that the process of the echo-signal after demodulation is: set up plane taking synthetic aperture center O as initial pointRectangular coordinate system, in described plane right-angle coordinate, the direction of motion that x direction of principal axis is motion platform, at described antenna phaseThe absolute value of the x axial coordinate value at center is X; Then set up polar coordinate system taking synthetic aperture center O as initial point, in antenna phaseThe heart is to point target P (r_p,θ_p) instantaneous oblique distance R (X; r_p,θ_p) be:

$R(X;r_p,{\mathrm{\&theta;}}_p)=\sqrt{r_p^2+X^2-2r_{p}X\sin {\mathrm{\&theta;}}_p},-\frac{L}{2}\&le;X<\frac{L}{2}$

Wherein, r_pAnd θ_pBe respectively two coordinates of point target P under polar coordinate system; Then define the sinusoidal coordinate α in angle_p，α_p＝sinθ_p, above formula is rewritten as:

$R(X;r_p,{\mathrm{\&alpha;}}_p)=\sqrt{r_p^2+X^2-2r_{p}X{\mathrm{\&alpha;}}_p},-\frac{L}{2}\&le;X<\frac{L}{2}$

The echo-signal s (τ, X) after demodulation is:

$s(\mathrm{\&tau;},X)=\mathrm{rect}\left[\frac{X}{L}\right]\&CenterDot;s_T(\mathrm{\&tau;}-{\mathrm{\&Delta;t}}_p)$

Wherein, s_T() is the waveform that transmits, and τ is the fast time, Δ t_p＝2R(X；r_p,α_p)/c, c is the light velocity, rect[] represents rectangular window function;

In step S1, after the echo-signal drawing after demodulation, the echo-signal after demodulation is carried out to matched filtering,Draw range pulse compressed signal s_M(τ,X)：

$s_M(\mathrm{\&tau;},X)=\sin c[B\&CenterDot;(\mathrm{\&tau;}-\mathrm{\&Delta;}{t}_p)]\&CenterDot;\mathrm{rect}\left[\frac{X}{L}\right]\&CenterDot;\exp [-j{K}_{\mathrm{rc}}R(X;r_p,{\mathrm{\&alpha;}}_p)]$

Wherein, the transmitted signal bandwidth that B is synthetic aperture radar, K_rc＝4π/λ_mid，λ_midFor synthetic aperture radar transmitting letterNumber time wavelength corresponding to carrier frequency.

In step S1, motion platform in the time flying at a constant speed, to form length be L synthetic aperture, described synthetic apertureCenter is expressed as O; In the process of motion platform flight, synthetic aperture radar outwards transmits, and receives echo-signal,Go out the echo-signal after demodulation;

In step S1, show that the process of the echo-signal after demodulation is: set up plane taking synthetic aperture center O as initial pointRectangular coordinate system, in described plane right-angle coordinate, the direction of motion that x direction of principal axis is motion platform, at described antenna phaseThe absolute value of the x axial coordinate value at center is X; Then set up polar coordinate system taking synthetic aperture center O as initial point, in antenna phaseThe heart is to point target P (r_p,θ_p) instantaneous oblique distance R (X; r_p,θ_p) be:

$R(X;r_p,{\mathrm{\&theta;}}_p)=\sqrt{r_p^2+X^2-2r_{p}X\sin {\mathrm{\&theta;}}_p},-\frac{L}{2}\&le;X<\frac{L}{2}$

Wherein, r_pAnd θ_pBe respectively two coordinates of point target P under polar coordinate system; Then define the sinusoidal coordinate α in angle_p，α_p＝sinθ_p, above formula is rewritten as:

$R(X;r_p,{\mathrm{\&alpha;}}_p)=\sqrt{r_p^2+X^2-2r_{p}X{\mathrm{\&alpha;}}_p},-\frac{L}{2}\&le;X<\frac{L}{2}$

The echo-signal s (τ, X) after demodulation is:

$s(\mathrm{\&tau;},X)=\mathrm{rect}\left[\frac{X}{L}\right]\&CenterDot;s_T(\mathrm{\&tau;}-{\mathrm{\&Delta;t}}_p)$

Wherein, s_T() is the waveform that transmits, and τ is the fast time, Δ t_p＝2R(X；r_p,α_p)/c, c is the light velocity, rect[] represents rectangular window function;

In step S1, after the echo-signal drawing after demodulation, according to platform parameter, calculate kinematic error and causeOblique distance error, described platform parameter comprises position, attitude, speed and the acceleration of motion platform; According to described kinematic errorThe oblique distance error causing, carries out motion compensation to the echo-signal after demodulation, draws motion compensation back echo signal; Then to instituteState motion compensation back echo signal and carry out matched filtering, draw range pulse compressed signal s_M(τ,X)：

$s_M(\mathrm{\&tau;},X)=\sin c[B\&CenterDot;(\mathrm{\&tau;}-\mathrm{\&Delta;}{t}_p)]\&CenterDot;\mathrm{rect}\left[\frac{X}{L}\right]\&CenterDot;\exp [-j{K}_{\mathrm{rc}}R(X;r_p,{\mathrm{\&alpha;}}_p)]$

Wherein, the transmitted signal bandwidth that B is synthetic aperture radar, K_rc＝4π/λ_mid，λ_midFor synthetic aperture radar transmitting letterNumber time wavelength corresponding to carrier frequency.

In step S2, first full aperture is divided into N₀Individual sub-aperture equal in length, N₀For being greater than 1 natural number, everyThe length in individual sub-aperture is l;

In described polar coordinate system, coordinate is (r_p, θ) point be expressed as (r_p, θ) and locate pixel; Make α=sin θ, in instituteState in polar coordinate system u (r corresponding to sub-aperture_p, θ) and locate the impulse response function I of pixel^(u)(r_p, α) be:

$I^{\left(u\right)}(r_p,\mathrm{\&alpha;})={\&Integral;}_{-l/2}^{l/2}{s}_M[\frac{2R(X+x_u;r_p,\mathrm{\&alpha;})}{c},X+x_u]\&CenterDot;\exp [j{K}_{\mathrm{rc}}\&CenterDot;R(X+x_u;r_p,\mathrm{\&alpha;})]\mathrm{dX}$

Wherein, x_u＝(u-N₀/ 2-1/2) l, u gets 1 to N₀, c is the light velocity; With X to the X+x in above formula_uCarry out variable generationChange, above formula is rewritten as:

$\begin{array}{c}{I}^{\left(u\right)}(r_p,\mathrm{\&alpha;})={\&Integral;}_{x_u-l/2}^{x_u+l/2}{s}_M[\frac{2R(X;r_p,\mathrm{\&alpha;})}{c},X]\&CenterDot;\exp \left[j{K}_{\mathrm{rc}}R(X;r_p,\mathrm{\&alpha;})\right]\mathrm{dX}\\ ={\&Integral;}_{x_u-l/2}^{x_u+l/2}\exp [{\mathrm{jK}}_{\mathrm{rc}}\&CenterDot;\mathrm{\&Delta;R}(X;r_p,\mathrm{\&alpha;})]\mathrm{dX}\end{array}$

Wherein, Δ R (X; r_p,α)＝R(X；r_p,α)-R(X；r_p,α_p); Then to Δ R (X; r_p, α) and carry out second order Taylor levelNumber launches, and obtains:

$\begin{array}{c}\mathrm{\&Delta;R}(X;r_p,\mathrm{\&alpha;})=R(X;r_p,\mathrm{\&alpha;})-R(X;r_p,{\mathrm{\&alpha;}}_p)\\ =-(\mathrm{\&alpha;}-{\mathrm{\&alpha;}}_p)X-\frac{{\mathrm{\&alpha;}}^2-{\mathrm{\&alpha;}}_p^2}{2r_p}{X}^2\end{array}$

Ignore the X in above formula², I^(u)(r_p, α) be reduced to:

$I^{\left(u\right)}(r_p,\mathrm{\&alpha;})={\&Integral;}_{x_u-l/2}^{x_u+l/2}\exp [-{\mathrm{jK}}_{\mathrm{rc}}\&CenterDot;(\mathrm{\&alpha;}-{\mathrm{\&alpha;}}_p)X]\mathrm{dX}$

Then, angular wave number domain variable is defined as follows:

$\left\{\begin{array}{c}{K}_{\mathrm{\&alpha;}}=K_{\mathrm{rc}}\&CenterDot;X\\ \mathrm{\&Delta;}{K}_{\mathrm{\&alpha;}}=K_{\mathrm{rc}}\&CenterDot;l\\ K_{\mathrm{\&alpha;c}}^{\left(u\right)}=K_{\mathrm{rc}}\&CenterDot;x_u\end{array}\right.$

Make I^(u)(α)＝I^(u)(r_p, α), by K_αSubstitution I^(u)(α), I^(u)(α) be:

$I^{\left(u\right)}\left(\mathrm{\&alpha;}\right)=I^{\left(u\right)}(r_p,\mathrm{\&alpha;})={\&Integral;}_{K_{\mathrm{\&alpha;c}}^{\left(u\right)}-\mathrm{\&Delta;}{K}_{\mathrm{\&alpha;}}/2}^{K_{\mathrm{\&alpha;c}}^{\left(u\right)}+\mathrm{\&Delta;}{K}_{\mathrm{\&alpha;}}/2}\exp [-j{K}_{\mathrm{\&alpha;}}\&CenterDot;(\mathrm{\&alpha;}-{\mathrm{\&alpha;}}_p)]{\mathrm{dK}}_{\mathrm{\&alpha;}}$

Wherein, Be u sub-aperture center looking to scene centerThe sine value at angle, Δ α is the angular domain areas imaging in every sub-aperture.

