CN104777479B - Front side based on multi-core DSP regards SAR realtime imaging methods - Google Patents

Abstract

The invention discloses a kind of front side based on multi-core DSP regards SAR realtime imaging methods, existing front side is mainly solved regarding SAR imaging algorithm before processing side-looking limited angles, computationally intensive, and do not carry out the problem of motion compensation.Which realizes that process is：1) echo data is pressed into orientation piecemeal, and each block number evidence is mapped to into each DSP process cores；2) range migration correction is carried out and apart from pulse pressure to each block number evidence；3) using the data estimation after pulse pressure apart from non-space-variant kinematic error；4) envelope correction and error compensation are carried out to echo data using apart from non-space-variant kinematic error；5) gone forward side by side row distance space-variant error compensation apart from space-variant kinematic error using the data estimation after compensation；6) data after space-variant error compensation of adjusting the distance carry out azimuth focus, obtain SAR image.The present invention can effectively estimate kinematic error, improve SAR image resolution, and operation efficiency is higher, can be used for the detection on a surface target of airborne/missile-borne radar with identification.

Description

Front side based on multi-core DSP regards SAR realtime imaging methods

Technical field

The invention belongs to digital signal processing technique field, is related to a kind of synthetic aperture radar (Synthetic Aperture Radar, SAR) realtime imaging method, can be used for the detection on a surface target of airborne/missile-borne radar with identification.

Background technology

With the development of SAR imaging techniques, positive side-looking and little Squint SAR technology are constantly ripe and perfect, obtain more It is widely applied to get over.At the same time, just towards multi-mode, multichannel, multifunctional direction development, modern SAR system is not for SAR High-resolution earth observation is limited only to, in being continuously developed based on functions such as the target detection of SAR image, identification, tracking. Front side, is of concern because of its application demand in airborne fire control radar and missile-borne precise guidance radar in recent years regarding SAR, is filled Aircraft and armament systems on front side of having depending on SAR system is considered as the trump to success on battlefield in future.

Front side makes it have following two different from traditional just side-looking and little stravismus depending on the unique observation geometry of SAR signals The characteristics of SAR：Large range cell migration and narrow doppler bandwidth.The space-variant of large range cell migration especially range migration is in imaging process Middle needs carry out accurate correction and echo signal envelope could be caused to align；Narrow doppler bandwidth causes front side to regard SAR azimuth discriminations Rate is reduced, and orientation Doppler mutation easily occurs.Problem above causes traditional range Doppler RD class algorithms, line frequency modulation to become mark CS classes algorithm can not obtain well focussed image depending on SAR model mismatches with front side, therefore study new front side and regard SAR imaging algorithms It is significant.

Front side can be equivalent to look side ways greatly model depending on SAR models, for high squint SAR imaging algorithm, article " Extended NCS Based on Method of Series Reversion for Imaging of Highly Squinted SAR, IEEE Geoscience and Remote Sensing Letters, Vol.8, NO.3, May2011 " is anti-by introducing series A kind of algorithm, it is proposed that the Non-linear chirp scaling of extension (Nolinear CS, NCS) algorithm, improves Squint SAR signal Distance to data processing performance, but the algorithm can process stravismus angle it is still limited, emulation experiment verify the algorithm be suitable for Front side visual angle be not smaller than 40 °.Article " Focus Improvement of Highly Squinted Data Based on Azimuth Nonlinear Scaling, IEEE Transactions on Geoscience and Remote Sensing, Vol.49, NO.6, June 2011 " further marks the accessible stravismus angle of algorithm raising using non-linear change the in orientation, but institute Carry that algorithm complex is high, computationally intensive, poor real.Additionally, both the above algorithm is not used measured data checking, therefore ignore Impact of the radar motion error in measured data to algorithm performance, not with broad applicability.

The content of the invention

Present invention aims to the deficiency of above-mentioned prior art, is considering radar platform kinematic error to algorithm On the premise of affecting, the real time processing system of side-looking SAR imagings in the past is application background, at currently advanced multi-core DSP Reason chip, with reference to front side regarding SAR's " narrow beam level land " it is assumed that proposing that a kind of front side based on multi-core DSP regards SAR realtime imagings Method, to reduce the front side angle of imaging processing, reduces operand, expands its range of application.

