CN101216553A - Synthetic aperture radar polar coordinates format image-forming algorithm based on variable metric principle - Google Patents

Abstract

A synthetic aperture radar polar format algorithm based on scaling principle comprises the following steps of : constructing a data collection geometric model of spotlight synthetic aperture radar; carrying out range-dimension processing pulse by pulse, inputting time-domain echo signals, subjecting the time-domain echo signals to range scaling to obtain output signals, i.e. range frequency domain signals achieving range re-sampling; processing the range frequency domain signals (scaling and focusing) to obtain an azimuth-focused image while achieving azimuth scaling (azimuth re-sampling); and subjecting the azimuth-focused data to fast Fourier transform in range dimension to obtain a two-dimensional focused image. The invention can achieve re-sampling by using two-dimensional transformation to substitute for two-dimensional interpolation in conventional PFA algorithm. The method only needs FFT and complex multiplication operation, and the computation efficiency can be improved significantly. Meanwhile, the possible phase error resulting from the finite interpolation kernel length can be obviated.

Description

A kind of synthetic aperture radar polar coordinates format image-forming algorithm based on variable metric principle

Technical field

The present invention relates to a kind of synthetic aperture radar polar coordinates format image-forming algorithm, specifically a kind of synthetic aperture radar polar coordinates format image-forming algorithm based on variable metric principle.

Background technology

Polar coordinates format image-forming algorithm (PFA) is succinct owing to its algorithm flow, and is easy to compensate the non-linear uniform motion of Texas tower, is a kind of perfect method in bunching type synthetic aperture radar (SAR) imaging.PFA algorithm such as document 1:J.L.Walker, Range-Doppler imaging of rotating objects, IEEETransactions on Aerospace and Electronic systems, vol.16, no.1, pp.23-52, January1980. with document 2:D.A.Ausherman, A.Kozma, J.L.Walker, H.M.Jones, and E.C.Poggio, Development in radar imaging, IEEE Transactions on Aerospace andElectronic Systems, vol.20, no.4, pp.363-400, July 1984. and document 3:W.G.Carrara, R.S.Goodman, and R.M.Majewski, Spotlight Synthetic Aperture Radar:SignalProcessing algorithms.Norwood, MA:Artech House, 1995, disclosed technology among the Chapter 3.

The major limitation that the PFA algorithm runs into aspect calculated amount is two-dimensional interpolation computing wherein, and its calculated amount is bigger, influences imaging efficiency.The purpose of interpolation is that the discrete sampling data to non-uniform Distribution under the rectangular coordinate system resample, and obtains equally distributed sampled data, so that follow-up fast two-dimensional fourier transformation (FastFourier Transform is called for short FFT) is handled.Use separately (distance of two dimension at present, the orientation) interpolation method, as document 1:J.L.Walker, Range-Doppler imaging of rotating objects, IEEETransactions on Aerospace and Electronic systems, vol.16, no.1, pp.23-52, January1980. with document 2:D.A.Ausherman, A.Kozma, J.L.Walker, H.M.Jones, and E.C.Poggio, Development in radar imaging, IEEE Transactions on Aerospace andElectronic Systems, vol.20, no.4, pp.363-400, disclosed technology among the July 1984..And when realizing interpolation arithmetic with programming, its process is also comparatively complicated.Substitute two-dimensional interpolation and realize equally resampling if can search out a kind of computing method more efficiently, just can improve the counting yield of PFA algorithm.Research to the PFA algorithm at present mainly also concentrates in this respect.

To go gained under the mitered receipts pattern go slope signal with the PFA algorithm process time, the interpolation of two-dimensional interpolation middle distance direction can realize on hardware.Realize that by adjusting methods such as signal sampling time and sampling rate the echo samples that obtains is exactly the signal of finishing apart from interpolation apart from interpolation.This technology such as document 1:Tsunoda SI, Lynx:A High Resolution Synthetic Aperture Radar, Aerospace ConferenceProceedings, 2000 IEEE, vol.5, disclosed technology among the pp.51-58.But it is restricted to the scene width to go mitered to receive pattern, and this method can't eliminate the influence of (ResidualVideo Phase is called for short RVP) of remaining video phase error in the slope signal, is suitable under therefore only low in resolution and the situation that scene is less.In the large scene high-resolution imaging, must consider linear frequency modulation (chirp) signal application PFA algorithm process to direct reception.

During to the chirp signal application PFA algorithm process of direct reception, method commonly used at present remain distance to the orientation to carrying out interpolation arithmetic respectively.There is considerable influence in this method to the counting yield of PFA algorithm.

Summary of the invention

Goal of the invention: the lower deficiency of counting yield that the present invention is directed to existing PFA algorithm, seek a kind of more high-efficiency method and substitute two-dimensional interpolation in the PFA algorithm, the same resampling that realizes the discrete sampling data of non-uniform Distribution under the rectangular coordinate system, obtain equally distributed sampled value, so that can more accurately handle the chirp signal that directly receives efficiently, a kind of synthetic aperture radar polar coordinates format image-forming algorithm based on variable metric principle is provided thus.