In step S3, first define two-dimentional wave number variable as follows:

$\left\{\begin{array}{cc}{K}_{\mathrm{\&alpha;}}=K_r\&CenterDot;X& \\ \mathrm{\&Delta;}{K}_{\mathrm{\&alpha;}}=K_r\&CenterDot;l& K_r\&Element;[\frac{4\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_{\max }},\frac{4\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_{\min }}]\\ K_{\mathrm{\&alpha;c}}^{\left(u\right)}=K_r\&CenterDot;x_u& \end{array}\right.$

Wherein, λ_maxWavelength corresponding to minimum frequency while transmitting for synthetic aperture radar, λ_minFor synthetic aperture radarWavelength corresponding to peak frequency while transmitting; K_r=4 π/λ, λ is the wavelength of synthetic aperture radar while transmitting;

By to I^(u)(α) carry out inverse Fourier transform, obtain u two-dimentional wave-number spectrum H corresponding to sub-aperture^(u)(K_r,K_α)，H^(u)(K_r,K_α) be:

$\begin{array}{c}{H}^{\left(u\right)}\left(K_{\mathrm{\&alpha;}}\right)={\&Integral;}_{{\mathrm{\&alpha;}}_c^{\left(u\right)}-\mathrm{\&Delta;\&alpha;}/2}^{{\mathrm{\&alpha;}}_c^{\left(u\right)}+\mathrm{\&Delta;\&alpha;}/2}{I}^{\left(u\right)}\left(\mathrm{\&alpha;}\right)\&CenterDot;\exp \left(j{K}_{\mathrm{\&alpha;}}\mathrm{\&alpha;}\right)\mathrm{d\&alpha;}\\ =\mathrm{rect}\left[\frac{K_{\mathrm{\&alpha;}}-K_{\mathrm{\&alpha;c}}^{\left(u\right)}}{\mathrm{\&Delta;}{K}_{\mathrm{\&alpha;}}}\right]\&CenterDot;\exp (-j{K}_{\mathrm{\&alpha;}}{\mathrm{\&alpha;}}_p)\end{array}$

$\left\{\begin{array}{c}{K}_{\mathrm{\&alpha;}}\&Element;[-\frac{\mathrm{\&Delta;}{K}_{\mathrm{\&alpha;}}}{2}+K_{\mathrm{\&alpha;c}}^{\left(u\right)},\frac{\mathrm{\&Delta;}{K}_{\mathrm{\&alpha;}}}{2}+K_{\mathrm{\&alpha;c}}^{\left(u\right)}]\\ K_r\&Element;[-\frac{\mathrm{\&Delta;}{K}_r}{2}+K_{\mathrm{rc}},\frac{\mathrm{\&Delta;}{K}_r}{2}+K_{\mathrm{rc}}]\end{array}\right.$

Wherein, Δ K_r=4 π B/c, c is the light velocity.

After step S3, by two-dimensional interpolation, total space resolution image under described polar coordinate system is converted to described planeIn rectangular coordinate system, draw total space resolution image under described plane right-angle coordinate.

Beneficial effect of the present invention is:

(1) imaging plane is selected in r-sin θ coordinate system by the present invention, directly calculates and treat according to the sine value at projection visual angleThe position of subpoint on sin θ axle, without calculating projection view angle theta itself. This method has been avoided the arcsine at projection visual angleBy pixel operation, effectively reduce the computational burden of algorithm itself.

(2) use overall r-sin θ coordinate, the present invention has set up aperture location X and angular wave number K_αBetween Fourier becomeChange relation, i.e. K_r＝K_αX, wherein K_rFor apart from wave number. Due to K_αRespective distances compression phase course territory, above formula can be carriedFor phase history and the one-to-one relationship of orientation time, this also the present invention can realize before the fusion of aperture by wave-number spectrumCarry.

(3), based on Fourier transformation and cyclic shift, the present invention can realize image by the one dimension processing to wave-number spectrumMerge, without two-dimensional interpolation and Recursive Fusion, avoided the destruction of interpolation error to wave-number spectrum form. Therefore, the present invention hasApproach the focusing performance of the operation efficiency of frequency domain algorithm and the time domain rear orientation projection method that matches in excellence or beauty.

Brief description of the drawings

Fig. 1 is the flow chart of accelerated decomposition of the present invention rear orientation projection spot beam SAR formation method;

Fig. 2 is the geometric representation of the sub-aperture imaging of synthetic aperture radar of the present invention under polar coordinate system;

Fig. 3 is the schematic diagram that one dimension angular wave number spectrum of the present invention splicing realizes image co-registration;

Fig. 4 is the schematic diagram that two-dimemsional number spectrum of the present invention splicing realizes image co-registration;

Fig. 5 is the geometric representation that in emulation experiment of the present invention, imaging region and point target distribute;

Fig. 6 a is that the aperture location number in every sub-aperture in emulation experiment is to use three kinds of methods to rebuild at 32 o'clock to drawThe orientation impulse response function schematic diagram that P1, P2 and P3 are 3; Fig. 6 b is the aperture location in every sub-aperture in emulation experimentNumber is the orientation impulse response function schematic diagram of 3 of the P1, the P2 that use three kinds of methods to rebuild at 16 o'clock to draw and P3; Fig. 6 c is for imitativeIn true experiment, the aperture location number in every sub-aperture is the side of 3 of the P1, the P2 that use three kinds of methods to rebuild at 8 o'clock to draw and P3Digit pulse receptance function schematic diagram;

Fig. 7 a adopts fast decoupled rear orientation projection method to rebuild full sky under the polar coordinate system drawing in measured data testBetween resolution image; Fig. 7 b is total space resolution image under the polar coordinate system that adopts the present invention to rebuild in measured data test to draw;

Fig. 8 a adopts in measured data test under the polar coordinate system of the sub-scenario A that fast decoupled rear orientation projection method drawsTotal space resolution image; Fig. 8 b adopts the total space under the polar coordinate system of the sub-scenario A that the present invention draws in measured data testResolution image; Fig. 8 c is the polar coordinate system that adopts the sub-scenario B that fast decoupled rear orientation projection method draws in measured data testLower total space resolution image; Fig. 8 d be in measured data test, adopt under the polar coordinate system of the sub-scenario B that the present invention draws complete emptyBetween resolution image; Fig. 8 e is the polar coordinates that adopt the subfield scape C that fast decoupled rear orientation projection method draws in measured data testThe lower total space resolution image of system; Fig. 8 f be in measured data test, adopt under the polar coordinate system of the subfield scape C that the present invention draws completeSpatial discrimination image;

Fig. 9 a is two two-dimensional interpolations that point target adopts fast decoupled rear orientation projection method to draw in measured data experimentAfter imaging results schematic diagram; Fig. 9 b is that in measured data experiment, two point targets adopt after the two-dimensional interpolation that the present invention drawsImaging results schematic diagram; Fig. 9 c is that in measured data experiment, two point targets adopt two kinds of orientation impulse response letters that method drawsNumber schematic diagram;

Figure 10 a is that in measured data experiment, point target 3 adopts after the two-dimensional interpolation that fast decoupled rear orientation projection method drawsImaging results schematic diagram; Figure 10 b is that in measured data experiment, point target 3 adopts the imaging after the two-dimensional interpolation that the present invention drawsResult schematic diagram; Figure 10 c is the orientation impulse response function signal that in measured data experiment, point target 3 adopts two kinds of methods to drawFigure.