The technical thought for realizing the object of the invention is：SAR echo datas estimation fortune is regarded by front side is surveyed using iterative manner Dynamic error, carries out Range Walk Correction with the data after phase compensation to envelope cancellation, using optimization oblique distance expression formula, carries out Space-variant range curvature correction and secondary range compression, are focused on by the second order matched filtering of orientation short-bore footpath and obtain SAR image, its tool It is as follows that body realizes that step includes：

1) distance is equally divided into into L block according to orientation to the echo data S of N points, orientation M point, and by ExtremelyAccording to the q cores for being mapped to multi-core DSP, to each block number according to Range Walk Correction is carried out, wherein N, M, L is block number Positive integer more than 1, q ∈ [0,1 ..., Q-1], Q are the DSP core number for participating in processing；

2) space-variant range curvature is corrected using the data after calibration of walking about：

2a) by this bidimensional frequency domain of data conversion to distance and bearing, and construct frequency-domain correction phase place：

Wherein, R₀For point target wave beam ray to oblique distance, f_rFor frequency of distance, f_aFor orientation frequency, f_aMIt is maximum for orientation Doppler, c is the light velocity, and j represents imaginary number；

2b) by frequency-domain correction phase place H₂(R₀,f_r,f_a) be multiplied with orientation frequency-region signal, complete space-variant range curvature correction；

3) row distance is entered to matched filtering to the data after space-variant range curvature correction；Filtered data are converted into Distance and bearing bidimensional time domain, estimates instantaneous Doppler chirp rate using the bidimensional time domain data, then to instantaneous Doppler frequency modulation Rate enters row interpolation, obtains full aperture kinematic error vector Δ R；

4) envelope correction and phase compensation are carried out to original radar return data S using kinematic error vector Δ R, obtain away from Data Y after non-space-variant motion compensation；

5) range migration correction is carried out using data Y after non-space-variant motion compensation, will be the data after correction equal Be divided into G × L blocks, G be distance to block number, L is orientation block number；Using each block number instantaneous Doppler chirp rate according to estimates, G is obtained × L ties up frequency modulation rate matrix Ω, carries out M point interpolations to the row vector of frequency modulation rate matrix Ω, obtains G × M dimension space-variant kinematic errors Matrix ψ, wherein G are the positive integer more than 1；

6) data Y after non-space-variant kinematic error compensation of being adjusted the distance using space-variant kinematic error matrix ψ carry out error compensation, Data Z after space-variant motion compensation are obtained, the entropy E of data Z is calculated_z；

7) repeatedly 1)～6), think that meeting compensation precision wants when the entropy difference of compensation result is less than 0.01 twice in front and back Ask, azimuth focus carried out to data Z after motion compensation, is such as unsatisfactory for, then continue iteration 1)～6), until meet compensation will Ask.

The present invention has advantages below compared with prior art：

1) imaging can before processing side-looking angle be decreased to 20 °.

Existing front side is all based on oblique distance approximate formula depending on SAR imaging methods and carries out range migration correction, exists larger System-level range error.In the present invention, using the oblique distance formula of optimization, accurate compensation system level range error will imaging Can before processing side-looking angle be decreased to 20 °.

2) operand is little.

Existing front side needs to carry out echo-signal " becoming mark " process depending on SAR imaging methods, and " becoming mark " process is complicated, fortune Calculation amount is larger.The present invention carries out imaging processing in distance and Doppler domain, is not related to " becoming mark " operation, reduces algorithm computing Amount.

3) applied range.

Existing front side is to be verified using emulation experiment depending on SAR imaging methods, does not consider actual measurement echo data In impact of the kinematic error to imaging algorithm, do not carry out motion compensation, practical ranges are limited.Fortune proposed by the present invention Dynamic compensation method can effectively estimate the non-space-variant kinematic error of distance in measured data and apart from space-variant kinematic error, improve SAR image precision, and the checking of measured data is obtained, it is with a wide range of applications.

4) beneficial to miniaturization SAR real time processing system designs.

Data processing is carried out by the way of multi-DSP cascade more than traditional SAR signal processors, multi-DSP is cascaded to be increased The volume and power consumption of signal processor, stability are poor, are unfavorable for the design of SAR real time processing systems and airborne/missile-borne radar Device miniaturization, low power dissipation design.The imaging algorithm of the present invention is based entirely on distance to the separable dimension processing with orientation, beneficial to Parallelization realization in multi-core DSP, improves data-handling efficiency.Imaging method of the present invention is realized in monolithic multi-core DSP, is reduced SAR real time processing system complexities, beneficial to miniaturization SAR system design.

Description of the drawings

Fig. 1 is the process chart of the present invention；

Fig. 2 is that geometry is observed regarding SAR in front side；

Fig. 3 is envelope error and phase error estimation and phase error result figure；

Fig. 4 is the Matlab comparison diagrams that SAR imaging results and conventional RD algorithm imaging results are regarded on front side of the present invention；

Fig. 5 is that imaging results figure of the SAR imaging algorithms in multi-core DSP is regarded on front side of the present invention.

