CN102226841B - Synchronous orbit SAR imaging method based on high-order polynomial range equation - Google Patents

Abstract

The invention discloses a synchronous orbit SAR (Synthetic Aperture Radar) imaging method based on high-order polynomial range equation. The implementation process thereof is as follows: 1. establishing a synchronous orbit SAR high-order polynomial range equation; 2. solving a Cardan equation and deducing the precise analytical expression of a synchronous orbit SAR echo signal two-dimensional frequency spectrum; 3. structuring a two-dimensional frequency domain compensation function and finishing a scene centre point matching processing in the two-dimensional frequency domain; 4. performing a range IFFT (Inverse Fast Fourier Transform) processing on a result after finishing the centre point matching and transforming the result to a range-Doppler domain from the two-dimensional frequency domain; 5. structuring an error phase spatially variant with range and compensating for a range spatially variant phase in the range-Doppler domain; and 6. performing an azimuth IFFT processing to obtain a focused synchronous orbit SAR image. All the operations in the invention are finished by fast Fourier transform and phase dot product, and the method is high in efficiency and suitable for engineering implementation; and moreover, the two-dimensional frequency spectrum is a precise analytic solution capable of realizing full-aperture and high-resolution imaging.

Description

Synchronous orbit SAR formation method based on the higher order polynomial range equation

Technical field

The invention belongs to the spaceborne radar technical field, further relate to a kind of synchronous orbit SAR formation method based on the higher order polynomial range equation, can be used for synchronous orbit SAR to ground Scene realization high-resolution imaging.

Background technology

Because the orbit altitude of synchronous orbit SAR is 35768km, anti-strike and lethality are strong, and stronger battlefield survival is arranged.Simultaneously, the synthetic aperture of overlength makes it possess the potentiality of moving-target being carried out Continuous Tracking and high-resolution imaging, can satisfy strategy of big range supervision, early warning and battle reconnaissance.In addition, it is short that synchronous orbit SAR also has the cycle of returning to, wide coverage, and the temporal resolution advantages of higher has potential advantage at aspects such as earthquake and volcano forecast, ocean applied researcies.Imaging technique is depended in the embodiment of these advantages, and existing synchronous orbit SAR imaging technique has following two kinds.

The first, high-resolution synchronous orbit SAR imaging algorithm.For example, Li Jun, Xing Mengdao, Li Yachao, Wang Wanlin, Tan Xiaomin is in paper " synchronous orbit SAR systematic parameter is analyzed and imaging algorithm research " " systems engineering and electronic technology " 2010,32 (5): propose among the 931-936 to utilize the BP algorithm that it is carried out the method for imaging, although the BP algorithm is in theory without any approximate, can carry out imaging to the signal in any track situation, and not be subjected to the restriction of scene, be the optimum imaging algorithm of time domain, but its operand is larger, is not suitable for Project Realization.

The second, low resolution synchronous orbit SAR imaging algorithm.For example, Lee's wealth product, Zhang Hongtai, Tan Xiaomin is in " a kind of improvement CS algorithm that is applicable to synchronous orbit SAR " Acta Astronautica 2011,32 (1): proposed a kind of method that adopts the RD algorithm to carry out imaging behind the straight line that curvilinear path is compensated for as among the 179-186, but because it is to compensate by the scene center point, its focusing effect to the scene marginal point is relatively poor, and only is suitable for the situation of low resolution.

Summary of the invention

The object of the invention is to overcome the deficiencies in the prior art, movement characteristic according to synchronous orbit SAR platform, true oblique distance course is carried out high-order approaches, thereby set up the higher order polynomial range equation of synchronous orbit SAR, utilize Ka Er folk prescription journey, derived the accurate and analytical expression of synchronous orbit SAR echoed signal 2-d spectrum.On this basis, propose a kind of formation method that is applicable to synchronous orbit SAR, realized the full aperture high-resolution imaging.

