CN105487074B - A kind of double-base synthetic aperture radar numerical distance Doppler imaging method - Google Patents

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

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CN105487074B
CN105487074B CN201510843794.2A CN201510843794A CN105487074B CN 105487074 B CN105487074 B CN 105487074B CN 201510843794 A CN201510843794 A CN 201510843794A CN 105487074 B CN105487074 B CN 105487074B
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CN105487074A (en
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武俊杰
钟徐琦
杨建宇
黄钰林
杨海光
杨晓波
孔令讲
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University of Electronic Science and Technology of China
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/904—SAR modes
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/904—SAR modes
    • G01S13/9058—Bistatic or multistatic SAR

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  • Other Investigation Or Analysis Of Materials By Electrical Means (AREA)
  • Radar Systems Or Details Thereof (AREA)

Abstract

The invention discloses a kind of double-base synthetic aperture radar numerical distance Doppler imaging method, comprise the following steps：S1, data prediction；S2, to echo data carry out Range compress；S3, using numerical method calculate range migration correction function, and using range migration correction function pair echo data progress range migration correction；Echo data after S4, generation secondary range compression function and migration of adjusting the distance correction carries out secondary range compression；Reference target point position corresponding to S5, each range gate of calculating；S6, using reference target point placement configurations Azimuth Compression function, and carry out Azimuth Compression, obtain imaging results.The advantage of the invention is that：Accurate range migration function is obtained using numerical method, then range migration correction is carried out with accurate range migration function pair echo data；A certain degree of motion compensation is carried out to echo data simultaneously；Realize the accurate distance migration correction of RD imaging methods under double-base SAR.

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, more particularly to 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 military surveillance, landform Mapping, vegetational analysis, ocean and hydrological observation, environment and disaster monitoring, resource exploration and the earth's crust it is micro- become detection etc. field, SAR has played more and more important effect.
Double-base SAR has the advantages that much to protrude due to bistatic, and it can obtain the non-back scattering letter of target Breath, with operating distance is remote, disguised and strong interference immunity the features such as.Further, since double-base SAR receiving station is without high-power Device, it is its low in energy consumption, small volume, lightweight, it is easy to polytype aircraft to carry, cost is relatively low.In a word, double-base SAR is made For a kind of new tool of earth observation from space, wide development space is suffered from civil and military field.
Research in the world to range Doppler (RD) imaging method of double-base SAR at present, open source literature has：Zare, A.；Masnadi-Shirazi,M.A.；Samadi,S.,"Range-Doppler algorithm for processing bistatic SAR data based on the LBF in the constant-offset constellation," Radar Conference (RADAR), 2012IEEE, vol., no., pp.17-21, give a kind of based on Loffeld two dimensions The RD algorithms of spectral model, it in the derivation of frequency spectrum the phase factor of echo data divide into it is related to cell site and Two parts related to receiving station, and carry out solving point in phase bit respectively, so that 2-d spectrum is obtained, so unavoidably Presence error.In addition, this method can not use motion path information, i.e., it can not be transported during range migration correction Dynamic compensation.
Pertinent literature：Neo,Y.L.；Wong,F.H.；Cumming,I.G.,"Processing of Azimuth- Invariant Bistatic SAR Data Using the Range Doppler Algorithm,"Geoscience and Remote Sensing, IEEE Transactions on, vol.46, no.1, pp.14,21, give a kind of anti-using series Drill to derive 2-d spectrum model, so as to obtain corresponding RD algorithms.But it has only been accurate to 4 times when carrying out Taylor expansion , it have ignored the high-order term of more than 4 times.This obviously brings error to 2-d spectrum, when lengthening the synthetic aperture time, error Influence will be inevitable.Equally, this method can not use motion measurement information.
The content of the invention
Motion path information is made full use of it is an object of the invention to overcome the deficiencies of the prior art and provide one kind, is realized Motion compensation in imaging process, realizes the accurate distance migration correction of RD imaging methods under double-base SAR, can apply Double-base synthetic aperture radar numerical distance Doppler imaging method in fields such as double-base SAR echo-wave imaging, geometric corrections.
