CN105487074A - Bistatic synthetic aperture radar numerical range Doppler imaging method - Google Patents

Abstract

The invention discloses a bistatic synthetic aperture radar numerical range Doppler imaging method, which comprises the following steps: S1) carrying out data pre-processing; S2) carrying out range compression on echo data; S3) calculating a range migration correction function through a numerical method, and carrying out range migration correction on the echo data by utilizing the range migration correction function; S4) generating a secondary range compression function and carrying out secondary range compression on the echo data obtained after range migration correction; S5) calculating reference target point position corresponding to each range gate; and S6) constructing an azimuth compression function by utilizing the reference target point position and carrying out azimuth compression to obtain an imaging result. The advantages of the method are that the accurate range migration function is obtained through the numerical method, and then, range migration correction is carried out on the echo data by utilizing the accurate range migration function; and meanwhile, a certain degree of motion compensation is carried out on the echo data, and thus accurate range migration correction based on the bistatic SAR RD imaging method is realized.

Description

A kind of double-base synthetic aperture radar numerical distance Doppler imaging method

Technical field

The invention belongs to Radar Signal Processing Technology field, particularly a kind of double-base synthetic aperture radar numerical distance Doppler imaging method.

Background technology

SAR is a kind of round-the-clock, round-the-clock modem high-resolution microwave remote sensing imaging radar.In fields such as military surveillance, topographic mapping, vegetational analysis, ocean and hydrologic observation, environment and disaster supervision, resource exploration and the micro-change detections of the earth's crust, SAR has played more and more important effect.

Double-base SAR has a lot of outstanding advantages due to bistatic, it can obtain the non-post of target to scattered information, has the features such as far away, the disguised and strong interference immunity of operating distance.In addition, because double-base SAR receiving station is not containing high power device, it is low in energy consumption, volume is little, lightweight, and be convenient to polytype aircraft and carry, cost is lower.In a word, double-base SAR, as a kind of new tool of earth observation from space, has wide development space in civil and military field.

At present in the world to the research of range Doppler (RD) formation method of double-base SAR, open source literature has: Zare, A., Masnadi-Shirazi, M.A., Samadi, S., " Range-DoppleralgorithmforprocessingbistaticSARdatabasedo ntheLBFintheconstant-offsetconstellation, " RadarConference (RADAR), 2012IEEE, vol., no., pp.17-21, give a kind of RD algorithm based on Loffeld 2-d spectrum model, it divide into two relevant to cell site and relevant with receiving station parts to the phase factor echo data in the derivation of frequency spectrum, and carry out respectively solving site in phasing, thus obtain 2-d spectrum, so inevitably there is error.In addition, this method cannot use motion path information, namely cannot carry out motion compensation in range migration correction process.

Pertinent literature: Neo, Y.L.; Wong, F.H.; Cumming, I.G., " ProcessingofAzimuth-InvariantBistaticSARDataUsingtheRang eDopplerAlgorithm, " GeoscienceandRemoteSensing, IEEETransactionson, vol.46, no.1, pp.14,21, giving one utilizes progression inverting to 2-d spectrum model of deriving, thus obtains corresponding RD algorithm.But it is when carrying out Taylor expansion, is only accurate to 4 items, has have ignored the high-order term of more than 4 times.This obviously brings error to 2-d spectrum, and when the synthetic aperture time lengthens, the impact of error will be inevitable.Equally, this method cannot use motion measurement information.

Summary of the invention

The object of the invention is to overcome the deficiencies in the prior art, one is provided to make full use of motion path information, achieve the motion compensation in imaging process, the accurate distance migration achieving RD formation method under double-base SAR corrects, and can be applied to the double-base synthetic aperture radar numerical distance Doppler imaging method in the fields such as double-base SAR echo-wave imaging, geometry correction.

The object of the invention is to be achieved through the following technical solutions: a kind of double-base synthetic aperture radar numerical distance Doppler imaging method, comprises the following steps:

S1, data prediction, calculate double-base synthetic aperture radar echo data;

S2, Range compress is carried out to echo data;

S3, employing numerical method calculate range migration correction function, and utilize range migration correction function to carry out range migration correction to echo data;

S4, generate secondary range compression function migration of adjusting the distance correct after echo data carry out secondary range compression;

S5, calculate reference target point position corresponding to each range gate;

S6, utilize reference target point placement configurations Azimuth Compression function, and carry out Azimuth Compression, obtain imaging results.

Further, described step S1 concrete methods of realizing is: make scene center point be irradiated the moment by beam center, flat pad is fixed, and flat pad position is designated as (x _t, y _t, z _t), wherein, x _t, y _tand h _tbe respectively the x-axis, y-axis and z-axis coordinate of cell site; Receiving station position is designated as (0,0, h _r), wherein, 0,0 and h _rbe respectively the x-axis, y-axis and z-axis coordinate of receiving station; Receiving station and cell site's speed are designated as v, and move along y-axis; Thus, establish with immediately below receiving station for initial point, height are for z-axis, the velocity reversal three-dimensional system of coordinate that is y-axis;

Orientation time arrow is designated as: $T_a=\[-PRI\frac{N_a}{2},-PRI(\frac{N_a}{2}-1),\mathrm{...},PRI(\frac{N_a}{2}-1)\],$ Wherein, PRI is pulse recurrence interval, N _afor counting in target echo orientation;

Double-basis distance history and be R _b(t; X, y)=R _t(t; X, y)+R _r(t; X, y), wherein t is the orientation time, R _t(t; X, y) and R _r(t; X, y) be respectively the distance history of cell site and receiving station:

$R_T(t;x,y)=\sqrt{{(x-x_T)}^2+{(y+vt-y_T)}^2+h_T^2}---\left(1\right)$

$R_R(t;x,y)=\sqrt{{(x-x_R)}^2+{(y+vt-y_R)}^2+h_R^2}---\left(2\right)$

Thus the expression formula obtaining echo data is:

$\begin{array}{c}{s}_r(t,\mathrm{\τ};x,y)=A_0{\mathrm{\ω}}_r(\mathrm{\τ}-\frac{R_b(t;x,y)}{c}){\mathrm{\ω}}_a\left(\frac{t-t_0}{T_a}\right)\exp \[-j2{\mathrm{\πf}}_c\frac{R_b(t;x,y)}{c}\]\\ \×\exp \[{\mathrm{j\πK}}_r{(\mathrm{\τ}-\frac{R_b(t;x,y)}{c})}^2\]\end{array}---\left(3\right)$

Wherein, A ₀the amplitude of scattering coefficient, ω _r() for distance is to envelope, ω _a() orientation is to envelope, and τ is fast time variable, t be orientation to time variable, f _cbe carrier frequency, c is the light velocity, K _rbe distance to frequency modulation rate, T _athe synthetic aperture time, t ₀that the beam center of impact point (x, y) passes through the moment.

