CN106324597A - Translational motion compensation and imaging method for PFA-based large-turning-angle ISAR radar - Google Patents

Abstract

The present invention discloses a translational motion compensation and imaging method for a PFA-based large-turning-angle ISAR radar. The method mainly comprises the steps of sending a frequency-modulated pulse signal by a foundation ISAR radar, and subjecting a received target echo signal to the mixing treatment to obtain a frequency-mixed baseband echo signal s(tr, ta); subjecting the signal s(tr, ta) to the distance pulse-pressure treatment to obtain a baseband echo signal after being subjected to the distance pulse-pressure treatment; subjecting the signal to the translational compensation treatment to obtain a baseband echo signal S(fr, ta) after being subjected to the translational compensation treatment; calculating a wave-number-domain baseband echo signal W(ky, kx) represented in a rectangular coordinate system, and further calculating a distance-independent phase error at an error phase phi error (ky, kx), namely the phase error of the wave-number-domain baseband echo signal after being subjected to the inverse fast Fourier transformation treatment in the range direction; obtaining a distance-dependent target translational error; calculating the wave-number-domain baseband echo signal Wcomp (ky, kx) after being subjected to phase compensation, further calculating the ISAR imaging of the wave-number-domain baseband echo signal and conducting the self-focusing treatment so as to obtain the self-focused ISAR imaging.

Description

The translational compensation of big corner ISAR radar based on PFA and formation method

Technical field

The invention belongs to Radar Signal Processing Technology field, particularly to a kind of big corner ISAR radar based on PFA Translational compensation and formation method, i.e. based on polar format algorithm (Polar Format Algorithm, PFA) big corner is inverse The translational compensation method of synthetic aperture radar (Inverse Synthetic Radar, ISAR) radar and formation method, it is adaptable to Directly carry out the ISAR imaging processing of sampling radar.

Background technology

ISAR can carry out bidimensional imaging to the noncooperative target of motion, thus obtains more target letter Breath, provides basis for target recognition afterwards and classification, therefore suffers from paying close attention to widely and applying.Continuous along with Radar Technology Development, the focus obtaining always research of high resolution radar ISAR imaging and difficulties, the distance of ISAR imaging is to resolution Rate improves by increasing transmitted bandwidth, and azimuth resolution realizes by increasing the observation angle to target, but observation The increase of angle can cause scattering point that more distance unit migration (Migration Through Range Cell, MTRC) occurs, Its corresponding Doppler can not be approximately steady state value simultaneously, if not to more distance unit migration is corrected and phase place is mended Repaying, ISAR imaging will defocus to occurring at distance and bearing.So to obtain high-quality ISAR imaging, mesh to be considered The more distance unit migration MTRC caused of mark translation, it is also contemplated that the angle impact that target rotational produces, the biggest corner feelings Under condition, the strong coupling of translation component and rotative component makes translational compensation that tradition translation based on envelope alignment and self-focusing is mended Compensation method is difficult to accurately correct translation component, and then the result that follow-up big corner ISAR imaging algorithm is processed goes out Existing distance and bearing to defocus.

Summary of the invention

For the deficiency of above-mentioned prior art, it is an object of the invention to propose a kind of big corner ISAR based on PFA The translational compensation of radar and formation method, translational compensation and the formation method of this kind big corner ISAR radar based on PFA pass through PFA correction rotation causes bidimensional to couple, it is possible to increase the processing accuracy of target translational compensation and efficiency.

For reaching above-mentioned technical purpose, the present invention is achieved by the following technical solutions.

The translational compensation of a kind of big corner ISAR radar based on PFA and formation method, comprise the following steps:

Step 1, ground ISAR radar emission chirp signal, and the target echo signal received is carried out at mixing Reason, the base band echo-signal s (t after being mixed_r,t_a)；Wherein, t_rRepresent apart from fast time, t_aRepresent the orientation time；

Step 2, to the base band echo-signal s (t after mixing_r,t_a) carry out distance pulse pressure process, obtain distance pulse pressure and process After base band echo-signalThen the base band echo-signal after pulse pressure of adjusting the distance processCarry out at translational compensation Reason, obtains the base band echo-signal S (f after translational compensation processes_r,t_a) and target translational error △ R (t_a)；Wherein, f_rRepresent away from Off-frequency rate；

Step 3, the base band echo-signal S (f after translational compensation is processed_r,t_a) transform to wave-number domain, obtain wave-number domain base Band echo-signal W (k_r, θ), then by polar format algorithm PFA to wave-number domain base band echo-signal W (k_r, θ) and carry out interpolation Conversion, obtains the wave-number domain base band echo-signal W (k represented under rectangular coordinate system_y,k_x), and calculate target translational error △ R (t_a) error phase φ that causes_error(k_y,k_x), and then it is calculated error phase φ_error(k_y,k_xIn) with apart from unrelated Error phase φ_{r_indep}(k_y0,k_x)；

Wherein, k_rRepresenting radial space wave number, θ represents the target corner relative to radar, k_yRepresent under rectangular coordinate system Distance is to space wave number, k_xRepresent that the orientation under rectangular coordinate system is to space wave number；

Step 4, according to error phase φ_error(k_y,k_xIn) with apart from unrelated error phase φ_{r_indep}(k_y0,k_x), meter Calculate the error phase obtaining distance wave-number domain base band echo-signal after inverse fast fourier transformk_y0Table Show that distance is to wave number center；

Step 5, according to error phase φ_error(k_y,k_xIn) with apart from unrelated error phase φ_{r_indep}(k_y0,k_x) and away from The error phase of the wave-number domain base band echo-signal after the inverse fast fourier transform of descriscentIt is calculated phase place to mend Wave-number domain base band echo-signal W after repaying_comp(k_y,k_x), and then calculate the ISAR imaging of wave-number domain base band echo-signal；

Step 6, the ISAR imaging to wave-number domain base band echo-signal carries out Autofocus processing, after obtaining Autofocus processing ISAR imaging, the ISAR imaging after described Autofocus processing can improve the image quality of ISAR imaging.