Specific embodiment

Step is further described to be realized to the present invention below in conjunction with the accompanying drawings.

With reference to Fig. 1, the present invention's realizes that step is as follows：

Step 1. walks dynamic(al) correction to echo data orientation piecemeal, row distance of going forward side by side.

Distance is equally divided into into L block according to orientation to the echo data S of N points, orientation M point 1a), and by ExtremelyBlock number is the positive integer more than 1, q ∈ [0,1 ..., Q- according to the q cores for being mapped to multi-core DSP, wherein N, M, L 1], Q is the DSP core number for participating in processing；

1b) to 1a) in each piece of echo data enter row distance to Fourier transformation, obtain apart from frequency-region signal：

Wherein, a_r() and a_a() is respectively the distance of linear FM signal to window function and orientation window function, k_rFor Signal frequency modulation rate, λ is radar wavelength, f_rIt is signal distance to frequency, f_cFor radar carrier frequency, t_mFor the orientation slow time, c is electromagnetism Ripple spread speed in media as well；R(t_m；X_n,R₀) be with certain range gate center point P transfer be X_nPoint target in t_mMoment is to flat The instantaneous oblique distance of platform, R₀For point target along wave beam ray to oblique distance, v be radar platform translational speed, θ_sqFor front side view angle theta_fsq Complementary angle, front side view angle theta_fsqFor the angle in beam center ray and course line, as shown in Figure 2；

S₁(f_r；t_m；X_n,R₀) in last exponential termWalk comprising distance It is dynamic；

1c) constitution step 1b) in exponential termRange Walk Correction phase place H₁：

Wherein, range walk amount Δ R (t_m)=- (vsin θ_sq)t_m；

1d) will be apart from frequency-region signal S₁(f_r；t_m；X_n,R₀) it is multiplied by Range Walk Correction phase place H₁(f_r；t_m), obtain distance and walk Signal after dynamic(al) correction：

Wherein,

Step 2. space-variant range curvature correction.

Signal S 2a) adjusted the distance away after dynamic(al) correction₂(f_r；t_m；X_n,R₀) orientation Fourier transformation is carried out, obtain two dimension Frequency-region signal：

Wherein, For the instantaneous angle of strabismus of wave beam ray, γ_e(f_a；R_s0) it is distance to equivalent FM rate, R_s0It is radar to scene centrage Reference distance, S₃(f_r；f_a；X_n, R₀) last exponential termFor range curvature item, the range curvature is oblique with target Away from R₀Change, illustrates bending with space-variant；

Construction frequency-domain correction phase place H₂：

2b) by two-dimensional frequency signal S₃(f_r；f_a；X_n,R₀) it is multiplied by phase calibration H₂(R₀,f_r,f_a), space-variant is obtained apart from curved Signal after Qu Jiaozheng：

Step 3. distance is to matched filtering.

Signal S after space-variant range curvature correction is constructed 3a)₄(f_r；f_a；X_n,R₀) in frequency modulation frequency modulation phase placeAdaptation function H₃：

3b) by S₄(f_r；f_a；X_n,R₀) and H₃(f_r；f_a；R_s0) be multiplied, line-spacing descriscent inverse Fourier transform of going forward side by side, obtain away from Signal after matched filtering：

Wherein,It is distance to fast time, Δ f_rFor linear FM signal bandwidth.

Step 4. is apart from non-space-variant motion error extraction.

4a) adjust the distance the signal after matched filteringOrientation inverse Fourier transform is carried out, when obtaining bidimensional Domain signal：

4b) using bidimensional time-domain signalFrequency Estimation is instantaneously adjusted, obtains adjusting frequency vector：

γ=[γ₁,…γ_l,…,γ_L],

Wherein l=1,2 ..., L；

4c) exchanging frequency vector γ carries out M point interpolations, obtains the tune frequency vector after interpolation：

ζ=[ζ₁,…ζ_m,…,ζ_M],

Wherein m=1,2 ..., M；

Quadratic integral is carried out to the tune frequency vector ζ after interpolation 4d), range error vector is obtained：

Wherein s ∈ [0, t_m]。

Step 5. is apart from non-space-variant kinematic error compensation.

Envelope correction is carried out to echo data S 5a)；

5b) using kinematic error vector Δ R construction phase compensation functions：

5c) by echo data S and phase compensation function H₄It is multiplied, obtains apart from non-space-variant moving compensating data：

WhereinRepresent Hadamard products.