Further, described step S2 concrete methods of realizing is: utilize the Chirp signal launched to carry out Range compress as with reference to function to echo data, the expression formula of Chirp signal is:

S(τ)＝A ₀w _r(τ)exp(jπK _rτ ²)(4)

Wherein, ω _a(), for distance is to envelope, τ is the fast time, K _rthat distance is to frequency modulation rate;

Get its reverse conjugation, obtaining expression formula is:

S ^*(-τ)＝A ₀w _r(-τ)exp(-jπK _r(-τ) ²)(5)

After the distance of the echo data obtained by step S1 carries out FFT respectively to data and formula (5), frequency domain is multiplied, then carry out IFFT just can obtain Range compress after echo data.

Further, described step S3 concrete methods of realizing is:

According to the configuration of double-base SAR, obtaining double-basis Distance geometry formula is:

$\begin{array}{c}{R}_b\left(t_a\right)=\sqrt{{\[x_R\left(t_a\right)-x_{dc}\]}^2+{\[y_R\left(t_a\right)-y_{dc}\]}^2+{(h_R-h_{dc})}^2}\\ +\sqrt{{\[x_T\left(t_a\right)-x_{dc}\]}^2+{\[y_T\left(t_a\right)-y_{dc}\]}^2+{(h_T-h_{dc})}^2}\end{array}---\left(6\right)$

Wherein, (x _dc, y _dc, h _dc) be aiming spot;

Doppler frequency formula is:

$\begin{array}{c}{f}_d\left(t_a\right)=\frac{v_T\·\[y_{dc}-y_T\left(t_a\right)\]}{\mathrm{\λ}\sqrt{{\[x_{dc}-x_T\left(t_a\right)\]}^2+{\[y_{dc}-y_T\left(t_a\right)\]}^2+{\[h_{dc}-h_T\left(t_a\right)\]}^2}}\\ +\frac{v_R\·\[y_{dc}-y_R\left(t_a\right)\]}{\mathrm{\λ}\sqrt{{\[x_{dc}-x_R\left(t_a\right)\]}^2+{\[y_{dc}-y_R\left(t_a\right)\]}^2+{\[h_{dc}-h_R\left(t_a\right)\]}^2}}\end{array}---\left(7\right)$

Wherein, (x _dc, y _dc, h _dc) be aiming spot, v _r, v _tbe respectively the flying speed of Receiver And Transmitter, t _sfor the synthetic aperture time;

Due to the impact of double joint formula, R cannot be derived _band f _dprecise relation function; Therefore, calculated by numerical method, described numerical method comprises following sub-step:

S31, get orientation to time t _adiscrete point, $\left[\begin{array}{cccc}-\frac{T_S}{2}+0*PRI& -\frac{T_S}{2}+1*PRI& \mathrm{...}& -\frac{T_S}{2}+n*PRI\end{array}\right],$ Wherein $n=\frac{T_S}{PRI};$

S32, the double-basis Distance geometry R calculated in each synthetic aperture time _bi(t _a), and by spline interpolation, double-basis Distance geometry curve interpolation is become doubly, wherein v _rfor receiver movement velocity, F _drfor orientation is to chirp rate; In like manner, identical interpolation is also done to Doppler frequency function; Thus, utilize relation obtain numerical value homography;

S33, because range-Dopler domain under, orientation to frequency is $-\frac{PRF}{2}+\left[\begin{array}{cccc}0*\frac{PRF}{N_a}& 1*\frac{PRF}{N_a}& \mathrm{...}& N_a\frac{PRF}{N_a}\end{array}\right],$ Wherein, N _afor orientation is to sampling number, utilize the numerical value homography obtained in S32, get wherein from each orientation to the double-basis Distance geometry corresponding to the nearest Doppler frequency of frequency as the range migration amount of this orientation under frequency, thus obtain range migration correction function;

S34, the echo data after Range compress is transformed to range-Dopler domain, utilize the range migration correction function obtained in S33, range migration correction is carried out to echo data.

Further, described step S4 concrete methods of realizing is: because numerical value RD does not adopt the 2-d spectrum expression formula of error, therefore cannot obtain secondary range compression function, the Bistatic SAR 2-d spectrum based on MSR adopting the people such as Neo, Y.L. to propose carries out secondary range compression to echo data; Secondary range compression function expression is:

$\begin{array}{c}{\mathrm{\φ}}_{src}\left(f_t\right)\≈\frac{c^2}{4k_2}\frac{2}{f_c^3}{f}_t^2+\frac{c^3{k}_3}{8k_2^3}\frac{6}{f_c^3}{f}_t^3(\frac{k_1}{c}+\frac{1}{f_c}{f}_t)\\ +\frac{c^4(9k_3^2-4k_2{k}_4)}{64k_2^5}\frac{12}{f_c^3}(\frac{k_1^2}{c^2}{f}_t^2+\frac{2k_1}{f_{c}c}{f}_t^3+\frac{1}{f_c^2}{f}_t^4)\end{array}---\left(8\right)$

Wherein, $k_1=\frac{\∂R_R\left(t\right)}{\∂t}{|}_{t=0}+\frac{\∂R_T\left(t\right)}{\∂t}{|}_{t=0}=-v_R{\mathrm{sin\θ}}_R-v_T{\mathrm{sin\θ}}_T$

$k_2=\frac{1}{2!}(\frac{{\∂}^2{R}_R\left(t\right)}{\∂t^2}+\frac{{\∂}^2{R}_T\left(t\right)}{\∂t^2}){|}_{t=0}=\frac{1}{2}(\frac{v_R^2{\cos }^2{\mathrm{\θ}}_R}{R_{Rc}}+\frac{v_T^2{\cos }^2{\mathrm{\θ}}_T}{R_{Tc}})$

$k_3=\frac{1}{3!}(\frac{{\∂}^3{R}_R\left(t\right)}{\∂t^3}+\frac{{\∂}^3{R}_T\left(t\right)}{\∂t^3}){|}_{t=0}=\frac{1}{6}(\frac{3v_R^3{\cos }^2{\mathrm{\θ}}_R{\mathrm{sin\θ}}_R}{R_{Rc}^2}+\frac{3v_T^3{\cos }^2{\mathrm{\θ}}_T{\mathrm{sin\θ}}_T}{R_{Tc}^2})$

$k_4=\frac{1}{4!}(\frac{{\∂}^4{R}_R\left(t\right)}{\∂t^{\left(4\right)}}+\frac{{\∂}^4{R}_T\left(t\right)}{\∂t^4}){|}_{t=0}=\frac{1}{24}\[\frac{3v_R^4{\cos }^2{\mathrm{\θ}}_R(4{\sin }^2{\mathrm{\θ}}_R-{\cos }^2{\mathrm{\θ}}_R)}{R_{Rc}^3}+\frac{3v_T^4{\cos }^2{\mathrm{\θ}}_T(4{\sin }^2{\mathrm{\θ}}_T-{\cos }^2{\mathrm{\θ}}_T)}{R_{Tc}^3}\]$