Implementation step of the present invention is as follows:

(1) set up the oblique distance expression formula: utilize 2 range formulas of synchronous satellite orbit establishing equation star ground oblique distance, this range formula is carried out the high-order Taylor expansion obtain synchronous orbit SAR higher order polynomial range equation:

$R\left(t_m\right)=R_0+k_1{t}_m+k_2{t}_m^2+k_3{t}_m^3+k_4{t}_m^4$

Wherein, R ₀Be reference distance, t _mBe slow time, k ₁t _mBe range walk item, k ₂t _mBe range curvature item, k ₃t _m, k ₄t _mBe the high-order phase term;

(2) derivation 2-d spectrum expression formula

2a) synchronous orbit SAR echo data is carried out apart from Fourier transform;

2b) find the solution the analytic solution of staying phase point that Ka Er folk prescription journey obtains the orientation Fourier transform based on higher order polynomial range equation in the step (1), in the phase term of substitution orientation Fourier transform, thereby obtain the analytical expression of synchronous orbit SAR echo data 2-d spectrum;

(3) scene center point coupling

3a) analytical expression of 2-d spectrum is got conjugation and obtain the two-dimensional frequency penalty function;

3b) synchronous orbit SAR echoed signal is carried out Two-dimensional FFT and process, it is transformed to two-dimensional frequency, obtain the echo data of two-dimensional frequency;

3c) two-dimensional frequency penalty function and the echo data that transforms to two-dimensional frequency are multiplied each other realize that scene center point mates;

(4) process apart from IFFT: the result who finishes the central point coupling is carried out processing apart from IFFT, it is transformed to the distance-Doppler territory from two-dimensional frequency;

(5) complementary range space-variant phase place

5a) find the solution phase differential: after the coefficient of the phase term of the orientation Fourier transform in the step (2) and Ka Er folk prescription journey is carried out approximate processing, find the solution the analytic solution of staying phase point that Ka Er folk prescription journey after the approximate processing obtains the orientation Fourier transform, in the phase term with the orientation Fourier transform after its substitution approximate processing, thereby obtain along the phase error apart from space-variant;

5b) will get after the conjugation and the signal multiplication that transforms to the distance-Doppler territory along the phase error of distance space-variant, realize the compensation of Spatially variant phase error;

(6) orientation is processed to IFFT: carry out the orientation and process to IFFT finishing signal apart from space-variant phase compensation, realize the focal imaging of synchronous orbit SAR.

The present invention compared with prior art has the following advantages:

The first, because the present invention has carried out high-order to the true oblique distance course of synchronous orbit SAR and approached, can access accurate target oblique distance expression formula, thereby reduce the phase error that the oblique distance approximate error causes, improved imaging precision.

Second, because oblique distance formula of the present invention is the higher order polynomial range equation, and obtain the accurate and analytical expression of 2-d spectrum by finding the solution Ka Er folk prescription journey, therefore compared to existing technology, synchronous orbit SAR movable information is more complete in the 2-d spectrum of the present invention, is conducive to the high-resolution imaging of synchronous orbit SAR.

The 3rd, because all operations is all finished by Fast Fourier Transform (FFT) and phase place dot product among the present invention, greatly shortened the processing time, have higher efficient, be fit to Project Realization.

Description of drawings:

Fig. 1 is process flow diagram of the present invention;

Fig. 2 is the phase error comparison diagram in the polynomial expression range equation different rank situation of the present invention, and wherein Fig. 2 (a) is three approximate error curve maps of target oblique distance of the present invention, and Fig. 2 (b) is four approximate error curve maps of target oblique distance of the present invention;

Fig. 3 is the comparison diagram of conventional RD method points target imaging result and point target imaging results of the present invention, and Fig. 3 (a) is as a result contour map of conventional RD method points target imaging, and Fig. 3 (b) is point target imaging results contour map of the present invention.

Embodiment:

The present invention will be further described below in conjunction with accompanying drawing.

With reference to Fig. 1, implementation step of the present invention is as follows:

Step 1. is set up the oblique distance expression formula.