Technical scheme: the invention provides a kind of synthetic aperture radar polar coordinates format image-forming algorithm based on variable metric principle, this algorithm may further comprise the steps:

(1) sets up spot beam SAR data acquisition geometric model;

(2) input time domain echoed signal, and the time domain echoed signal of input carried out distance to becoming yardstick, obtain output signal be finish the distance resampling apart from frequency-region signal;

(3) carry out the orientation to becoming yardstick to finishing in the step (2) apart from frequency-region signal, finish the orientation to becoming the image that yardstick obtains orientation focusing simultaneously apart from what resample;

(4) data that the orientation that obtains in the step (3) is focused on to making fast fourier transform, obtain the image of two-dimension focusing in distance.

In the step (1), setting up spot beam SAR data acquisition geometric model comprises: establish carrier aircraft along Ox direction rectilinear motion, θ is that angle of squint, instantaneous ground is the angle of ground projection of radar beam center line and ground track, ψ is that instantaneous grazing angle is the angle on radar beam center line and ground, and the flight path direction coordinate that prolongs of aperture center is x _cWith reference ground angle of squint θ _RefBe defined as

Thus with reference to grazing angle ψ _RefBe grazing angle on the yOz plane.

Initial time domain echoed signal is:

Wherein c is the light velocity, and λ is a wavelength, and τ is fast (distance) time, and t is slow (orientation) time, with t _c=x _c/ v is the center, T _aBe aperture time, r=r (t) is the instantaneous oblique distance between antenna phase center (Antenna Phase Center is called for short APC) and target.

In the SAR processor that uses PFA, can be by adjusting initial distance sampling ripple door to reduce apart from storage unit.With reference pulse, be designated as r such as the distance of first distance samples unit correspondence of first pulse ₀, then each definite distance samples time apart from the storage unit correspondence:

$\mathrm{\τ}=\frac{2r_0}{c}+n{T}_s,n=\mathrm{0,1,2},......,N-1;$ T wherein _sBe sampling time interval, N is total sampling number.Note r ₀=r ₀(t) be the instantaneous distance of first distance samples unit correspondence of each pulse subsequently.Make Δ r=r ₀-r ₀, and according to Δ r adjust all pulses subsequently initial distance sampling ripple door (also just be equivalent to echoed signal do distance to the time domain translation):

Just can reduce apart from storage unit.When Δ r=0, expression initial distance sampling ripple door immobilizes s _R(τ t) is the time domain echoed signal of importing in the step (2).

Input signal is time domain echoed signal s in the step (2) _R(τ, t), by to input signal s _R(τ t) carries out distance to becoming yardstick, make output signal just for finish that distance resamples apart from frequency domain (wavenumber domain) signal Yy (f _τ, t).Particularly the time domain echoed signal of input being carried out distance may further comprise the steps to the Pulse by Pulse processing:

(a) with time domain echoed signal s _R(τ is t) with the change scaling function

${\mathrm{\φ}}_{\mathrm{scl}}\left(\mathrm{\τ}\right)=\exp \{-\mathrm{j\πk}\frac{{\mathrm{\δ}}_r-1}{{\mathrm{\δ}}_r}\·{[\mathrm{\τ}-\frac{2(r_c-\mathrm{\Δr})}{c}]}^2\}$ Multiply each other;

(b) step (a) gained result is carried out fast fourier transform;

(c) with step (b) gained result and matched filter $H_2\left(f_{\mathrm{\τ}}\right)=\exp \left(j\frac{{\mathrm{\π\δ}}_r}{k}{f}_{\mathrm{\τ}}^2\right).$ Multiply each other;

(d) step (c) gained result is carried out invert fast fourier transformation;

(e) with step (d) gained result and contrary scaling (be and become yardstick) function

${\mathrm{\&phi;}}_{\mathrm{ins}}\left(\mathrm{\&tau;}\right)=\exp \{\mathrm{j\&pi;k}\frac{{\mathrm{\&delta;}}_r-1}{{\mathrm{\&delta;}}_r^2}{[\mathrm{\&tau;}-\frac{2(r_c-\mathrm{\&Delta;r})}{c}]}^2\}\&CenterDot;\exp [-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="S2007101919598E00031.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}{f}_c\frac{{\mathrm{\&delta;}}_r-1}{{\mathrm{\&delta;}}_r}\mathrm{\&tau;}]$ Multiply each other;

(f) step (e) gained result is carried out fast fourier transform;