Then following calculating is utilized to carry out secondary range compression to echo data:

$S_{src}(f_{\mathrm{\τ}},f_t)=S_{rcmc}(f_{\mathrm{\τ}},f_t)\·\exp (-j2{\mathrm{\π\φ}}_{src}(f_t\left)\frac{f_{\mathrm{\τ}}^2}{c}\right)---\left(9\right).$

Further, described step S5 concrete methods of realizing is:

Geographic coordinate and the location of pixels in its image of known scene center point, if when distance is the same with height overhead sex change to space-variant, only with the position solving the target the same with scene center point height, then construct orientation to reference function with them; Concrete derivation method is as follows:

The coordinate that certain pixel (i, j) known is corresponding is (x _i,j, y _i,j), wherein (i, j) be respectively image middle distance to orientation to position; Its distance to consecutive point be respectively (x _{i-1, j}, y _{i-1, j}) and (x _{i+1, j}, y _{i+1, j}), first, from beam model:

$\frac{y_{i-1,j}-y_{i,j}}{x_{i-1,j}-x_{i,j}}=\frac{y_{i+1,j}-y_{i,j}}{x_{i+1,j}-x_{i,j}}={\mathrm{tan\θ}}_c---\left(10\right)$

For near point, can obtain

$\left\{\begin{array}{c}R-{\mathrm{\ΔR}}_i=\sqrt{x_{i-1,j}^2+{(y_{i-1,j}-y_R)}^2+H_R^2}+\sqrt{{(x_{i-1,j}-x_T)}^2+{(y_{i-1,j}-y_T)}^2+H_T^2}\\ y_{i-1,j}-y_{i,j}=(x_{i-1,j}-x_{i,j}){\mathrm{tan\θ}}_c\end{array}\right.---\left(11\right)$

Wherein, θ _cfor receiving antenna Horizontal oblique visual angle, R-Δ R _iit is the double-basis Distance geometry of i-th range gate; Finally draw:

$\left\{\begin{array}{c}{x}_{i-1,j}=\frac{-b\±\sqrt{b^2-4ac}}{2a}\\ y_{i-1,j}=(x_{i-1,j}-x_{i,j}){\mathrm{tan\θ}}_c+y_{i,j}\end{array}\right.---\left(12\right)$

Wherein,

$\left\{\begin{array}{c}a=4{(R-{\mathrm{\ΔR}}_i)}^2(1+{\tan }^2{\mathrm{\θ}}_c)-4{(x_T+(y_T-y_R\left){\mathrm{tan\θ}}_c\right)}^2\\ b=8{\mathrm{tan\θ}}_c{(R-{\mathrm{\ΔR}}_i)}^2\[(y_{i,j}-x_{i,j}{\mathrm{tan\θ}}_c)-y_R\]\\ +4\[C_0-2(y_T-y_R)(y_{i,j}-x_{i,j}{\mathrm{tan\θ}}_c)\]\[x_T+(y_T-y_R){\mathrm{tan\θ}}_c\]\\ c=4{(R-{\mathrm{\ΔR}}_i)}^2\{{\[(y_{i,j}-x_{i,j}{\mathrm{tan\θ}}_c)-y_R\]}^2+H_R^2\}-{\[2(y_T-y_R)(y_{i,j}-{\mathrm{tan\θ}}_c{x}_{i,j})-C_0\]}^2\\ C_0=x_T^2+y_T^2+H_T^2-y_R^2-H_R^2-{(R-{\mathrm{\ΔR}}_i)}^2\end{array}\right.---\left(13\right)$

Thus just can derive orientation to zero time be engraved in the reference target point position (x of different distance door under antenna angle of squint _i, y _i, 0) (i=1,2 ..., N _r), wherein N _rfor distance is to sampling number.

Further, described step S6 concrete methods of realizing is:

The Azimuth Compression function different to different distance door structure, utilizes the reference target point position (x of the different distance door obtained in S5 _i, y _i, 0) (i=1,2 ..., N _r), obtain Azimuth Compression reference function:

$S\left(t_a\right)=A_0{w}_a\left(t_a\right)\exp \[j2\mathrm{\π}\frac{R_{bi}\left(t_a\right)}{\mathrm{\λ}}\]---\left(14\right)$

Wherein, w _afor orientation is to window function, t _afor orientation is to the time, λ is pulse signal wavelength, R _bi(t _a) for orientation is to t _athe double-basis Distance geometry in moment:

$R_{bi}\left(t_a\right)=\sqrt{{\[x_R\left(t_a\right)-x_i\]}^2+{\[y_R\left(t_a\right)-y_i\]}^2+{(h_R-h_i)}^2}+\sqrt{{\[x_T\left(t_a\right)-x_i\]}^2+{\[y_T\left(t_a\right)-y_i\]}^2+{(h_T-h_i)}^2}---\left(15\right)$

Wherein, (x _i, y _i, h _i) be the reference point locations of each range gate;

Get the reverse conjugation of reference function, be Azimuth Compression function:

$S^{*}(-t_a)=A_0{w}_a\left(t_a\right)\exp \[-j2\mathrm{\π}\frac{R_{bi}(-t_a)}{\mathrm{\λ}}\]---\left(16\right)$

After the Data in Azimuth Direction of the echo data obtained by step S4 and formula (16) carry out FFT respectively, frequency domain is multiplied, then carries out IFFT, obtain final imaging results.

The invention has the beneficial effects as follows: on the basis of double-base SAR range-Dopler domain, give up inaccurate 2-d spectrum model, and obtain accurate range migration function by numerical method, then with accurate range migration function, range migration correction is carried out to echo data; Meanwhile, again because the numerical evaluation of range migration function needs the motion path using SAR, so the motion compensation carrying out to a certain degree to echo data; The accurate distance migration achieving RD formation method under double-base SAR corrects, and fully profit has arrived motion path information simultaneously, achieves the motion compensation in imaging process, can be applied to the fields such as double-base SAR echo-wave imaging, geometry correction.

Accompanying drawing explanation

Fig. 1 is for moving constant pattern double-base SAR system structural drawing;

Fig. 2 is formation method process flow diagram of the present invention;

Fig. 3 is the target scene arrangenent diagram of the embodiment that the present invention adopts;

Fig. 4 is the two-dimensional time-domain figure after the echo of the embodiment of the present invention carries out first time Range compress;

Fig. 5 is the two-dimensional time-domain figure after specific embodiment of the invention middle distance migration corrects;

Fig. 6 is the two-dimensional time-domain figure in the specific embodiment of the invention after Azimuth Compression.

Embodiment

Technical scheme of the present invention is further illustrated below in conjunction with the drawings and specific embodiments.

Content of the present invention for convenience of description, first makes an explanation to following term:

Term 1: double-base SAR

Double-base SAR refers to the SAR system that systems radiate station and receiving station are placed in different platform, wherein has at least a platform to be motion platform, conceptually belongs to bistatic radar, as shown in Figure 1.

