CN102608576A - Geometric correction method for large rake forward synthetic aperture radar return image - Google Patents

Abstract

The invention discloses a geometric correction two-dimensional Sinc interpolation method for a large rake forward synthetic aperture radar (SAR), which belongs to the technical field of SAR imaging. According to the asymmetrical characteristic of a point spread function side band, a novel two-dimensional Sinc interpolation function is constructed for the geometric correction of a large rake forward SAR image. The method also introduces two parameters into the interpolation function, so interpolation and lowpass filtering can be realized at the same time, the spatial variability of image resolution can be eliminated, and under-sampling can be avoided when a ground distance pixel interval is larger.

Description

A kind of geometric correction method that is used for big preceding oblique synthetic-aperture radar echo

Technical field

The present invention relates to the synthetic aperture radar (SAR) imaging field, specifically, is a kind of big preceding tiltedly geometric correction method of synthetic-aperture radar echo that is used for.

Background technology

Among the oblique SAR, the front bevel angle is violent along with oblique distance changes, thereby makes Doppler center and doppler frequency rate with the oblique distance significant change, when carrying out imaging processing, must consider the space-variant property of these Doppler parameters before big.Because considered the space-variant property at Doppler center, the point spread function that imaging algorithm is derived has asymmetrical two-dimentional secondary lobe, this asymmetrical sidelobe structure can cause its frequency spectrum to be distorted, thereby no longer about the frequency axis symmetry.Because sampling rate is limited, the distortion of frequency spectrum develops into the folding of frequency spectrum through regular meeting.

Before big tiltedly the SAR slant-range image under the pattern serious geometric distortion is arranged, must carry out geometry correction to it after, just can be used for identification of targets and coupling further.Geometry correction need be carried out interpolation to two dimensional image, and the traditional two-dimensional interpolation method is all realized by two separable one dimension interpolation, and these one dimension interpolation all are equivalent to about the axisymmetric window function of frequency at frequency domain.But before big tiltedly the frequency spectrum of the point spread function of SAR slant-range image be asymmetric about frequency axis, and often fold, thereby the traditional two-dimensional interpolation method can be introduced tangible distortion when carrying out before big oblique SAR geometry correction.

Tiltedly the space-variant property of SAR distance image resolution ratio is bigger before big, when pixel separation is big, just possibly owes sampling and makes some track rejections, therefore need before geometry correction, carry out LPF to slant-range image, eliminates the space-variant property of resolution.But increase step low pass operation, will certainly increase operand.If can LPF and interpolation be combined, just can under the situation that does not increase calculated amount, realize LPF.

So two-dimensional interpolation method that needs a kind of ability to adapt to big preceding tiltedly SAR point spread function characteristic and be easy to combine with LPF.

Summary of the invention

In view of this; The invention provides a kind of big preceding tiltedly geometric correction method of synthetic-aperture radar echo that is used for, can carry out geometry correction to big preceding tiltedly SAR slant-range image, and can combine LPF; Eliminate the space-variant property of resolution, avoid the generation of owing to sample simultaneously.

A kind of big preceding tiltedly geometric correction method of synthetic-aperture radar echo that is used for of the present invention; Slant-range image utilizing spectrum analysis SPECAN imaging algorithm to the echo of oblique synthetic-aperture radar before big carries out in the step of geometry correction; Adopt function h (t; τ) slant-range image is carried out two-dimensional interpolation and handle, obtain the distance image then;

Said function h (t, expression formula τ) is:

h(t，τ)＝sinc(F _r·τ)sinc[F _a·(t+Kτ)]

F wherein _rBe slant-range image distance to sampling rate, F _aFor slant-range image in the orientation to sampling rate, t is the orientation time, τ is apart from the time, $K=\frac{2\mathrm{Vc}}{\mathrm{\&lambda;}}\&CenterDot;\mathrm{Cos}\mathrm{\&alpha;}\&CenterDot;\frac{h^2}{{{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HDA0000145069240000012.png,HDA0000145069240000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_0}^2\sqrt{{{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HDA0000145069240000012.png,HDA0000145069240000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_0}^2-h^2}}/[-2f_{\mathrm{Dr}}\left(r_0\right)],$ C is the light velocity, and v is the movement velocity of Texas tower, and λ is the carrier wavelength of radar, α be the velocity of Texas tower at floor projections and wave beam direction of visual lines angle in floor projections, h be big before the oblique height of Texas tower in the polarization sensitive synthetic aperture radar system, r ₀Be the oblique distance of imaging scene center, f _Dr(r ₀) be the doppler frequency rate at imaging scene center place.