(g) with step (f) the gained result and the motion compensated filtering factor

$H_3\left(f_{\mathrm{\&tau;}}\right)=\exp \left[j\frac{4\mathrm{\&pi;}}{c}(f_{\mathrm{\&tau;}}+f_c\frac{{\mathrm{\&delta;}}_r-1}{{\mathrm{\&delta;}}_r})(r_c-\mathrm{\&Delta;r})\right]\&CenterDot;\exp \left(j\frac{4\mathrm{\&pi;}{r}_c}{\mathrm{\&lambda;}}\right)$ Multiply each other f _cBe carrier frequency;

Obtain (f at last apart from frequency-region signal Yy _τ, t);

R wherein _c=r _c(t) be instantaneous oblique distance between antenna phase center and scene center point, f _τBe frequency of distance, δ _rFor with slow time t be parameter apart from scaling (be the become yardstick) factor:

${\mathrm{\&delta;}}_r={\mathrm{\&delta;}}_r\left(t\right)=\frac{\cos {\mathrm{\&psi;}}_{\mathrm{ref}}}{\cos [\mathrm{\&theta;}\left(t\right)-{\mathrm{\&theta;}}_{\mathrm{ref}}]\cos \mathrm{\&psi;}\left(t\right)}.$

Conventional P FA algorithm middle distance resamples and originally carries out at distance frequency domain (wavenumber domain).To echoed signal s _R(τ, t) the distance frequency domain carry out matched filtering and to the motion compensation of scene center point after, can be apart from the resampling input signal:

$\mathrm{Xx}(f_{\mathrm{\&tau;}},t)=\mathrm{rect}\left(\frac{t-t_c}{T_a}\right)\&CenterDot;\mathrm{rect}\left(\frac{f_t}{k{T}_r}\right)\&CenterDot;\exp [-j\frac{4\mathrm{\&pi;}{f}_{\mathrm{\&tau;}}}{c}(r-r_c)]\&CenterDot;\exp [-j\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}(r-r_c)];$

R wherein _c=r _c(t) be instantaneous oblique distance between antenna phase center (APC) and scene center point, f _τBe frequency of distance.Xx (f _τ, discrete form t) is: $\mathrm{Xx}(-\frac{{\mathrm{<figure-callout\; id="2"\; label="F\; s"\; filenames="S2007101919598E00031.png"\; state="\{\{state\}\}">F</figure-callout>}}_s}{2}+\frac{n{F}_s}{N},t);$ F wherein _sFor the distance to sampling rate, $F_s=\frac{1}{T_s}.$ So, the output signal that distance resamples, promptly finish should being expressed as of distance resampling apart from frequency-region signal: $\mathrm{Yy}(n,t)=\mathrm{Xx}(f_c({\mathrm{\&delta;}}_r-1)+(n-\frac{N}{2})\&CenterDot;\frac{{\mathrm{\&delta;}}_r{F}_s}{N},t);$

Its conitnuous forms are: $\mathrm{Yy}(f_{\mathrm{\&tau;}},t)=\mathrm{Xx}(f_c({\mathrm{\&delta;}}_r-1)+{\mathrm{\&delta;}}_r{f}_{\mathrm{\&tau;}},t)$ Wherein, δ _rFor with slow time t be parameter apart from the scaling factor:

${\mathrm{\&delta;}}_r={\mathrm{\&delta;}}_r\left(t\right)=\frac{\cos {\mathrm{\&psi;}}_{\mathrm{ref}}}{\cos [\mathrm{\&theta;}\left(t\right)-{\mathrm{\&theta;}}_{\mathrm{ref}}]\cos \mathrm{\&psi;}\left(t\right)}$

So far finish (the f of Yy as a result that just can obtain expecting at output point apart from scaling _τ, t), realized resampling apart from frequency domain.Distance is in pulse compression and being embedded into apart from scaling to the motion compensation of scene center point, rather than as carrying out respectively in the conventional P FA algorithm.Though this algorithm has increased a pair of FFT in processing, but avoided direct interpolation, thereby also avoided the phase error brought owing to the interpolation kernel limited length.If adopt the parallel digital signal processing apparatus, more can show its high efficiency.

Carry out the orientation to becoming yardstick to finishing in the step (2) apart from frequency-region signal in the step (3), finish the orientation, specifically may further comprise the steps to becoming the image that yardstick obtains orientation focusing simultaneously apart from what resample:

(a) make that input signal is apart from frequency-region signal p (t)=Yy (f _τ, t), and with input signal p (t) and function $h_1\left(t\right)=\exp \left[\mathrm{j\&pi;}{k}_a^{\&prime;}{(t-t_c)}^2\right]$ Multiply each other;