Term 2: secondary range compression (SRC)

Along with the increase of angle of squint, can introduce the coupling of stronger distance and bearing, what need to correct that coupling causes by filtering defocuses.This process is secondary range compression.

The present invention mainly adopts the method for emulation experiment to verify, institute in steps, conclusion all on Matlab2012 checking correct.Solution of the present invention first utilizes the relation function of double-basis Distance geometry R and orientation time t, the relation function of Doppler frequency f and orientation time t, calculate the corresponding relation of double-basis Distance geometry R and Doppler frequency f under each orientation moment t in the synthetic aperture time, recycle this corresponding relation and obtain range-Dopler domain by spline interpolation, double-basis Distance geometry R corresponding to each Doppler frequency f, then carries out range migration correction at range-Dopler domain to echo data; Then, Taylor expansion is carried out, using the quadratic term of Taylor expansion as secondary range compression function to the Bistatic SAR 2-d spectrum based on MSR; Finally, utilize motion path to each range gate generating direction compression function, and carry out Azimuth Compression.As shown in Figure 2, a kind of double-base synthetic aperture radar numerical distance Doppler imaging method of the present invention, comprises the following steps idiographic flow:

S1, data prediction, calculate double-base synthetic aperture radar echo data; Its concrete methods of realizing is: make scene center point be irradiated the moment by beam center, flat pad is fixed, and flat pad position is designated as (x _t, y _t, z _t), wherein, x _t, y _tand h _tbe respectively the x-axis, y-axis and z-axis coordinate of cell site; Receiving station position is designated as (0,0, h _r), wherein, 0,0 and h _rbe respectively the x-axis, y-axis and z-axis coordinate of receiving station; Receiving station and cell site's speed are designated as v, and move along y-axis; Thus, establish with immediately below receiving station for initial point, height are for z-axis, the velocity reversal three-dimensional system of coordinate that is y-axis; The present embodiment is under the geographic coordinate system set up, and receiving station's coordinate is set to (0,0,1) km, speed are (0,50,0) m/s, cell site's coordinate is (-1,1,1) km, speed are (0,50,0) m/s, target scene centre coordinate is (0,1,0) km.What the present embodiment adopted moves the design parameter of constant pattern double-base SAR as shown in Table 1.The target scene that adopts in the present embodiment is arranged as shown in Figure 3, the black round dot in figure for being arranged in ground 3 × 3 totally 9 point targets, these 9 points (cut flight path) in the x-direction 200 meters, interval, in the y-direction 20 meters, (along flight path) interval.Platform moves along y-axis.

Table one

Parameter	Symbol	Numerical value
			Carrier frequency	f c	9.65GHz
Moment position, cell site zero	(x T,y T,h T)	(-1km,0,1km)
			Receiving station zero moment position	(x R,y R,h R)	(0,-1km,1km)
Flat pad movement velocity	V T	50m/s
			Receiving platform movement velocity	V R	50m/s
Transmitted signal bandwidth	B r	100MHz
			Wide when transmitting	T r	5us
Impulse sampling frequency	PRF	1000Hz
			The synthetic aperture time	T s	1.8s

Orientation time arrow is designated as: $T_a=\[-PRI\frac{N_a}{2},-PRI(\frac{N_a}{2}-1),\mathrm{...},PRI(\frac{N_a}{2}-1)\],$ Wherein, PRI is pulse recurrence interval, N _afor counting in target echo orientation;

Double-basis distance history and be R _b(t; X, y)=R _t(t; X, y)+R _r(t; X, y), wherein t is the orientation time, R _t(t; X, y) and R _r(t; X, y) be respectively the distance history of cell site and receiving station:

$R_T(t;x,y)=\sqrt{{(x-x_T)}^2+{(y+vt-y_T)}^2+h_T^2}---\left(1\right)$

$R_R(t;x,y)=\sqrt{{(x-x_R)}^2+{(y+vt-y_R)}^2+h_R^2}---\left(2\right)$

Thus the expression formula obtaining echo data is:

$\begin{array}{c}{s}_r(t,\mathrm{\τ};x,y)=A_0{\mathrm{\ω}}_r(\mathrm{\τ}-\frac{R_b(t;x,y)}{c}){\mathrm{\ω}}_a\left(\frac{t-t_0}{T_a}\right)\exp \[-j2{\mathrm{\πf}}_c\frac{R_b(t;x,y)}{c}\]\\ \×\exp \[{\mathrm{j\πK}}_r{(\mathrm{\τ}-\frac{R_b(t;x,y)}{c})}^2\]\end{array}---\left(3\right)$

Wherein, A ₀the amplitude of scattering coefficient, ω _r() for distance is to envelope, ω _a() orientation is to envelope, and τ is fast time variable, t be orientation to time variable, f _cbe carrier frequency, c is the light velocity, K _rbe distance to frequency modulation rate, T _athe synthetic aperture time, t ₀that the beam center of impact point (x, y) passes through the moment.

S2, Range compress is carried out to echo data; Its concrete methods of realizing is: utilize the Chirp signal launched to carry out Range compress as with reference to function to echo data, the expression formula of Chirp signal is:

S(τ)＝A ₀w _r(τ)exp(jπK _rτ ²)(4)

Wherein, ω _a(), for distance is to envelope, τ is the fast time, K _rthat distance is to frequency modulation rate;

Get its reverse conjugation, obtaining expression formula is:

S ^*(-τ)＝A ₀w _r(-τ)exp(-jπK _r(-τ) ²)(5)

After the distance of the echo data obtained by step S1 carries out FFT respectively to data and formula (5), frequency domain is multiplied, then carry out IFFT just can obtain Range compress after echo data, the echo data of the present embodiment carries out the two-dimensional time-domain figure after Range compress as shown in Figure 4.

S3, employing numerical method calculate range migration correction function, and utilize range migration correction function to carry out range migration correction to echo data; Concrete methods of realizing is:

According to the configuration of double-base SAR, obtaining double-basis Distance geometry formula is:

$\begin{array}{c}{R}_b\left(t_a\right)=\sqrt{{\[x_R\left(t_a\right)-x_{dc}\]}^2+{\[y_R\left(t_a\right)-y_{dc}\]}^2+{(h_R-h_{dc})}^2}\\ +\sqrt{{\[x_T\left(t_a\right)-x_{dc}\]}^2+{\[y_T\left(t_a\right)-y_{dc}\]}^2+{(h_T-h_{dc})}^2}\end{array}---\left(6\right)$

Wherein, (x _dc, y _dc, h _dc) be aiming spot;