Detailed description of the invention

Below in conjunction with accompanying drawing, the invention will be further described:

With reference to Fig. 1, it is the flow chart of accelerated decomposition of the present invention rear orientation projection spot beam SAR formation method. ShouldAccelerated decomposition rear orientation projection spot beam SAR formation method comprises the following steps:

S1: utilize the synthetic aperture radar on motion platform to receive echo-signal, echo-signal is carried out to matched filtering,Go out range pulse compressed signal, described motion platform is aircraft or satellite. Be described as follows:

Synthetic aperture radar is installed on motion platform. When motion platform is with speed v (the flying of motion platform that fly at a constant speedLine direction is expressed as x direction) time, the synthetic aperture that to have formed length be L, the center of this synthetic aperture is expressed as O, flat in motionIn the process of platform flight, synthetic aperture radar outwards transmits, and the antenna of synthetic aperture radar (is reception antenna, is alsoTransmitting antenna) beam center points to scene center C all the time. With reference to Fig. 2, for synthetic aperture radar of the present invention is under polar coordinate systemThe geometric representation of sub-aperture imaging. Set up polar coordinate system taking synthetic aperture center O as initial point, antenna phase center is to pointTarget P (r_p,θ_p) instantaneous oblique distance be

$R(X;r_p,{\mathrm{\&theta;}}_p)=\sqrt{r_p^2+X^2-2r_{p}X\sin {\mathrm{\&theta;}}_p},-\frac{L}{2}\&le;X<\frac{L}{2}$

Wherein, r_pAnd θ_pBe respectively two coordinates of point target P under polar coordinate system; Below the implication of X is described:Set up plane right-angle coordinate taking synthetic aperture center O as initial point, in this plane right-angle coordinate, x direction of principal axis is flat for movingThe direction of motion of platform, the absolute value of the x axial coordinate value that X is antenna phase center.

The sinusoidal coordinate α in definition angle_p，α_p＝sinθ_p, above formula can be rewritten as

$R(X;r_p,{\mathrm{\&alpha;}}_p)=\sqrt{r_p^2+X^2-2r_{p}X{\mathrm{\&alpha;}}_p},-\frac{L}{2}\&le;X<\frac{L}{2}$

The echo-signal after demodulation is

$s(\mathrm{\&tau;},X)=\mathrm{rect}\left[\frac{X}{L}\right]\&CenterDot;s_T(\mathrm{\&tau;}-{\mathrm{\&Delta;t}}_p)$

Wherein, s_T() is the waveform that transmits, and τ is the fast time, Δ t_pRepresent round trip time delay, Δ t_p＝2R(X；r_p,α_p)/C, c is the light velocity, rect[] expression rectangular window function.

Then according to the platform parameter of GPS (global position system) or INS (inertial navigation system) record, calculate motionThe oblique distance error that error causes, described platform parameter comprises position, attitude, speed and the acceleration of motion platform. According to motionThe oblique distance error that error causes, carries out motion compensation to echo-signal, draws motion compensation back echo signal.

Motion compensation back echo signal is carried out to matched filtering, draw range pulse compressed signal s_M(τ,X)：

$s_M(\mathrm{\&tau;},X)=\sin c[B\&CenterDot;(\mathrm{\&tau;}-\mathrm{\&Delta;}{t}_p)]\&CenterDot;\mathrm{rect}\left[\frac{X}{L}\right]\&CenterDot;\exp [-j{K}_{\mathrm{rc}}R(X;r_p,{\mathrm{\&alpha;}}_p)]$

Wherein, the transmitted signal bandwidth that B is synthetic aperture radar, K_rcFor apart from wave number center, K_rc＝4π/λ_mid，λ_midForThe wavelength that centre frequency when synthetic aperture radar transmits (carrier frequency) is corresponding.

S2: set up polar coordinate system taking synthetic aperture center O as initial point, in described polar coordinate system, coordinate is (r_p, θ)Point is expressed as (r_p, θ) and locate pixel; Full aperture is divided into N₀Individual sub-aperture equal in length, N₀For being greater than 1 natural number, orderα=sin θ; By u (r corresponding to sub-aperture_p, θ) and the impulse response function of locating pixel is expressed as I^(u)(r_p, α), make I^(u)(α)＝I^(u)(r_p, α). Be described as follows:

In step S2, first full aperture is divided into N₀Individual sub-aperture equal in length, N₀For being greater than 1 natural number, everyThe length in individual sub-aperture is l, l=L/N₀。

The present invention by corresponding each sub-aperture from pulse compression signal rear orientation projection to taking synthetic aperture center as initial pointIn polar coordinate system. In this polar coordinate system, coordinate is (r_p, θ) point be expressed as (r_p, θ) and locate pixel. Make α=sin θ, with thisSet up r-sin θ coordinate system, by (r_p, θ) locate pixel and be converted in r-sin θ coordinate system, (r_p, θ) locate pixel and sit at r-sin θCoordinate in mark system is (r_p, α), will in r-sin θ coordinate system, coordinate be (r_p, α) point be expressed as (r_p, α) and locate pixel.

U (r corresponding to sub-aperture in above-mentioned polar coordinate system_p, θ) and locate the impulse response function I of pixel^(u)(r_p,α) be:

$I^{\left(u\right)}(r_p,\mathrm{\&alpha;})={\&Integral;}_{-l/2}^{l/2}{s}_M[\frac{2R(X+x_u;r_p,\mathrm{\&alpha;})}{c},X+x_u]\&CenterDot;\exp [j{K}_{\mathrm{rc}}\&CenterDot;R(X+x_u;r_p,\mathrm{\&alpha;})]\mathrm{dX}$

Wherein, x_u＝(u-N₀/ 2-1/2) l. By I^(u)(r_p, α) computing formula known, I^(u)(r_p, α) and be by edge tiltedlyApart from course R (X+x_u；r_p, α) and carry out integration acquisition, corresponding integration variable X ∈ [l/2, l/2]. With X to I^(u)(r_p, α) meterCalculate the X+x in formula_uCarry out substitution of variable, I^(u)(r_p, α) computing formula be further rewritten as:

$\begin{array}{c}{I}^{\left(u\right)}(r_p,\mathrm{\&alpha;})={\&Integral;}_{x_u-l/2}^{x_u+l/2}{s}_M[\frac{2R(X;r_p,\mathrm{\&alpha;})}{c},X]\&CenterDot;\exp \left[j{K}_{\mathrm{rc}}R(X;r_p,\mathrm{\&alpha;})\right]\mathrm{dX}\\ ={\&Integral;}_{x_u-l/2}^{x_u+l/2}\exp [{\mathrm{jK}}_{\mathrm{rc}}\&CenterDot;\mathrm{\&Delta;R}(X;r_p,\mathrm{\&alpha;})]\mathrm{dX}\end{array}$

Wherein, Δ R (X; r_p, α) and be projection oblique distance, Δ R (X; r_p,α)＝R(X；r_p,α)-R(X；r_p,α_p). To Δ R (X;r_p, α) and carry out second order Taylor series expansion, obtain:

$\begin{array}{c}\mathrm{\&Delta;R}(X;r_p,\mathrm{\&alpha;})=R(X;r_p,\mathrm{\&alpha;})-R(X;r_p,{\mathrm{\&alpha;}}_p)\\ \&ap;-(\mathrm{\&alpha;}-{\mathrm{\&alpha;}}_p)X-\frac{{\mathrm{\&alpha;}}^2-{\mathrm{\&alpha;}}_p^2}{2r_p}{X}^2\end{array}$

If above formula can be ignored X², I^(u)(r_p, α) can be reduced to:

$I^{\left(u\right)}(r_p,\mathrm{\&alpha;})\&ap;{\&Integral;}_{x_u-l/2}^{x_u+l/2}\exp [-{\mathrm{jK}}_{\mathrm{rc}}\&CenterDot;(\mathrm{\&alpha;}-{\mathrm{\&alpha;}}_p)X]\mathrm{dX}$

Then, angular wave number domain variable is defined as follows

$\left\{\begin{array}{c}{K}_{\mathrm{\&alpha;}}=K_{\mathrm{rc}}\&CenterDot;X\\ \mathrm{\&Delta;}{K}_{\mathrm{\&alpha;}}=K_{\mathrm{rc}}\&CenterDot;l\\ K_{\mathrm{\&alpha;c}}^{\left(u\right)}=K_{\mathrm{rc}}\&CenterDot;x_u\end{array}\right.$

Wherein K_αFor angular wave number, Δ K_αFor angular wave number bandwidth,Be wave number center corresponding to u sub-aperture. Make I^(u)(α)＝I^(u)(r_p, α), by K_αSubstitution I^(u)(α), I^(u)(α) can further be rewritten as about angular wave number K_αFunction:

$I^{\left(u\right)}\left(\mathrm{\&alpha;}\right)=I^{\left(u\right)}(r_p,\mathrm{\&alpha;})\&ap;{\&Integral;}_{K_{\mathrm{\&alpha;c}}^{\left(u\right)}-\mathrm{\&Delta;}{K}_{\mathrm{\&alpha;}}/2}^{K_{\mathrm{\&alpha;c}}^{\left(u\right)}+\mathrm{\&Delta;}{K}_{\mathrm{\&alpha;}}/2}\exp [-j{K}_{\mathrm{\&alpha;}}\&CenterDot;(\mathrm{\&alpha;}-{\mathrm{\&alpha;}}_p)]{\mathrm{dK}}_{\mathrm{\&alpha;}}$

Wherein,Be the sine value of u sub-aperture center to the visual angle of scene center, it can be straight according to geometrical relationshipConnect calculating; Δ α is the angular domain areas imaging (the angular domain areas imaging in every sub-aperture equates) in every sub-aperture.By introducing the concept of angular wave number, above formula is set up K_αAnd Fourier between αTransformation relation has produced the orientation impulse response function I of sinc shape simultaneously^(u)(α). It should be noted that the present invention utilizes angle justThe Fourier transformation relation that string coordinate has been set up rear orientation projection's image and angular wave number territory, has broken through wave-number spectrum and has operated in Time-Domain algorithmUnder the obstacle of use, and injected some frequency domain algorithm speciality for the present invention.