A kind of big preceding tiltedly geometric correction method of synthetic-aperture radar echo that is used for of the present invention carries out in the step of geometry correction at the slant-range image that utilizes spectrum analysis SPECAN imaging algorithm to the echo of oblique synthetic-aperture radar before big, adopts function h _LP(t τ) carries out two-dimensional interpolation to slant-range image and handles, and obtains the distance image then;

Said function h _LP(t, expression formula τ) is: $h_{\mathrm{LP}}(t,\mathrm{\&tau;})=\mathrm{Sin}c(\frac{F_r}{{\mathrm{\&gamma;}}_r}\&CenterDot;\mathrm{\&tau;})\mathrm{Sin}c[\frac{F_a}{{\mathrm{\&gamma;}}_a}\&CenterDot;(t+\mathrm{K\&tau;})];$

F wherein _rBe slant-range image distance to sampling rate, F _aFor slant-range image in the orientation to sampling rate, t is the orientation time, τ is apart from the time, $K=\frac{2\mathrm{Vc}}{\mathrm{\&lambda;}}\&CenterDot;\mathrm{Cos}\mathrm{\&alpha;}\&CenterDot;\frac{h^2}{{{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HDA0000145069240000012.png,HDA0000145069240000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_0}^2\sqrt{{{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HDA0000145069240000012.png,HDA0000145069240000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_0}^2-h^2}}/[-2f_{\mathrm{Dr}}\left(r_0\right)],$ C is the light velocity, and v is the movement velocity of Texas tower, and λ is the carrier wavelength of radar, α be the velocity of Texas tower at floor projections and wave beam direction of visual lines angle in floor projections, h be big before the oblique height of Texas tower in the polarization sensitive synthetic aperture radar system, r ₀Be the oblique distance of imaging scene center, f _Dr(r ₀) be the doppler frequency rate at imaging scene center place; For the distance to the sampling rate coefficient,

For the orientation to the sampling rate coefficient, ρ wherein _rBe distance range resolution, the ρ that requires _aBe the distance azimuthal resolution that requires, μ _rFor slant range resolution to ground range resolution apart from conversion factor and μ _aBe the orientation conversion factor of slant range resolution to ground range resolution.

The present invention is a kind of method that adopts the two-dimensional coupled interpolation to carry out geometry correction; Than traditional geometry bearing calibration method, taken into full account the non-perpendicular sidelobe performance and distortion spectral characteristic of the point spread function that the space-variant property owing to Doppler parameter causes, can realize well big before the tiltedly geometry correction of SAR image; And can combine with LPF at an easy rate; Eliminate the space-variant property of resolution, avoid owing sampling, improved the image quality of distance image.

Description of drawings

Fig. 1 is the big preceding tiltedly geometric relationship synoptic diagram of SAR imaging system of the present invention.

Fig. 2 carries out 4 times of frequency spectrums after rising sampling to oblique distance point target image respectively for classic method and two kinds of methods of the present invention.

Fig. 3 is that classic method and two kinds of methods of the present invention are respectively to the oblique distance point target image after the geometry correction of SAR slant-range image before big.