Doppler frequency formula is

$\begin{array}{c}{f}_d\left(t_a\right)=\frac{v_T\·\[y_{dc}-y_T\left(t_a\right)\]}{\mathrm{\λ}\sqrt{{\[x_{dc}-x_T\left(t_a\right)\]}^2+{\[y_{dc}-y_T\left(t_a\right)\]}^2+{\[h_{dc}-h_T\left(t_a\right)\]}^2}}\\ +\frac{v_R\·\[y_{dc}-y_R\left(t_a\right)\]}{\mathrm{\λ}\sqrt{{\[x_{dc}-x_R\left(t_a\right)\]}^2+{\[y_{dc}-y_R\left(t_a\right)\]}^2+{\[h_{dc}-h_R\left(t_a\right)\]}^2}}\end{array}---\left(7\right)$

Wherein, (x _dc, y _dc, h _dc) be aiming spot, v _r, v _tbe respectively the flying speed of Receiver And Transmitter, t _sfor the synthetic aperture time;

Due to the impact of double joint formula, R cannot be derived _band f _dprecise relation function; Therefore, calculated by numerical method, described numerical method comprises following sub-step:

S31, get orientation to time t _adiscrete point, $\left[\begin{array}{cccc}-\frac{T_S}{2}+0*PRI& -\frac{T_S}{2}+1*PRI& \mathrm{...}& -\frac{T_S}{2}+n*PRI\end{array}\right],$ Wherein $n=\frac{T_S}{PRI};$

S32, the double-basis Distance geometry R calculated in each synthetic aperture time _bi(t _a), and by spline interpolation, double-basis Distance geometry curve interpolation is become doubly, wherein v _rfor receiver movement velocity, F _drfor orientation is to chirp rate; In like manner, identical interpolation is also done to Doppler frequency function; Thus, utilize relation obtain numerical value homography;

S33, because range-Dopler domain under, orientation to frequency is $-\frac{PRF}{2}+\left[\begin{array}{cccc}0*\frac{PRF}{N_a}& 1*\frac{PRF}{N_a}& \mathrm{...}& N_a\frac{PRF}{N_a}\end{array}\right],$ Wherein, N _afor orientation is to sampling number, utilize the numerical value homography obtained in S32, get wherein from each orientation to the double-basis Distance geometry corresponding to the nearest Doppler frequency of frequency as the range migration amount of this orientation under frequency, thus obtain range migration correction function;

S34, the echo data after Range compress is transformed to range-Dopler domain, utilize the range migration correction function obtained in S33, carry out range migration correction to echo data, the echo data of the present embodiment carries out two-dimensional time-domain figure after range migration correction as shown in Figure 5.

S4, generate secondary range compression function migration of adjusting the distance correct after echo data carry out secondary range compression; Concrete methods of realizing is: because numerical value RD does not adopt the 2-d spectrum expression formula of error, therefore secondary range compression function cannot be obtained, the Bistatic SAR 2-d spectrum based on MSR adopting the people such as Neo, Y.L. to propose carries out secondary range compression to echo data: according to distance to frequency f _τtaylor expansion is carried out to 2-d spectrum expression formula, extracts quadratic term (f wherein _τ ²coefficient) as secondary range compression function; Secondary range compression function expression is:

$\begin{array}{c}{\mathrm{\φ}}_{src}\left(f_t\right)\≈\frac{c^2}{4k_2}\frac{2}{f_c^3}{f}_t^2+\frac{c^3{k}_3}{8k_2^3}\frac{6}{f_c^3}{f}_t^3(\frac{k_1}{c}+\frac{1}{f_c}{f}_t)\\ +\frac{c^4(9k_3^2-4k_2{k}_4)}{64k_2^5}\frac{12}{f_c^3}(\frac{k_1^2}{c^2}{f}_t^2+\frac{2k_1}{f_{c}c}{f}_t^3+\frac{1}{f_c^2}{f}_t^4)\end{array}---\left(8\right)$

Wherein, $k_1=\frac{\∂R_R\left(t\right)}{\∂t}{|}_{t=0}+\frac{\∂R_T\left(t\right)}{\∂t}{|}_{t=0}=-v_R{\mathrm{sin\θ}}_R-v_T{\mathrm{sin\θ}}_T$

$k_2=\frac{1}{2!}(\frac{{\∂}^2{R}_R\left(t\right)}{\∂t^2}+\frac{{\∂}^2{R}_T\left(t\right)}{\∂t^2}){|}_{t=0}=\frac{1}{2}(\frac{v_R^2{\cos }^2{\mathrm{\θ}}_R}{R_{Rc}}+\frac{v_T^2{\cos }^2{\mathrm{\θ}}_T}{R_{Tc}})$

$k_3=\frac{1}{3!}(\frac{{\∂}^3{R}_R\left(t\right)}{\∂t^3}+\frac{{\∂}^3{R}_T\left(t\right)}{\∂t^3}){|}_{t=0}=\frac{1}{6}(\frac{3v_R^3{\cos }^2{\mathrm{\θ}}_R{\mathrm{sin\θ}}_R}{R_{Rc}^2}+\frac{3v_T^3{\cos }^2{\mathrm{\θ}}_T{\mathrm{sin\θ}}_T}{R_{Tc}^2})$

$k_4=\frac{1}{4!}(\frac{{\∂}^4{R}_R\left(t\right)}{\∂t^{\left(4\right)}}+\frac{{\∂}^4{R}_T\left(t\right)}{\∂t^4}){|}_{t=0}=\frac{1}{24}\[\frac{3v_R^4{\cos }^2{\mathrm{\θ}}_R(4{\sin }^2{\mathrm{\θ}}_R-{\cos }^2{\mathrm{\θ}}_R)}{R_{Rc}^3}+\frac{3v_T^4{\cos }^2{\mathrm{\θ}}_T(4{\sin }^2{\mathrm{\θ}}_T-{\cos }^2{\mathrm{\θ}}_T)}{R_{Tc}^3}\]$

Then following calculating is utilized to carry out secondary range compression to echo data:

$S_{src}(f_{\mathrm{\τ}},f_t)=S_{rcmc}(f_{\mathrm{\τ}},f_t)\·\exp (-j2{\mathrm{\π\φ}}_{src}(f_t\left)\frac{f_{\mathrm{\τ}}^2}{c}\right)---\left(9\right).$

S5, calculate reference target point position corresponding to each range gate; Concrete methods of realizing is:

Geographic coordinate and the location of pixels in its image of known scene center point, if when distance is the same with height overhead sex change to space-variant, only with the position solving the target the same with scene center point height, then construct orientation to reference function with them; Concrete derivation method is as follows:

The coordinate that certain pixel (i, j) known is corresponding is (x _i,j, y _i,j), wherein (i, j) be respectively image middle distance to orientation to position; Its distance to consecutive point be respectively (x _{i-1, j}, y _{i-1, j}) and (x _{i+1, j}, y _{i+1, j}), first, from beam model:

$\frac{y_{i-1,j}-y_{i,j}}{x_{i-1,j}-x_{i,j}}=\frac{y_{i+1,j}-y_{i,j}}{x_{i+1,j}-x_{i,j}}={\mathrm{tan\θ}}_c---\left(10\right)$

