CN101866001B - Three-dimensional focused imaging method of look-down array antenna synthetic aperture radar - Google Patents

Abstract

The present invention discloses a three-dimensional focal imaging method of a look-down array antenna synthetic aperture radar, which relates to radar technology. The method comprises: A) performing slant-range compression of collected original echo data of the look-down array antenna synthetic aperture radar; B) performing azimuth range migration correction of a signal obtained by the step A); C) performing the azimuth compression of a signal obtained by the step B); D) performing the ground-range range migration correction of the signal which is subjected to slant-range compression and azimuth compression; and E) performing the ground-range slant removal and ground-range Fourier transform of the signal obtained by the step D), and reestablishing the three-dimensional radar image of an imaged area in a cylindrical coordinate system. In the method of the present invention, fewer antenna array elements are used for reestablishing the three-dimensional radar image of the imaged area, the range migration correction problem, which is not solved in the conventional three-dimensional imaging method, is solved, the ground-range wave beam forming calculation performed in the conventional three-dimension imaging method is converted into one time of complex multiplication and the Fourier transform, and a three-dimensional resolution image is thus acquired, and the required imaging time is reduced.

Description

A kind of three-dimensional focal imaging method that is used for look-down array antenna synthetic aperture radar

Technical field

The information that the present invention relates to synthetic-aperture radar is obtained and processing technology field, and especially a kind of three-dimensional focal imaging method that is used for look-down array antenna synthetic aperture radar can obtain the three-dimensional radar image of imaging region under the carrier.

Background technology

Look-down array antenna synthetic aperture radar is a kind of new synthetic aperture radar three-dimensional imaging technology, as shown in Figure 1.Wherein, Oxyz is the rectangular coordinate system in space at look-down array antenna synthetic aperture radar and imaging region place thereof, P _i(x _i, y _i, z _i) be i point target of imaging region and rectangular coordinate thereof.Qxr θ be look-down array antenna synthetic aperture radar and imaging region place thereof cylindrical coordinate system (orientation to, oblique distance to argument to), as shown in Figure 2, P _i(x _i, r _i, θ _i) be i point target of imaging region and cylindrical coordinates thereof.L _x, W _yBe respectively the look-down array antenna synthetic aperture radar orientation to length of synthetic aperture and distance to the imaging fabric width.By going up the distribution linear array antenna to (being the orientation) to-elevation normal direction to the plane at distance, make upwards to have formed at distance and differ from second the true aperture of orientation to synthetic aperture: distance is to true aperture, L is a linear array length, also be that distance is to length of real aperture, thereby formed a two-dimentional aperture that is positioned on the surface level (be the orientation to-distance to the plane), by the transmitted bandwidth signal, realized imaging region in the orientation to, distance to the three-dimensional resolution imaging that makes progress with elevation.

Since 1999, some research work have been carried out aspect look-down array antenna synthetic aperture radar three-dimensional imaging theory and the method in the world.1999, the Christoph H.Gierull of German aerospace institute (DLR) (C.Gierull.On a Concept for an Airborne Downward-Looking Imaging Radar. No.6, pp295-304,1999.) the imaging observation mode of having analyzed present airborne single-channel synthetic aperture radar mainly contains positive side-looking and stravismus, its common ground is can only carry out imaging to the scene objects of carrier aircraft flight path one side at synchronization, this is owing to single-channel synthetic aperture radar exists a left side/right fuzzy problem that is caused by flight two lateral extents symmetry, can't distinguish left side or the right side of target from flight track, thereby single-channel synthetic aperture radar do not possess to the carrier aircraft dead ahead and under the zone carry out the ability of high-resolution imaging, as shown in Figure 3.For solve the imaging blind area that airborne synthetic aperture radar exists under carrier aircraft, Gierull is incorporated into linear array antenna in the synthetic aperture radar image-forming, the notion of time looking imaging radar has been proposed, and provided and time looked the geometric model of imaging system, synthetic aperture and true aperture are combined, the orientation is to adopting the synthetic aperture principle, and distance is upwards introduced linear array antenna and constituted a true aperture, has formed a two-dimentional aperture.Because the following imaging radar system of looking that Gierull proposes is mainly used in the ultimate principle that the look-down array antenna synthetic aperture radar imaging is described, thereby adopts pure-tone polse signal rather than bandwidth signal, has realized two-dimensional imaging.

2006, people such as the J.Klare of German FGAN-FHR (J.Klare, A.Brenner, J.Ender.A new Airborne Radar for 3D Imaging-Image Formation using the ARTINO Principle-.EUSAR2006, Dresden, Germany, 2006; M.Wei β, J.Ender, O.Peters, et al.An airborne Radar for Three Dimensional Imaging and Observation-technical realisation and status of ARTINO.EUSAR2006, Dresden, Germany, 2006.) proposed to make up airborne three-dimensional imaging radar (Airborne Radar for Three-dimensional Imaging and Nadir Observation, the ARTINO) system that adopts nadir observation.The ARTINO principle with the launching antenna array separated into two parts, is placed at the wing two ends based on the one group of thinned array that distributes along wing respectively, and receiving antenna array is placed at the wing centre position.Form final 3-D view to synthetic aperture principle and distance to wave beam formation computing to pulse compression technique, orientation by distance.The ARTINO system can directly generate real three-dimensional resolution element rather than interference image, and this makes that can observe scene from different angles by the rotation 3-D view exists feasibility.By obtaining radar data in parallel flight path, a few width of cloth images that make progress at distance can be connected together, guaranteed to obtain the large-area three-dimensional image on all directions.FGAN-FHR is installed in the ARTINO system on the small-sized UAV, provides technic relization scheme.2007, people such as J.Klare (Jens Klare, Delphine Cerutti-Maori, Andreas Brenner, et al.Image quality analysis of the vibrating sparse MIMO antenna array of the airborne 3D imaging radar ARTINO.IGARSS2007, Barcelona, Spain, 2007.) considered of the influence of the carrier aircraft wing flutter of ARTINO system to three-dimensional focal imaging, and provided compensation scheme.2008, people such as J.Klare (Jens Klare, Andreas Brenner, Joachim Ender.Impact of Platform Attitude Disturbances on the 3D Imaging Quality of the UAV ARTINO.EUSAR2008, Friedrichshafen, Germany, 2008.) further considered the influence of the variation (comprising driftage, pitching and roll) of carrier aircraft attitude to three-dimensional focal imaging, and considered compensation scheme.