Use the PCS principle in principle except requiring h ₁(t) be linear frequency modulation (Linear Frequency Modulated, be called for short LFM) signal and have beyond the big time-bandwidth product k _a' the scope of selected value be rational number arbitrarily.And, therefore at first should consider to select k because the orientation of input signal has been removed to Doppler's slope _a' it is modulated to recovering original Doppler in the orientation.If k _aDoppler's slope for aperture center $k_a=-\frac{2{\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="S2007101919598E00031.png"\; state="\{\{state\}\}">v</figure-callout>}}^2{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="S2007101919598E00031.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2{\mathrm{\&phi;}}_c}{\mathrm{\&lambda;}{r}_c\left(t_c\right)};$ φ wherein _cBe aperture center Doppler coning angle, r _c(t _c) for aperture center point and scene center dot spacing from.In order to prevent to recover the signal generation aliasing after Doppler's modulation, select k _a' be $k_a^{\&prime;}=\frac{k_a}{\mathrm{\&xi;}};$ Wherein $\mathrm{\&xi;}=\frac{k_a{T}_a}{\mathrm{PRF}-B_s},$ B _sBe the orientation bandwidth of input signal, PRF is a pulse repetition rate.

(b) step (a) gained result is carried out fast fourier transform;

(c) with step (b) gained result and scaling function ${\mathrm{\&Phi;}}_{\mathrm{scl}}\left(f_t\right)=\exp (-\mathrm{j\&pi;}\frac{1-{\mathrm{\&delta;}}_a}{{\mathrm{\&delta;}}_a{k}_a^{\&prime;}}{f}_t^2)$ Multiply each other

Wherein, f _tBe the orientation frequency;

(d) step (c) gained result is carried out invert fast fourier transformation;

(e) with step (d) gained and function as a result $h_2\left(t\right)=\exp [-\mathrm{j\&pi;}{\mathrm{\&delta;}}_a{k}_a^{\&prime;}{(t-t_c)}^2]$ Multiply each other;

(f) step (e) gained result is carried out fast fourier transform;

(g) with the contrary scaling function of step (f) gained result

${\mathrm{\&Phi;}}_{\mathrm{ins}}\left(f_t\right)=\exp \left[\mathrm{j\&pi;}\frac{1-{\mathrm{\&delta;}}_a}{{\mathrm{\&delta;}}_a^2{k}_a^{\&prime;}}{f}_t^2\right]\&CenterDot;\exp \left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="S2007101919598E00031.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}{f}_t\frac{{\mathrm{\&delta;}}_a-1}{{\mathrm{\&delta;}}_a}{t}_c\right)$ Multiply each other;

Obtain the image that the orientation focuses on when finishing orientation scaling at last, promptly export the result and be Yy (f _τ, δ _aT) fourier transform of azimuth: ZZ (f _τ, f _t)=F _a[Yy (f _τ, δ _aT)];

δ _aFor with the frequency of distance being the orientation scaling factor of parameter

${\mathrm{\&delta;}}_a={\mathrm{\&delta;}}_a\left(f_{\mathrm{\&tau;}}\right)=\frac{f_c}{f_c+f_{\mathrm{\&tau;}}}.$

The output signal that the orientation resamples in the conventional P FA algorithm should be expressed as p (δ _aT), δ wherein _aFor with the frequency of distance being the orientation scaling factor of parameter

${\mathrm{\&delta;}}_a={\mathrm{\&delta;}}_a\left(f_{\mathrm{\&tau;}}\right)=\frac{f_c}{f_c+f_{\mathrm{\&tau;}}}$

Subsequently to p (δ _aT) make the orientation and can realize that to IFFT the orientation focuses on.

Beneficial effect: the present invention by two-dimentional change of scale substituted two-dimensional interpolation in the conventional P FA algorithm process, realized resampling.The method has been avoided interpolation operation, only needs FFT and takes advantage of operation again, and operation efficiency significantly improves.Also avoided simultaneously because interpolation kernel limited length and the phase error that may bring.

Description of drawings

Fig. 1 is a Spotlight SAR Imaging data acquisition geometric model of the present invention.

Fig. 2 is that the distance of chirp signal of the present invention becomes the yardstick process flow diagram.

Fig. 3 is that the orientation of chirp signal of the present invention becomes yardstick and focuses on process flow diagram.

Fig. 4 is point target simulation imaging result of the present invention.

Fig. 5 is point target impulse response function distance profile figure of the present invention.

Fig. 6 is a point target impulse response function of the present invention orientation sectional view.

Fig. 7 is a system emulation parameter among the present invention.

Fig. 8 is a general flowchart of the present invention.

Embodiment

Below in conjunction with the drawings and specific embodiments the present invention is done further detailed explanation.

The SAR system works is under medium strabismus mode among the present invention, antenna is with fixedly forward speed v motion, then can use the PFA algorithm based on the PCS principle set forth in the present invention echoed signal is carried out imaging processing, the distance, the orientation change yardstick (scaling) that separate with two dimension substitute distance, orientation interpolation in the conventional P FA algorithm respectively, realize resampling.

The synthetic aperture radar polar coordinates format image-forming algorithm based on variable metric principle that the present invention proposes has carried out theoretical validation by emulation experiment, and theoretical analysis and The simulation experiment result have proved validity of the present invention.This radar parameter as shown in Figure 7.