Embodiment

The invention provides a kind of be used for big before the oblique geometric correction method of synthetic-aperture radar echo, below in conjunction with the accompanying drawing embodiment that develops simultaneously, describe the present invention:

As shown in Figure 1, OXYZ is a rectangular coordinate system in space, and wherein the OXY plane is on ground level, and the Z axle makes progress perpendicular to ground level; Texas tower O _r0 of distance is high on the Z axle be the h place, is parallel to the Y axle and moves, and speed is v; P is imaging scene center point, and θ is the front bevel angle of target, and α is the Texas tower velocity at floor projections and wave beam direction of visual lines at the angle of floor projections, is called the position angle, and β is the angle on wave beam direction of visual lines and ground, is called the angle of pitch.(Spectral Analysis SPECAN) becomes algorithm to be carried out to picture and handles, and sub-aperture length is elected 1024 PRT as to adopt spectrum analysis.Ka wave band SAR system is adopted in this experiment, and experiment parameter is as shown in table 1:

Table 1 experiment parameter

At first according to the above big preceding tiltedly two-dimensional interpolation function of parametric configuration in the geometry correction step of SAR system, detailed process is following:

According to the oblique geometric relationship of SAR system before big, can obtain the front bevel angle θ of target and the relation of oblique distance r and be:

$\sin \mathrm{\&theta;}=\cos \mathrm{\&alpha;}\&CenterDot;\sqrt{1-{\left(\frac{h}{r}\right)}^2}---\left(1\right)$

According to the computing formula and the convolution (1) at Doppler center, can obtain the Doppler center f of scene _Dc(r) relational expression with oblique distance r is:

$f_{\mathrm{dc}}\left(r\right)=\frac{2v}{\mathrm{\&lambda;}}\cos \mathrm{\&alpha;}\&CenterDot;\sqrt{1-{\left(\frac{h}{r}\right)}^2}---\left(2\right)$

Formula (2) is at scene center oblique distance r ₀The place carries out the single order Taylor expansion, with Doppler center f _Dc(r) be approximately the linear function of oblique distance r:

$f_{\mathrm{dc}}\left(r\right)=f_{\mathrm{dc}}\left(r_0\right)+{f_{\mathrm{dc}}}^{\&prime;}\left(r_0\right)\&CenterDot;(r-r_0)$

$=f_{\mathrm{dc}}\left(r_0\right)+\frac{2v}{\mathrm{\&lambda;}}\&CenterDot;\cos \mathrm{\&alpha;}\&CenterDot;\frac{h^2}{{{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HDA0000145069240000012.png,HDA0000145069240000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_0}^2\sqrt{{{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HDA0000145069240000012.png,HDA0000145069240000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_0}^2-h^2}}\&CenterDot;(r-r_0)---\left(3\right)$

Order

$\frac{2v}{\mathrm{\&lambda;}}\&CenterDot;\cos \mathrm{\&alpha;}\&CenterDot;\frac{h^2}{{{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HDA0000145069240000012.png,HDA0000145069240000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_0}^2\sqrt{{{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HDA0000145069240000012.png,HDA0000145069240000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_0}^2-h^2}}=k---\left(4\right)$

Because the Doppler center is with the altering a great deal of oblique distance in whole imaging scene, so imaging algorithm must be considered the space-variant property of Doppler center with oblique distance.For compensating for doppler center space-variant property, spectrum analysis goes oblique function to adopt following expression formula as the orientation in the algorithm:

h _dechirp(t；r)＝exp[-j2πf _dc(r)t-jπf _dr(r)t ²] (5)

Can derive and obtain point spread function expression formula s (t, τ; r ₀):

s(t，τ；r ₀)＝sinc[B _r(τ-τ ₀)·sinc{B _a[t+K(τ-τ ₀)]} (6)

Wherein, t and τ are respectively the orientation time and apart from the time, K=ck/ [2f _Dr(r ₀)] be defined as the distortion factor;

Utilize two-dimensional Fourier transform, obtain the 2-d spectrum expression formula S (f of point spread function _t, f _τr ₀):

$S(f_t,f_{\mathrm{\&tau;}};r_0)=\mathrm{rect}\left(\frac{f_t}{B_a}\right)\mathrm{rect}\left(\frac{f_{\mathrm{\&tau;}}-{\mathrm{Kf}}_t}{B_r}\right)\exp (-j2\mathrm{\&pi;}{f}_{\mathrm{\&tau;}}{\mathrm{\&tau;}}_0)---\left(7\right)$

Wherein, f _tBe corresponding frequency variable of point spread function orientation time, f _τBe the point spread function frequency variable corresponding apart from the time.