Compared with prior art, the invention have the advantages that

Space-variant is got over distance unit migration MTRC by polar format algorithm PFA and is corrected by the inventive method, solves Keystone algorithm of having determined can not be adjusted the distance and be bent the problem being corrected；Target translational error is carried out two step compensation simultaneously, Accurately compensate for the target translation impact on ISAR imaging, there is bigger corner treatment ability and higher precision.

Accompanying drawing explanation

The present invention is described in further detail by explanation and detailed description of the invention below in conjunction with the accompanying drawings.

Fig. 1 is translational compensation and the formation method flow chart of a kind of based on PFA the big corner ISAR radar of the present invention；

Fig. 2 is that the target scattering point of emulation experiment is relative to position view；

Fig. 3 is the target flight path figure relative to radar；

Fig. 4 (a) is that the distance of error free process is to envelope result schematic diagram；

Fig. 4 (b) is that the distance that processes of the present invention is to envelope result schematic diagram；

Fig. 4 (c) is that the distance of conventional method process is to envelope result schematic diagram；

Fig. 5 (a) is by translational error and accurately compensates the imaging results schematic diagram obtained；

Fig. 5 (b) is to use the inventive method to obtain imaging results schematic diagram；

Fig. 5 (c) is the imaging results schematic diagram using conventional method to obtain；

Fig. 6 (a) is by the two-dimentional contour map of labelling point 1 in Fig. 2 of the accurate compensation deals of translational error；

Fig. 6 (b) is the two-dimentional contour map of labelling point 1 in Fig. 2 that conventional method processes；

Fig. 6 (c) is the two-dimentional contour map of labelling point 1 in Fig. 2 that the inventive method processes；

Fig. 6 (d) is that accurately the compensating in translational error respectively of labelling point 1 in Fig. 2, conventional method process and the inventive method The orientation obtained under disposition is to the comparative result schematic diagram of profile；

Fig. 7 (a) is by the two-dimentional contour map of labelling point 2 in Fig. 2 of the accurate compensation deals of translational error；

Fig. 7 (b) is the two-dimentional contour map of labelling point 2 in Fig. 2 that conventional method processes；

Fig. 7 (c) is the two-dimentional contour map of labelling point 2 in Fig. 2 that the inventive method processes；

Fig. 7 (d) is that in Fig. 2, labelling point 2 accurately compensates in translational error respectively, conventional method processes and at the inventive method The orientation obtained in the case of reason is to the comparative result schematic diagram of profile；

Fig. 8 (a) be the accurate compensation deals of translational error Fig. 2 in the two-dimentional contour map of labelling point 3；

Fig. 8 (b) is the two-dimentional contour map of labelling point 3 in Fig. 2 that conventional method processes；

Fig. 8 (c) is the two-dimentional contour map of labelling point 3 in Fig. 2 that the inventive method processes；

Fig. 8 (d) is that in Fig. 2, labelling point 3 accurately compensates in translational error respectively, conventional method processes and at the inventive method The orientation obtained in the case of reason is to the comparative result schematic diagram of profile；

Fig. 9 (a) be the accurate compensation deals of translational error Fig. 2 in the two-dimentional contour map of labelling point 4；

Fig. 9 (b) is the two-dimentional contour map of labelling point 4 in Fig. 2 that conventional method processes

Fig. 9 (c) is the two-dimentional contour map of labelling point 4 in Fig. 2 that the inventive method processes；

Fig. 9 (d) is that in Fig. 2, labelling point 4 accurately compensates in translational error respectively, conventional method processes and at the inventive method The orientation obtained in the case of reason is to the comparative result schematic diagram of profile.

Detailed description of the invention

With reference to Fig. 1, for the translational compensation of a kind of based on PFA big corner ISAR radar and the formation method flow process of the present invention Figure；The translational compensation of described big corner ISAR radar based on PFA and formation method, comprise the following steps:

Step 1, ground ISAR radar emission chirp signal, and the target echo signal received is carried out at mixing Reason, the base band echo-signal s (t after being mixed_r,t_a)；Wherein, t_rRepresent apart from fast time, t_aRepresent the orientation time.