Step 6. is apart from space-variant motion error extraction.

6a) range migration correction is carried out with distance to matched filtering using data Y after non-space-variant motion compensation, Filtered data are divided into into G × L blocks, G be distance to block number, G takes the positive integer more than 1, and L is orientation block number；

6b) using each block number instantaneous Doppler chirp rate according to estimates, G × L dimension frequency modulation rate matrix Ω are obtained；

M point interpolations 6c) are carried out to the row vector of frequency modulation rate matrix Ω, G × M dimension space-variant kinematic error matrix ψ are obtained.

Step 7. data Y after non-space-variant motion compensation of being adjusted the distance using space-variant kinematic error matrix ψ carry out error compensation.

Space-variant motion compensation phasing matrix is constructed 7a)：

H₅=exp (j ψ),

7b) by data Y and H after non-space-variant motion compensation₅It is multiplied, obtains the data after space-variant motion compensation：

Step 8. calculates the entropy E of data Z after motion compensation_z：

Wherein z (m, n) represents the m rows of Z, the n-th column element.

Step 9. iterative estimate kinematic error.

Repeat step 1～8, when the entropy difference of motion compensated result is less than 0.01 twice in front and back, it is believed that meet compensation essence Degree requires that execution step 10 is such as unsatisfactory for, and continues step 1～8, requires until meeting compensation.

Step 10. azimuth focus.

Orientation Fourier transformation is carried out to data Z after motion compensation 10a), orientation frequency-region signal is obtained：

Wherein Z (m,:) for the m rows of data Z,Last exponential termFor orientation matched filtering item；

10b) constitution step 10a) in orientation matched filtering item penalty function H₅：

10c) by orientation frequency-region signalWith penalty function H₅(f_a,R₀) be multiplied, and it is inverse to perform orientation Fourier transformation, obtains bidimensional time domain target response function：

Wherein Δ f_aFor doppler bandwidth；

10d) to bidimensional time domain target response functionAmplitude is taken, SAR image is obtained.

The effect of the present invention is further illustrated by the experiment of following measured data：

1st, experiment condition：

Radar parameter is set, as shown in table 1：

1 radar parameter of table

Wave band	X-band	Front side visual angle	20°
				Bandwidth	200MHz	Speed	About 43m/s
Shi Kuan	24μs	Scene center away from	7258m
				PRF	1KHz	Sample rate	250MHz

Radar return data are 2048 × 2048 complex matrix.

Because inventive algorithm is obtained by the RD algorithm improvements of time domain correlation range walk, therefore choose time domain correlation range walk RD algorithms contrasted with the present invention.

2nd, experiment content：

Experiment 1, using the envelope error in present invention estimation echo data, apart from non-space-variant error and apart from space-variant mistake Difference, as shown in figure 3, wherein, Fig. 3 (a) represents envelope error estimation result to estimated result；Fig. 3 (b) is represented apart from non-NULL changeable phases Error estimation result；Fig. 3 (c) expressions list 3 different distance units apart from Spatially variant phase error estimated result in Fig. 3 (c) Phase error.

From figure 3, it can be seen that envelope error reaches 2m, 800rad is reached apart from non-Spatially variant phase error, miss apart from space-variant Excursion is differed from for -25～27rad, rad represents radian.

Experiment 2, carries out Matlab imaging with the RD algorithms of existing time domain correlation range walk using the present invention, as a result such as Shown in Fig. 4, wherein, Fig. 4 (a) represents imaging results of the present invention, and Fig. 4 (b) represents the RD algorithms imaging of time domain correlation range walk As a result.

From fig. 4, it can be seen that imaging results of the present invention focus on good, the RD algorithm imaging results of time domain correlation range walk Presence is significantly defocused.

Experiment 3, carries out DSP imagings with the present invention, as a result as shown in Figure 5 in multi-core DSP.

From fig. 5, it can be seen that DSP imaging results are identical with the Matlab imaging results of Fig. 4 (a).

Process time to testing 3 each steps is counted, as a result as shown in table 2.

2 multi-core DSP treatment effeciency of table

Step	Time (ms)
		Apart from non-space-variant error estimation and compensation	323.65
Apart from space-variant error estimation and compensation	452.49
		Range Walk Correction	85.22
Space-variant range curvature correction	90.81
		Distance is to matched filtering	79.45
Azimuth focus	92.74
		Total time	1124.36

As shown in Table 2, DSP processes total time for 1124.36ms.