Based on Δ R (X; r_p, α) and can ignore X²The hypothesis of item, derives and ignores X emphatically below²Constraints. For justIn analysis, make α=α_p+ Δ ρ, Δ R (X; r_p, α) in X²Item can abbreviation be

$-\frac{{\mathrm{\&alpha;}}^2-{\mathrm{\&alpha;}}_p^2}{2r_p}{X}^2\&ap;-\frac{{\mathrm{\&alpha;}}_p\&CenterDot;\mathrm{\&Delta;\&rho;}}{r_p}{X}^2$

The quadratic phase error QPE that above formula is corresponding is

$\mathrm{QPE}=-\frac{4\mathrm{\&pi;}{\mathrm{\&alpha;}}_p\&CenterDot;\mathrm{\&Delta;\&rho;}}{\mathrm{\&lambda;}{r}_p}{X}^2$

It is generally acknowledged in the time of QPE≤π/8, the energy of impulse response function mainly concentrates on α_pCentered by, width isAngular resolution ρ_αIn the adjacent domain of size. Form principle, angular resolution ρ according to wave beam_αFor:

${\mathrm{\&rho;}}_{\mathrm{\&alpha;}}=\frac{{\mathrm{\&lambda;}}_{\min }}{2L}$

Wherein, λ_minWavelength (the synthetic aperture radar transmitting that while transmitting for synthetic aperture radar, peak frequency is correspondingThe wavelength minimum (X-Guang Pu) of signal).

While being positioned at synthetic aperture two ends due to antenna, QPE gets maximum, and Δ ρ is replaced with to ρ_α, QPE meets:

$\mathrm{QPE}\&le;\frac{\mathrm{\&pi;L}}{2r_p}\&CenterDot;\left|{\mathrm{\&alpha;}}_p\right|\&le;\frac{\mathrm{\&pi;L}}{2r_p}\&le;\frac{\mathrm{\&pi;}}{8}$

Above formula is done to further abbreviation:

$L\&le;\frac{r_p}{4}$

Be that length of synthetic aperture is not more than r_pFour/for the moment, Δ R (X; r_p, α) in about the approximate essence once of XDegree is enough to ensure: I^(u)(r_p, α) can further be rewritten as about angular wave number K_αFunction. And this constraints is in most of imagingsOccasion all can be met.

S3: definition is apart from wave number variable K_rWith angular wave number variable K_α; By to I^(u)(α) carry out inverse Fourier transform, drawU two-dimentional wave-number spectrum H corresponding to sub-aperture^(u)(K_r,K_α); In two-dimentional wave-number spectrum corresponding to all sub-apertures, for eachThe two-dimentional wave-number spectrum corresponding apart from wave number, along orientation to each two-dimentional wave-number spectrum corresponding to sub-aperture spliced, draws everyThe individual one dimension wave-number spectrum corresponding apart from wave number; Then by each apart from one dimension wave-number spectrum corresponding to wave number along distance to spellingConnect, draw full aperture two dimension wave-number spectrum; Described full aperture two dimension wave-number spectrum is carried out to two-dimensional Fourier transform, draw polar coordinate systemLower total space resolution image. Be described as follows:

First to I^(u)(α) carry out inverse Fourier transform, obtain corresponding angular wave number spectrum H^(u)(K_α)，H^(u)(K_α) be:

$\begin{array}{c}{H}^{\left(u\right)}\left(K_{\mathrm{\&alpha;}}\right)={\&Integral;}_{{\mathrm{\&alpha;}}_c^{\left(u\right)}-\mathrm{\&Delta;\&alpha;}/2}^{{\mathrm{\&alpha;}}_c^{\left(u\right)}+\mathrm{\&Delta;\&alpha;}/2}{I}^{\left(u\right)}\left(\mathrm{\&alpha;}\right)\&CenterDot;\exp \left(j{K}_{\mathrm{\&alpha;}}\mathrm{\&alpha;}\right)\mathrm{d\&alpha;}\\ =\mathrm{rect}\left[\frac{K_{\mathrm{\&alpha;}}-K_{\mathrm{\&alpha;c}}^{\left(u\right)}}{\mathrm{\&Delta;}{K}_{\mathrm{\&alpha;}}}\right]\&CenterDot;\exp (-j{K}_{\mathrm{\&alpha;}}{\mathrm{\&alpha;}}_p)\end{array}$

Wherein, rectangular window function represents width and the position of u sub-aperture inferior horn wave-number spectrum, and the corresponding P point of exponential term existsAngle sinusoidal position α under polar coordinate system_p。

With reference to Fig. 3, for one dimension angular wave number spectrum of the present invention is spliced the schematic diagram of realizing image co-registration. OrderIt is uThe angular domain resolution cell size that sub-aperture is corresponding, whenOrTime, there is Fold in angular wave number spectrum. But, as long as angular domain sampling meets Nyquist (Nyquist) sampling thheorem, this phenomenonBring the difficulty that is difficult to overcome can't to angular wave number spectrum of the present invention splicing. According to Nyquist sampling thheorem,ChooseNeed to meet

${\mathrm{\&rho;}}_{\mathrm{\&alpha;}}^{\left(u\right)}\&le;\frac{{\mathrm{\&lambda;}}_{\min }}{2l}$

According to above stated specification, first synthetic aperture is divided into N₀Individual sub-aperture. Every corresponding width subimage in sub-apertureWith an independent angular wave number spectrum, wherein the wave number center of angular wave number spectrum and wave number width corresponding sub-aperture center and sub-hole respectivelyElectrical path length. Under polar coordinate system, can move the orderly combination that realizes angular wave number spectrum by a series of simple wave-number spectrums, i.e. figurePicture merges. Carrying out angular wave number when splicing spectrum, need to be by cyclic shift by the angular wave number Pu center in u sub-aperture by zeroFrequently move. Consider the fourier transform property of signal, image area is multiplied by linear phase can realize angular wave number spectrumMove. Moving of angular wave number spectrum can be eliminated the previous Fold of spectrum. Be spliced into one dimension along Xiang Jiangge aperture, orientation wave-number spectrumVector, thus the orderly restructuring of wave-number spectrum completed.

By one dimension wave-number spectrum H^(u)(K_α) be generalized to two-dimentional wave-number spectrum, first define two-dimentional wave number variable as follows:

$\left\{\begin{array}{cc}{K}_{\mathrm{\&alpha;}}=K_r\&CenterDot;X& \\ \mathrm{\&Delta;}{K}_{\mathrm{\&alpha;}}=K_r\&CenterDot;l& K_r\&Element;[\frac{4\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_{\max }},\frac{4\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_{\min }}]\\ K_{\mathrm{\&alpha;c}}^{\left(u\right)}=K_r\&CenterDot;x_u& \end{array}\right.$

Wherein, λ_maxWavelength corresponding to minimum frequency while transmitting for synthetic aperture radar, K_rFor apart from wave number, K_r＝4π/λ, λ is the wavelength (λ be variable) of synthetic aperture radar while transmitting. U two-dimentional wave-number spectrum H corresponding to sub-aperture^(u)(K_r,K_α) be:

$H^{\left(u\right)}(K_r,K_{\mathrm{\&alpha;}})=\mathrm{rect}\left[\frac{K_r-K_{\mathrm{rc}}}{\mathrm{\&Delta;}{K}_r}\right]\&CenterDot;\exp (-j\&CenterDot;K_r{r}_p)\&CenterDot;\mathrm{rect}\left[\frac{K_{\mathrm{\&alpha;}}-K_{\mathrm{\&alpha;c}}^{\left(u\right)}}{\mathrm{\&Delta;}{K}_{\mathrm{\&alpha;}}}\right]\&CenterDot;\exp (-j\&CenterDot;K_{\mathrm{\&alpha;}}{\mathrm{\&alpha;}}_p)$

$\left\{\begin{array}{c}{K}_{\mathrm{\&alpha;}}\&Element;[-\frac{\mathrm{\&Delta;}{K}_{\mathrm{\&alpha;}}}{2}+K_{\mathrm{\&alpha;c}}^{\left(u\right)},\frac{\mathrm{\&Delta;}{K}_{\mathrm{\&alpha;}}}{2}+K_{\mathrm{\&alpha;c}}^{\left(u\right)}]\\ K_r\&Element;[-\frac{\mathrm{\&Delta;}{K}_r}{2}+K_{\mathrm{rc}},\frac{\mathrm{\&Delta;}{K}_r}{2}+K_{\mathrm{rc}}]\end{array}\right.$

Wherein Δ K_r=4 π B/c, c is the light velocity, Δ K_rRepresent apart from wave number width.