Making the frequency spectrum supporting domain of two-dimensional interpolation function and the frequency spectrum supporting domain of point spread function is similar parallelogram, under the situation of ignoring the linear phase influence, can construct the spectrum expression formula H (f of two-dimensional interpolation function _t, f _τ):

$H(f_t,f_{\mathrm{\&tau;}})=\mathrm{rect}\left(\frac{f_t}{F_a}\right)\mathrm{rect}\left(\frac{f_{\mathrm{\&tau;}}-{\mathrm{Kf}}_t}{F_r}\right)---\left(8\right)$

Wherein, F _rBe according to radar return handle the slant-range image obtain target distance to sampling rate, F _aFor handle according to radar return obtain target slant-range image in the orientation to sampling rate.

Utilize two-dimentional inverse Fourier transform at last, by the frequency spectrum of two-dimensional interpolation function obtain two-dimensional interpolation function h (t, τ):

h(t，τ)＝sinc(F _r·τ)sinc[F _a·(t+Kτ)] (9)

Based on two-dimensional interpolation function h (t τ) has obtained considering the two-dimensional interpolation function of LPF:

$h_{\mathrm{LP}}(t,\mathrm{\&tau;})=\sin c(\frac{F_r}{{\mathrm{\&gamma;}}_r}\&CenterDot;\mathrm{\&tau;})\sin c[\frac{F_a}{{\mathrm{\&gamma;}}_a}\&CenterDot;(t+\mathrm{K\&tau;})]---\left(10\right)$

Wherein

For the distance to the sampling rate coefficient, For the orientation to the sampling rate coefficient, ρ _rAnd ρ _aBe respectively the distance range resolution and the distance azimuthal resolution of requirement, μ _rAnd μ _aBe respectively slant range resolution to ground range resolution apart from conversion factor and orientation conversion factor.

(a) is the frequency spectrum that is interrupted that utilizes the traditional two-dimensional interpolating function to handle in the geometry correction to obtain among Fig. 2, can see that this frequency spectrum folds, and (a) is corresponding point target distance image among Fig. 3,

In correlation parameter substitution formula (2) and (4) in the table 1, calculate f _Dc(r ₀)=17.81kHz, k=2.23Hz/m, i.e. the every increase of oblique distance 1m, the Doppler center will change 2.23Hz; Calculate distortion factor K=1.0625 * 10 then ⁶, obtain F according to calculation of parameter in the table 1 _a=71.6Hz is with K, F _a, F _rBe updated in the formula (9), obtain h (t, τ)=sinc (1 * 10 ⁸τ) sinc [71.6 (t+1.0625 * 10 ⁶τ)], utilize this two-dimensional interpolation function that the frequency spectrum of the slant-range image of point target is carried out 4 times and rise sampling processing, obtain complete parallelogram frequency spectrum, (b) as shown in Figure 2, and then obtain corresponding point target distance image shown in (b) among Fig. 3.

The base area is apart from 4 meters resolution requirement of image, and the decrease of the passband width of design two-dimensional interpolation function is realized LPF.According to the computing formula of ground range resolution calculate distance to the orientation to the sampling rate coefficient be respectively γ _r=2 and γ _a=3.3, with γ _rAnd γ _aBe updated to the two-dimensional interpolation function that has obtained considering LPF in the formula (10): h _LP(t, τ)=sinc (5 * 10 ⁷τ) sinc [21.7 (t+1.0625 * 10 ⁶τ)], utilize this two-dimensional interpolation function of having considered LPF that the frequency spectrum of the slant-range image of point target is carried out 4 times and rise sampling processing, obtain Fig. 2 (c); With respect to (b) figure among Fig. 2; Frequency spectrum reduces to some extent, and promptly resolution descends, and has realized LPF; Be corresponding point target distance image among Fig. 3 (c), table 2 has provided the assessment result of each distance point target.