In the above-mentioned ongoing research, three problems of main existence: at first, do not consider the range migration correction problem in the imaging algorithm that the ARTINO system is adopted, owing to exist in the look-down array antenna synthetic aperture radar by the orientation to a two-dimentional aperture that synthetic aperture and distance are formed to true aperture, make oblique distance all have coupling to fast time u and distance to fast time v, make based on the imaging algorithm calculating of matched filtering more complicated to fast time t and orientation; Secondly, the compression that distance makes progress in the imaging algorithm is adopted wave beam to form and is realized, when antenna array unit number more for a long time, operation efficiency is lower; At last, distance also is that bay spacing d requires to be not more than λ to sampling interval _c/ 2, make the bay number that comprises in the linear array greatly increase, be unfavorable for practical application.

Summary of the invention

The object of the present invention is to provide a kind of three-dimensional focal imaging method that is used for look-down array antenna synthetic aperture radar, this method has been considered the correction of two-dimensional distance migration, improve distance and relax the requirement of distance simultaneously to sampling interval to compression efficiency, having solved existing three-dimensional focal imaging method, not carry out the problem and the distance of range migration correction lower to compaction algorithms efficient, the look-down array antenna synthetic aperture radar distance requires too small grade to be unfavorable for the problem of practical application to sampling interval

In order to realize described purpose, technical solution of the present invention is:

A kind of three-dimensional focal imaging method that is used for look-down array antenna synthetic aperture radar comprises that step is as follows:

Step S1: the look-down array antenna synthetic aperture radar system acquisition to machine under the original echoed signals of imaging region be S ₀(t, u, v), oblique distance to compression unit with original echoed signals along oblique distance to carrying out Fourier transform, generating the 1st signal is S ₁(f _t, u v), adopts oblique distance to matched filter H ₁(f _t) the 1st signal is carried out oblique distance handle to focal imaging, generating the 2nd signal is S ₂(f _t, u v), carries out oblique distance to inverse Fourier transform to the 2nd signal then, and generating the 3rd signal is S ₃(v), wherein, oblique distance is t to fast time domain for t, u, and oblique distance is f to frequency field _t, the orientation is that u and distance are v to time domain to time domain;

Step S2: the orientation to the range migration correction unit will generate the 3rd signal along the orientation to carrying out Fourier transform, generating the 4th signal is S ₄(t, f _u, v), wherein, the orientation is f to frequency field _u, then to the 4th signal along oblique distance to carrying out Fourier transform, generating the 5th signal is S ₅(f _t, f _u, v), adopt range migration correction factor H ₂(f _t) the 5th signal is carried out the orientation to range migration correction, generating the 6th signal is S ₆(f _t, f _u, v), then the 6th signal is carried out oblique distance to inverse Fourier transform, generating the 7th signal is S ₇(t, f _u, v);

Step S3: the orientation adopts the orientation to matched filter H to compression unit ₃(f _t) the 7th signal is carried out the orientation handle to focal imaging, generating the 8th signal is S ₈(t, f _u, v), then the 8th signal is carried out the orientation to inverse Fourier transform, generating the 9th signal is S ₉(t, u, v);

Step S4: distance to the range migration correction unit with the 9th signal along oblique distance to carrying out Fourier transform, generate the 10th signal S ₁₀(f _t, u v), carries out distance to range migration correction to the 10th signal, and generating the 11st signal is S ₁₁(f _t, u v), carries out oblique distance to inverse Fourier transform to the 11st signal, and generating the 12nd signal is S ₁₂(t, u, v);

Step S5: distance at first adopts oblique solution reference function H to compression unit ₆(v) the 12nd signal is carried out oblique solution and handle, generating the 13rd signal is S ₁₃(t, u v), carry out distance to Fourier transform to the 13rd signal then, and generating the 14th signal is S ₁₄(θ), the imaging region that this signal is acquisition comprises the look-down array antenna synthetic aperture radar three-dimensional focal image of amplitude and phase information in cylindrical coordinate system for u, r, and wherein, i target orientation in cylindrical coordinate system is x to coordinate figure in the imaging region _i, oblique distance is r to coordinate figure _i, argument is θ to coordinate figure _i

The described three-dimensional focal imaging method that is used for look-down array antenna synthetic aperture radar, its in imaging geometry, in the look-down array antenna synthetic aperture radar system array antenna array element be system at interval along distance to sampling interval d smaller or equal to λ _c/ [2sin (β/2)], wherein λ _cBe the carrier wavelength of radar emission signal, β is that the distance of emitting antenna is to beam angle.

The described three-dimensional focal imaging method that is used for look-down array antenna synthetic aperture radar, its described sampling interval d is smaller or equal to D _e, D wherein _eThe size that makes progress at distance for emitting antenna.

The described three-dimensional focal imaging method that is used for look-down array antenna synthetic aperture radar, its described sampling interval d smaller or equal to

Wherein H is the system platform flying height, W _yThe imaging fabric width that makes progress at distance for system.

The described three-dimensional focal imaging method that is used for look-down array antenna synthetic aperture radar, in its described look-down array antenna synthetic aperture radar system, array antenna employing single-shot is overcharged, the linear array structure of bistatic, wherein single emitting antenna is positioned at the central authorities of linear array, and receiving antenna array element battle array along the line is spacedly distributed.

The described three-dimensional focal imaging method that is used for look-down array antenna synthetic aperture radar, its in imaging geometry, distance to true aperture be centered close to the distance of look-down array antenna synthetic aperture radar imaging region to the center.

The described three-dimensional focal imaging method that is used for look-down array antenna synthetic aperture radar, its in imaging geometry, the distance of imaging region to the imaging fabric width greater than look-down array antenna synthetic aperture radar systematically apart to the linear array length of real aperture.

The described three-dimensional focal imaging method that is used for look-down array antenna synthetic aperture radar, its described distance to range migration correction cell processing step is:

Step S41: with the 9th signal along oblique distance to carrying out Fourier transform, generate the 10th signal S ₁₀(f _t, u, v);

Step S42: adopt range migration correction factor H ₄(f _t) the 10th signal is carried out distance to the range migration correction first time, generating the 101st signal is S ₁₀₁(f _t, u v), removes range migration item relevant with the oblique distance position in the 10th signal;

Step S43: adopt range migration correction factor H ₅(f _t) the 101st signal is carried out distance to the range migration correction second time, generating the 11st signal is S ₁₁(f _t, u v), removes range migration item relevant with the argument position in the 101st signal;

Step S44: the 11st signal is carried out oblique distance to inverse Fourier transform, and generating the 12nd signal is S ₁₂(t, u, v).