Under rear orientation projection's framework, step S2 is by ignoring Δ R (X; r_p, α) X²Under the constraints of item, set up figureThe Fourier transformation relation in image field and angular wave number territory, therefore the Analytical Expression H of two-dimentional wave-number spectrum^(u)(K_r,K_α) be one approximate,The rectangle wave-number spectrum of resolving. But it should be noted that Fourier transformation and cyclic shift in actual process all do not drawEnter approximately, therefore spliced two-dimentional wave-number spectrum is an accurate spectrum that is trapezoidal shape, as shown in Figure 4. With reference to Fig. 4, be thisBright two-dimemsional number spectrum splicing realizes the schematic diagram of image co-registration, angular wave number centerApart from wave number K_rLinear function. BorrowAngular domain wave-number spectrum joining method shown in mirror Fig. 3, the joining method of two-dimentional wave-number spectrum as shown in Figure 4. Particularly, drawing uThe two-dimentional wave-number spectrum H that individual sub-aperture is corresponding^(u)(K_r,K_α) afterwards, in two-dimentional wave-number spectrum corresponding to all sub-apertures, for eachThe two-dimentional wave-number spectrum corresponding apart from wave number, along orientation to each two-dimentional wave-number spectrum corresponding to sub-aperture spliced, draws everyThe individual one dimension wave-number spectrum corresponding apart from wave number (form with one-dimensional vector represents). Then by each corresponding apart from wave numberOne dimension wave-number spectrum, along distance to splicing, draws full aperture two dimension wave-number spectrum; Described full aperture two dimension wave-number spectrum is carried out to twoDimension Fourier transformation, draws total space resolution image under polar coordinate system (the full resolution image of angular domain).

Below the computational complexity of step S2 and step S3 is analyzed:

Suppose in full aperture, aperture location number (orientation is to pulse number, orientation to sampling number) is M, imaging netThe pixel number of lattice is M × M. The aperture location number in every sub-aperture is m, m=M/N₀, every resolution corresponding to sub-apertureThe pixel number that sub-picture pack contains is M × m. In the two-dimentional wave-number spectrum splicing stage of step S3, because circulative shift operation only accounts forThe small part of integral operation amount, therefore ignore this part. Treatment in accordance with the present invention order, corresponding operand analysis asUnder:

A) the required operand of step S2 is (M/N₀×M/N₀×M)×N₀；

B), in step S3, while drawing two-dimentional wave-number spectrum corresponding to every sub-aperture, required operand is: $[M\&times;M/N_0\&times;({\log }_2^{M/N_0}+{\log }_2^M)]\&times;N_0;$

C), in step S3, show that the required operand of full aperture two dimension wave-number spectrum is M × N₀. Its principle is: drawing entirelyWhen aperture two dimension wave-number spectrum, first open up full aperture wave-number spectrum matrix (memory headroom), calculate the angular wave number center of wave-number spectrum, logicalCross cyclic shift along orientation to the orderly splicing that realizes sub-aperture wave-number spectrum; Along distance to repeating this process, the final two dimension that realizesThe splicing of full aperture wave-number spectrum, draws full aperture two dimension wave-number spectrum. If ignore the operand of circulative shift operation, calculate angle rippleThe required operand in number center is M × N₀。

D), in step S3, when described full aperture two dimension wave-number spectrum is carried out to two-dimensional Fourier transform, required operand is

In sum, total operand OP of step S2 and step S3_AFBPFor:

${\mathrm{OP}}_{\mathrm{AFBP}}=M^3/N_0+{3M}^2{\log }_2^M+M^2{\log }_2^{M/N_0}+{\mathrm{MN}}_0$

Observe above formula, OP_AFBPAbout N₀Monotonic decreasing function. Therefore, work as N₀When larger, step S2 and step S3'sTotal operand is less, and operation efficiency is higher. Very hour, during as m=4 or m=8, angular wave number bands of a spectrum are wide for the length in group apertureVery narrow, in the time that wave-number spectrum splices, easily cause the fuzzy of full aperture wave-number spectrum, and cause the reduction of picture quality. At actual numberDuring according to processing, get m=16 or m=32 and can ensure that wave-number spectrum has good precision, can take into account again the operation efficiency of algorithm.

After step S3, by two-dimensional interpolation, total space resolution image under described polar coordinate system is converted to described planeIn rectangular coordinate system, draw total space resolution image under described plane right-angle coordinate. Then by described plane right-angle coordinateLower total space resolution image shows on display.

Effect of the present invention can be further described by following emulation experiment and measured data experiment:

Simulated conditions:

This emulation experiment is used X-band radar, and its parameter as shown in Table 1.

Table one X-band radar parameter

Centre frequency	5GHz	Center oblique distance	1000m
				Two-dimensional resolution	0.175m	Length of synthetic aperture	192m

9 point targets that are spacedly distributed in the imaging region of 100m × 100m, as shown in Figure 5. With reference to Fig. 5, be thisThe geometric representation that in bright emulation experiment, imaging region and point target distribute. A synthetic aperture comprises 2048 row pulse echos,The pixel distribution of imaging grid is 2048 × 2048.

The major parameter of computer simulation platform is: 2.53GHz processor, 4GB internal memory (RAM), 64 bit manipulation systems withAnd 64 MATLAB.7.10.0 softwares.

Emulation content and analysis of simulation result:

In emulation experiment, use respectively the present invention, time domain rear orientation projection (Back-Projection, BP) method, quickDecompose rear orientation projection (FastFactorizedBP, FFBP) method and carry out imaging simulation. Adopting fast decoupled rear orientation projectionWhen method is carried out imaging simulation, rebuild local pole coordinate system subimage by sub-aperture BP integration, and in the present invention, be by sonImage reconstruction is in overall polar coordinate system. The present invention and fast decoupled rear orientation projection method only need be carried out distance in the corresponding stage and be insertedValue, without carrying out angular domain interpolation. In order to ensure fairness and the comparability of emulation experiment, the backward throwing of the present invention and fast decoupledImage method is all by the liter realization of sampling in the time carrying out apart from interpolation, and its basic step comprises: in the zero padding of frequency domain two ends, contrary FuLeaf transformation, low order interpolation, wherein rise sampling multiple and get 8 to ensure interpolation precision.

In the time drawing under polar coordinate system total space resolution image, fast decoupled rear orientation projection method relies on two-dimensional distance interpolationRealize the Recursive Fusion of image, wherein still rise sampling by 8 times apart from interpolation and realize, angular domain interpolation is by the sinc interpolation of blockingRealize. After finishing, Recursive Fusion obtains total space resolution image under polar coordinate system. Drawing total space resolution figure under polar coordinate systemWhen picture, the present invention is by Fourier transformation and cyclic shift restructuring full aperture wave-number spectrum, and this process is without interpolation processing. To full holeFootpath wave-number spectrum carries out two-dimentional inverse Fourier transform, obtains total space resolution image under polar coordinate system.

For the present invention and fast decoupled rear orientation projection method, different sub-aperture lengths (now every sub-aperture is setAperture location number m be set to respectively 32,16 and 8), and obtain three groups of different imagings knots by three different experimentsReally, the image of reconstruction is total space resolution image under polar coordinate system. For the present invention and fast decoupled rear orientation projection side are describedThe image focus quality of method, chooses tri-point targets of P1 in Fig. 5, P2 and P3 and carries out image quality analysis. As space is limited restriction andGive top priority to what is the most important, only provide the orientation impulse response function of three point targets under the length l in the sub-aperture of difference here, as Fig. 6 instituteShow. With reference to Fig. 6 a, for the aperture location number in every sub-aperture in emulation experiment is to use three kinds of methods to rebuild at 32 o'clock to drawThe orientation impulse response function schematic diagram that P1, P2 and P3 are 3. With reference to Fig. 6 b, it is the position, aperture in every sub-aperture in emulation experimentPut number and be the orientation impulse response function schematic diagram of 3 of the P1, the P2 that use three kinds of methods to rebuild at 16 o'clock to draw and P3. ReferenceFig. 6 c, for the aperture location number in every sub-aperture in emulation experiment is to use three kinds of methods to rebuild P1, the P2 and the P3 that draw at 8 o'clockThe orientation impulse response function schematic diagram of 3. In Fig. 6 a, Fig. 6 b and Fig. 6 c, transverse axis represents angular domain location of interpolation, longitudinal axis tableShow normalization amplitude, unit is dB.