Specifically, the base band echo-signal s (t after described mixing_r,t_a) expression formula is:

$s(t_r,t_a)=a_r(t_r-\frac{2R\left(t_a\right)}{c})\exp \[j\mathrm{\γ}{(t_r-\frac{2R\left(t_a\right)}{c})}^2\]\exp \[-j\frac{4\mathrm{\π}}{\mathrm{\λ}}R\left(t_a\right)\]$

Wherein, t_rRepresent apart from fast time, t_aRepresent orientation time, a_rT () represents base band echo-signal s after mixing (t_r,t_a) distance to window function,T_pRepresenting the pulse width of chirp signal, γ represents frequency modulation on pulse The frequency modulation rate of signal, c represents the light velocity, t express time variable, and λ represents the wavelength of chirp signal；R(t_a) represent that target arrives The oblique distance course of radar, is configured to multinomial model by the oblique distance course of described target to radar, and its expression formula is:R₀Represent the center of rotation initial distance to radar of target, V represents the target radial velocity relative to radar, and a represents the target radial acceleration relative to radar, R_n(t_a) represent more than n rank High-order translation component, n > 2；(x, y) represents the original position relative to target center of rotation of target scattering point, and θ represents target Relative to the corner of radar, target relative to the rotational angle theta of radar be [8,12] be big corner；Exp represents exponential function.

Step 2, to the base band echo-signal s (t after mixing_r,t_a) carry out distance pulse pressure process, obtain distance pulse pressure and process After base band echo-signalThen the base band echo-signal after pulse pressure of adjusting the distance processCarry out at translational compensation Reason, obtains the base band echo-signal S (f after translational compensation processes_r,t_a) and target translational error △ R (t_a)。

Specifically, the base band echo-signal after described distance pulse pressure processesExpression formula is:

$\hat{s}(t_r,t_a)=A_p\sin c\left(B\right(t_r-\frac{2R\left(t_a\right)}{c}\left)\right)\exp \[-j\frac{4\mathrm{\π}}{\mathrm{\λ}}R\left(t_a\right)\]$

Wherein, A_pRepresent the base band echo-signal after distance pulse pressure processAmplitude, B represent distance pulse pressure process After base band echo-signalBandwidth, sinc () represents sinc function, t_rRepresent apart from fast time, R (t_a) represent mesh Mark is to the oblique distance course of radar, and c represents that the light velocity, λ represent the wavelength of chirp signal, and exp represents exponential function.

Base band echo-signal after pulse pressure of adjusting the distance processEnvelope curve carry out fitting of a polynomial, estimate target The speed of translationTranslatory acceleration with targetRe-use the speed of described target translationTranslatory acceleration with target Base band echo-signal after pulse pressure of adjusting the distance processCarry out translational compensation process, obtain the base band after translational compensation processes Echo-signal S (f_r,t_a), its expression formula is:

$S(f_r,t_a)=A_{p}rect\left(\frac{f_r}{B}\right)\exp (-j\frac{4\mathrm{\π}(f_c+f_r)}{c}(\mathrm{\Δ}R\left(t_a\right)+xsin\mathrm{\θ}\left(t_a\right)+ycos\mathrm{\θ}\left(t_a\right)\left)\right)$

Wherein, △ R (t_a) represent between the target translation that the actual translation of target translational error, i.e. target and estimation obtain Difference,Rect represents rectangular function, R_n(t_a) represent high-orders more than n rank Translation component, n > 2；f_rRepresent frequency of distance, f_cRepresent carrier frequency, t_aRepresenting the orientation time, v represents the target radial direction relative to radar Speed, a represents the target radial acceleration relative to radar,The speed of the target translation obtained is estimated in expression,Represent and estimate The translatory acceleration of the target arrived.

Step 3, the base band echo-signal S (f after translational compensation is processed_r,t_a) transform to wave-number domain, obtain wave-number domain base Band echo-signal W (k_r, θ), then by polar format algorithm PFA to wave-number domain base band echo-signal W (k_r, θ) and carry out interpolation Conversion, obtains the wave-number domain base band echo-signal W (k represented under rectangular coordinate system_y,k_x), and calculate target translational error △ R (t_a) error phase φ that causes_error(k_y,k_x), and then it is calculated error phase φ_error(k_y,k_xIn) with apart from unrelated Error phase φ_{r_indep}(k_y0,k_x)；Wherein, k_rRepresenting radial space wave number, θ represents the target corner relative to radar, k_yTable Show that the distance under rectangular coordinate system is to space wave number, k_xRepresent that the orientation under rectangular coordinate system is to space wave number.

Specifically, described wave-number domain base band echo-signal W (k_r, θ) and expression formula is:

W(k_r, θ) and=P (k_r)exp(-jk_r(xsinθ+ycosθ))exp(-jk_r△R(θ))

Wherein, k_rRepresent radial space wave number,P(k_r) represent wave-number domain base band echo-signal W (k_r, Distance θ) to window function,△k_rBRepresent radial wave SerComm degree, △ k_rB=max (k_r)-min(k_r)； k_rcRepresent radial space wave number center,f_cRepresent carrier frequency；Maxima operation asked for by max table, and min represents and asks for Little Value Operations.