For near point, can obtain

$\left\{\begin{array}{c}R-{\mathrm{\ΔR}}_i=\sqrt{x_{i-1,j}^2+{(y_{i-1,j}-y_R)}^2+H_R^2}+\sqrt{{(x_{i-1,j}-x_T)}^2+{(y_{i-1,j}-y_T)}^2+H_T^2}\\ y_{i-1,j}-y_{i,j}=(x_{i-1,j}-x_{i,j}){\mathrm{tan\θ}}_c\end{array}\right.---\left(11\right)$

Wherein, θ _cfor receiving antenna Horizontal oblique visual angle, when the geometric configuration of double-base SAR is forward sight, θ _c=0; R-Δ R _iit is the double-basis Distance geometry of i-th range gate; Finally draw:

$\left\{\begin{array}{c}{x}_{i-1,j}=\frac{-b\±\sqrt{b^2-4ac}}{2a}\\ y_{i-1,j}=(x_{i-1,j}-x_{i,j}){\mathrm{tan\θ}}_c+y_{i,j}\end{array}\right.---\left(12\right)$

Wherein,

$\left\{\begin{array}{c}a=4{(R-{\mathrm{\ΔR}}_i)}^2(1+{\tan }^2{\mathrm{\θ}}_c)-4{(x_T+(y_T-y_R\left){\mathrm{tan\θ}}_c\right)}^2\\ b=8{\mathrm{tan\θ}}_c{(R-{\mathrm{\ΔR}}_i)}^2\[(y_{i,j}-x_{i,j}{\mathrm{tan\θ}}_c)-y_R\]\\ +4\[C_0-2(y_T-y_R)(y_{i,j}-x_{i,j}{\mathrm{tan\θ}}_c)\]\[x_T+(y_T-y_R){\mathrm{tan\θ}}_c\]\\ c=4{(R-{\mathrm{\ΔR}}_i)}^2\{{\[(y_{i,j}-x_{i,j}{\mathrm{tan\θ}}_c)-y_R\]}^2+H_R^2\}-{\[2(y_T-y_R)(y_{i,j}-{\mathrm{tan\θ}}_c{x}_{i,j})-C_0\]}^2\\ C_0=x_T^2+y_T^2+H_T^2-y_R^2-H_R^2-{(R-{\mathrm{\ΔR}}_i)}^2\end{array}\right.---\left(13\right)$

Thus just can derive orientation to zero time be engraved in the reference target point position (x of different distance door under antenna angle of squint _i, y _i, 0) (i=1,2 ..., N _r), wherein N _rfor distance is to sampling number.

S6, utilize reference target point placement configurations Azimuth Compression function, and carry out Azimuth Compression, obtain imaging results; Its concrete methods of realizing is:

The Azimuth Compression function different to different distance door structure, utilizes the reference target point position (x of the different distance door obtained in S5 _i, y _i, 0) (i=1,2 ..., N _r), obtain Azimuth Compression reference function:

$S\left(t_a\right)=A_0{w}_a\left(t_a\right)\exp \[j2\mathrm{\π}\frac{R_{bi}\left(t_a\right)}{\mathrm{\λ}}\]---\left(14\right)$

Wherein, w _afor orientation is to window function, t _afor orientation is to the time, λ is pulse signal wavelength, R _bi(t _a) for orientation is to t _athe double-basis Distance geometry in moment:

$R_{bi}\left(t_a\right)=\sqrt{{\[x_R\left(t_a\right)-x_i\]}^2+{\[y_R\left(t_a\right)-y_i\]}^2+{(h_R-h_i)}^2}+\sqrt{{\[x_T\left(t_a\right)-x_i\]}^2+{\[y_T\left(t_a\right)-y_i\]}^2+{(h_T-h_i)}^2}---\left(15\right)$

Wherein, (x _i, y _i, h _i) be the reference point locations of each range gate;

Get the reverse conjugation of reference function, be Azimuth Compression function:

$S^{*}(-t_a)=A_0{w}_a\left(t_a\right)\exp \[-j2\mathrm{\π}\frac{R_{bi}(-t_a)}{\mathrm{\λ}}\]---\left(16\right)$

After the Data in Azimuth Direction of the echo data obtained by step S4 and formula (16) carry out FFT respectively, frequency domain is multiplied, then carry out IFFT, obtain final imaging results, the two-dimensional time-domain figure after the echo data type Azimuth Compression of the present embodiment as shown in Figure 6.

Those of ordinary skill in the art will appreciate that, embodiment described here is to help reader understanding's principle of the present invention, should be understood to that protection scope of the present invention is not limited to so special statement and embodiment.Those of ordinary skill in the art can make various other various concrete distortion and combination of not departing from essence of the present invention according to these technology enlightenment disclosed by the invention, and these distortion and combination are still in protection scope of the present invention.

Claims (7)

1. a double-base synthetic aperture radar numerical distance Doppler imaging method, is characterized in that, comprises the following steps:

S1, data prediction, calculate double-base synthetic aperture radar echo data;

S2, Range compress is carried out to echo data;

S3, employing numerical method calculate range migration correction function, and utilize range migration correction function to carry out range migration correction to echo data;

S4, generate secondary range compression function migration of adjusting the distance correct after echo data carry out secondary range compression;

S5, calculate reference target point position corresponding to each range gate;

S6, utilize reference target point placement configurations Azimuth Compression function, and carry out Azimuth Compression, obtain imaging results.

2. double-base synthetic aperture radar numerical distance Doppler imaging method according to claim 1, it is characterized in that, described step S1 concrete methods of realizing is: make scene center point be irradiated the moment by beam center, flat pad is fixed, and flat pad position is designated as (x _t, y _t, z _t), wherein, x _t, y _tand h _tbe respectively the x-axis, y-axis and z-axis coordinate of cell site; Receiving station position is designated as (0,0, h _r), wherein, 0,0 and h _rbe respectively the x-axis, y-axis and z-axis coordinate of receiving station; Receiving station and cell site's speed are designated as v, and move along y-axis; Thus, establish with immediately below receiving station for initial point, height are for z-axis, the velocity reversal three-dimensional system of coordinate that is y-axis;

Orientation time arrow is designated as: $T_a=\[-PRI\frac{N_a}{2},-PRI(\frac{N_a}{2}-1),...,PRI(\frac{N_a}{2}-1)\],$ Wherein, PRI is pulse recurrence interval, N _afor counting in target echo orientation;

Double-basis distance history and be R _b(t; X, y)=R _t(t; X, y)+R _r(t; X, y), wherein t is the orientation time, R _t(t; X, y) and R _r(t; X, y) be respectively the distance history of cell site and receiving station:

$R_T(t;x,y)=\sqrt{{(x-x_T)}^2+{(y+vt-y_T)}^2+h_T^2}---\left(1\right)$

$R_R(t;x,y)=\sqrt{{(x-x_R)}^2+{(y+vt-y_R)}^2+h_R^2}---\left(2\right)$

Thus the expression formula obtaining echo data is:

$\begin{array}{c}{s}_r(t,\mathrm{\τ};x,y)=A_0{\mathrm{\ω}}_r(\mathrm{\τ}-\frac{R_b(t;x,y)}{c}){\mathrm{\ω}}_a\left(\frac{t-t_0}{T_a}\right)\exp \[-j2{\mathrm{\πf}}_c\frac{R_b(t;x,y)}{c}\]\\ \×\exp \[{\mathrm{j\πK}}_r{(\mathrm{\τ}-\frac{R_b(t;x,y)}{c})}^2\]\end{array}---\left(3\right)$

Wherein, A ₀the amplitude of scattering coefficient, ω _r() for distance is to envelope, ω _a() orientation is to envelope, and τ is fast time variable, t be orientation to time variable, f _cbe carrier frequency, c is the light velocity, K _rbe distance to frequency modulation rate, T _athe synthetic aperture time, t ₀that the beam center of impact point (x, y) passes through the moment.