The synchronous satellite orbit equation is as follows:

$\left[\begin{array}{c}{x}_s\\ y_s\\ z_s\end{array}\right]=R\left[\begin{array}{c}\cos L_0[1+(\cos i-1){\sin }^2\mathrm{\&omega;}({\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000462172800021.png"\; state="\{\{state\}\}">t</figure-callout>}}_0+t_m)]-\frac{1}{2}\sin L_0(\cos i-1)\sin 2\mathrm{\&omega;}({\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000462172800021.png"\; state="\{\{state\}\}">t</figure-callout>}}_0+t_m)\\ \sin L_0[1+(\cos i-1){\sin }^2\mathrm{\&omega;}({\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000462172800021.png"\; state="\{\{state\}\}">t</figure-callout>}}_0+t_m)]+\frac{1}{2}\cos L_0(\cos i-1)\sin 2\mathrm{\&omega;}({\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000462172800021.png"\; state="\{\{state\}\}">t</figure-callout>}}_0+t_m)\\ \sin i\sin \mathrm{\&omega;}({\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000462172800021.png"\; state="\{\{state\}\}">t</figure-callout>}}_0+t_m)\end{array}\right]$

Wherein, t ₀For ascending node of orbit initial " 0 " constantly;

t _mBe the slow time;

x _s, y _s, z _sFor satellite with t ₀Centered by the trajectory coordinates of one section movement locus;

ω is the earth rotation angular speed;

R=R _e+ h, R _eBe earth radius, h is orbit altitude;

I is orbit inclination;

L ₀Be the ascending node of orbit right ascension.

Above-mentioned synchronous satellite orbit equation is carried out the high-order Taylor expansion, with the coordinate figure substitution satellite after launching and the instantaneous oblique distance equation of impact point:

$R\left(t_m\right)=\sqrt{{(x_s-x_p)}^2+{(y_s-y_p)}^2+{(z_s-z_p)}^2}$

Wherein, R (t _m) be instantaneous oblique distance equation;

x _p, y _p, z _pCoordinate for impact point in the mapping band.

Then to oblique distance R (t _m) at aperture center t _mTaylor series expansion is done at=0 place, and the sequence after the expansion remains to item four times, and the higher order polynomial range equation that just obtains synchronous orbit SAR is

$R\left(t_m\right)=R_0+k_1{t}_m+k_2{t}_m^2+k_3{t}_m^3+k_4{t}_m^4$

Wherein, R ₀Be reference distance;

k ₁t _mBe the range walk item;

k ₂t _mBe the range curvature item;

k ₃t _m, k ₄t _mBe the high-order phase term.

The true oblique distance course of synchronous orbit SAR has been carried out high-order approaches, can access accurate target oblique distance expression formula, the precision of oblique distance model is mainly reflected in phase error, if the phase error that the approximate error of oblique distance causes less than 0.25 π, can be thought on not impact of imaging precision.

Step 2. derivation 2-d spectrum expression formula.

At first synchronous orbit SAR echo data is carried out apart from Fourier transform, utilize Ka Er folk prescription journey to find the solution the analytic solution of staying phase point of orientation Fourier transform based on the higher order polynomial range equation, in the phase term with its substitution orientation Fourier transform, thereby obtain the accurate expression of synchronous orbit SAR echo data 2-d spectrum.

2a) radar emission linear FM signal, the echo baseband signal of point target is:

$s(\hat{t},t_m)=a_r(\hat{t}-\frac{2R\left(t_m\right)}{c})a_a\left(t_m\right)\exp \left[\mathrm{j\&pi;\&gamma;}{(\hat{t}-\frac{2R\left(t_m\right)}{c})}^2\right]\exp [-j\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}R\left(t_m\right)]$

Wherein,

Be respectively window function and the orientation window function of radar linear frequency-modulated signal; γ is the frequency modulation rate; λ is wavelength; C is the light velocity; Be the fast time.

The echo baseband signal is carried out apart from Fourier transform, it is transformed to apart from frequency domain gets:

$S(f_r,t_m)=a_r\left(f_r\right)a_a\left(t_m\right)\exp [-\mathrm{j\&pi;}\frac{f_r^2}{\mathrm{\&gamma;}}]\exp [-j\frac{4\mathrm{\&pi;}}{c}R\left(t_m\right)(f_r+f_c)]$

Wherein, a _r(f _r) be the distance spectrum envelope, f _rBe frequency of distance, f _cBe carrier frequency.

2b) do the orientation apart from the signal of frequency domain and to Fourier transform be transforming to:

$S(f_r,f_a)={\&Integral;}_{-\&infin;}^{\&infin;}S(f_r,t_m)\exp (-j2\mathrm{\&pi;}{f}_a{t}_m)d{t}_m$

Wherein, f _aBe the orientation frequency.