As can be seen from Figure 6, though the value difference of the length l in sub-aperture, the present invention and fast decoupled rear orientation projection sideMethod all can realize good focusing performance. And along with the increase of the length l in sub-aperture, the present invention and fast decoupled rear orientation projection sideThe quality of the reconstruction image of method improves thereupon. When the length l in group aperture equals length of synthetic aperture L, do not divide sub-apertureTime, the quality of the reconstruction image of the present invention and fast decoupled rear orientation projection method is all equivalent to time domain rear orientation projection method. And withSuccessively decreasing of sub-aperture length, in fast decoupled rear orientation projection method, the notch depth of the main lobe of IRF (impulse response function) existsConstantly become " shallow ", IRF secondary lobe constantly raises, and the 4th and the response forms of IRF secondary lobe is undesirable afterwards. When backward with fast decoupledWhen the starting stage aperture length of projecting method equates, the impulse response function curve of the present invention (orientation that P1, P2 and P3 are 3Profile) more approach time domain rear orientation projection method. Now, the zero point depth of main lobe of the present invention and other position compares fast decoupledRear orientation projection's method is lower. As shown in Figure 6 a, in the time that initial sub-aperture location number is 32, P1, P2 and P3 that the present invention drawsImpulse response function curve and the time domain rear orientation projection method of 3 are basically identical, and do not exist as fast decoupled rear orientation projection sideThe undesirable situation of the high-order secondary lobe (IRF secondary lobe) when method focuses on far field point P3. From the above analysis to Fig. 6, the present inventionFrom thering is than fast decoupled rear orientation projection method the focusing performance that is more tending towards desirable intuitively. In order to provide picture quality and computingThe quantitative assessment of efficiency, show that corresponding peak sidelobe ratio (PSLR), integration secondary lobe are than parameters such as (ISLR) and processing times, asShown in table two. From table two, find out, at peak sidelobe ratio aspect of performance, the present invention omits one than fast decoupled rear orientation projection methodPoint, but the present invention is very obvious to the improvement of integration secondary lobe ratio. In the situation that peak value side lobe performance approaches, integration secondary lobe is than getting overLow, the contrast of image is higher, and this phenomenon will provide better illustration in the processing of measured data. From the processing time,In the situation that sub-aperture length is equal, the present invention has higher operation efficiency than fast decoupled rear orientation projection method. ApertureBe decomposed into fast decoupled rear orientation projection method and bring good operation efficiency, but two-dimensional interpolation is realized Recursive Fusion to algorithm bandCarry out extra computational burden. For fast decoupled rear orientation projection method, sub-aperture length is shorter, the fortune that Recursive Fusion is requiredCalculation amount is just larger. Corresponding above three different sub-aperture lengths, the present invention in the time carrying out step S2, consuming time be respectively 73.8s,36.6s and 18.7s. Processing time total in the table of comparisons two is visible, and the operand overwhelming majority of the present invention concentrates on step S2,And the spectrum splicing stage is consuming time very little. To sum up analyze, the present invention and fast decoupled rear orientation projection method have all improved greatlyThe operation efficiency of BP integration, but the present invention is more excellent than fast decoupled rear orientation projection method aspect imaging precision and operation efficiencyElegant.

Table two image quality evaluation and processing time contrast

Measured data experiment:

To verify performance of the present invention by the imaging of X-band high-resolution Spotlight SAR Imaging below. Test in measured dataIn, in corresponding echo-signal, comprising 16384 pulse echos, the synthetic aperture time is 7.8 seconds. Transmitted signal bandwidth is1.16GHz, center oblique distance is 10.5Km. It is 16384 that the distance samples using when data processing is counted, areas imaging is 1.6 ×1.2km. Consider the impact of two-dimentional windowing on IRF main lobe broadening, distance and bearing resolution ratio theoretical value is about 0.15m.

In order to illustrate that two-dimensional interpolation is processed and two-dimentional wave-number spectrum splices the difference that realizes image co-registration, avoid follow-up coordinateThe interpolation error that system's conversion is introduced, the result providing is all positioned at polar coordinate system, and rebuilding image is the total space under polar coordinate systemResolution image. In measured data experiment, adopt respectively the present invention and fast decoupled rear orientation projection method to carry out image reconstruction,To image be respectively Fig. 7 a and Fig. 7 b. With reference to Fig. 7 a, for adopting fast decoupled rear orientation projection method weight in measured data testBuild total space resolution image under the polar coordinate system drawing. With reference to Fig. 7 b, draw for adopting the present invention to rebuild in measured data testPolar coordinate system under total space resolution image.

Find out from Fig. 7 a and Fig. 7 b, inherited the accuracy of fast decoupled rear orientation projection method, fast decoupled rear orientation projectionMethod and the present invention have all realized the well focussed of image. In data handling procedure, 1024 sub-apertures are divided, every heightAperture comprises 16 aperture location. Fast decoupled rear orientation projection method needs 10 Recursion process to realize image co-registration, its computingTime is 5751.4s; The present invention only needs once to compose splicing and realizes image co-registration, and be 1723.4s its operation time, and the present invention is realBe less than fast decoupled rear orientation projection method the operation time of existing image co-registration.

Find out from Fig. 7 a and Fig. 7 b, fast decoupled rear orientation projection method and the present invention all can realize the well focussed of image.But the imaging from Fig. 7 portion on the lower side to field texture and intensive building, the present invention is slightly better than the contribution of picture contrastFast decoupled rear orientation projection method. For a step is only evaluated the picture quality of the present invention and fast decoupled rear orientation projection method, fromFig. 7 a amplifies processing with the three different subfield scapes in place (being expressed as A, B and C in Fig. 7 a and Fig. 7 b) that Fig. 7 b extracts, and obtainsThree antithetical phrase scene images, as shown in Figure 8. With reference to Fig. 8 a, for adopting fast decoupled rear orientation projection method to obtain in measured data testTotal space resolution image under the polar coordinate system of the sub-scenario A going out, with reference to Fig. 8 b, for adopting the present invention to draw in measured data testThe polar coordinate system of sub-scenario A under total space resolution image; With reference to Fig. 8 c, for adopting fast decoupled backward in measured data testTotal space resolution image under the polar coordinate system of the sub-scenario B that projecting method draws, with reference to Fig. 8 d, for adopting in measured data testTotal space resolution image under the polar coordinate system of the sub-scenario B that the present invention draws; With reference to Fig. 8 e, fast for adopting in measured data testTotal space resolution image under the polar coordinate system of the subfield scape C that speed decomposition rear orientation projection method draws, with reference to Fig. 8 f, is measured dataIn test, adopt total space resolution image under the polar coordinate system of the subfield scape C that the present invention draws. Find out to Fig. 8 f from Fig. 8 a, thisBright and fast decoupled rear orientation projection method has all realized the well focussed of point target, but the energy of the point target that the present invention focuses on moreConcentrate, IRF side lobe levels contrast lower, image is better, and this phenomenon gives the credit to the present invention and has reasonably avoided interpolationThe impact on wave-number spectrum precision of error and build-up effect thereof. In sub-scenario A, there are two that orientation is adjacent, spacing is 0.15mCorner reflector (being labeled as point target 1 and point target 2 in Fig. 8 b) and the corner reflector (point target 3) of independently putting, San ZheIn Fig. 8 a, identified by annulus. For resolution performance of the present invention is described, point target 1 and 2 is carried out to imaging and orientation impulse responseFunctional Analysis, as shown in Figure 9. With reference to Fig. 9 a, for two point targets in measured data experiment adopt fast decoupled rear orientation projection sideImaging results schematic diagram after the two-dimensional interpolation that method draws. With reference to Fig. 9 b, for two point targets in measured data experiment adopt thisImaging results schematic diagram after the two-dimensional interpolation that invention draws. With reference to Fig. 9 c, for two point targets in measured data experiment adoptTwo kinds of orientation impulse response function schematic diagrames that method draws. In Fig. 9 a and Fig. 9 b, transverse axis represents angular domain location of interpolation, the longitudinal axisRepresent apart from location of interpolation. In Fig. 9 c, transverse axis represents angular domain location of interpolation, and the longitudinal axis represents normalization amplitude. AFBP refers to thisBright, FFBP refers to fast decoupled rear orientation projection method. From Fig. 9 c, two IRF main lobes corresponding to target separate, illustrate adjacentThe corner reflector of putting can well be differentiated.

For focusing performance of the present invention is described, point target 3 is carried out to imaging and orientation impulse response function analysis, as figureShown in 10. With reference to Figure 10 a, for adopting the two dimension that fast decoupled rear orientation projection method draws, point target 3 in measured data experiment insertsImaging results schematic diagram after value. With reference to Figure 10 b, for adopting the two dimension that the present invention draws, point target 3 in measured data experiment insertsImaging results schematic diagram after value. With reference to Figure 10 c, it is the orientation that in measured data experiment, point target 3 adopts two kinds of methods to drawImpulse response function schematic diagram. In Figure 10 a and Figure 10 b, transverse axis represents angular domain location of interpolation, and the longitudinal axis represents apart from interpolation positionPut. In Figure 10 c, transverse axis represents angular domain location of interpolation, and the longitudinal axis represents normalization amplitude. AFBP refers to the present invention, and FFBP refers to fastDecompose rear orientation projection's method. From Figure 10 c, approach-25dB of IRF the first secondary lobe of the present invention, and fast decoupled rear orientation projectionMethod IRF left side be about-15dB of the first secondary lobe, but received by IRF main lobe. Can find the present invention by Fig. 9 c and Figure 10 cIRF side lobe performance in the time processing measured data is still better than fast decoupled rear orientation projection method, the knot that this and emulation experiment drawOpinion is consistent. Certainly, fast decoupled rear orientation projection method can be improved orientation arteries and veins by the aperture length of suitable increase starting stageRush the side lobe performance of receptance function, and the method will inevitably increase the processing time of algorithm. Compare fast decoupled rear orientation projection sideMethod, the present invention just can obtain more excellent picture quality and the operation efficiency of Geng Gao under relatively short sub-aperture condition.