The purpose of the present invention is 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, to echo data carry out Range compress；
S3, range migration correction function calculated using numerical method, and entered using range migration correction function pair echo data Row distance migration is corrected；
Echo data after S4, generation secondary range compression function and migration of adjusting the distance correction carries out secondary range compression；
Reference target point position corresponding to S5, each range gate of calculating；
S6, using 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, send out Penetrate platform to fix, flat pad position is designated as (xT,yT,zT), wherein, xT、yTAnd hTRespectively x-axis, y-axis and z-axis of cell site Coordinate；Receive station location and be designated as (0,0, hR), wherein, 0,0 and hRThe respectively x-axis, y-axis and z-axis coordinate of receiving station；Receiving station V is designated as with cell site's speed, and is moved along y-axis；Thus, establish with immediately below receiving station for origin, highly be z-axis, speed Direction is the three-dimensional system of coordinate of y-axis；
Orientation time arrow is designated as：
Wherein, PRI is pulse recurrence interval, NaCounted for target echo orientation；
It is biradical apart from history and for Rb(t；X, y)=RT(t；x,y)+RR(t；X, y), wherein t is orientation time, RT(t；x, And R y)R(t；X, y) it is respectively cell site and receiving station apart from history：
So as to which the expression formula for obtaining echo data is：
Wherein, A0It is the amplitude of scattering coefficient, ωr() is distance to envelope, ωa() orientation envelope, when τ is fast Between variable, t is orientation time variable, fcIt is carrier frequency, c is the light velocity, KrIt is distance to frequency modulation rate, TaWhen being synthetic aperture Between, t0It is that the beam center of target point (x, y) passes through the moment.
Further, described step S2 concrete methods of realizing is：Chirp signals by the use of transmitting are used as reference function pair Echo data carries out Range compress, and the expression formula of Chirp signals is：
S (τ)=A0wr(τ)exp(jπKrτ2) (4)
Wherein, ωa() be distance to envelope, τ is fast time, KrIt is distance to frequency modulation rate；
It is taken reversely to be conjugated, obtaining expression formula is：
S*(- τ)=A0wr(-τ)exp(-jπKr(-τ)2) (5)
The distance of the obtained echo datas of step S1 is carried out after FFT respectively to data and formula (5), is multiplied on frequency domain, Then carry out IFFT and can be obtained by the echo data after Range compress.
Further, described step S3 concrete methods of realizing is：
According to the configuration of double-base SAR, obtain biradical distance and formula is：
Wherein, (xdc,ydc,hdc) it is aiming spot；
Doppler frequency formula is：
Wherein, (xdc,ydc,hdc) it is aiming spot, vR、vTThe respectively flying speed of Receiver And Transmitter,TSFor the synthetic aperture time；
Due to the influence of double joint formula, it is impossible to derive RbAnd fdPrecise relation function；Therefore, carried out by numerical method Calculate, described numerical method includes following sub-step：
S31, take orientation time taDiscrete point,
Wherein
S32, the biradical distance and R calculated in each synthetic aperture timebi(ta), and with spline interpolation biradical distance and Curve interpolation intoTimes, wherein vRFor receiver movement velocity, FdrFor orientation chirp rate；Similarly, to how general Strangle frequency function and also do identical interpolation；So as to utilize relationObtainNumerical value homography；
S33, because range-Dopler domain under, orientation frequency is
Wherein, NaFor orientation sampling number, using the numerical value homography obtained in S32, take wherein from each orientation frequency Biradical distance corresponding to the nearest Doppler frequency of rate and as the range migration amount under the orientation frequency, thus obtain away from From migration correction function；
S34, the echo data after Range compress transformed into range-Dopler domain, utilize the range migration obtained in S33 Correction function, range migration correction is carried out to echo data.