Described wave-number domain base band echo-signal W (k_r, θ) and it is at polar coordinate (k_r, θ) under represent wave-number domain base band echo letter Number, by polar format algorithm PFA at polar coordinate (k_r, θ) under represent wave-number domain base band echo-signal carry out interpolation change Change, obtain the wave-number domain base band echo-signal W (k represented under rectangular coordinate system_y,k_x), k_yRepresent distance under rectangular coordinate system to Space wave number, k_xRepresent that the orientation under rectangular coordinate system is to space wave number；The wave-number domain base band represented under described rectangular coordinate system Echo-signal W (k_y,k_x), its expression formula is:

$\begin{array}{c}W(k_y,k_x)=W(k_{r}cos\mathrm{\θ},k_{r}sin\mathrm{\θ})\\ =P\left(k_y\right)\exp (-{\mathrm{jk}}_{x}x-{\mathrm{jk}}_{y}y)\exp (-j\sqrt{k_x^2+k_y^2}\mathrm{\Δ}R(\mathrm{\θ}\left)\right)\\ =P\left(k_y\right)\exp (-{\mathrm{jk}}_{x}x-{\mathrm{jk}}_{y}y)\exp (-{\mathrm{j\φ}}_{error}(k_y,k_x\left)\right)\end{array}$

Wherein, W () represents wave-number domain base band echo-signal,k_rcRepresent radial space Wave number center,f_cRepresent carrier frequency；k_x=k_rSin θ, k_y=k_rCos θ, △ k_rBRepresent radial wave SerComm degree, soφ_error(k_y,k_x) represent target translational error △ R (t_a) error phase that causes,△ R (θ) represents target translational error △ R (t_a) with rotational angle theta for during independent variable Representation, θ represents the target corner relative to radar.

Then by target translational error △ R (t_a) error phase φ that causes_error(k_y,k_x) at k_y=k_y0Place carries out Taylor Series expansion, and remain into quadratic term, obtain target translational error △ R (t_a) error phase φ that causes_error(k_y,k_x) Taylor series expansion:

$\sqrt{k_x^2+k_y^2}R\left(arctan\right(k_x/k_y\left)\right)\≈{\mathrm{\φ}}_{r\_indep}(k_{y0},k_x)+{\mathrm{\φ}}_{r\_dep}(k_y,k_x)$

${\mathrm{\φ}}_{r\_indep}(k_{y0},k_x)=\sqrt{k_x^2+k_{y0}^2}R\left(arctan\right(k_x/k_{y0}\left)\right)$

$\begin{array}{c}{\mathrm{\φ}}_{r\_dep}(k_y,k_x)=\left(\frac{k_{y0}}{\sqrt{k_x^2+k_{y0}^2}}\mathrm{\Δ}R\right(\arctan \left(k_x/k_{y0}\right))-\frac{k_x}{\sqrt{k_x^2+k_{y0}^2}}{\mathrm{\ΔR}}^{\′}(\arctan \left(k_x/k_{y0}\right)\left)\right)(k_y-k_{y0})+\\ \left(\frac{k_x^2}{{(k_x^2+k_{y0}^2)}^{3/2}}\mathrm{\Δ}R\right(\arctan \left(k_x/k_{y0}\right))+\frac{k_x^2}{{(k_x^2+k_{y0}^2)}^{3/2}}{\mathrm{\ΔR}}^{\′\′}(\arctan \left(k_x/k_{y0}\right)\left)\right){(k_y-k_{y0})}^2\end{array}$

Wherein, φ_{r_indep}(k_y0,k_x) represent error phase φ_error(k_y,k_xIn) with apart from unrelated error phase, φ_{r_dep}(k_y,k_x) represent error phase φ_error(k_y,k_xWith the error phase of distance dependent in), φ_error(k_y,k_x) represent mesh Mark translational error △ R (t_a) error phase that causes, △ R'(arctan (k_x/k_y0)) represent △ R (arctan (k_x/k_y)) relatively In arctan (k_x/k_y) first derivative, △ R " (arctan (k_x/k_y0)) represent △ R (arctan (k_x/k_y)) relative to arctan(k_x/k_y) at k_y=k_y0Time second dervative, △ R (arctan (k_x/k_y)) represent target translational error △ R (t_a) to turn AngleFor representation during independent variable, k_y0Expression distance is to wave number center, and distance is to wave number center k simultaneously_y0It is Distance under rectangular coordinate system is to space wave number k_yIntermediate value；k_xRepresent that the orientation under rectangular coordinate system is to space wave number.

Step 4, according to error phase φ_error(k_y,k_xIn) with apart from unrelated error phase φ_{r_indep}(k_y0,k_x), meter Calculate the error phase obtaining distance wave-number domain base band echo-signal after inverse fast fourier transformk_y0Table Show that distance is to wave number center.

The concrete sub-step of step 4 is:

4.1 intercept the wave-number domain base band echo-signal W (k represented under described rectangular coordinate system_y,k_x) a part of ripple in centre Number field base band echo-signalObtain distance wave-number domain base band echo-signal after inverse fast fourier transformThe wave-number domain base band echo-signal W (k represented under the described rectangular coordinate system of described intercepting_y,k_x) a part of ripple in centre Number field base band echo-signalIts requirement is: the wave-number domain base band making described distance after inverse fast fourier transform Echo-signalIn each point exist only in a distance unit, and described distance is to inverse fast fourier transform After wave-number domain base band echo-signalIn image along orientation to bright line parallel with azimuth axis.

Described distance wave-number domain base band echo-signal after inverse fast fourier transformIts expression formula is:IFFT represents your fast Fourier transform operation, k_yRepresent distance under rectangular coordinate system to Space wave number, k_xRepresent that the orientation under rectangular coordinate system is to space wave number.