The first step, consider that the PFA algorithm is subjected to the restriction of range curvature, to imaging area size restricted (the theoretical imaging scene radius of PFA under Fig. 7 parameter condition is about 90m), in the effective imaging scene domain in ground, be provided with 9 point targets, one is scene center O point, other 8 point targets are uniformly distributed in scene center O point to be the center of circle, to be on the circle of radius with 90m.

Under Fig. 7 parameter condition, the SAR system is equivalent to be operated under the positive side-looking pattern.In order to realize the azimuthal resolution of 0.5m, the azimuth accumulation angle is greater than 34 °, in order to satisfy this condition, makes carrier aircraft flight 3000m, flight time T in the emulation _a=40.96s.Under the parameter condition of pulse repetition rate PRF=100Hz, overall pulse number M=PRF * T _a=4096, promptly the orientation is to receiving 4096 echo pulse signals altogether.If aperture center is t constantly _c=0, the corresponding orientation of each pulse t (unit: s) constantly then

$t=t_c+(m-\frac{M}{2})/\mathrm{PRF}=0.01\&times;(m-2048),$ m＝0，1……4096-1

For easy, make initial distance sampling ripple door immobilize, even Δ r=0.Get 2048 range gate, promptly N=2048 obtains 2048 Discrete Complex samples to each pulse echo signal sampling.

In second step, Pulse by Pulse carries out apart from scaling.

At first according to the corresponding instantaneous grazing angle of each pulse (be each orientation constantly t) and angle of squint, instantaneous ground determine its correspondence apart from the scaling factor

${\mathrm{\&delta;}}_r={\mathrm{\&delta;}}_r\left(t\right)=\frac{\cos {\mathrm{\&psi;}}_{\mathrm{ref}}}{\cos [\mathrm{\&theta;}\left(t\right)-{\mathrm{\&theta;}}_{\mathrm{ref}}]\cos \mathrm{\&psi;}\left(t\right)}$

Wherein ${\mathrm{\&psi;}}_{\mathrm{ref}}={\sin }^{-1}\left(\frac{H}{r_c\left(t_c\right)}\right)=0.643501,$ ${\mathrm{\&theta;}}_{\mathrm{ref}}=\frac{\mathrm{\&pi;}}{2}.$

Carry out apart from scaling according to process flow diagram 2.Pass through following steps successively: (a) with time domain echoed signal s _R(τ is t) with the change scaling function ${\mathrm{\&phi;}}_{\mathrm{scl}}\left(\mathrm{\&tau;}\right)=\exp \{-\mathrm{j\&pi;k}\frac{{\mathrm{\&delta;}}_r-1}{{\mathrm{\&delta;}}_r}\&CenterDot;{[\mathrm{\&tau;}-\frac{2(r_c-\mathrm{\&Delta;r})}{c}]}^2\}$ Multiply each other;

(b) step (a) gained result is carried out fast fourier transform;

(c) with step (b) gained result and matched filter $H_2\left(f_{\mathrm{\&tau;}}\right)=\exp \left(j\frac{{\mathrm{\&pi;\&delta;}}_r}{k}{f}_{\mathrm{\&tau;}}^2\right).$ Multiply each other;

(d) step (c) gained result is carried out invert fast fourier transformation;

(e) with step (d) gained result and contrary scaling function

${\mathrm{\&phi;}}_{\mathrm{ins}}\left(\mathrm{\&tau;}\right)=\exp \{\mathrm{j\&pi;k}\frac{{\mathrm{\&delta;}}_r-1}{{\mathrm{\&delta;}}_r^2}{[\mathrm{\&tau;}-\frac{2(r_c-\mathrm{\&Delta;r})}{c}]}^2\}\&CenterDot;\exp [-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="S2007101919598E00031.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}{f}_c\frac{{\mathrm{\&delta;}}_r-1}{{\mathrm{\&delta;}}_r}\mathrm{\&tau;}].$ Multiply each other;

(f) step (e) gained result is carried out fast fourier transform;

(g) with step (f) the gained result and the motion compensated filtering factor

$H_3\left(f_{\mathrm{\&tau;}}\right)=\exp \left[j\frac{4\mathrm{\&pi;}}{c}(f_{\mathrm{\&tau;}}+f_c\frac{{\mathrm{\&delta;}}_r-1}{{\mathrm{\&delta;}}_r})(r_c-\mathrm{\&Delta;r})\right]\&CenterDot;\exp \left(j\frac{4\mathrm{\&pi;}{r}_c}{\mathrm{\&lambda;}}\right)$ Multiply each other.