Further, described step S4 concrete methods of realizing is：Because numerical value RD does not use the 2-d spectrum of error Expression formula, therefore secondary range compression function, the Bistatic SAR two based on MSR proposed using Neo, Y.L. et al. can not be obtained Tie up frequency spectrum and secondary range compression is carried out to echo data；Secondary range compression function expression is：
Wherein,
Then using be calculated as below to echo data carry out secondary range compression：
Further, described step S5 concrete methods of realizing is：
Location of pixels in the geographical coordinate of known scene center point and its image, if distance is to space-variant and height overhead In the case that denaturation is the same, only with the position for solving the target as scene center point height, construction side is then used to Position is to reference function；Specific derivation method is as follows：
Some known corresponding coordinate of pixel (i, j) is (xi,j,yi,j), wherein (i, j) is respectively image middle-range descriscent With orientation position；Its distance to consecutive points be respectively (xi-1,j,yi-1,j) and (xi+1,j,yi+1,j), first, by beam model Understand：
For near point, it can obtain
Wherein, θcFor reception antenna Horizontal oblique visual angle, R- Δs RiFor i-th of range gate biradical distance and；Finally draw：
Wherein,
So as to can just derive the reference target point position of orientation zero moment different distance door under antenna angle of squint (xi,yi, 0) (i=1,2 ..., Nr), wherein NrIt is distance 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 of the different distance door obtained in S5 Point position (xi,yi, 0) (i=1,2 ..., Nr), obtain Azimuth Compression reference function：
Wherein, waFor orientation window function, taFor the orientation time, λ is pulse signal wavelength, Rbi(ta) it is orientation ta The biradical distance at moment and：
Wherein, (xi,yi,hi) be each range gate reference point locations；
Take the reverse conjugation of reference function, as Azimuth Compression function：
The Data in Azimuth Direction of the obtained echo datas of step S4 and formula (16) are carried out after FFT respectively, are multiplied on frequency domain, Then IFFT is carried out, final imaging results are obtained.
The beneficial effects of the invention are as follows：On the basis of double-base SAR range-Dopler domain, give up inaccurate two dimension frequency Spectrum model, and accurate range migration function is obtained with numerical method, then entered with accurate range migration function pair echo data Row distance migration is corrected；Meanwhile, and because the numerical computations of range migration function need to use SAR motion path, it is right Echo data carries out a certain degree of motion compensation；The accurate distance migration correction of RD imaging methods under double-base SAR is realized, Fully profit has arrived motion path information simultaneously, realizes the motion compensation in imaging process, can apply to double-base SAR echo The fields such as imaging, geometric correction.
Brief description of the drawings
Fig. 1 is the constant pattern double-base SAR system structure chart of shifting；
Fig. 2 is imaging method flow chart of the invention；
The target scene layout drawing for the embodiment that Fig. 3 uses for the present invention；
Fig. 4 carries out the two-dimensional time-domain figure after first time Range compress for the echo of the embodiment of the present invention；
Fig. 5 is the two-dimensional time-domain figure after range migration correction in the specific embodiment of the invention；
Fig. 6 is the two-dimensional time-domain figure after Azimuth Compression in the specific embodiment of the invention.
Embodiment
Below in conjunction with the accompanying drawings technical scheme is further illustrated with specific embodiment.
Present disclosure is described for convenience, and following term is explained first：
Term 1：Double-base SAR
Double-base SAR refers to the SAR system that system cell site and receiving station are placed in different platform, and wherein at least has one Individual platform is motion platform, conceptually belongs to bistatic radar, as shown in Figure 1.
Term 2：Secondary range compression (SRC)
With the increase of angle of squint, stronger distance and bearing coupling can be introduced and made, it is necessary to correct coupling by filtering Into defocus.The process is secondary range compression.