4.2 due to described distance wave-number domain base band echo-signal after inverse fast fourier transformWith distance Unrelated error phase φ_{r_indep}(k_y0,k_x), and described rectangular coordinate system (k_y,k_xThe wave-number domain base band echo-signal represented under) W(k_y,k_x) identical with apart from unrelated error phase, therefore use autofocus algorithm to described distance to inverse fast Fourier Wave-number domain base band echo-signal after conversionEstimate with apart from unrelated error phase, obtain distance to inverse fast The error phase of the wave-number domain base band echo-signal after speed Fourier transformation

Step 5, according to error phase φ_error(k_y,k_xIn) with apart from unrelated error phase φ_{r_indep}(k_y0,k_x) and away from The error phase of the wave-number domain base band echo-signal after the inverse fast fourier transform of descriscentIt is calculated phase place to mend Wave-number domain base band echo-signal W after repaying_comp(k_y,k_x), and then calculate the ISAR imaging of wave-number domain base band echo-signal；Wherein, φ_error(k_y,k_x) represent target translational error △ R (t_a) error phase that causes.

The concrete sub-step of step 5 is:

5.1 according to error phase φ_error(k_y,k_xIn) with apart from unrelated error phase φ_{r_indep}(k_y0,k_x), calculate target and put down In dynamic error with apart from unrelated translational error Represent the error phase of distance wave-number domain base band echo-signal after inverse fast fourier transform.

In 5.2 pairs of described target translational error with apart from unrelated translational errorCarry out interpolation plan Close, obtain the target translational error with distance dependent after interpolation fitting

5.3 according to target translational error with distance dependent after interpolation fittingIt is calculated target to put down The phase compensation function H of dynamic error_TrCo2(k_y,k_x), its expression formula is:

$H_{TrCo2}(k_y,k_x)=\exp \left(j\sqrt{k_x^2+k_y^2}\mathrm{\Δ}\tilde{R}\right(\arctan \left(k_x/k_y\right)\left)\right)$

The 5.4 phase compensation function H utilizing target translational error_TrCo2(k_y,k_x) to described rectangular coordinate system (k_y,k_xUnder) The wave-number domain base band echo-signal W (k represented_y,k_x) carry out phase compensation, obtain the letter of the wave-number domain base band echo after phase compensation Number W_comp(k_y,k_x), its expression formula is:

W_comp(k_y,k_x)=W (k_y,k_x)·H_TrCo2(k_y,k_x)

Wherein, dot product is represented.

Wave-number domain base band echo-signal W after 5.5 pairs of described compensation_comp(k_y,k_x) carry out bidimensional inverse fast fourier transform (IFFT) the ISAR imaging of wave-number domain base band echo-signal, is obtained.

Step 6, the ISAR imaging to wave-number domain base band echo-signal carries out Autofocus processing, after obtaining Autofocus processing ISAR imaging, the ISAR imaging after described Autofocus processing can improve the image quality of ISAR imaging.

Effectiveness of the invention can be described further by following emulation.

Emulation content and interpretation of result:

Emulation experiment: simulation parameter is as shown in table 1:

Table 1

Fig. 2 be the target scattering point of emulation experiment relative to position view, wherein aircraft length 35 meters, wide 30 meters；

Fig. 2 comprises 4 labelling points, respectively labelling point 1, labelling point 2, labelling point 3 and labelling point 4；

Fig. 3 is the target flight path figure relative to radar, and target is 11.73 degree relative to the corner of radar.

Use conventional translational compensation algorithm i.e. envelope alignment and Autofocus processing scheme and the present invention that method is emulated respectively Data process, by the result of accurately compensation translation as reference, and result such as Fig. 4 (a), Fig. 4 (b) and Fig. 4 (c) Shown in, Fig. 4 (a) be the distance of error free process to envelope result schematic diagram, Fig. 4 (b) is that the distance that processes of the present invention is to envelope Result schematic diagram, Fig. 4 (c) is that the distance of conventional method process is to envelope result schematic diagram；Translational error accurately compensates and uses Conventional method processes and uses the imaging results that the inventive method obtains after processing, such as Fig. 5 (a), Fig. 5 (b) and Fig. 5 (c) institute Show；Fig. 5 (a) is by translational error and accurately compensates the imaging results schematic diagram obtained, and Fig. 5 (b) is to use the inventive method to obtain To imaging results schematic diagram, Fig. 5 (c) is the imaging results schematic diagram using conventional method to obtain.In order to further result be entered 4 labelling points in Fig. 2 are amplified analyzing by row explanation, draw its two dimension contour map and orientation to impulse response function (Impulse Response Function, IRF), shown in result such as Fig. 6 (a)-Fig. 9 (d)；Wherein, Fig. 6 (a) is by translation The two-dimentional contour map of labelling point 1 in Fig. 2 of the accurate compensation deals of error；Fig. 6 (b) is labelling in Fig. 2 that conventional method processes The two-dimentional contour map of point 1；Fig. 6 (c) is the two-dimentional contour map of labelling point 1 in Fig. 2 that the inventive method processes；Fig. 6 (d) is Accurately the compensating in translational error respectively of labelling point 1 in Fig. 2, conventional method process and obtain under the inventive method disposition Orientation is to the comparative result schematic diagram of profile；Fig. 7 (a) is by labelling point 2 in Fig. 2 of the accurate compensation deals of translational error Two dimension contour map；