Obviously, those skilled in the art can carry out various changes and modification and not depart from essence of the present invention the present inventionGod and scope. Like this, if these amendments of the present invention and modification belong to the scope of the claims in the present invention and equivalent technologies thereofWithin, the present invention be also intended to comprise these change and modification interior.

Claims (6)

1. an accelerated decomposition rear orientation projection spot beam SAR formation method, is characterized in that, comprises the following steps:

S1: utilize the synthetic aperture radar on motion platform to receive echo-signal, echo-signal is carried out to matched filtering, draw distanceFrom pulse compression signal, described motion platform is aircraft or satellite;

S2: set up polar coordinate system taking synthetic aperture center O as initial point, in described polar coordinate system, coordinate is (r_p, θ) point representFor (r_p, θ) and locate pixel, full aperture is divided into N₀Individual sub-aperture equal in length, N₀For being greater than 1 natural number, make α=sinθ; By u (r corresponding to sub-aperture_p, θ) and the impulse response function of locating pixel is expressed as I^(u)(r_p, α), u gets 1 to N₀; Make I^(u)(α)＝I^(u)(r_p,α)；

S3: definition is apart from wave number variable K_rWith angular wave number variable K_αAs follows:

$\left\{\begin{array}{c}{K}_{\mathrm{\&alpha;}}=K_r\&CenterDot;X\\ {\mathrm{\&Delta;K}}_{\mathrm{\&alpha;}}=K_r\&CenterDot;l\\ K_{\mathrm{\&alpha;}c}^{\left(u\right)}=K_r\&CenterDot;x_u\end{array}\right.,K_r\&Element;\&lsqb;\frac{4\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_{max}},\frac{4\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_{min}}\&rsqb;$

Wherein, λ_maxWavelength corresponding to minimum frequency while transmitting for synthetic aperture radar, λ_minFor synthetic aperture radar transmittingWavelength corresponding to peak frequency when signal; K_r=4 π/λ, λ is the wavelength of synthetic aperture radar while transmitting; Full aperture is dividedFor N₀Individual sub-aperture equal in length, N₀For being greater than 1 natural number, the length in every sub-aperture is l, x_u＝(u-N₀/2-1/2) l, u gets 1 to N₀; X direction of principal axis is the direction of motion of motion platform, at the absolute value of the x of antenna phase center axial coordinate valueFor X;

By to I^(u)(α) carry out inverse Fourier transform, draw u two-dimentional wave-number spectrum H corresponding to sub-aperture^(u)(K_r,K_α)；

In two-dimentional wave-number spectrum corresponding to all sub-apertures, for each two-dimentional wave-number spectrum corresponding apart from wave number, along orientation toEach two-dimentional wave-number spectrum corresponding to sub-aperture spliced, draw each one dimension wave-number spectrum corresponding apart from wave number; Then willEach apart from one dimension wave-number spectrum corresponding to wave number along distance to splicing, draw full aperture two dimension wave-number spectrum; To described full holeFootpath two dimension wave-number spectrum carries out two-dimensional Fourier transform, draws total space resolution image under polar coordinate system.

2. a kind of accelerated decomposition as claimed in claim 1 rear orientation projection spot beam SAR formation method, its feature existsIn, in step S1, motion platform in the time flying at a constant speed, to form length be L synthetic aperture, the center table of described synthetic apertureBe shown O; In the process of motion platform flight, synthetic aperture radar outwards transmits, and receives echo-signal, draws demodulationAfter echo-signal;

In step S1, show that the process of the echo-signal after demodulation is: set up flat square taking synthetic aperture center O as initial pointCoordinate system, in plane right-angle coordinate, the direction of motion that x direction of principal axis is motion platform, at the x of antenna phase center axial coordinateThe absolute value of value is X; Then set up polar coordinate system taking synthetic aperture center O as initial point, antenna phase center is to point target P(r_p,θ_p) instantaneous oblique distance R (X; r_p,θ_p) be:

$R(X;r_p,{\mathrm{\&theta;}}_p)=\sqrt{r_p^2+X^2-2r_{p}X{\mathrm{sin\&theta;}}_p},-\frac{L}{2}\&le;X<\frac{L}{2}$

Wherein, r_pAnd θ_pBe respectively two coordinates of point target P under polar coordinate system; Then define the sinusoidal coordinate α in angle_p，α_p＝sinθ_p, above formula is rewritten as:

$R(X;r_p,{\mathrm{\&alpha;}}_p)=\sqrt{r_p^2+X^2-2r_p{\mathrm{X\&alpha;}}_p},-\frac{L}{2}\&le;X<\frac{L}{2}$

The echo-signal s (τ, X) after demodulation is:

$s(\mathrm{\&tau;},X)=rect\&lsqb;\frac{X}{L}\&rsqb;\&CenterDot;s_T(\mathrm{\&tau;}-{\mathrm{\&Delta;t}}_p)$

Wherein, s_T() is the waveform that transmits, and τ is the fast time, △ t_p＝2R(X；r_p,α_p)/c, c is the light velocity, rect[] tableShow rectangular window function;

In step S1, after the echo-signal drawing after demodulation, the echo-signal after demodulation is carried out to matched filtering, drawRange pulse compressed signal s_M(τ,X)：

$s_M(\mathrm{\&tau;},X)=\sin c\&lsqb;B\&CenterDot;(\mathrm{\&tau;}-{\mathrm{\&Delta;t}}_p)\&rsqb;\&CenterDot;rect\&lsqb;\frac{X}{L}\&rsqb;\&CenterDot;\exp \&lsqb;-{\mathrm{jK}}_{rc}R(X;r_p,{\mathrm{\&alpha;}}_p)\&rsqb;$

Wherein, the transmitted signal bandwidth that B is synthetic aperture radar, K_rc＝4π/λ_mid，λ_midWhile transmitting for synthetic aperture radarThe wavelength that carrier frequency is corresponding.

3. a kind of accelerated decomposition as claimed in claim 1 rear orientation projection spot beam SAR formation method, its feature existsIn, in step S1, motion platform in the time flying at a constant speed, to form length be L synthetic aperture, the center table of described synthetic apertureBe shown O; In the process of motion platform flight, synthetic aperture radar outwards transmits, and receives echo-signal, draws demodulationAfter echo-signal;

In step S1, show that the process of the echo-signal after demodulation is: set up flat square taking synthetic aperture center O as initial pointCoordinate system, in plane right-angle coordinate, the direction of motion that x direction of principal axis is motion platform, at the x of antenna phase center axial coordinateThe absolute value of value is X; Then set up polar coordinate system taking synthetic aperture center O as initial point, antenna phase center is to point target P(r_p,θ_p) instantaneous oblique distance R (X; r_p,θ_p) be:

$R(X;r_p,{\mathrm{\&theta;}}_p)=\sqrt{r_p^2+X^2-2r_{p}X{\mathrm{sin\&theta;}}_p},-\frac{L}{2}\&le;X<\frac{L}{2}$

Wherein, r_pAnd θ_pBe respectively two coordinates of point target P under polar coordinate system; Then define the sinusoidal coordinate α in angle_p，α_p＝sinθ_p, above formula is rewritten as:

$R(X;r_p,{\mathrm{\&alpha;}}_p)=\sqrt{r_p^2+X^2-2r_p{\mathrm{X\&alpha;}}_p},-\frac{L}{2}\&le;X<\frac{L}{2}$

The echo-signal s (τ, X) after demodulation is:

$s(\mathrm{\&tau;},X)=rect\&lsqb;\frac{X}{L}\&rsqb;\&CenterDot;s_T(\mathrm{\&tau;}-{\mathrm{\&Delta;t}}_p)$

Wherein, s_T() is the waveform that transmits, and τ is the fast time, △ t_p＝2R(X；r_p,α_p)/c, c is the light velocity, rect[] tableShow rectangular window function;

In step S1, after the echo-signal drawing after demodulation, according to platform parameter, calculate oblique that kinematic error causesApart from error, described platform parameter comprises position, attitude, speed and the acceleration of motion platform; Cause according to described kinematic errorOblique distance error, the echo-signal after demodulation is carried out to motion compensation, draw motion compensation back echo signal; Then to described fortuneMoving compensation back echo signal carries out matched filtering, draws range pulse compressed signal s_M(τ,X)：

$s_M(\mathrm{\&tau;},X)=\sin c\&lsqb;B\&CenterDot;(\mathrm{\&tau;}-{\mathrm{\&Delta;t}}_p)\&rsqb;\&CenterDot;rect\&lsqb;\frac{X}{L}\&rsqb;\&CenterDot;\exp \&lsqb;-{\mathrm{jK}}_{rc}R(X;r_p,{\mathrm{\&alpha;}}_p)\&rsqb;$

Wherein, the transmitted signal bandwidth that B is synthetic aperture radar, K_rc＝4π/λ_mid，λ_midWhile transmitting for synthetic aperture radarThe wavelength that carrier frequency is corresponding.