The main method for using emulation experiment of the invention is verified that all steps, conclusion are all tested on Matlab2012 Card is correct.The solution of the present invention is relation function, the Doppler frequency f first with biradical distance and R and orientation time t With orientation time t relation function, calculate in synthetic aperture time under each orientation moment t biradical distance and R with it is many The general corresponding relation for strangling frequency f, recycles this corresponding relation to pass through spline interpolation to obtain range-Dopler domain, each is more The general biradical distance and R strangled corresponding to frequency f, then carries out range migration correction in range-Dopler domain to echo data；So Afterwards, Taylor expansion is carried out to the Bistatic SAR 2-d spectrum based on MSR, assign the quadratic term of Taylor expansion as secondary range compression Function；Finally, Azimuth Compression function is generated to each range gate using motion path, and carries out Azimuth Compression.Idiographic flow is such as Shown in Fig. 2, a kind of double-base synthetic aperture radar numerical distance Doppler imaging method of the invention comprises the following steps：
S1, data prediction, calculate double-base synthetic aperture radar echo data；Its concrete methods of realizing is：Make scene Central point is irradiated the moment by beam center, and flat pad is fixed, and flat pad position is designated as (xT,yT,zT), wherein, xT、yTAnd hT The respectively x-axis, y-axis and z-axis coordinate of cell site；Receive station location and be designated as (0,0, hR), wherein, 0,0 and hRRespectively receiving station X-axis, y-axis and z-axis coordinate；Receiving station is designated as v with cell site's speed, and is moved along y-axis；Thus, establish with receiving station just Lower section is origin, be highly z-axis, the three-dimensional system of coordinate that velocity attitude is y-axis；The present embodiment under the geographic coordinate system of foundation, Receive station coordinates and be set to (0,0,1) km, speed for (0,50,0) m/s, transmitting station coordinates be (- 1,1,1) km, speed be (0,50, 0) m/s, target scene centre coordinate is (0,1,0) km.The specific ginseng for the constant pattern double-base SAR of shifting that the present embodiment is used Number is as shown in Table 1.The target scene arrangement that is used in the present embodiment is as shown in figure 3, black round dot in figure is is arranged in ground On 3 × 3 totally 9 point targets, (cutting flight path) is spaced 200 meters to this 9 points in the x-direction, is spaced 20 meters (along flight path) in the y-direction. Platform is moved along y-axis.
Table one
Parameter Symbol Numerical value
Carrier frequency fc 9.65GHz
Cell site zero moment position (xT,yT,hT) (-1km,0,1km)
Receiving station's zero moment position (xR,yR,hR) (0,-1km,1km)
Flat pad movement velocity VT 50m/s
Receiving platform movement velocity VR 50m/s
Transmitted signal bandwidth Br 100MHz
Transmission signal time width Tr 5us
Impulse sampling frequency PRF 1000Hz
The synthetic aperture time Ts 1.8s
Orientation time arrow is designated as：
Wherein, PRI is pulse recurrence interval, NaCounted for target echo orientation；
It is biradical apart from history and for Rb(t；X, y)=RT(t；x,y)+RR(t；X, y), wherein t is orientation time, RT(t；x, And R y)R(t；X, y) it is respectively cell site and receiving station apart from history：
So as to which the expression formula for obtaining echo data is：
Wherein, A0It is the amplitude of scattering coefficient, ωr() is distance to envelope, ωa() orientation envelope, when τ is fast Between variable, t is orientation time variable, fcIt is carrier frequency, c is the light velocity, KrIt is distance to frequency modulation rate, TaWhen being synthetic aperture Between, t0It is that the beam center of target point (x, y) passes through the moment.
S2, to echo data carry out Range compress；Its concrete methods of realizing is：Chirp signals by the use of transmitting are used as ginseng Examine function pair echo data and carry out Range compress, the expression formula of Chirp signals is：
S (τ)=A0wr(τ)exp(jπKrτ2) (4)
Wherein, ωa() be distance to envelope, τ is fast time, KrIt is distance to frequency modulation rate；
It is taken reversely to be conjugated, obtaining expression formula is：
S*(- τ)=A0wr(-τ)exp(-jπKr(-τ)2) (5)
The distance of the obtained echo datas of step S1 is carried out after FFT respectively to data and formula (5), is multiplied on frequency domain, Then carry out IFFT and can be obtained by the echo data after Range compress, the echo data of the present embodiment is carried out after Range compress Two-dimensional time-domain figure is as shown in Figure 4.