Fig. 7 (b) is the two-dimentional contour map of labelling point 2 in Fig. 2 that conventional method processes；Fig. 7 (c) is at the inventive method The two-dimentional contour map of labelling point 2 in Fig. 2 of reason；Fig. 7 (d) is that in Fig. 2, labelling point 2 accurately compensates in translational error, often respectively The orientation obtained under the process of rule method and the inventive method disposition is to the comparative result schematic diagram of profile；Fig. 8 (a) is flat The two-dimentional contour map of labelling point 3 in Fig. 2 of the dynamic accurate compensation deals of error；Fig. 8 (b) is Fig. 2 acceptance of the bid that conventional method processes The two-dimentional contour map of note point 3；Fig. 8 (c) is the two-dimentional contour map of labelling point 3 in Fig. 2 that the inventive method processes；Fig. 8 (d) It is that in Fig. 2, labelling point 3 accurately compensates in translational error respectively, conventional method processes and obtains under the inventive method disposition Orientation is to the comparative result schematic diagram of profile；Fig. 9 (a) be the accurate compensation deals of translational error Fig. 2 in the two dimension of labelling point 4 Contour map；Fig. 9 (b) is the two-dimentional contour map of labelling point 4 in Fig. 2 that conventional method processes；Fig. 9 (c) is the inventive method The two-dimentional contour map of labelling point 4 in the Fig. 2 processed；Fig. 9 (d) be in Fig. 2 labelling point 4 accurately compensate in translational error respectively, The orientation obtained under conventional method process and the inventive method disposition is to the comparative result schematic diagram of profile；And calculate Its orientation to response pulse duration (Impulse Response Width, IRW), result of calculation is as shown in table 2.

Table 2

From Fig. 6 (a)-Fig. 9 (d) it can be seen that the result that processes of the inventive method and the process that accurately compensates of translational error Result is the most close, illustrates the effectiveness of the inventive method；And the two-dimentional contour map of conventional method result is the most mixed Disorderly, main lobe and secondary lobe are difficult to separately.Be can be seen that the orientation of the inventive method result is to dividing by the IRW result of calculation of table 2 The azimuth resolution of resolution and the accurate compensation result of translation is close and the azimuth resolution of conventional method result is deteriorated, Resolution loss is more than 25%.Illustrate effectiveness of the invention.

In sum, emulation experiment demonstrates the correctness of the present invention, validity and reliability.

Obviously, those skilled in the art can carry out various change and the modification essence without deviating from the present invention to the present invention God and scope；So, if these amendments of the present invention and modification belong to the scope of the claims in the present invention and equivalent technologies thereof Within, then the present invention is also intended to comprise these change and modification.

Claims (9)

1. the translational compensation of a big corner ISAR radar based on PFA and formation method, it is characterised in that include following step Rapid:

Step 1, ground ISAR radar emission chirp signal, and the target echo signal received is carried out Frequency mixing processing, Base band echo-signal s (t after being mixed_r,t_a)；Wherein, t_rRepresent apart from fast time, t_aRepresent the orientation time；

Step 2, to the base band echo-signal s (t after mixing_r,t_a) carry out distance pulse pressure process, after obtaining distance pulse pressure process Base band echo-signalThen the base band echo-signal after pulse pressure of adjusting the distance processCarry out translational compensation process, Base band echo-signal S (f after processing to translational compensation_r, t_a) and target translational error Δ R (t_a)；Wherein, f_rRepresent distance frequency Rate；

Step 3, the base band echo-signal S (f after translational compensation is processed_r, t_a) transform to wave-number domain, obtain wave-number domain base band and return Ripple signal W (k_r, θ), then by polar format algorithm PFA to wave-number domain base band echo-signal W (k_r, θ) and carry out interpolation change Change, obtain the wave-number domain base band echo-signal W (k represented under rectangular coordinate system_y, k_x), and calculate target translational error Δ R (t_a) Error phase φ caused_error(k_y, k_x), and then it is calculated error phase φ_error(k_y, k_xIn) with apart from unrelated error Phase_{r_indep}(k_y0, k_x)；

Wherein, k_rRepresenting radial space wave number, θ represents the target corner relative to radar, k_yRepresent the distance under rectangular coordinate system To space wave number, k_xRepresent that the orientation under rectangular coordinate system is to space wave number；

Step 4, according to error phase φ_error(k_y, k_xIn) with apart from unrelated error phase φ_{r_indep}(k_y0, k_x), calculate Error phase to distance wave-number domain base band echo-signal after inverse fast fourier transformk_y0Represent away from Wave number center, descriscent；

Step 5, according to error phase φ_error(k_y, k_xIn) with apart from unrelated error phase φ_{r_indep}(k_y0, k_x) and distance to The error phase of the wave-number domain base band echo-signal after inverse fast fourier transformAfter being calculated phase compensation Wave-number domain base band echo-signal W_comp(k_y, k_x), and then calculate the ISAR imaging of wave-number domain base band echo-signal；

Step 6, the ISAR imaging to wave-number domain base band echo-signal carries out Autofocus processing, obtains the ISAR after Autofocus processing Imaging.