To sum up, the present invention can effectively estimate envelope error, apart from non-space-variant error and apart from space-variant error, the present invention into Image space method focusing performance is better than conventional RD algorithm, and multi-core DSP process disclosure satisfy that requirement of real-time.

Claims (9)

1. a kind of front side based on multi-core DSP regards SAR realtime imaging methods, comprises the steps：

1) distance is equally divided into into L block according to orientation to the echo data S of N points, orientation M point, and byExtremelyAccording to the q cores for being mapped to multi-core DSP, to each block number according to Range Walk Correction is carried out, wherein N, M, L is greatly block number In 1 positive integer, q ∈ [0,1 ..., Q-1], Q are the DSP core number for participating in processing；

2) space-variant range curvature is corrected using the data after calibration of walking about：

2a) by this bidimensional frequency domain of data conversion to distance and bearing, and construct frequency-domain correction phase place：

$H_2(R_0,f_r,f_a)=\exp \left\{j\frac{4\mathrm{\π}}{c}\left(\frac{R_0}{\sqrt{1-{(f_a/f_{aM})}^2}}\right)f_r\right\}$

Wherein, R₀For point target wave beam ray to oblique distance, f_rFor frequency of distance, f_aFor orientation frequency, f_aMIt is most mostly general for orientation Strangle, c is the light velocity, j represents imaginary number；

2b) by frequency-domain correction phase place H₂(R₀,f_r,f_a) be multiplied with orientation frequency-region signal, complete space-variant range curvature correction；

3) row distance is entered to matched filtering to the data after space-variant range curvature correction；Filtered data are converted into into distance With orientation bidimensional time domain, instantaneous Doppler chirp rate is estimated using the bidimensional time domain data, then instantaneous Doppler chirp rate is entered Row interpolation, obtains full aperture kinematic error vector Δ R；

4) envelope correction and phase compensation are carried out to original radar return data S using kinematic error vector Δ R, is obtained apart from non- Data Y after space-variant motion compensation；

5) range migration correction is carried out using data Y after non-space-variant motion compensation, the data after correction are divided into into G × L blocks, G are distance to block number, and L is orientation block number；Using each block number instantaneous Doppler chirp rate according to estimates, G × L dimensions are obtained Frequency modulation rate matrix Ω, carries out M point interpolations to the row vector of frequency modulation rate matrix Ω, obtains G × M dimension space-variant kinematic error matrix ψ, Wherein G is the positive integer more than 1；

6) data Y after non-space-variant kinematic error compensation of being adjusted the distance using space-variant kinematic error matrix ψ carry out error compensation, obtain Data Z after space-variant motion compensation, calculate the entropy E of data Z_z；

7) repeatedly 1)～6), when the entropy difference of compensation result is less than 0.01 twice in front and back think to meet compensation precision requirement, Azimuth focus are carried out to data Z after motion compensation, are such as unsatisfactory for, then continue iteration 1)～6), until meet compensation require.

2. method according to claim 1, wherein the step 1) in Range Walk Correction is carried out to each piece of echo data, Carry out as follows：

Row distance is entered to Fourier transformation to each piece of echo data 1a), is obtained apart from frequency-region signal：

$\begin{array}{c}{S}_1(f_r;t_m;X_n,R_0)=a_r\left(f_r/k_r\right)a_a\left(t_m\right)\exp \[-j\mathrm{\π}\frac{f_r^2}{k_r}\]\·\\ \exp \[-j\frac{4\mathrm{\π}}{c}R(t_m;X_n,R_0)f_r\]\exp \[-j\frac{4\mathrm{\π}}{\mathrm{\λ}}R(t_m;X_n,R_0)\]\\ =a_r\left(f_r/k_r\right)a_a\left(t_m\right)\exp \[-j\mathrm{\π}\frac{f_r^2}{k_r}\]\exp \[-j\frac{4\mathrm{\π}}{\mathrm{\λ}}R(t_m;X_n,R_0)(f_r+f_c)\]\end{array}$

$\begin{array}{c}R(t_m;X_n,R_0)=\sqrt{R_0^2+{({\mathrm{vt}}_m-X_n)}^2-2R_0({\mathrm{vt}}_m-X_n){\mathrm{sin\θ}}_{sq}}\\ \≈\sqrt{R_0^2+v^2{\cos }^2{\mathrm{\θ}}_{sq}{(t_m-X_n/v)}^2}-(t_m-X_n/v)v{\mathrm{sin\θ}}_{sq}\end{array},$