3. double-base synthetic aperture radar numerical distance Doppler imaging method according to claim 2, it is characterized in that, described step S2 concrete methods of realizing is: utilize the Chirp signal launched to carry out Range compress as with reference to function to echo data, the expression formula of Chirp signal is:

S(τ)＝A ₀w _r(τ)exp(jπK _rτ ²)(4)

Wherein, ω _a(), for distance is to envelope, τ is the fast time, K _rthat distance is to frequency modulation rate;

Get its reverse conjugation, obtaining expression formula is:

S ^*(-τ)＝A ₀w _r(-τ)exp(-jπK _r(-τ) ²)(5)

After the distance of the echo data obtained by step S1 carries out FFT respectively to data and formula (5), frequency domain is multiplied, then carry out IFFT just can obtain Range compress after echo data.

4. double-base synthetic aperture radar numerical distance Doppler imaging method according to claim 3, is characterized in that, described step S3 concrete methods of realizing is:

According to the configuration of double-base SAR, obtaining double-basis Distance geometry formula is:

$\begin{array}{c}{R}_b\left(t_a\right)=\sqrt{{\[x_R\left(t_a\right)-x_{dc}\]}^2+{\[y_R\left(t_a\right)-y_{dc}\]}^2+{(h_R-h_{dc})}^2}\\ +\sqrt{{\[x_T\left(t_a\right)-x_{dc}\]}^2+{\[y_T\left(t_a\right)-y_{dc}\]}^2+{(h_T-h_{dc})}^2}\end{array}---\left(6\right)$

Wherein, (x _dc, y _dc, h _dc) be aiming spot;

Doppler frequency formula is

$\begin{array}{c}{f}_d\left(t_a\right)=\frac{v_T\·\[y_{dc}-y_T\left(t_a\right)\]}{\mathrm{\λ}\sqrt{{\[x_{dc}-x_T\left(t_a\right)\]}^2+{\[y_{dc}-y_T\left(t_a\right)\]}^2+{\[h_{dc}-h_T\left(t_a\right)\]}^2}}\\ +\frac{v_R\·\[y_{dc}-y_R\left(t_a\right)\]}{\mathrm{\λ}\sqrt{{\[x_{dc}-x_R\left(t_a\right)\]}^2+{\[y_{dc}-y_R\left(t_a\right)\]}^2+{\[h_{dc}-h_R\left(t_a\right)\]}^2}}\end{array}---\left(7\right)$

Wherein, (x _dc, y _dc, h _dc) be aiming spot, v _r, v _tbe respectively the flying speed of Receiver And Transmitter, t _sfor the synthetic aperture time;

Due to the impact of double joint formula, R cannot be derived _band f _dprecise relation function; Therefore, calculated by numerical method, described numerical method comprises following sub-step:

S31, get orientation to time t _adiscrete point, $\left[\begin{array}{cccc}-\frac{T_S}{2}+0*PRI& -\frac{T_S}{2}+1*PRI& ...& -\frac{T_S}{2}+n*PRI\end{array}\right],$ Wherein $n=\frac{T_S}{PRI};$

S32, the double-basis Distance geometry R calculated in each synthetic aperture time _bi(t _a), and by spline interpolation, double-basis Distance geometry curve interpolation is become doubly, wherein v _rfor receiver movement velocity, F _drfor orientation is to chirp rate; In like manner, identical interpolation is also done to Doppler frequency function; Thus, utilize relation obtain numerical value homography;

S33, because range-Dopler domain under, orientation to frequency is $-\frac{PRF}{2}+\left[\begin{array}{cccc}0*\frac{PRF}{N_a}& 1*\frac{PRF}{N_a}& ...& N_a\frac{PRF}{N_a}\end{array}\right],$ Wherein, N _afor orientation is to sampling number, utilize the numerical value homography obtained in S32, get wherein from each orientation to the double-basis Distance geometry corresponding to the nearest Doppler frequency of frequency as the range migration amount of this orientation under frequency, thus obtain range migration correction function;

S34, the echo data after Range compress is transformed to range-Dopler domain, utilize the range migration correction function obtained in S33, range migration correction is carried out to echo data.

5. double-base synthetic aperture radar numerical distance Doppler imaging method according to claim 4, it is characterized in that, described step S4 concrete methods of realizing is: because numerical value RD does not adopt the 2-d spectrum expression formula of error, therefore cannot obtain secondary range compression function, adopt the Bistatic SAR 2-d spectrum based on MSR to carry out secondary range compression to echo data; Secondary range compression function expression is:

$\begin{array}{c}{\mathrm{\φ}}_{src}\left(f_t\right)\≈\frac{c^2}{4k_2}\frac{2}{f_c^3}{f}_t^2+\frac{c^3{k}_3}{8k_2^3}\frac{6}{f_c^3}{f}_t^2(\frac{k_1}{c}+\frac{1}{f_c}{f}_t)\\ +\frac{c^4(9k_3^2-4k_2{k}_4)}{64k_2^5}\frac{12}{f_c^3}(\frac{k_1^2}{c^2}{f}_t^2+\frac{2k_1}{f_{c}c}{f}_t^3+\frac{1}{f_c^2}{f}_t^4)\end{array}---\left(8\right)$

Wherein, $k_1=\frac{\∂R_R\left(t\right)}{\∂t}{|}_{t=0}+\frac{\∂R_T\left(t\right)}{\∂t}{|}_{t=0}=-v_R{\mathrm{sin\θ}}_R-v_T{\mathrm{sin\θ}}_T$

$k_2=\frac{1}{2!}(\frac{{\∂}^2{R}_R\left(t\right)}{\∂t^2}+\frac{{\∂}^2{R}_T\left(t\right)}{\∂t^2}){|}_{t=0}=\frac{1}{2}(\frac{v_R^2{\cos }^2{\mathrm{\θ}}_R}{R_{Rc}}+\frac{v_T^2{\cos }^2{\mathrm{\θ}}_T}{R_{Tc}})$