The translational compensation of a kind of big corner ISAR radar based on PFA and formation method, its feature It is, in step 1, the base band echo-signal s (t after described mixing_r,t_a) expression formula is:

$s(t_r,t_a)=a_r\left(t_r-\frac{2R\left(t_a\right)}{c}\right)\exp \[j\mathrm{\γ}{\left(t_r-\frac{2R\left(t_a\right)}{c}\right)}^2\]\exp \[-j\frac{4\mathrm{\π}}{\mathrm{\λ}}R\left(t_a\right)\]$

Wherein, t_rRepresent apart from fast time, t_aRepresent orientation time, a_rT () represents the base band echo-signal s (t after mixing_r,t_a) Distance to window function,T_pRepresenting the pulse width of chirp signal, γ represents chirp signal Frequency modulation rate, c represents the light velocity, t express time variable, and λ represents the wavelength of chirp signal；R(t_a) represent that target arrives radar Oblique distance course, is configured to multinomial model by the oblique distance course of described target to radar, and its expression formula is:R₀Represent the center of rotation initial distance to radar of target, V represents the target radial velocity relative to radar, and a represents the target radial acceleration relative to radar, R_n(t_a) represent more than n rank High-order translation component, n > 2；(x, y) represents the original position relative to target center of rotation of target scattering point, and θ represents target Relative to the corner of radar, exp represents exponential function.

The translational compensation of a kind of big corner ISAR radar based on PFA and formation method, its feature It is, in step 2, the base band echo-signal after described distance pulse pressure processBase after the process of described translational compensation Band echo-signal S (f_r, t_a) and described target translational error Δ R (t_a), its expression formula is respectively as follows:

$\hat{s}(t_r,t_a)=A_p\sin c\left(B\right(t_r-\frac{2R\left(t_a\right)}{c}\left)\right)\exp \[-j\frac{4\mathrm{\π}}{\mathrm{\λ}}R\left(t_a\right)\]$

$S(f_r,t_a)=A_{p}rect\left(\frac{f_r}{B}\right)\exp (-j\frac{4\mathrm{\π}(f_c+f_r)}{c}(\mathrm{\Δ}R\left(t_a\right)+xsin\mathrm{\θ}\left(t_a\right)+ycos\mathrm{\θ}\left(t_a\right)))$

$\mathrm{\Δ}R\left(t_a\right)=({\mathrm{vt}}_a+\frac{1}{2}{\mathrm{at}}_a^2+R_n(t_a\left)\right)-(\tilde{v}{t}_a+\frac{1}{2}\tilde{a}{t}_a^2)$

Wherein, A_pRepresent the base band echo-signal after distance pulse pressure processAmplitude, B represent distance pulse pressure process after Base band echo-signalBandwidth, sinc () represents sinc function, t_rRepresent apart from fast time, R (t_a) represent that target arrives The oblique distance course of radar, c represents that the light velocity, λ represent the wavelength of chirp signal, and exp represents exponential function, Δ R (t_a) represent Target translational error, R_n(t_a) represent high-order translation components more than n rank, n > 2；Rect represents rectangular function, f_rRepresent distance frequency Rate, f_cRepresent carrier frequency, t_aRepresenting the orientation time, v represents the target radial velocity relative to radar, and a represents the target footpath relative to radar To acceleration,The speed of the target translation obtained is estimated in expression,The translatory acceleration of the target obtained is estimated in expression.

The translational compensation of a kind of big corner ISAR radar based on PFA and formation method, its feature Be, described in obtain translational compensation process after base band echo-signal S (f_r, t_a), its process is:

Base band echo-signal after pulse pressure of adjusting the distance processEnvelope curve carry out fitting of a polynomial, estimate target translation SpeedTranslatory acceleration with targetRe-use the speed of described target translationTranslatory acceleration with targetTo away from Base band echo-signal after pulse pressure processesCarry out translational compensation process, obtain the base band echo after translational compensation processes Signal S (f_r, t_a)。

The translational compensation of a kind of big corner ISAR radar based on PFA and formation method, its feature It is, in step 3, described wave-number domain base band echo-signal W (k_r, θ), the wave-number domain base band that represents under described rectangular coordinate system Echo-signal W (k_y, k_x), described target translational error Δ R (t_a) error phase φ that causes_error(k_y, k_x) and described error phase Position φ_error(k_y, k_xIn) with apart from unrelated error phase φ_{r_indep}(k_y0, k_x), its expression formula is respectively as follows:

W(k_r, θ) and=P (k_r)exp(-jk_r(xsinθ+ycosθ))exp(-jk_rΔR(θ))

$\begin{array}{c}W(k_y,k_x)=W(k_r\cos \mathrm{\θ},k_r\sin \mathrm{\θ})\\ =P\left(k_y\right)\exp (-{\mathrm{jk}}_{x}x-{\mathrm{jk}}_{y}y)\exp (-j\sqrt{k_x^2+k_y^2}\mathrm{\Δ}R(\mathrm{\θ}\left)\right)\\ =P\left(k_y\right)\exp (-{\mathrm{jk}}_{x}x-{\mathrm{jk}}_{y}y)\exp (-{\mathrm{j\φ}}_{error}(k_y,k_x\left)\right)\end{array}$

${\mathrm{\φ}}_{error}(k_y,k_x)=\sqrt{k_x^2+k_y^2}\mathrm{\Δ}R\left(arctan\right(\frac{k_x}{k_y}\left)\right)$

${\mathrm{\φ}}_{r\_indep}(k_{y0},k_x)=\sqrt{k_x^2+k_{y0}^2}\mathrm{\Δ}R\left(arctan\right(k_x/k_{y0}\left)\right)$