Wherein, a_r() and a_a() is respectively the distance of linear FM signal to window function and orientation window function, k_rFor signal Frequency modulation rate, λ is radar wavelength, f_rIt is signal distance to frequency, f_cFor radar carrier frequency, t_mFor the orientation slow time, c exists for electromagnetic wave Spread speed in medium, R (t_m；X_n,R₀) be with certain range gate central point transfer be X_nPoint target in t_mMoment arrives platform Instantaneous oblique distance, R₀For point target along wave beam ray to oblique distance, v be radar platform translational speed, θ_sqFor the complementary angle at front side visual angle, Front side visual angle is beam center ray and the angle in course line, S₁(f_r；t_m；X_n,R₀) in last exponential termComprising range walk；

1b) constitution step 1a) in exponential termRange Walk Correction phase place H₁：

$H_1(f_r;t_m)=\exp \[j4\mathrm{\π}\frac{\mathrm{\Δ}R\left(t_m\right)}{c}(f_r+f_c)\],$

Wherein, range walk amount Δ R (t_m)=- (vsin θ_sq)t_m；

1c) will be apart from frequency-region signal S₁(f_r；t_m；X_n,R₀) it is multiplied by Range Walk Correction phase place H₁(f_r；t_m), obtain range walk school Signal after just：

$\begin{array}{c}{S}_2(f_r;t_m;X_n,R_0)=S_1(f_r;t_m;X_n,R_0)\×H_1(f_r;t_m)\\ =a_r(f_r/k_r)a_a\left(t_m\right)\exp \[-j\mathrm{\π}\frac{f_r^2}{k_r}\]\exp \[-j\frac{4\mathrm{\π}}{c}{R}_L(t_m;X_n,R_0)(f_r+f_c)\]\end{array}$

Wherein,

3. method according to claim 1, wherein the step 2) in the signal S that adjusts the distance away after dynamic(al) correction₂(f_r； t_m；X_n,R₀) space-variant range curvature correction is carried out, carry out as follows：

Signal S 2a) adjusted the distance away after dynamic(al) correction₂(f_r；t_m；X_n,R₀) orientation Fourier transformation is carried out, obtain two-dimensional frequency Signal：

$\begin{array}{c}{S}_3(f_r;f_a;X_n,R_0)=a_r\left(\frac{f_r}{{\mathrm{\γ}}_e(f_a;R_{s0})}\right)a_a\left(\frac{R_0{\mathrm{\λf}}_a}{2v^2{\cos }^2{\mathrm{\θ}}_{sq}\sqrt{1-{(f_a/f_{aM})}^2}}\right)\·\\ \exp \[-j\frac{4\mathrm{\π}}{c}{X}_n{\mathrm{sin\θ}}_{sq}{(f_r+f)}_c\]\·\\ \exp \[-j\frac{2\mathrm{\π}}{{\mathrm{vcos\θ}}_{sq}}{R}_0\sqrt{f_{aM}^2-f_a^2}\]\exp \[-j2{\mathrm{\πf}}_a\frac{X_n}{v}\]\·\\ \exp \[-j\mathrm{\π}\frac{{f_r}^2}{{\mathrm{\γ}}_e(f_a;R_{s0})}\]\·\exp \left\{-j\frac{4\mathrm{\π}}{c}\left(\frac{R_0}{\sqrt{1-{(f_a/f_{aM})}^2}}\right)f_r\right\}\end{array}$

Wherein, For the instantaneous angle of strabismus of wave beam ray, R_s0For the reference distance of radar to scene centrage,S₃ (f_r；f_a；X_n,R₀) last exponential termFor range curvature item, this is apart from curved Song is with target oblique distance R₀Change, illustrates bending with space-variant；t_mFor the orientation slow time, λ is carrier frequency wavelength, and v is radar platform shifting Dynamic speed, θ_sqFor the complementary angle at front side visual angle, f_cFor radar carrier frequency, X_nFor target and range gate central point which is located orientation away from From a_r() and a_a() is respectively the distance of linear FM signal to window function and orientation window function, γ_e(f_a；R_s0) be away from Descriscent equivalent FM rate, k_rFor signal frequency modulation rate；

Construction frequency-domain correction phase place H₂：

$H_2(R_0,f_r,f_a)=\exp \left\{j\frac{4\mathrm{\π}}{c}\left(\frac{R_0}{\sqrt{1-{(f_a/f_{aM})}^2}}\right)f_r\right\},$

2b) by two-dimensional frequency signal S₃(f_r；f_a；X_n,R₀) it is multiplied by phase calibration H₂(R₀,f_r,f_a), obtain space-variant range curvature school Signal after just：