$k_3=\frac{1}{3!}(\frac{{\∂}^3{R}_R\left(t\right)}{\∂t^3}+\frac{{\∂}^3{R}_T\left(t\right)}{\∂t^3}){|}_{t=0}=\frac{1}{6}(\frac{3v_R^3{\cos }^2{\mathrm{\θ}}_R{\mathrm{sin\θ}}_R}{R_{Rc}^2}+\frac{3v_T^3{\cos }^2{\mathrm{\θ}}_T{\mathrm{sin\θ}}_T}{R_{Tc}^2})$

$k_4=\frac{1}{4!}(\frac{{\∂}^4{R}_R\left(t\right)}{\∂t^4}+\frac{{\∂}^4{R}_T\left(t\right)}{\∂t^4}){|}_{t=0}=\frac{1}{24}\[\frac{3v_R^4{\cos }^2{\mathrm{\θ}}_R(4{\sin }^2{\mathrm{\θ}}_R-{\cos }^2{\mathrm{\θ}}_R)}{R_{Rc}^3}+\frac{3v_T^4{\cos }^2{\mathrm{\θ}}_T(4{\sin }^2{\mathrm{\θ}}_T-{\cos }^2{\mathrm{\θ}}_T)}{R_{Tc}^3}\]$

Then following calculating is utilized to carry out secondary range compression to echo data:

$S_{src}(f_{\mathrm{\τ}},f_t)=S_{rcmc}(f_{\mathrm{\τ}},f_t)\·\exp (-j2{\mathrm{\π\φ}}_{src}(f_t\left)\frac{f_{\mathrm{\τ}}^2}{c}\right)---\left(9\right).$

6. double-base synthetic aperture radar numerical distance Doppler imaging method according to claim 5, is characterized in that, described step S5 concrete methods of realizing is:

Geographic coordinate and the location of pixels in its image of known scene center point, if when distance is the same with height overhead sex change to space-variant, only with the position solving the target the same with scene center point height, then construct orientation to reference function with them; Concrete derivation method is as follows:

The coordinate that certain pixel (i, j) known is corresponding is (x _i,j, y _i,j), wherein (i, j) be respectively image middle distance to orientation to position; Its distance to consecutive point be respectively (x _{i-1, j}, y _{i-1, j}) and (x _{i+1, j}, y _{i+1, j}), first, from beam model:

$\frac{y_{i-1,j}-y_{i,j}}{x_{i-1,j}-x_{i,j}}=\frac{y_{i+1,j}-y_{i,j}}{x_{i+1,j}-x_{i,j}}={\mathrm{tan\θ}}_c---\left(10\right)$

For near point, can obtain

$\left\{\begin{array}{c}R-{\mathrm{\ΔR}}_i=\sqrt{x_{i-1,j}^2+{(y_{i-1,j}-y_R)}^2+H_R^2}+\sqrt{{(x_{i-1,j}-x_T)}^2+{(y_{i-1,j}-y_T)}^2+H_T^2}\\ y_{i-1,j}-y_{i,j}=(x_{i-1,j}-x_{i,j}){\mathrm{tan\θ}}_c\end{array}\right.---\left(11\right)$

Wherein, θ _cfor receiving antenna Horizontal oblique visual angle, R-Δ R _iit is the double-basis Distance geometry of i-th range gate; Finally draw:

$\left\{\begin{array}{c}{x}_{i-1,j}=\frac{-b\±\sqrt{b^2-4ac}}{2a}\\ y_{i-1,j}=(x_{i-1,j}-x_{i,j}){\mathrm{tan\θ}}_c+y_{i,j}\end{array}\right.---\left(12\right)$

Wherein,

$\left\{\begin{array}{c}a=4{(R-{\mathrm{\ΔR}}_i)}^2(1+{\tan }^2{\mathrm{\θ}}_c)-4{(x_T+(y_T-y_R\left){\mathrm{tan\θ}}_c\right)}^2\\ b=8{\mathrm{tan\θ}}_c{(R-{\mathrm{\ΔR}}_i)}^2{\mathrm{\[(y}}_{i,j}-x_{i,j}{\mathrm{tan\θ}}_c)-y_R\mathrm{\]}\\ +4\[C_0-2(y_T-y_R)(y_{i,j}-x_{i,j}{\mathrm{tan\θ}}_c)\]\[x_T+(y_T-y_R){\mathrm{tan\θ}}_c\]\\ c=4{(R-{\mathrm{\ΔR}}_i)}^2\{{\[(y_{i,j}-x_{i,j}{\mathrm{tan\θ}}_c)-y_R\]}^2+H_R^2\}-{\[2(y_T-y_R)(y_{i,j}-{\mathrm{tan\θ}}_c{x}_{i,j})-C_0\]}^2\\ C_0=x_T^2+y_T^2+H_T^2-y_R^2-H_R^2-{(R-{\mathrm{\ΔR}}_i)}^2\end{array}\right.---\left(13\right)$

Thus just can derive orientation to zero time be engraved in the reference target point position (x of different distance door under antenna angle of squint _i, y _i, 0) (i=1,2 ..., N _r), wherein N _rfor distance is to sampling number.

7. double-base synthetic aperture radar numerical distance Doppler imaging method according to claim 6, is characterized in that, described step S6 concrete methods of realizing is:

The Azimuth Compression function different to different distance door structure, utilizes the reference target point position (x of the different distance door obtained in S5 _i, y _i, 0) (i=1,2 ..., N _r), obtain Azimuth Compression reference function:

$S\left(t_a\right)=A_0{W}_a\left(t_a\right)\exp \[j2\mathrm{\π}\frac{R_{bi}\left(t_a\right)}{\mathrm{\λ}}\]---\left(14\right)$

Wherein, w _afor orientation is to window function, t _afor orientation is to the time, λ is pulse signal wavelength, R _bi(t _a) for orientation is to t _athe double-basis Distance geometry in moment:

$R_{bi}\left(t_a\right)=\sqrt{{\[x_R\left(t_a\right)-x_i\]}^2+{\[y_R\left(t_a\right)-y_i\]}^2+{(h_R-h_i)}^2}+\sqrt{{\[x_T\left(t_a\right)-x_i\]}^2+{\[y_T\left(t_a\right)-y_i\]}^2+{(h_T-h_i)}^2}---\left(15\right)$

Wherein, (x _i, y _i, h _i) be the reference point locations of each range gate;

Get the reverse conjugation of reference function, be Azimuth Compression function:

$S^{*}(-t_a)=A_0{w}_a\left(t_a\right)\exp \[-j2\mathrm{\π}\frac{R_{bi}(-t_a)}{\mathrm{\λ}}\]---\left(16\right)$

After the Data in Azimuth Direction of the echo data obtained by step S4 and formula (16) carry out FFT respectively, frequency domain is multiplied, then carries out IFFT, obtain final imaging results.