Promptly since the distance to sampling rate F _s=400MHz, range gate N=2048, the frequency of distance discrete value of using in the flow process:

$f_{\mathrm{\&tau;}}=-\frac{F_s}{2}+\frac{n{F}_s}{N}=-400\&times;{10}^6/2+n\&times;400\&times;{10}^6/2048$

$n=\mathrm{0,1,2},......,2048-1$

All FFT, IFFT are 2048 fast fourier transform in the flow process.Output signal be finish that distance resamples apart from frequency-region signal, be the required input signal of the orientation scaling that next will do.

In the 3rd step, carry out orientation scaling and focusing by frequency of distance.

At first need determine parameter k _a' and the orientation scaling factor delta of each frequency of distance correspondence _aBy table 1 parameter, can estimate aperture center Doppler's slope $k_a=-\frac{2{\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="S2007101919598E00031.png"\; state="\{\{state\}\}">v</figure-callout>}}^2{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="S2007101919598E00031.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2{\mathrm{\&phi;}}_c}{\mathrm{\&lambda;}{r}_c\left(t_c\right)}=-3.58,$ Input signal orientation bandwidth $B_s=\frac{k_a\&times;2\mathrm{radius}}{v\sin \left({\mathrm{\&phi;}}_c\right)}=8.79\mathrm{Hz},$ Can get thus $\mathrm{\&xi;}=\frac{k_a{T}_a}{\mathrm{PRF}-B_s}=1.6.$ Thereby get $k_a^{\&prime;}=\frac{k_a}{\mathrm{\&xi;}}=-2.23.$ And δ _aDetermine by frequency of distance

${\mathrm{\&delta;}}_a={\mathrm{\&delta;}}_a\left(f_{\mathrm{\&tau;}}\right)=\frac{f_c}{f_c+f_{\mathrm{\&tau;}}}$

Just can follow according to process flow diagram 3 then, the signal behind the scaling that adjusts the distance carries out orientation scaling by frequency of distance and the orientation focuses on.Pass through following steps successively: make (a) that input signal is apart from frequency-region signal p (t)=Yy (f _τ, t), and with input signal p (t) and function $h_1\left(t\right)=\exp \left[\mathrm{j\&pi;}{k}_a^{\&prime;}{(t-t_c)}^2\right]$ Multiply each other;

(b) step (a) gained result is carried out fast fourier transform;

(c) with step (b) gained result and scaling function ${\mathrm{\&Phi;}}_{\mathrm{scl}}\left(f_t\right)=\exp (-\mathrm{j\&pi;}\frac{1-{\mathrm{\&delta;}}_a}{{\mathrm{\&delta;}}_a{k}_a^{\&prime;}}{f}_t^2)$ Multiply each other wherein f _tBe the orientation frequency;

(d) step (c) gained result is carried out invert fast fourier transformation;

(e) with step (d) gained and function as a result $h_2\left(t\right)=\exp [-\mathrm{j\&pi;}{\mathrm{\&delta;}}_a{k}_a^{\&prime;}{(t-t_c)}^2]$ Multiply each other;

(f) step (e) gained result is carried out fast fourier transform;

(g) with the contrary scaling function of step (f) gained result

${\mathrm{\&Phi;}}_{\mathrm{ins}}\left(f_t\right)=\exp \left[\mathrm{j\&pi;}\frac{1-{\mathrm{\&delta;}}_a}{{\mathrm{\&delta;}}_a^2{k}_a^{\&prime;}}{f}_t^2\right]\&CenterDot;\exp \left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="S2007101919598E00031.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}{f}_t\frac{{\mathrm{\&delta;}}_a-1}{{\mathrm{\&delta;}}_a}{t}_c\right)$ Multiply each other;

The orientation frequency-distributed value of using in the flow process

$f_t=-\frac{\mathrm{<figure-callout\; id="2"\; label="PRF"\; filenames="S2007101919598E00031.png"\; state="\{\{state\}\}">PRF</figure-callout>}}{2}+m\&times;\frac{\mathrm{PRF}}{M}=-100/2+m\&times;100/4096$

$m=\mathrm{0,1,2},......,4096-1---\left(5\right)$

All FFT, IFFT are 4096 fast fourier transform in the flow process.By this flow process, obtained the image that the orientation focuses on when finishing orientation scaling.

In the 4th step, remake 2048 distance can obtain complex pattern from two-dimension focusing to FFT.

Fig. 4 has provided point target simulation imaging result.In order to be analyzed with the conventional P FA algorithm that resamples with the interpolation realization, Fig. 5, Fig. 6 have provided with conventional P FA algorithm respectively and after using two kinds of methods of PFA algorithm based on variable metric principle to be processed into picture side by side, the distance profile figure of the impulse response function of resultant marginal point S and orientation sectional view.Can see that the sectional view with these two kinds of method gained overlaps substantially fully.