$\begin{array}{c}{S}_4(f_r;f_a;X_n,R_0)=S_3(f_r;f_a;X_n,R_0)\×H_2(R_0;f_r;f_a)\\ =a_r\left(\frac{f_r}{{\mathrm{\γ}}_e(f_a;R_{s0})}\right)a_a\left(\frac{R_0{\mathrm{\λf}}_a}{2v^2{\cos }^2{\mathrm{\θ}}_{sq}\sqrt{1-{(f_a/f_{aM})}^2}}\right)\·\\ \exp \[-j\frac{4\mathrm{\π}}{c}{X}_n{\mathrm{sin\θ}}_{sq}{(f_r+f)}_c\]\·\exp \[-j2{\mathrm{\πf}}_a\frac{X_n}{v}\]\·\\ \exp \[-j\mathrm{\π}\frac{{f_r}^2}{{\mathrm{\γ}}_e(f_a;R_{s0})}\]\·\exp \[-j\frac{2\mathrm{\π}}{{\mathrm{vcos\θ}}_{sq}}{R}_0\sqrt{f_{aM}^2-f_a^2}\]\end{array}.$

4. method according to claim 1, wherein the step 3) in enter row distance to matched filtering, enter as follows OK：

Signal S after space-variant range curvature correction is constructed 3a)₄(f_r；f_a；X_n,R₀) in frequency modulation frequency modulation phase place Adaptation function H₃：

$H_3(f_r;f_a;R_{s0})=\exp \[j\mathrm{\π}\frac{{f_r}^2}{{\mathrm{\γ}}_e(f_a;R_{s0})}\],$

Wherein, γ_e(f_a；R_s0) it is distance to equivalent FM rate, R_s0For the reference distance of radar to scene centrage；

3b) by S₄(f_r；f_a；X_n,R₀) and H₃(f_r；f_a；R_s0) be multiplied, line-spacing descriscent inverse Fourier transform of going forward side by side obtains distance matching Filtered signal：

$\begin{array}{c}{S}_5(\hat{t};f_a;X_n,R_0)=IFFT\[S_4(f_r;f_a;X_n,R_0)\×H_3(f_r;f_a;R_0)\]\\ =\sin c\left({\mathrm{\Δf}}_r\left(\hat{t}-\frac{2(R_0+X_n{\mathrm{sin\θ}}_{sq})}{c}\right)\right)\·\\ a_a\left(\frac{R_0{\mathrm{\λf}}_a}{2v^2{\cos }^2{\mathrm{\θ}}_{sq}\sqrt{1-{(f_a/f_{aM})}^2}}\right)\·\exp \[-j2{\mathrm{\πf}}_a\frac{X_n}{v}\]\·\\ \exp \[-j\frac{4\mathrm{\π}}{c}{X}_n{\mathrm{sin\θ}}_{sq}{f}_c\]\exp \[-j\frac{2\mathrm{\π}}{{\mathrm{vcos\θ}}_{sq}}{R}_0\sqrt{f_{aM}^2-f_a^2}\]\end{array}$

Wherein,It is distance to fast time, Δ f_rFor linear FM signal bandwidth, λ is carrier frequency wavelength, and v is radar platform movement speed Degree, θ_sqFor the complementary angle at front side visual angle, f_cFor radar carrier frequency, X_nFor the azran of target and range gate central point which is located.

5. method according to claim 1, wherein the step 3) in estimation difference vector Δ R, carry out as follows：

3c) adjust the distance the signal after matched filteringOrientation inverse Fourier transform is carried out, bidimensional time domain letter is obtained Number：

$S_6(\hat{t};t_m;X_n,R_0)=IFFT\[S_5(\hat{t};f_a;X_n,R_0)\],$

Wherein,It is distance to fast time, t_mFor orientation slow time, X_nFor target and range gate central point which is located orientation away from From；

3d) using bidimensional time-domain signalFrequency Estimation is instantaneously adjusted, obtains adjusting frequency vector：

γ=[γ₁,…γ_l,…,γ_L],

Wherein l=1,2 ..., L；

M point interpolations are carried out to γ 3e), the tune frequency vector after interpolation is obtained：

ζ=[ζ₁,…ζ_m,…,ζ_M],

Wherein m=1,2 ..., M；

Quadratic integral is carried out to ζ 3f), range error vector is obtained：

$\begin{array}{c}\mathrm{\Δ}R={\∫}_0^{t_m}{\∫}_0^s{a}_{R}duds\\ ={\∫}_0^{t_m}{\∫}_0^s\frac{\mathrm{\λ}}{2}\mathrm{\ζ}dsdt\end{array},$