Beneficial effect of the present invention: the present invention is a kind of three-dimensional focal imaging method that is used for look-down array antenna synthetic aperture radar, this method arrives oblique distance to frequency field with the look-down array antenna synthetic aperture radar original echo data conversion that collects, and carries out oblique distance to matched filtering; Then the echoed signal of oblique distance after matched filtering transformed to the orientation to frequency field, selects the oblique distance reference planes to carry out the orientation to range migration correction, with the signal after proofreading and correct carry out the orientation to matched filtering and orientation to inverse Fourier transform; Oblique distance to carrying out distance to range migration correction with the signal of orientation after matched filtering, is carried out oblique distance then to inverse Fourier transform, obtain the two-dimensional radar image that each passage becomes; With the resulting two dimensional image of all passages carry out distance to oblique solution and distance to Fourier transform, reconstruct the three-dimensional radar image of imaging region in cylindrical coordinate system; By coordinate transform, obtain the three-dimensional radar image of imaging region in rectangular coordinate system in space.

The present invention has considered in the existing three-D imaging method that the two-dimensional distance migration of not considering proofreaies and correct problem, has strengthened the ubiquity that this method is suitable for.

The present invention forms operation transform with the distance in the existing three-D imaging method to wave beam and promptly obtains three-dimensional resolution image for once taking advantage of again with Fourier transform, shortens the required time of imaging.

Applicable elements of the present invention be look-down array antenna synthetic aperture radar along distance to sampling interval, promptly array antenna array element distance d is smaller or equal to λ _c/ [2sin (β/2)], distance of the present invention as can be seen is greater than the distance of prior art to sampling interval λ to sampling interval from formula _c/ 2, thus the needed bay number of array antenna in the look-down array antenna synthetic aperture radar reduced, help practical application.

Description of drawings

Fig. 1 is the look-down array antenna synthetic aperture radar three-dimensional imaging geometric representation that the present invention adopts;

Fig. 2 be in the look-down array antenna synthetic aperture radar imaging geometry that adopts of the present invention distance to-elevation to sectional view;

Fig. 3 is an airborne synthetic aperture radar imaging region synoptic diagram;

Fig. 4 is the look-down array antenna synthetic aperture radar three-dimensional focal imaging processing flow chart that the present invention adopts;

Fig. 5 is that the distance that adopts of the present invention is to range migration correction cell processing process flow diagram;

Fig. 6 is the locus distribution plan of 7 point targets of emulation input of the embodiment of the invention;

Fig. 7 is the look-down array antenna synthetic aperture radar three-dimensional imaging focusedimage that comprises 7 point targets of the embodiment of the invention;

Fig. 8 is that Fig. 7 of the embodiment of the invention is at 5 the point target distribution plans of argument on ° section of θ=0;

Fig. 9 be Fig. 7 of the embodiment of the invention in the orientation 5 point target distribution plans on the u=10m section;

Figure 10 is that Fig. 7 of the embodiment of the invention is at 5 the point target distribution plans of oblique distance on the r=490m section.

Embodiment

Describe each related detailed problem in the technical solution of the present invention in detail below in conjunction with accompanying drawing.Be to be noted that described embodiment only is intended to be convenient to the understanding of the present invention, and it is not played any qualification effect.

As shown in Figure 1, Oxyz is the rectangular coordinate system in space at look-down array antenna synthetic aperture radar and imaging region place thereof, imaging region be positioned at the look-down array antenna synthetic aperture radar line of flight under the zone, and about flight track, be x direction of principal axis symmetry, P _i(x _i, y _i, z _i) be i point target of imaging region and rectangular coordinate thereof.Qxr θ is the cylindrical coordinate system at look-down array antenna synthetic aperture radar and imaging region place thereof, perpendicular to the orientation to, promptly the axial distance of x to-elevation as shown in Figure 2 to the plane, P _i(x _i, r _i, θ _i) be i point target of imaging region and cylindrical coordinates thereof.Point target P _i(x _i, r _i, θ _i) rectangular space coordinate and the transformational relation between the cylindrical coordinates be:

$\left\{\begin{array}{c}{x}_i=x_i\\ y_i=r_i\sin {\mathrm{\θ}}_i\\ z_i=H-r_i\cos {\mathrm{\θ}}_i\end{array}\right.---\left(1\right)$

In the formula, H is a look-down array antenna synthetic aperture radar carrier aircraft flying height.L _xFor the look-down array antenna synthetic aperture radar orientation to length of synthetic aperture, L be the look-down array antenna synthetic aperture radar distance to length of real aperture, i.e. array antenna length, W _yFor the look-down array antenna synthetic aperture radar distance to the imaging fabric width, wherein distance is to imaging fabric width W _yGreater than look-down array antenna synthetic aperture radar systematically apart to length of real aperture L.

In the look-down array antenna synthetic aperture radar system, array antenna employing single-shot is overcharged, the linear array structure of bistatic, wherein single emitting antenna is positioned at the central authorities of linear array, also be distance to true aperture center Q place, the distance that is positioned at the look-down array antenna synthetic aperture radar imaging region is near center O.Receiving antenna array element battle array along the line is spacedly distributed v _nFor n pairing distance of receiving array antenna array element in the look-down array antenna synthetic aperture radar to coordinate, n=1 wherein, 2 ..., N, d are the receiving array antenna array element distance.In this look-down array antenna synthetic aperture radar imaging geometry, the orientation by look-down array antenna synthetic aperture radar to (x axle) motion formed be parallel to course made good (orientation to) the orientation to synthetic aperture; Form distance to true aperture by going up distribution linear array antenna to (y axle), and then the two-dimentional synthetic aperture plane that forms is positioned at surface level (be the orientation to-distance to the plane) along distance.The linear FM signal p of transmission antennas transmit (t) is:

$p\left(t\right)=\mathrm{rect}\left(\frac{t}{T}\right)\&CenterDot;\exp \left\{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}(f_{c}t+\frac{1}{2}{\mathrm{\&gamma;t}}^2)\right\}---\left(2\right)$

In the formula, j representation unit imaginary number, f _cThe carrier frequency of expression radar emission signal, γ represents the frequency modulation rate of radar emission linear FM signal, and T is the duration of pulse, and rect () is a rectangular window function.The bandwidth B of linear FM signal=γ T then.