Fig. 8 is a general flowchart of the present invention, may further comprise the steps: 1, set up spot beam SAR data acquisition geometric model; 2, input time domain echoed signal, and the time domain echoed signal of input carried out distance to becoming yardstick, obtain output signal be finish the distance resampling apart from frequency-region signal; 3, carry out the orientation to becoming yardstick to finishing in the step 2 apart from frequency-region signal, finish the orientation obtains orientation focusing when becoming yardstick image apart from what resample; 4, the data that the orientation that obtains in the step 3 is focused on to making fast fourier transform, obtain the image of two-dimension focusing in distance.

Theoretical analysis and The simulation experiment result show, use based on the PFA algorithm of variable metric principle and to use conventional P FA algorithm based on interpolation to carry out the result of imaging processing gained suitable substantially, and taking resource still less based on the PFA algorithm of variable metric principle, counting yield is higher.

The above only is a preferred implementation of the present invention; should be pointed out that for those skilled in the art, under the prerequisite that does not break away from the principle of the invention; can also make some improvements and modifications, these improvements and modifications also should be considered as protection scope of the present invention.

Claims (6)

1. the synthetic aperture radar polar coordinates format image-forming algorithm based on variable metric principle is characterized in that, this algorithm may further comprise the steps:

(1) sets up spot beam SAR data acquisition geometric model;

(2) input time domain echoed signal, and the time domain echoed signal of input carried out distance to becoming yardstick, obtain output signal be finish the distance resampling apart from frequency-region signal;

(3) carry out the orientation to becoming yardstick to finishing in the step (2) apart from frequency-region signal, finish the orientation obtains orientation focusing when becoming yardstick image apart from what resample;

(4) data that the orientation that obtains in the step (3) is focused on to making fast fourier transform, obtain the image of two-dimension focusing in distance.

2. a kind of synthetic aperture radar polar coordinates format image-forming algorithm according to claim 1 based on variable metric principle, it is characterized in that, in the step (1), setting up spot beam SAR data acquisition geometric model comprises: establish carrier aircraft along Ox direction rectilinear motion, θ is that angle of squint, instantaneous ground is the angle of ground projection of radar beam center line and ground track, ψ is that instantaneous grazing angle is the angle on radar beam center line and ground, and the flight path direction coordinate that prolongs of aperture center is x _cWith reference ground angle of squint θ _RefBe defined as

Thus with reference to grazing angle ψ _RefBe grazing angle on the yOz plane.

3. a kind of synthetic aperture radar polar coordinates format image-forming algorithm based on variable metric principle according to claim 1 is characterized in that, in the step (2), input time domain echoed signal is s _R(τ, t); And s _R(τ, t) be equivalent to echoed signal do distance to the time domain translation:

Wherein, Δ r=r ₀-r ₀, r ₀Be the distance of first distance samples unit correspondence of first pulse, then each definite distance samples time apart from the storage unit correspondence $\mathrm{\&tau;}=\frac{{2r}_0}{c}+n{T}_s,$ And n=0,1,2 ... N-1, T _sBe sampling time interval, N is total sampling number, r ₀=r ₀(t) be the instantaneous distance of first distance samples unit correspondence of each pulse subsequently; The time domain echoed signal is:

Wherein c is the light velocity, and λ is a wavelength, τ be the fast time promptly apart from the time, t is that the slow time is the orientation time, with t _c=x _c/ v is the center, T ₀Be aperture time, r=r (t) is the instantaneous oblique distance between antenna phase center and target.

4. a kind of synthetic aperture radar polar coordinates format image-forming algorithm based on variable metric principle according to claim 1 is characterized in that, step (2) is carried out distance to the time domain echoed signal of input and specifically be may further comprise the steps to the Pulse by Pulse processing:

(a) with time domain echoed signal s _R(τ is t) with the change scaling function

${\mathrm{\&phi;}}_{\mathrm{scl}}\left(\mathrm{\&tau;}\right)=\exp \{-\mathrm{j\&pi;k}\frac{{\mathrm{\&delta;}}_r-1}{{\mathrm{\&delta;}}_r}\&CenterDot;{[\mathrm{\&tau;}-\frac{2(r_c-\mathrm{\&Delta;r})}{c}]}^2\}$ Multiply each other;

(b) step (a) gained result is carried out fast fourier transform;

(c) with step (b) gained result and matched filter $H_c\left(f_{\mathrm{\&tau;}}\right)=\exp \left(j\frac{{\mathrm{\&pi;\&delta;}}_r}{k}{f}_{\mathrm{\&tau;}}^2\right).$ Multiply each other;

(d) step (c) gained result is carried out invert fast fourier transformation;

(e) with step (d) gained result and inversion scaling function

${\mathrm{\&phi;}}_{\mathrm{ins}}\left(\mathrm{\&tau;}\right)=\exp \{\mathrm{j\&pi;k}\frac{{\mathrm{\&delta;}}_r-1}{{\mathrm{\&delta;}}_r^2}\&CenterDot;{[\mathrm{\&tau;}-\frac{2(r_c-\mathrm{\&Delta;r})}{c}]}^2\}\&CenterDot;\exp [-j2\mathrm{\&pi;}{f}_c\frac{{\mathrm{\&delta;}}_r-1}{{\mathrm{\&delta;}}_r}\mathrm{\&tau;}].$ Multiply each other;