Table 2 distance image point target assessment result

From Fig. 3 and table 2, can find out; Use classic method that oblique SAR slant-range image before big is carried out the geometry correction meeting and make target distortion significantly; Interpolation method of the present invention has then obtained good distance image, and has combined the interpolation method of low pass that resolution has been reduced to desired value.

In sum, more than being merely preferred embodiment of the present invention, is not to be used to limit protection scope of the present invention.All within spirit of the present invention and principle, any modification of being done, be equal to replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (2)

1. one kind is used for the big preceding tiltedly geometric correction method of synthetic-aperture radar echo, it is characterized in that,

Utilize spectrum analysis SPECAN imaging algorithm that the slant-range image of the echo of oblique synthetic-aperture radar before big is carried out in the step of geometry correction, (t τ) carries out two-dimensional interpolation to slant-range image and handles, and obtains the distance image then to adopt function h;

Said function h (t, expression formula τ) is:

h(t，τ)＝sinc(F _r·τ)sinc[F _a·(t+Kτ)]

F wherein _rBe slant-range image distance to sampling rate, F _aFor slant-range image in the orientation to sampling rate, t is the orientation time, τ is apart from the time, $K=\frac{2\mathrm{Vc}}{\mathrm{\&lambda;}}\&CenterDot;\mathrm{Cos}\mathrm{\&alpha;}\&CenterDot;\frac{h^2}{{r_0}^2\sqrt{{r_0}^2-h^2}}/[-2f_{\mathrm{Dr}}\left(r_0\right)],$ C is the light velocity, and v is the movement velocity of Texas tower, and λ is the carrier wavelength of radar, α be the velocity of Texas tower at floor projections and wave beam direction of visual lines angle in floor projections, h be big before the oblique height of Texas tower in the polarization sensitive synthetic aperture radar system, r ₀Be the oblique distance of imaging scene center, f _Dr(r ₀) be the doppler frequency rate at imaging scene center place.

2. one kind is used for the big preceding tiltedly geometric correction method of synthetic-aperture radar echo, it is characterized in that,

Utilize spectrum analysis SPECAN imaging algorithm that the slant-range image of the echo of oblique synthetic-aperture radar before big is carried out in the step of geometry correction, adopt function h _LP(t τ) carries out two-dimensional interpolation to slant-range image and handles, and obtains the distance image then;

Said function h _LP(t, expression formula τ) is: $h_{\mathrm{LP}}(t,\mathrm{\&tau;})=\mathrm{Sin}c(\frac{F_r}{{\mathrm{\&gamma;}}_r}\&CenterDot;\mathrm{\&tau;})\mathrm{Sin}c[\frac{F_a}{{\mathrm{\&gamma;}}_a}\&CenterDot;(t+\mathrm{K\&tau;})];$

F wherein _rBe slant-range image distance to sampling rate, F _aFor slant-range image in the orientation to sampling rate, t is the orientation time, τ is apart from the time, $K=\frac{2\mathrm{Vc}}{\mathrm{\&lambda;}}\&CenterDot;\mathrm{Cos}\mathrm{\&alpha;}\&CenterDot;\frac{h^2}{{r_0}^2\sqrt{{r_0}^2-h^2}}/[-2f_{\mathrm{Dr}}\left(r_0\right)],$ C is the light velocity, and v is the movement velocity of Texas tower, and λ is the carrier wavelength of radar, α be the velocity of Texas tower at floor projections and wave beam direction of visual lines angle in floor projections, h be big before the oblique height of Texas tower in the polarization sensitive synthetic aperture radar system, r ₀Be the oblique distance of imaging scene center, f _Dr(r ₀) be the doppler frequency rate at imaging scene center place;

For the distance to the sampling rate coefficient,

For the orientation to the sampling rate coefficient, ρ wherein _rBe distance range resolution, the ρ that requires _aBe the distance azimuthal resolution that requires, μ _rFor slant range resolution to ground range resolution apart from conversion factor and μ _aBe the orientation conversion factor of slant range resolution to ground range resolution.

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