For backscattering coefficient in the observation scene is δ _iTarget P _i(x _i, y _i, z _i), its desirable echoed signal that receives is:

$S_0(t,u,v)={\mathrm{\&delta;}}_i\&CenterDot;\mathrm{rect}\left(\frac{v-x_i}{L_x}\right)\&CenterDot;p\{t-\frac{R_i(u,v)}{C}\}\&CenterDot;\exp (-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}{f}_{c}t)---\left(3\right)$

In the formula,

Be observation scene internal object P _i(x _i, y _i, z _i) and look-down array antenna synthetic aperture radar between round distance, wherein:

$R_i^T\left(u\right)=\sqrt{{(u-x_i)}^2+y_i^2+{(H-z_i)}^2}$

(4)

$=\sqrt{{(u-x_i)}^2+r_i^2}$

Be target P _i(x _i, y _i, z _i) and emitting antenna between distance.

$R_i^R(u,v)=\sqrt{{(u-x_i)}^2+{(v-y_i)}^2+{(H-z_i)}^2}$

(5)

$=\sqrt{{(u-x_i)}^2+v^2-{2\mathrm{vr}}_i\sin {\mathrm{\&theta;}}_i+r_{\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">i</figure-callout>}}^2}$

Be target P _i(x _i, y _i, z _i) and receiving antenna between distance.According to Taylor's formula, R _i(u v) can be approximately:

$R_i(u,v)\&ap;{2r}_i+\frac{{(u-x_i)}^2}{r_i}+\frac{{\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">v</figure-callout>}}^2}{{2r}_i}-v{\sin \mathrm{\&theta;}}_i---\left(6\right)$

Shown in the process flow diagram of the three-dimensional focal imaging method that is used for look-down array antenna synthetic aperture radar that proposes as Fig. 4 the present invention, data for the look-down array antenna synthetic aperture radar collection, wherein, be input as the look-down array antenna synthetic aperture radar original echo, through the obtained look-down array antenna synthetic aperture radar 3-D view after the three-dimensional imaging focusing processing, concrete implementation step is as follows:

Step S1: the look-down array antenna synthetic aperture radar system acquisition to machine under the original echoed signals of imaging region be S ₀(t, u, v), oblique distance to compression unit with original echoed signals along oblique distance to carrying out Fourier transform, generating the 1st signal is S ₁(f _t, u, v), expression formula is:

$S_1(f_t,u,v)={\mathrm{\&delta;}}_i\&CenterDot;\mathrm{rect}\left(\frac{u-x_i}{L_x}\right)\&CenterDot;\mathrm{rect}\left(\frac{f_t}{\mathrm{\&gamma;T}}\right).$

(7)

$\exp (-\mathrm{j\&pi;}\frac{{\mathrm{<figure-callout\; id="2"\; label="f\; t"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">f</figure-callout>}}_t^{}}{\mathrm{\&gamma;}})\&CenterDot;\exp \{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}(f_c+f_t)\frac{R_i(u,v)}{C}\}$

Adopt oblique distance to matched filter H ₁(f _t) the 1st signal is carried out oblique distance handle H to focal imaging ₁(f _t) expression formula is:

$H_1\left(f_t\right)=\mathrm{rect}\left(\frac{f_t}{\mathrm{\&gamma;T}}\right)\&CenterDot;\exp \left(\mathrm{j\&pi;}\frac{{\mathrm{<figure-callout\; id="2"\; label="f\; t"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">f</figure-callout>}}_t^{}}{\mathrm{\&gamma;}}\right)---\left(8\right)$

Generating the 2nd signal is S ₂(f _t, u, v), expression formula is:

$S_2(f_t,u,v)={\mathrm{\&delta;}}_i\&CenterDot;\mathrm{rect}\left(\frac{u-x_i}{L_x}\right)\&CenterDot;\mathrm{rect}\left(\frac{f_t}{\mathrm{\&gamma;T}}\right)\&CenterDot;\exp \{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}(f_c+f_t)\frac{R_i(u,v)}{C}\}---\left(9\right)$

Then the 2nd signal is carried out oblique distance to inverse Fourier transform, generating the 3rd signal is S ₃(v), expression formula is for t, u:

$S_3(t,u,v)={\mathrm{\&delta;}}_i\&CenterDot;\mathrm{rect}\left(\frac{u-x_i}{L_x}\right)\&CenterDot;\sin c\left\{B(t-\frac{R_i(u,v)}{C})\right\}\&CenterDot;\exp \{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}{f}_c\frac{R_i(u,v)}{C}\}---\left(10\right)$

Wherein, oblique distance is t to fast time domain, and oblique distance is f to frequency field _t, the orientation is that u and distance are v to time domain to time domain;

Step S2: the orientation to the range migration correction unit will generate the 3rd signal along the orientation to carrying out Fourier transform, generating the 4th signal is S ₄(t, f _u, v), expression formula is:

$S_4(t,f_u,v)={\mathrm{\&delta;}}_i\&CenterDot;\mathrm{rect}\left(\frac{f_u}{{\mathrm{\&gamma;}}_x{L}_x}\right)\&CenterDot;\exp \left(\mathrm{j\&pi;}\frac{{\mathrm{<figure-callout\; id="2"\; label="f\; u"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">f</figure-callout>}}_u^{}}{{\mathrm{\&gamma;}}_x}\right)\&CenterDot;\exp (-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}{f}_u{x}_i)\&CenterDot;$

(11)

$\sin c\left\{B(t-\frac{R_i^{\&prime;}(f_u,v)}{C})\right\}\&CenterDot;\exp (-j\frac{\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_c}\frac{v^2-2v{r}_i\sin {\mathrm{\&theta;}}_i}{r_i})\&CenterDot;\exp (-\mathrm{<figure-callout\; id="4"\; label="j"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{4\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_c}{r}_i)$

Wherein, the orientation is f to frequency field _u, the orientation is to frequency modulation rate γ _x=2/ (λ _cr _i), the range migration item R ' in the orientation frequency field _i(f _u, v) expression formula is:

$R_i^{\&prime;}(f_u,v)=2r_i+\frac{{\mathrm{\&lambda;}}_c^2{r}_{\mathrm{<figure-callout\; id="2"\; label="i\; f\; u"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">i</figure-callout>}}{f}_u^{}{}_2^{}}{4}+\frac{{\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">v</figure-callout>}}^2}{{2r}_i}-v\sin {\mathrm{\&theta;}}_i---\left(12\right)$

Then to the 4th signal along oblique distance to carrying out Fourier transform, generating the 5th signal is S ₅(f _t, f _u, v), expression formula is:

$S_5(f_t,f_u,v)={\mathrm{\&delta;}}_i\&CenterDot;\mathrm{rect}\left(\frac{f_u}{{\mathrm{\&gamma;}}_x{L}_x}\right)\&CenterDot;\exp \left(\mathrm{j\&pi;}\frac{{\mathrm{<figure-callout\; id="2"\; label="f\; u"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">f</figure-callout>}}_u^{}}{{\mathrm{\&gamma;}}_x}\right)\&CenterDot;\exp (-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}{f}_u{x}_i)\&CenterDot;$

(13)

$\mathrm{rect}\left(\frac{f_t}{B}\right)\&CenterDot;\exp (-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}{f}_t\frac{R_i^{\&prime;}(f_u,v)}{C})\&CenterDot;\exp (-j\frac{\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_c}\frac{v^2-2v{r}_i\sin {\mathrm{\&theta;}}_i}{r_i})\&CenterDot;\exp (-\mathrm{<figure-callout\; id="4"\; label="j"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{4\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_c}{r}_i)$

Adopt range migration correction factor H ₂(f _t) the 5th signal is carried out the orientation to range migration correction, H ₂(f _t) expression formula is:

$H_2\left(f_t\right)=\exp \left(\mathrm{j\&pi;}\frac{{\mathrm{\&lambda;}}_c^2{r}_{\mathrm{<figure-callout\; id="2"\; label="i\; f\; u"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">i</figure-callout>}}{f}_u^{}{}_2^{}}{2C}{f}_t\right)---\left(14\right)$

Generating the 6th signal is S ₆(f _t, f _u, v), expression formula is:

$S_6(f_t,f_u,v)={\mathrm{\&delta;}}_i\&CenterDot;\mathrm{rect}\left(\frac{f_u}{{\mathrm{\&gamma;}}_x{L}_x}\right)\&CenterDot;\exp \left(\mathrm{j\&pi;}\frac{{\mathrm{<figure-callout\; id="2"\; label="f\; u"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">f</figure-callout>}}_u^{}}{{\mathrm{\&gamma;}}_x}\right)\&CenterDot;\exp (-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}{f}_u{x}_i)\&CenterDot;\mathrm{rect}\left(\frac{f_t}{B}\right)\&CenterDot;$

(15)

$\exp \{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\frac{f_t}{C}({2r}_i+\frac{{\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">v</figure-callout>}}^2}{{2r}_i}-v\sin {\mathrm{\&theta;}}_i)\}\&CenterDot;\exp (-j\frac{\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_c}\frac{v^2-2v{r}_i\sin {\mathrm{\&theta;}}_i}{r_i})\&CenterDot;\exp (-\mathrm{<figure-callout\; id="4"\; label="j"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{4\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_c}{r}_i)$

Then the 6th signal is carried out oblique distance to inverse Fourier transform, generating the 7th signal is S ₇(t, f _u, v), expression formula is:

$S_7(t,f_u,v)={\mathrm{\&delta;}}_i\&CenterDot;\mathrm{rect}\left(\frac{f_u}{{\mathrm{\&gamma;}}_x{L}_x}\right)\&CenterDot;\exp \left(\mathrm{j\&pi;}\frac{{\mathrm{<figure-callout\; id="2"\; label="f\; u"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">f</figure-callout>}}_u^{}}{{\mathrm{\&gamma;}}_x}\right)\&CenterDot;\exp (-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}{f}_u{x}_i)\&CenterDot;\exp (-\mathrm{<figure-callout\; id="4"\; label="j"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{4\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_c}\&CenterDot;r_i)\&CenterDot;$

(16)

$\sin c\left\{B\right[t-({2r}_i+\frac{{\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">v</figure-callout>}}^2}{{2r}_i}-v\sin {\mathrm{\&theta;}}_i)/C\left]\right\}\&CenterDot;\exp (-j\frac{\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_c}\frac{v^2-2v{r}_i\sin {\mathrm{\&theta;}}_i}{r_i})$

Step S3: the orientation adopts the orientation to matched filter H to compression unit ₃(f _t) the 7th signal is carried out the orientation handle H to focal imaging ₃(f _t) expression formula is:

$H_3\left(f_t\right)=\mathrm{rect}\left(\frac{f_u}{{\mathrm{\&gamma;}}_x{L}_x}\right)\&CenterDot;\exp (-\mathrm{j\&pi;}\frac{{\mathrm{<figure-callout\; id="2"\; label="f\; u"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">f</figure-callout>}}_u^{}}{{\mathrm{\&gamma;}}_x})---\left(17\right)$

Generating the 8th signal is S ₈(t, f _u, v), expression formula is:

$S_8(t,f_u,v)={\mathrm{\&delta;}}_i\&CenterDot;\mathrm{rect}\left(\frac{f_u}{{\mathrm{\&gamma;}}_x{L}_x}\right)\&CenterDot;\exp (-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}{f}_u{x}_i)\&CenterDot;\exp (-\mathrm{<figure-callout\; id="4"\; label="j"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{4\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_c}\&CenterDot;r_i)\&CenterDot;$

(18)

$\sin c\left\{B\right[t-({2r}_i+\frac{{\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">v</figure-callout>}}^2}{{2r}_i}-v\sin {\mathrm{\&theta;}}_i)/C\left]\right\}\&CenterDot;\exp (-j\frac{\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_c}\frac{v^2-2v{r}_i\sin {\mathrm{\&theta;}}_i}{r_i})$

Then the 8th signal is carried out the orientation to inverse Fourier transform, generating the 9th signal is S ₉(v), expression formula is for t, u:

$S_9(t,u,v)={\mathrm{\&delta;}}_i\&CenterDot;\sin c\left\{B_x(u-x_i)\right\}\&CenterDot;\sin c\left\{B\right[t-({2r}_i+\frac{{\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">v</figure-callout>}}^2}{{2r}_i}-v\sin {\mathrm{\&theta;}}_i)/C\left]\right\}\&CenterDot;$

(19)

$\exp (-j\frac{\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_c}\frac{v^2-2v{r}_i\sin {\mathrm{\&theta;}}_i}{r_i})\&CenterDot;\exp (-\mathrm{<figure-callout\; id="4"\; label="j"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{4\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_c}{r}_i)$

In the formula, B _xFor the orientation to doppler bandwidth, expression formula is B _x=γ _xL _x

Step S4: distance to the range migration correction unit step as shown in Figure 5, specific implementation process is:

Step S41: with the 9th signal along oblique distance to carrying out Fourier transform, generate the 10th signal S ₁₀(f _t, u, v), expression formula is:

$S_{10}(f_t,u,v)={\mathrm{\&delta;}}_i\sin c\left\{B_x(u-x_i)\right\}\&CenterDot;\exp (-\mathrm{<figure-callout\; id="4"\; label="j"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{4\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_c}{r}_i)\&CenterDot;\mathrm{rect}\left(\frac{f_t}{B}\right)\&CenterDot;$

(20)

$\exp \{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\frac{f_t}{C}({2r}_i+\frac{{\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">v</figure-callout>}}^2}{{2r}_i}-v\sin {\mathrm{\&theta;}}_i)\}\&CenterDot;\exp (-j\frac{\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_c}\frac{v^2-2v{r}_i\sin {\mathrm{\&theta;}}_i}{r_i})$

Step S42: adopt range migration correction factor H ₄(f _t) the 10th signal is carried out distance to the range migration correction first time, H ₄(f _t) expression formula is:

$H_4\left(f_t\right)=\exp \left(\mathrm{j\&pi;}\frac{v^2}{C{\mathrm{\&gamma;}}_i}{f}_t\right)---\left(21\right)$

Generating the 101st signal is S ₁₀₁(f _t, u, v), expression formula is:

$S_{101}(f_t,u,v)={\mathrm{\&delta;}}_i\sin c\left\{B_x(u-x_i)\right\}\&CenterDot;\exp (-\mathrm{<figure-callout\; id="4"\; label="j"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{4\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_c}{r}_i)\&CenterDot;\mathrm{rect}\left(\frac{f_t}{B}\right)\&CenterDot;$

(22)

$\exp \{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\frac{f_t}{C}({2r}_i-v\sin {\mathrm{\&theta;}}_i)\}\&CenterDot;\exp (-j\frac{\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_c}\frac{v^2-2v{r}_i\sin {\mathrm{\&theta;}}_i}{r_i})$

Range migration item relevant with the oblique distance position in the 10th signal is removed;

Step S43: adopt range migration correction factor H ₅(f _t) the 101st signal is carried out distance to the range migration correction second time, H ₅(f _t) expression formula is:

$H_5\left(f_t\right)=\exp (-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\frac{{v\sin \mathrm{\&theta;}}_i}{C}{f}_t)---\left(23\right)$

Generating the 11st signal is S ₁₁(f _t, u, v), expression formula is:

$S_{11}(f_t,u,v)={\mathrm{\&delta;}}_i\&CenterDot;\sin c\left\{B_x(u-x_i)\right\}\&CenterDot;\exp (-\mathrm{<figure-callout\; id="4"\; label="j"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{4\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_c}{r}_i)\&CenterDot;\mathrm{rect}\left(\frac{f_t}{B}\right)\&CenterDot;$

(24)

$\exp (-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\frac{{2r}_i}{C}{f}_t)\&CenterDot;\exp (-j\frac{\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_c}\frac{v^2-2v{r}_i\sin {\mathrm{\&theta;}}_i}{r_i})$

Range migration item relevant with the argument position in the 101st signal is removed;

Step S44: the 11st signal is carried out oblique distance to inverse Fourier transform, and generating the 12nd signal is S ₁₂(v), expression formula is for t, u:

$S_9(t,u,v)={\mathrm{\&delta;}}_i\&CenterDot;\sin c\left\{B_x(u-x_i)\right\}\&CenterDot;\sin c\left\{B(t-\frac{{2r}_i}{C})\right\}\&CenterDot;$

(25)

$\exp (-j\frac{\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_c}\frac{v^2-2v{r}_i\sin {\mathrm{\&theta;}}_i}{r_i})\&CenterDot;\exp (-\mathrm{<figure-callout\; id="4"\; label="j"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{4\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_c}{r}_i)$

Step S5: distance at first adopts oblique solution reference function H to compression unit ₆(v) the 12nd signal is carried out oblique solution and handle H ₆(v) expression formula is:

$H_6\left(v\right)=\exp \left(\mathrm{j\&pi;}\frac{{\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">v</figure-callout>}}^2}{{\mathrm{\&lambda;}}_c{r}_i}\right)---\left(26\right)$

Generating the 13rd signal is S ₁₃(v), expression formula is for t, u:

$S_{13}(t,u,v)={\mathrm{\&delta;}}_i\&CenterDot;\sin c\left\{B_x(u-x_i)\right\}\&CenterDot;\sin c\left\{B(t-\frac{{2r}_i}{C})\right\}\&CenterDot;$

(27)

$\exp \left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_c}v\sin {\mathrm{\&theta;}}_i\right)\&CenterDot;\exp (-\mathrm{<figure-callout\; id="4"\; label="j"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{4\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_c}{r}_i)$

Then the 13rd signal is carried out distance to Fourier transform, generating the 14th signal is S ₁₄(θ), expression formula is for u, r:

$S_{14}(u,r,\mathrm{\&theta;})={\mathrm{\&delta;}}_i\&CenterDot;\sin c\left\{B_x(u-x_i)\right\}\&CenterDot;\sin c\left\{B_r(r-r_i)\right\}\&CenterDot;$

$\frac{\sin \left[\frac{\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_c}\mathrm{Nd}(\sin \mathrm{\&theta;}-\sin {\mathrm{\&theta;}}_i)\right]}{\sin \left[\frac{\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_c}d(\sin \mathrm{\&theta;}-\sin {\mathrm{\&theta;}}_i)\right]}\&CenterDot;\exp (-\mathrm{<figure-callout\; id="4"\; label="j"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{4\mathrm{\&pi;}}{{\mathrm{\&lambda;}}_c}{r}_i)---\left(28\right)$

In the formula, B _r=2B/C.The imaging region that this signal is acquisition cylindrical coordinate system (orientation to, oblique distance to argument to) in comprise the look-down array antenna synthetic aperture radar three-dimensional focal image of amplitude and phase information, wherein, i target orientation in cylindrical coordinate system is x to coordinate figure in the imaging region _i, oblique distance is r to coordinate figure _i, argument is θ to coordinate figure _i

In the look-down array antenna synthetic aperture radar array element distance d of array antenna by system in make progress spatial sampling theorem decision of distance, apart can not be too near between the array element, otherwise the mutual lotus root effect between the array-element antenna can have a strong impact on the directional performance of system, but can not be too far away apart, otherwise system upwards can the angle of arrival fuzzy problem at argument.