The phase place of orientation Fourier transform is:

$\mathrm{\&phi;}(t_m;R_0)=-\frac{4\mathrm{\&pi;}}{c}R\left(t_m\right)(f_r+f_c)-2\mathrm{\&pi;}{f}_a{t}_m$

Utilize in facies principle and obtain f _aAnd t _mThe pass be:

$-\frac{4\mathrm{\&pi;}}{c}(k_1+2k_2{t}_m+3k_3{t}_m^2+4k_4{t}_m^3)(f_r+f_c)-2\mathrm{\&pi;}{f}_a=0$

Make α=4k ₄β=3k ₃γ=2k ₂

F then _aAnd t _mRelationship conversion be a Ka Er folk prescription journey:

y ³+3py+2q＝0

Wherein,

Monomial coefficient for equation;

Constant term for equation.

This Ka Er folk prescription journey discriminant is Δ=q ²+ p ³, and it only has a real solution to be when Δ 〉=0:

$y_1=\sqrt[3]{-q+\sqrt{q^2+p^3}}+\sqrt[3]{-q-\sqrt{q^2+p^3}}$

It exists three real solutions to be when Δ＜0:

$\left\{\begin{array}{c}{y}_1=2\sqrt{-p}\cos \left[\frac{\mathrm{\&theta;}}{3}\right]\\ y_2=2\sqrt{-p}\cos [\frac{\mathrm{\&theta;}}{3}+\frac{2\mathrm{\&pi;}}{3}]\\ y_3=2\sqrt{-p}\cos [\frac{\mathrm{\&theta;}}{3}+\frac{4\mathrm{\&pi;}}{3}]\end{array}\right.$

Wherein,

$\cos \mathrm{\&theta;}=\frac{-q}{\sqrt{{-p}^3}}$

In Practical Project uses, when Δ＜0, select one of them to have the solution of actual physics meaning according to radar parameter.

Utilize the solution of Ka Er folk prescription journey can obtain staying phase point to be:

$t_m^{*}=y-\frac{k_3}{4k_4}$

Wherein, y is the solution of Ka Er folk prescription journey.

Will be in phase point

In the substitution orientation fourier integral, the 2-d spectrum that can obtain synchronous orbit SAR echoed signal is:

$S(f_r,f_a)=a_r\left(f_r\right)a_a\left(f_a\right)\exp [-\mathrm{j\&pi;}\frac{f_r^2}{\mathrm{\&gamma;}}]\exp \left[\mathrm{j\&phi;}(t_m^{*};R_0)\right]$

Can be found out by above derivation, in the computation process of 2-d spectrum, only oblique distance carried out high-order approximation, comprise the oblique distance change information in the gained spectrum expression formula, have higher degree of accuracy.

Step 3. scene center point coupling.

3a) accurate and analytical expression of 2-d spectrum being got conjugation, to obtain the two-dimensional frequency penalty function as follows:

$H_1(f_r,f_a)=\exp \left[\mathrm{j\&pi;}\frac{f_r^2}{\mathrm{\&gamma;}}\right]\exp [-\mathrm{j\&phi;}(t_m^{*};R_s)]$

3b) synchronous orbit SAR echo data is carried out Two-dimensional FFT and process, it is transformed to two-dimensional frequency;

3c) with two-dimensional frequency penalty function H ₁Multiply each other with the synchronous orbit SAR echo data that transforms to two-dimensional frequency and to realize that scene center point mates.

Step 4. is processed apart from IFFT.The result who finishes the center coupling is carried out processing apart from IFFT, it is transformed to the distance-Doppler territory from two-dimensional frequency.

Step 5. complementary range space-variant.

5a) find the solution phase differential: after the coefficient of the phase place of the orientation Fourier transform in the step 2 and Ka Er folk prescription journey is carried out approximate processing, utilize Ka Er folk prescription journey to find the solution the analytic solution of staying phase point of orientation Fourier transform, in the phase term with the orientation Fourier transform after its substitution approximate processing, thereby obtain along the phase error apart from space-variant.