Wherein s ∈ [0, t_m]。

6. method according to claim 1, wherein the step 4) in using kinematic error vector Δ R to original radar return Data S carry out phase compensation, carry out as follows：

4a) using kinematic error vector Δ R construction phase compensation functions：

$H_4=\exp \left(-j\frac{4\mathrm{\π}\mathrm{\Δ}R}{\mathrm{\λ}}\right),$

Wherein, λ is carrier frequency wavelength；

4b) by echo data S and phase compensation function H₄It is multiplied, obtains apart from non-space-variant moving compensating data：

$Y=S\⊗H_4,$

Wherein,Represent Hadamard products.

7. method according to claim 1, wherein the step 6) in adjusted the distance non-space-variant using space-variant kinematic error matrix ψ Data Y after motion compensation carry out error compensation, carry out as follows：

Space-variant motion compensation phasing matrix is constructed 6a)：

H₅=exp (j ψ),

6b) by data Y and H after non-space-variant motion compensation₅It is multiplied, obtains the data after space-variant motion compensation：

$Z=Y\⊗H_5.$

8. method according to claim 1, wherein the step 6) in data Z entropy E_z, it is calculated as follows：

$E_z=-\underset{m,n}{\Σ}\left\{\left(\frac{|z(m,n){|}^2}{\underset{m,n}{\Σ}|z(m,n){|}^2}\right)\log \[\frac{\left|z(m,n)\right|}{\underset{m,n}{\Σ}\left|z(m,n)\right|}\]\right\},$

Wherein z (m, n) represents the m rows of Z, the n-th column element.

9. method according to claim 1, wherein the step 7) in data Z after motion compensation carried out with orientation gather Jiao, is carried out as follows：

Orientation Fourier transformation is carried out to data Z after motion compensation 7a), orientation frequency-region signal is obtained：

$\begin{array}{c}{S}_7(\hat{t};t_a;X_n,R_0)=\underset{m}{FFT}\[Z(m,:)\]\\ =\sin c\left({\mathrm{\Δf}}_r\left(\hat{t}-\frac{2(R_0+X_n{\mathrm{sin\θ}}_{sq})}{c}\right)\right)\·\\ a_a\left(\frac{R_0{\mathrm{\λf}}_a}{2v^2{\cos }^2{\mathrm{\θ}}_{sq}\sqrt{1-{(f_a/f_{aM})}^2}}\right)\·\exp \[-j2{\mathrm{\πf}}_a\frac{X_n}{v}\]\·\\ \exp \[-j\frac{4\mathrm{\π}}{c}{X}_n{\mathrm{sin\θ}}_{sq}{f}_c\]\exp \[-j\frac{2\mathrm{\π}}{{\mathrm{vcos\θ}}_{sq}}{R}_0\sqrt{f_{aM}^2-f_a^2}\]\end{array}$

Wherein, Z (m,:) for the m rows of data Z,Last exponential termFor Orientation matched filtering item,It is distance to fast time, X_nFor the azran of target and range gate central point which is located, Δ f_rFor line Property FM signal bandwidth, θ_sqFor the complementary angle at front side visual angle, a_a() is orientation window function, and λ is carrier frequency wavelength, and v is that radar is put down Platform translational speed, f_cFor radar carrier frequency；

7b) constitution step 7a) in orientation matched filtering item penalty function H₅：

$H_5(f_a,R_0)=\exp \[j\frac{2\mathrm{\π}}{{\mathrm{vcos\θ}}_{sq}}{R}_0\sqrt{f_{aM}^2-f_a^2}\],$

7c) by orientation frequency-region signalWith penalty function H₅(f_a,R₀) be multiplied, and orientation is performed against Fourier Conversion, obtains SAR image：

$\begin{array}{c}{S}_8(\hat{t},t_m;R_0)=IFFT\[S_7(\hat{t};f_a;X_n,R_0)\×H_5(f_a,R_0)\]\\ =\sin c\[{\mathrm{\Δf}}_r\left(\hat{t}-\frac{2(R_0+X_n{\mathrm{sin\θ}}_{sq})}{c}\right)\]\·\sin c\[{\mathrm{\Δf}}_a\left(t_m-\frac{X_n}{v}\right)\]\·\\ \exp \[-j\frac{4\mathrm{\π}}{c}{X}_n{\mathrm{sin\θ}}_{sq}{f}_c\]\end{array}$

Wherein Δ f_aFor doppler bandwidth, t_mFor the orientation slow time.