By formula (28) as can be seen, the 14th signal S ₁₄(x, r, θ) sin[π Nd (the sin θ-sin θ in _i)/λ _c]/sin[π d (sin θ-sin θ _i)/λ _c] be periodic function about sin θ, when satisfying π d (sin θ _Main-sin θ _i)/λ _c-π d (sin θ _Amb-sin θ _i)/λ _c=| during l| π, remove at argument θ _MainOccur outside the main lobe peak value, also can be at θ _AmbGraing lobe appears, in the formula,

The progression of expression graing lobe.Thereby the pass that can calculate target argument and fuzzy angle is:

The look-down array antenna synthetic aperture radar argument is determined to beam angle β by the emitting antenna distance to the imaging scope, for [β/2, β/2], if θ _AmbDrop in this scope, then final imaging results can be at θ _AmbGraing lobe appears in the position, and this moment, system's argument was to there being the angle fuzzy problem.For avoiding the argument fuzzy problem, formula (29) should satisfy:

(30)

Because look-down array antenna synthetic aperture radar is bowed argument to imaging scope [β/2, β/2] at [pi/2, pi/2] within, the sine function sin θ of argument θ is a monotone variation in this scope, therefore, if first order graing lobe (promptly | l|=1) argument is dropped on outside imaging scope [β/2, β/2] in the angle position, and then argument also can be dropped on outside the imaging scope in the graing lobe that progression is higher (promptly | l|＞1) angle position.Therefore, when distance to spatial sampling below at interval d satisfies during condition, system makes progress at argument can the angle of arrival fuzzy problem.

$d\&le;\frac{{\mathrm{\&lambda;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">c</figure-callout>}}}{2\sin \frac{\mathrm{\&beta;}}{2}}---\left(31\right)$

Because the emitting antenna distance to beam angle β ∈ [0, π], satisfies

And β and emitting antenna distance are to dimension D _eBetween the pass be β=λ _c/ D _eSo the constraint condition that d need satisfy in the formula (31) can be written as in addition:

$d\&le;\frac{{\mathrm{\&lambda;}}_c}{\mathrm{\&beta;}}\&DoubleRightArrow;d\&le;D_e---\left(32\right)$

By shown in Figure 1, by following geometric relationship:

Substitution formula (31) can get distance and adopt interval d and stride course imaging fabric width W to the space _yAnd the pass between the carrier flying height H is:

$d\&le;\frac{{\mathrm{\&lambda;}}_c{R}_c}{W_y}=\frac{{\mathrm{\&lambda;}}_{\mathrm{<figure-callout\; id="2"\; label="c\; H"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">c</figure-callout>}}\sqrt{H^{}}\sqrt{{}^2+{\mathrm{<figure-callout\; id="2"\; label="W\; y"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">W</figure-callout>}}_y^{}/4}}{W_y}=\frac{{\mathrm{\&lambda;}}_c\sqrt{{4\mathrm{<figure-callout\; id="2"\; label="H"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">H</figure-callout>}}^2+{\mathrm{<figure-callout\; id="2"\; label="W\; y"\; filenames="H2009100819977E00061.png,H2009100819977E00071.png"\; state="\{\{state\}\}">W</figure-callout>}}_y^{}}}{{2W}_y}---\left(33\right)$

With the point target that is arranged in three dimensions is example, and the radar carrier wavelength is λ _c=8mm, linear FM signal bandwidth B=375MHz, carrier flying height H=500m, the real aperture length L=6m of array antenna, the emitting antenna distance is to beam angle β=6 °, can calculate array antenna array element distance d=7.64cm by formula (31), then form by 1 emitting antenna and 28 receiving antennas in the array antenna.Imaging region has 7 point targets, and its locus is δ=1 to scattering coefficient thereafter as shown in Figure 6.Then the imaging results of 7 point targets that obtain by three-dimensional focal imaging method of the present invention is shown in Fig. 7-10, wherein Fig. 7 is after comprising the look-down array antenna synthetic aperture radar three-dimensional imaging normalization of 7 point targets-3dB profile display result, the orientation to oblique distance to coordinate unit be m, argument to coordinate unit be °, cylindrical coordinates position in the relative look-down array antenna synthetic aperture radar imaging geometry of numeral on the coordinate axis, by seeing with Fig. 6 contrast, behind above-mentioned treatment step, can accurately reconstruct the locus and the amplitude information of 7 point targets.Fig. 8 is Fig. 7 at 5 the point target distribution plans of argument on θ=0 ° section (orientation to-oblique distance to the plane), because the amplitude unanimity of each point target in the emulation, therefore dynamic display image is also consistent, and simultaneously, the position of each point target also is consistent with the position of realistic objective.Fig. 9 is Fig. 7 at 5 the point target distribution plans of oblique distance on u=10m section (oblique distance to-argument to the plane), because the amplitude unanimity of each point target in the emulation, therefore dynamic display image is also consistent, and simultaneously, the position of each point target also is consistent with the position of realistic objective.Figure 10 is Fig. 7 at 5 the point target distribution plans of oblique distance on r=490m section (orientation to-argument to the plane), because the amplitude unanimity of each point target in the emulation, therefore dynamic display image is also consistent, and simultaneously, the position of each point target also is consistent with the position of realistic objective.

The present invention has considered in the existing three-D imaging method that the two-dimensional distance migration of not considering proofreaies and correct problem, has strengthened the ubiquity that this method is suitable for.

The present invention forms operation transform with the distance in the existing three-D imaging method to wave beam and promptly obtains three-dimensional resolution image for once taking advantage of again with Fourier transform, shortens the required time of imaging.

The invention enables look-down array antenna synthetic aperture radar along distance to sampling interval, promptly array antenna array element distance d is smaller or equal to λ _c/ [2sin (β/2)] also can be suitable for, and distance of the present invention as can be seen is greater than the distance of prior art to sampling interval λ to sampling interval from formula _c/ 2, thus the needed bay number of array antenna in the look-down array antenna synthetic aperture radar reduced, help practical application.

The method that the present invention is above-mentioned has been used MATLAB software on computers and has been verified, and Fig. 7-Figure 10 is the result who uses the method for the invention to obtain under the MATLAB software environment.This method mainly realizes by 5 program modules on computing machine or specialized equipment, as shown in Figure 4, described oblique distance to compression unit, orientation to range migration correction unit, orientation to compression unit, distance to range migration correction unit and distance to compression unit, the function of completing steps S1, step S2, step S3, step S4 and step S5 respectively.