Wherein, k_rRepresent radial space wave number,P(k_r) represent wave-number domain base band echo-signal W (k_r, θ) Distance to window function,Δk_rBRepresent radial wave SerComm degree, Δ k_rB=max (k_r)-min(k_r)；k_rc Represent radial space wave number center,f_cRepresent carrier frequency；Maxima operation asked for by max table, and min represents and asks for minimum Value Operations, W () represents wave-number domain base band echo-signal,k_rcRepresent radial space wave number center,f_cRepresent carrier frequency；k_x=k_rSin θ, k_y=k_rCos θ, Δ k_rBRepresent radial wave SerComm degree, soφ_error(k_y, k_x) represent target translational error Δ R (t_a) error phase that causes,Δ R (θ) represents target translational error Δ R (t_a) with rotational angle theta for independent variable time Representation, θ represents the target corner relative to radar, φ_{r_indep}(k_y0, k_x) represent error phase φ_error(k_y, k_xIn) With apart from unrelated error phase, φ_error(k_y, k_x) represent target translational error Δ R (t_a) error phase that causes, Δ R' (arctan(k_x/k_y0)) represent Δ R (arctan (k_x/k_y)) relative to arctan (k_x/k_y) first derivative, Δ R " (arctan (k_x/k_y0)) represent Δ R (arctan (k_x/k_y)) relative to arctan (k_x/k_y) at k_y=k_y0Time second dervative, Δ R (arctan(k_x/k_y)) represent target translational error Δ R (t_a) with cornerFor representation during independent variable, k_y0 Represent that distance is to wave number center, k_yRepresent that the distance under rectangular coordinate system is to the intermediate value of space wave number；k_xRepresent under rectangular coordinate system Orientation to space wave number.

The translational compensation of a kind of big corner ISAR radar based on PFA and formation method, its feature Being, the sub-step of step 4 is:

4.1 intercept the wave-number domain base band echo-signal W (k represented under described rectangular coordinate system_y,k_x) a part of wave-number domain in centre Base band echo-signalObtain distance wave-number domain base band echo-signal after inverse fast fourier transform

4.2 use autofocus algorithms to described distance wave-number domain base band echo-signal after inverse fast fourier transform Estimate with apart from unrelated error phase, obtain distance after inverse fast fourier transform wave-number domain base band echo letter Number error phase

Wherein, the wave-number domain base band echo-signal W (k represented under the described rectangular coordinate system of described intercepting_y,k_x) in the middle of a part Wave-number domain base band echo-signalIts requirement is: the wave-number domain base making described distance after inverse fast fourier transform Band echo-signalIn each point exist only in a distance unit, and described distance becomes to inverse fast Fourier Wave-number domain base band echo-signal after changingIn image along orientation to bright line parallel with azimuth axis.

The translational compensation of a kind of big corner ISAR radar based on PFA and formation method, its feature It is, in step 4, described distance wave-number domain base band echo-signal after inverse fast fourier transformIt is expressed Formula is:IFFT represents your fast Fourier transform operation, k_yRepresent under rectangular coordinate system away from Space, descriscent wave number, k_xRepresent that the orientation under rectangular coordinate system is to space wave number.

The translational compensation of a kind of big corner ISAR radar based on PFA and formation method, its feature Being, the sub-step of step 5 is:

5.1 according to error phase φ_error(k_y,k_xIn) with apart from unrelated error phase φ_{r_indep}(k_y0,k_x), calculate target and put down In dynamic error with apart from unrelated translational error

In 5.2 pairs of described target translational error with apart from unrelated translational errorCarry out interpolation fitting, obtain With the target translational error of distance dependent after interpolation fitting

5.3 according to target translational error with distance dependent after interpolation fittingIt is calculated target translation by mistake The phase compensation function H of difference_TrCo2(k_y,k_x)；

The 5.4 phase compensation function H utilizing target translational error_TrCo2(k_y,k_x) to described rectangular coordinate system (k_y,k_xRepresent under) Wave-number domain base band echo-signal W (k_y,k_x) carry out phase compensation, obtain the wave-number domain base band echo-signal after phase compensation W_comp(k_y,k_x)；

Wave-number domain base band echo-signal W after 5.5 pairs of described compensation_comp(k_y,k_x) carry out bidimensional inverse fast fourier transform, ISAR imaging to wave-number domain base band echo-signal.

The translational compensation of a kind of big corner ISAR radar based on PFA and formation method, its feature It is, the translational error that in described target translational error, distance non-NULL becomesDescribed target translational error Phase compensation function H_TrCo2(k_y,k_x) and described phase compensation after wave-number domain base band echo-signal W_comp(k_y,k_x), it is expressed Formula is respectively as follows:

$\mathrm{\Δ}\tilde{R}\left(arctan\right(k_x/k_{y0}\left)\right)={\widetilde{\mathrm{\φ}}}_{r\_indep}(k_{y0},k_x)/\sqrt{k_x^2+k_{y0}^2}$

$H_{TrCo2}(k_y,k_x)=\exp \left(j\sqrt{k_x^2+k_y^2}\mathrm{\Δ}\tilde{R}\right(arctan\left(k_x/k_y\right)\left)\right)$

W_comp(k_y,k_x)=W (k_y,k_x)·H_TrCo2(k_y,k_x)

Wherein,Represent the error phase of distance wave-number domain base band echo-signal after inverse fast fourier transform Position, represents dot product.