(f) step (e) gained result is carried out fast fourier transform;

(g) with step (f) the gained result and the motion compensated filtering factor

$H_3\left(f_{\mathrm{\&tau;}}\right)=\exp \left[j\frac{4\mathrm{\&pi;}}{c}(f_{\mathrm{\&tau;}}+f_c\frac{{\mathrm{\&delta;}}_r-1}{{\mathrm{\&delta;}}_r})(r_c-\mathrm{\&Delta;r})\right]\&CenterDot;\exp \left(j\frac{4\mathrm{\&pi;}{r}_c}{\mathrm{\&lambda;}}\right)$ Multiply each other f _cBe carrier frequency;

Obtain (f at last apart from frequency-region signal Yy _τ, t);

R wherein _c=r _c(t) be instantaneous oblique distance between antenna phase center and scene center point, f _τBe frequency of distance, δ _rFor with slow time t being the distance change scale factor of parameter

${\mathrm{\&delta;}}_r={\mathrm{\&delta;}}_r\left(t\right)=\frac{\cos {\mathrm{\&psi;}}_{\mathrm{ref}}}{\cos [\mathrm{\&theta;}\left(t\right)-{\mathrm{\&theta;}}_{\mathrm{ref}}]\cos \mathrm{\&psi;}\left(t\right)}.$

5. a kind of synthetic aperture radar polar coordinates format image-forming algorithm based on variable metric principle according to claim 1 is characterized in that, the frequency-region signal of adjusting the distance in the step (3) is handled specifically and be may further comprise the steps:

(a) order input finish that distance resamples apart from frequency-region signal p (t)=Yy (f _τ, t), and with p (t) and function $h_1\left(t\right)=\exp \left[\mathrm{j\&pi;}{k}_a^{\&prime;}{(t-t_c)}^2\right]$ Multiply each other;

(b) step (a) gained result is carried out fast fourier transform;

(c) with step (b) gained result and change scaling function ${\mathrm{\&Phi;}}_{\mathrm{scl}}\left(f_t\right)=\exp (-\mathrm{j\&pi;}\frac{1-{\mathrm{\&delta;}}_a}{{\mathrm{\&delta;}}_a{k}_a^{\&prime;}}{f}_t^2)$ Multiply each other wherein f _tBe the orientation frequency;

(d) step (c) gained result is carried out invert fast fourier transformation;

(e) with step (d) gained and function as a result $h_2\left(t\right)=\exp [-\mathrm{j\&pi;}{\mathrm{\&delta;}}_a{k}_a^{\&prime;}{(t-t_c)}^2]$ Multiply each other;

(f) step (e) gained result is carried out fast fourier transform;

(g) with step (f) gained inversion scaling function as a result

${\mathrm{\&Phi;}}_{\mathrm{ins}}\left(f_t\right)=\exp \left[\mathrm{j\&pi;}\frac{1-{\mathrm{\&delta;}}_a}{{\mathrm{\&delta;}}_a^2{k}_a^{\&prime;}}{f}_t^2\right]\&CenterDot;\exp \left(j2\mathrm{\&pi;}{f}_t\frac{{\mathrm{\&delta;}}_a-1}{{\mathrm{\&delta;}}_a}{t}_c\right)$ Multiply each other;

Finish at last when the orientation becomes yardstick and obtain the image that the orientation focuses on, promptly export the result and be Yy (f _τ, δ _aT) fourier transform of azimuth: $\mathrm{ZZ}(f_{\mathrm{\&tau;}},f_t)=F_a\left[\mathrm{Yy}(f_{\mathrm{\&tau;}},{\mathrm{\&delta;}}_{a}t)\right];$

K wherein _aThe scope of ' value is a rational number; k _aDoppler's slope for aperture center $k_a=-\frac{2v^2{\sin }^2{\mathrm{\&phi;}}_c}{\mathrm{\&lambda;}{r}_c\left(t_c\right)}.;$ φ wherein _cBe aperture center Doppler coning angle, r _c(t _c) for aperture center point and scene center dot spacing from; δ _aFor with the frequency of distance being the orientation change scale factor of parameter.

6. a kind of synthetic aperture radar polar coordinates format image-forming algorithm based on variable metric principle according to claim 5 is characterized in that, in the step (a) $k_a^{\&prime;}=\frac{k_a}{\mathrm{\&xi;}},$ Wherein $\mathrm{\&xi;}=\frac{k_a{T}_a}{\mathrm{PRF}-B_s},$ B _sBe the orientation bandwidth of input signal, PRF is a pulse repetition rate.

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