Because common f in the SAR imaging _c＞＞f _r, therefore

Can be approximately

δ in the step 2 can be approximately

So, the phase term φ (t of orientation Fourier transform in this up-to-date style step 2 _m) and q can be similar to and be written as:

$\mathrm{\&phi;}\left(t_m\right)\&ap;-\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}R\left(t_m\right)-2\mathrm{\&pi;}{f}_a{t}_m$

$q\&ap;\frac{k_1}{8k_4}+\frac{1}{64}{\left(\frac{k_3}{k_4}\right)}^3-\frac{1}{16}\frac{k_2{k}_3}{k_4^2}+\frac{\mathrm{\&lambda;}{f}_a}{16k_4}$

Adopt and step 2 same procedure, obtain the new phase point of staying and be designated as:

${\tilde{t}}_m^{*}=\tilde{y}-\frac{k_3}{4k_4}$

Wherein,

Solution for new Ka Er folk prescription journey.

Then can obtain with distance R ₀The phase differential of space-variant is:

$\mathrm{\&Delta;\&phi;}(f_a;R_s;R_0)=\exp [-j(\mathrm{\&phi;}({\tilde{t}}_m^{*};R_s)-\mathrm{\&phi;}({\tilde{t}}_m^{*};R_0))]$

Wherein,

Be distance R ₀Phase term,

Be the scene center distance R _sPhase term.

5b) with Δ φ (f _aR _sR ₀) with transform to the signal multiplication in distance-Doppler territory, just can compensate the error phase with the distance space-variant.

Step 6. is done the synchronous orbit SAR image after the orientation can obtain focusing on to IFFT.

Effect of the present invention can be illustrated by following emulation experiment:

Simulated conditions

Choose satellite when " 8 " word top, to being positioned at scene point target R _In(54.36 ° of N, 105.00 ° of E) carry out simulation imaging, and simulation parameter arranges as shown in the table.

Parameter	Parameter value
		Orbit inclination	60°
Ascending node	105°
		Orbit altitude	35768km
Carrier frequency	2.5GHz
		Transmitted signal bandwidth	45MHz
Distance is to sampling rate	65MHz
		Pulse repetition rate	300Hz
Slant range resolution	3m
		Azimuthal resolution	3m

Simulation result

Wherein Fig. 2 (a) is three approximate error curve maps of target oblique distance of the present invention, and Fig. 2 (b) is four approximate error curve maps of target oblique distance of the present invention.Can be found out by Fig. 2 (a) and Fig. 2 (b), in the time, the approximate error that radar is carried out three rank Taylor expansions to the oblique distance of target reaches 0.0275m at the edge in aperture a synthetic aperture, and the approximate error of quadravalence Taylor expansion is 1.23 * 10 ^-6M.For the radar of 2.5GHz carrier frequency, its wavelength is 0.12m, and the approximate error of three rank Taylor expansions, three rank Taylor expansions has surpassed 1/8 wavelength.Expect to focus on good image, in this systematic parameter situation, will carry out the quadravalence Taylor expansion at least.Utilize the approximate oblique distance equation of quafric curve in the conventional spaceborne formation method to carry out the decline that imaging must bring image quality.Therefore the present invention uses quadravalence to approach and obtains synchronous orbit SAR higher order polynomial range equation.

Fig. 3 (a) is as a result contour map of conventional RD method points target imaging, and Fig. 3 (b) is point target imaging results contour map of the present invention.Following table provides the present invention to the focusing performance statistics of point target, and wherein, PSLR is peak sidelobe ratio, and ISLR is integration secondary lobe ratio, does not all carry out windowing process in the imaging processing.Can be seen by Fig. 3 and following table imaging achievement data, because the synchronous orbit SAR synthetic aperture time is long, the orientation phase error of utilizing conventional Space-borne SAR Imaging method oblique distance equation to bring is larger, be difficult to obtain enough spectrum informations, cause the middle orientation of Fig. 3 (a) to the main lobe broadening, cause focusing quality to descend, be difficult to satisfy imaging requirements.And in the contour map of Fig. 3 (b) the inventive method point target, the secondary lobe rule, main secondary lobe obviously separates, and presents good " cross " shape, and focusing effect is good, and the index of imaging performance shown in the following table has all reached the requirement of imaging.As seen, the present invention can realize synchronous orbit SAR full aperture high-resolution imaging.