Oblique distance is input as look-down array antenna synthetic aperture radar original echo data to compression unit, be output as be in oblique distance to time domain, orientation to time domain and distance the 3rd signal to time domain;

The orientation is input as the 3rd signal to the range migration correction unit, be output as be in oblique distance to time domain, orientation to frequency field and distance the 7th signal to time domain;

The orientation is input as the 7th signal to compression unit, be output as be in oblique distance to time domain, orientation to time domain and distance the 9th signal to time domain;

Distance is input as the 9th signal to the range migration correction unit, be output as be in oblique distance to time domain, orientation to time domain and distance the 12nd signal to time domain;

Distance is input as the 12nd signal to compression unit, be output as focus in the cylindrical coordinate system orientation to, oblique distance to argument to the look-down array antenna synthetic aperture radar 3-D view that comprises amplitude and phase information.

The above; only be the embodiment among the present invention; but protection scope of the present invention is not limited thereto; anyly be familiar with the people of this technology in the disclosed technical scope of the present invention; can understand conversion or the replacement expected; all should be encompassed in of the present invention comprising within the scope, therefore, protection scope of the present invention should be as the criterion with the protection domain of claims.

Claims (8)

1. a three-dimensional focal imaging method that is used for look-down array antenna synthetic aperture radar is characterized in that, comprises that step is as follows:

Step S1: the look-down array antenna synthetic aperture radar system acquisition to the imaging region original echoed signals be S ₀(t, u, v), oblique distance to compression unit with original echoed signals along oblique distance to carrying out Fourier transform, generating the 1st signal is S ₁(f _t, u v), adopts oblique distance to matched filter H ₁(f _t) the 1st signal is carried out oblique distance handle to focal imaging, generating the 2nd signal is S ₂(f _t, u v), carries out oblique distance to inverse Fourier transform to the 2nd signal then, and generating the 3rd signal is S ₃(v), wherein, oblique distance is t to fast time domain for t, u, and oblique distance is f to frequency field _t, the orientation is that u and distance are v to time domain to time domain;

Step S2: to carrying out Fourier transform, generate the 4th signal is S to the 3rd signal that the orientation will generate to the range migration correction unit along the orientation ₄(t, f _u, v), wherein, the orientation is f to frequency field _u, then to the 4th signal along oblique distance to carrying out Fourier transform, generating the 5th signal is S ₅(f _t, f _u, v), adopt range migration correction factor H ₂(f _t) the 5th signal is carried out the orientation to range migration correction, generating the 6th signal is S ₆(f _t, f _u, v), then the 6th signal is carried out oblique distance to inverse Fourier transform, generating the 7th signal is S ₇(t, f _u, v);

Step S3: the orientation adopts the orientation to matched filter H to compression unit ₃(f _t) the 7th signal is carried out the orientation handle to focal imaging, generating the 8th signal is S ₈(t, f _u, v), then the 8th signal is carried out the orientation to inverse Fourier transform, generating the 9th signal is S ₉(t, u, v);

Step S4: distance to the range migration correction unit with the 9th signal along oblique distance to carrying out Fourier transform, generate the 10th signal S ₁₀(f _t, u v), carries out distance to range migration correction to the 10th signal, and generating the 11st signal is S ₁₁(f _t, u v), carries out oblique distance to inverse Fourier transform to the 11st signal, and generating the 12nd signal is S ₁₂(t, u, v);

Step S5: distance at first adopts oblique solution reference function H to compression unit ₆(v) the 12nd signal is carried out oblique solution and handle, generating the 13rd signal is S ₁₃(t, u v), carry out distance to Fourier transform to the 13rd signal then, and generating the 14th signal is S ₁₄(θ), the imaging region that this signal is acquisition comprises the look-down array antenna synthetic aperture radar three-dimensional focal image of amplitude and phase information in cylindrical coordinate system for u, r, and wherein, i target orientation in cylindrical coordinate system is x to coordinate figure in the imaging region _i, oblique distance is r to coordinate figure _i, argument is θ to coordinate figure _i

2. according to the three-dimensional focal imaging method that is used for look-down array antenna synthetic aperture radar described in the claim 1, it is characterized in that, in imaging geometry, in the look-down array antenna synthetic aperture radar system array antenna array element be system at interval along distance to sampling interval d smaller or equal to λ _c/ [2sin (β/2)], wherein λ _cBe the carrier wavelength of radar emission signal, β is that the distance of emitting antenna is to beam angle.

3. according to the three-dimensional focal imaging method that is used for look-down array antenna synthetic aperture radar described in the claim 2, it is characterized in that described sampling interval d is smaller or equal to D _e, D wherein _eThe size that makes progress at distance for emitting antenna.

4. according to the three-dimensional focal imaging method that is used for look-down array antenna synthetic aperture radar described in the claim 2, it is characterized in that, described sampling interval d smaller or equal to

Wherein H is the system platform flying height, W _yThe imaging fabric width that makes progress at distance for system.

5. according to the three-dimensional focal imaging method that is used for look-down array antenna synthetic aperture radar described in the claim 1, it is characterized in that, in the described look-down array antenna synthetic aperture radar system, array antenna employing single-shot is overcharged, the linear array structure of bistatic, wherein single emitting antenna is positioned at the central authorities of linear array, and receiving antenna array element battle array along the line is spacedly distributed.

6. according to the three-dimensional focal imaging method that is used for look-down array antenna synthetic aperture radar described in the claim 1, it is characterized in that, in imaging geometry, distance to true aperture be centered close to the distance of look-down array antenna synthetic aperture radar imaging region to the center.

7. according to the three-dimensional focal imaging method that is used for look-down array antenna synthetic aperture radar described in the claim 1, it is characterized in that, in imaging geometry, the distance of imaging region to the imaging fabric width greater than look-down array antenna synthetic aperture radar systematically apart to the linear array length of real aperture.

8. according to the three-dimensional focal imaging method that is used for look-down array antenna synthetic aperture radar described in the claim 1, it is characterized in that among the described step S4, distance to the treatment step of range migration correction unit is:

Step S41: with the 9th signal along oblique distance to carrying out Fourier transform, generate the 10th signal S ₁₀(f _t, u, v);

Step S42: adopt range migration correction factor H ₄(f _t) the 10th signal is carried out distance to the range migration correction first time, generating the 101st signal is S ₁₀₁(f _t, u v), removes range migration item relevant with the oblique distance position in the 10th signal;

Step S43: adopt range migration correction factor H ₅(f _t) the 101st signal is carried out distance to the range migration correction second time, generating the 11st signal is S ₁₁(f _t, u v), removes range migration item relevant with the argument position in the 101st signal;

Step S44: the 11st signal is carried out oblique distance to inverse Fourier transform, and generating the 12nd signal is S ₁₂(t, u, v).

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