4. a kind of accelerated decomposition as claimed in claim 3 rear orientation projection spot beam SAR formation method, its feature existsIn, in step S2, first full aperture is divided into N₀Individual sub-aperture equal in length, N₀For being greater than 1 natural number, every heightThe length in aperture is l;

In described polar coordinate system, coordinate is (r_p, θ) point be expressed as (r_p, θ) and locate pixel; Make α=sin θ, at the described utmost pointIn coordinate system, u (r corresponding to sub-aperture_p, θ) and locate the impulse response function I of pixel^(u)(r_p, α) be:

$I^{\left(u\right)}\left(r_p,\mathrm{\&alpha;}\right)={\&Integral;}_{-l/2}^{l/2}{s}_M\&lsqb;\frac{2R\left(X+x_u;r_p,\mathrm{\&alpha;}\right)}{c},X+x_u\&rsqb;\&CenterDot;\exp \&lsqb;{\mathrm{jK}}_{rc}\&CenterDot;R\left(X+x_u;r_p,\mathrm{\&alpha;}\right)\&rsqb;dX$

Wherein, x_u＝(u-N₀/ 2-1/2) l, u gets 1 to N₀, c is the light velocity; With X to the X+x in above formula_uCarry out substitution of variable,Above formula is rewritten as:

$\begin{array}{c}{I}^{\left(u\right)}\left(r_p,\mathrm{\&alpha;}\right)={\&Integral;}_{x_u-l/2}^{x_u+l/2}{s}_M\&lsqb;\frac{2R\left(X;r_p,\mathrm{\&alpha;}\right)}{c},X\&rsqb;\&CenterDot;\exp \&lsqb;{\mathrm{jK}}_{rc}R\left(X;r_p,\mathrm{\&alpha;}\right)\&rsqb;dX\\ ={\&Integral;}_{x_u-l/2}^{x_u+l/2}\exp \&lsqb;{\mathrm{jK}}_{rc}\&CenterDot;\mathrm{\&Delta;}R\left(X;r_p,\mathrm{\&alpha;}\right)\&rsqb;dX\end{array}$

Wherein, △ R (X; r_p,α)＝R(X；r_p,α)-R(X；r_p,α_p); Then to △ R (X; r_p, α) and carry out the exhibition of second order Taylor seriesOpen, obtain:

$\begin{array}{c}\mathrm{\&Delta;}R(X;r_p,\mathrm{\&alpha;})=R(X;r_p,\mathrm{\&alpha;})-R(X;r_p,{\mathrm{\&alpha;}}_p)\\ =-\left(\mathrm{\&alpha;}-{\mathrm{\&alpha;}}_p\right)X-\frac{{\mathrm{\&alpha;}}^2-{\mathrm{\&alpha;}}_p^2}{2r_p}{X}^2\end{array}$

Ignore the X in above formula², I^(u)(r_p, α) be reduced to:

$I^{\left(u\right)}\left(r_p,\mathrm{\&alpha;}\right)={\&Integral;}_{x_u-l/2}^{x_u+l/2}\exp \&lsqb;-{\mathrm{jK}}_{rc}\&CenterDot;(\mathrm{\&alpha;}-{\mathrm{\&alpha;}}_p)X\&rsqb;dX$

Then, angular wave number domain variable is defined as follows:

$\left\{\begin{array}{c}{K}_{\mathrm{\&alpha;}}=K_{rc}\&CenterDot;X\\ {\mathrm{\&Delta;K}}_{\mathrm{\&alpha;}}=K_{rc}\&CenterDot;l\\ K_{\mathrm{\&alpha;}c}^{\left(u\right)}=K_{rc}\&CenterDot;x_u\end{array}\right.$

Make I^(u)(α)＝I^(u)(r_p, α), by K_αSubstitution I^(u)(α), I^(u)(α) be:

$I^{\left(u\right)}\left(\mathrm{\&alpha;}\right)=I^{\left(u\right)}(r_p,\mathrm{\&alpha;})={\&Integral;}_{K_{\mathrm{\&alpha;}c}^{\left(u\right)}-{\mathrm{\&Delta;K}}_{\mathrm{\&alpha;}}/2}^{K_{\mathrm{\&alpha;}c}^{\left(u\right)}+{\mathrm{\&Delta;K}}_{\mathrm{\&alpha;}}/2}\exp \&lsqb;-{\mathrm{jK}}_{\mathrm{\&alpha;}}\&CenterDot;\left(\mathrm{\&alpha;}-{\mathrm{\&alpha;}}_p\right)\&rsqb;{\mathrm{dK}}_{\mathrm{\&alpha;}}$

Wherein, Be u sub-aperture center to the visual angle of scene centerSine value, △ α is the angular domain areas imaging in every sub-aperture.

5. a kind of accelerated decomposition as claimed in claim 4 rear orientation projection spot beam SAR formation method, its feature existsIn, in step S3, first define two-dimentional wave number variable as follows:

$\left\{\begin{array}{c}{K}_{\mathrm{\&alpha;}}=K_r\&CenterDot;X\\ {\mathrm{\&Delta;K}}_{\mathrm{\&alpha;}}=K_r\&CenterDot;l\\ K_{\mathrm{\&alpha;}c}^{\left(u\right)}=K_r\&CenterDot;x_u\end{array}\right.,K_r\&Element;\&lsqb;\frac{4\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_{max}},\frac{4\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_{min}}\&rsqb;$

Wherein, λ_maxWavelength corresponding to minimum frequency while transmitting for synthetic aperture radar, λ_minFor synthetic aperture radar transmittingWavelength corresponding to peak frequency when signal; K_r=4 π/λ, λ is the wavelength of synthetic aperture radar while transmitting;

By to I^(u)(α) carry out inverse Fourier transform, obtain u two-dimentional wave-number spectrum H corresponding to sub-aperture^(u)(K_r,K_α)，H^(u)(K_r,K_α) be:

$\begin{array}{c}{H}^{\left(u\right)}\left(K_{\mathrm{\&alpha;}}\right)={\&Integral;}_{{\mathrm{\&alpha;}}_c^{\left(u\right)}-\mathrm{\&Delta;}\mathrm{\&alpha;}/2}^{{\mathrm{\&alpha;}}_c^{\left(u\right)}+\mathrm{\&Delta;}\mathrm{\&alpha;}/2}{I}^{\left(u\right)}\left(\mathrm{\&alpha;}\right)\&CenterDot;\exp \left({\mathrm{jK}}_{\mathrm{\&alpha;}}\mathrm{\&alpha;}\right)d\mathrm{\&alpha;}\\ =rect\&lsqb;\frac{K_{\mathrm{\&alpha;}}-K_{\mathrm{\&alpha;}c}^{\left(u\right)}}{{\mathrm{\&Delta;K}}_{\mathrm{\&alpha;}}}\&rsqb;\&CenterDot;\exp \left(-{\mathrm{jK}}_{\mathrm{\&alpha;}}{\mathrm{\&alpha;}}_p\right)\end{array}$

$\left\{\begin{array}{c}{K}_{\mathrm{\&alpha;}}\&Element;\&lsqb;-\frac{{\mathrm{\&Delta;K}}_{\mathrm{\&alpha;}}}{2}+K_{\mathrm{\&alpha;}c}^{\left(u\right)},\frac{{\mathrm{\&Delta;K}}_{\mathrm{\&alpha;}}}{2}+K_{\mathrm{\&alpha;}c}^{\left(u\right)}\&rsqb;\\ K_r\&Element;\&lsqb;-\frac{{\mathrm{\&Delta;K}}_r}{2}+K_{rc},\frac{{\mathrm{\&Delta;K}}_r}{2}+K_{rc}\&rsqb;\end{array}\right.$

Wherein, △ K_r=4 π B/c, c is the light velocity.

6. a kind of accelerated decomposition as claimed in claim 1 rear orientation projection spot beam SAR formation method, its feature existsIn, after step S3, by two-dimensional interpolation, total space resolution image under described polar coordinate system is converted to plane rectangular coordinatesIn system, draw total space resolution image under plane right-angle coordinate.