Claims (5)

1. the synchronous orbit SAR formation method based on the higher order polynomial range equation comprises the steps:

(1) set up the oblique distance expression formula: utilize 2 range formulas of synchronous satellite orbit establishing equation star ground oblique distance, this range formula is carried out the high-order Taylor expansion obtain synchronous orbit SAR higher order polynomial range equation:

$R\left(t_m\right)=R_0+k_1{t}_m+k_2{t}_m^2+k_3{t}_m^3+k_4{t}_m^4$

Wherein, R ₀Be reference distance, t _mBe slow time, k ₁t _mBe range walk item, k ₂t _mBe range curvature item, k ₃t _m, k ₄t _mBe the high-order phase term;

(2) derivation 2-d spectrum expression formula

2a) synchronous orbit SAR echo data is carried out apart from Fourier transform;

2b) find the solution the analytic solution of staying phase point that Ka Er folk prescription journey obtains the orientation Fourier transform based on higher order polynomial range equation in the step (1), in the phase term of substitution orientation Fourier transform, thereby obtain the analytical expression of synchronous orbit SAR echo data 2-d spectrum;

(3) scene center point coupling

3a) analytical expression of 2-d spectrum is got conjugation and obtain the two-dimensional frequency penalty function;

3b) synchronous orbit SAR echoed signal is carried out Two-dimensional FFT and process, it is transformed to two-dimensional frequency, obtain the echo data of two-dimensional frequency;

3c) two-dimensional frequency penalty function and the echo data that transforms to two-dimensional frequency are multiplied each other realize that scene center point mates;

(4) process apart from IFFT: the result who finishes the central point coupling is carried out processing apart from IFFT, it is transformed to the distance-Doppler territory from two-dimensional frequency;

(5) complementary range space-variant phase place

5a) find the solution phase differential: after the coefficient of the phase term of the orientation Fourier transform in the step (2) and Ka Er folk prescription journey is carried out approximate processing, find the solution the analytic solution of staying phase point that Ka Er folk prescription journey after the approximate processing obtains the orientation Fourier transform, in the phase term with the orientation Fourier transform after its substitution approximate processing, thereby obtain along the phase error apart from space-variant;

5b) will get after the conjugation and the signal multiplication that transforms to the distance-Doppler territory along the phase error of distance space-variant, realize the compensation of Spatially variant phase error;

(6) orientation is processed to IFFT: the signal of finishing apart from space-variant phase compensation is carried out the orientation after IFFT processes, realize the focal imaging of synchronous orbit SAR.

2. the synchronous orbit SAR formation method based on the higher order polynomial range equation according to claim 1 is characterized in that: the sequence after 2 range formula Taylor expansions of step (1) culminant star ground oblique distance is remained to item four times.

3. the synchronous orbit SAR formation method based on the higher order polynomial range equation according to claim 1 is characterized in that: the 2-d spectrum analytical expression of the synchronous orbit SAR echoed signal of deriving described step 2b) is:

Wherein, f _rBe frequency of distance, f _aBe orientation frequency, a _r(f _r), a _a(f _a) be respectively window function and the orientation window function of radar linear frequency-modulated signal;

Be the 2-d spectrum phase place.

4. the synchronous orbit SAR formation method based on the higher order polynomial range equation according to claim 1 is characterized in that: adopt the method for finding the solution Ka Er folk prescription journey to obtain described step 5a) along the error phase apart from space-variant to be:

$\mathrm{\&Delta;\&phi;}(f_a;R_s;R_0)=\exp [-j(\mathrm{\&phi;}({\tilde{t}}_m^{*};R_s)-\mathrm{\&phi;}({\tilde{t}}_m^{*};R_0))]$

Wherein, f _aBe the orientation frequency,

For staying phase point,

Be distance R ₀Phase term, Be the scene center distance R _sPhase term.

5. the synchronous orbit SAR formation method based on the higher order polynomial range equation according to claim 1 is characterized in that: the approximate processing described step 5a) refer to

Be approximately

Wherein, f _rBe frequency of distance, λ is radar wavelength, and c is the light velocity.

Images