S3, range migration correction function calculated using numerical method, and entered using range migration correction function pair echo data Row distance migration is corrected；Concrete methods of realizing is：
According to the configuration of double-base SAR, obtain biradical distance and formula is：
Wherein, (xdc,ydc,hdc) it is aiming spot；
Doppler frequency formula is
Wherein, (xdc,ydc,hdc) it is aiming spot, vR、vTThe respectively flying speed of Receiver And Transmitter,TSFor the synthetic aperture time；
Due to the influence of double joint formula, it is impossible to derive RbAnd fdPrecise relation function；Therefore, carried out by numerical method Calculate, described numerical method includes following sub-step：
S31, take orientation time taDiscrete point,
Wherein
S32, the biradical distance and R calculated in each synthetic aperture timebi(ta), and with spline interpolation biradical distance and Curve interpolation intoTimes, wherein vRFor receiver movement velocity, FdrFor orientation chirp rate；Similarly, to how general Strangle frequency function and also do identical interpolation；So as to utilize relationObtainNumerical value homography；
S33, because range-Dopler domain under, orientation frequency isWherein, Na For orientation sampling number, using the numerical value homography obtained in S32, take wherein nearest from each orientation frequency how general Strangle frequency corresponding to biradical distance and as the range migration amount under the orientation frequency, so as to obtain range migration correction letter Number；
S34, the echo data after Range compress transformed into range-Dopler domain, utilize the range migration obtained in S33 Correction function, range migration correction is carried out to echo data, and the echo data of the present embodiment is carried out after range migration correction Two-dimensional time-domain figure is as shown in Figure 5.
Echo data after S4, generation secondary range compression function and migration of adjusting the distance correction carries out secondary range compression； Concrete methods of realizing is：Because numerical value RD does not use the 2-d spectrum expression formula of error, therefore secondary range pressure can not be obtained Contracting function, using Neo, the Bistatic SAR 2-d spectrum based on MSR that Y.L. et al. is proposed carries out secondary range pressure to echo data Contracting：According to distance to frequency fτTaylor expansion is carried out to 2-d spectrum expression formula, quadratic term (f therein is extractedτ 2Coefficient) make For secondary range compression function；Secondary range compression function expression is：
Wherein,
Then using be calculated as below to echo data carry out secondary range compression：
Reference target point position corresponding to S5, each range gate of calculating；Concrete methods of realizing is：
Location of pixels in the geographical coordinate of known scene center point and its image, if distance is to space-variant and height overhead In the case that denaturation is the same, only with the position for solving the target as scene center point height, construction side is then used to Position is to reference function；Specific derivation method is as follows：
Some known corresponding coordinate of pixel (i, j) is (xi,j,yi,j), wherein (i, j) is respectively image middle-range descriscent With orientation position；Its distance to consecutive points be respectively (xi-1,j,yi-1,j) and (xi+1,j,yi+1,j), first, by beam model Understand：
For near point, it can obtain
Wherein, θcFor reception antenna Horizontal oblique visual angle, in the case where the geometric configuration of double-base SAR is forward sight, θc=0； R-ΔRiFor i-th of range gate biradical distance and；Finally draw：
Wherein,
So as to can just derive the reference target point position of orientation zero moment different distance door under antenna angle of squint (xi,yi, 0) (i=1,2 ..., Nr), wherein NrIt is distance to sampling number.
S6, using 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 of the different distance door obtained in S5 Point position (xi,yi, 0) (i=1,2 ..., Nr), obtain Azimuth Compression reference function：
Wherein, waFor orientation window function, taFor the orientation time, λ is pulse signal wavelength, Rbi(ta) it is orientation ta The biradical distance at moment and：
Wherein, (xi,yi,hi) be each range gate reference point locations；
Take the reverse conjugation of reference function, as Azimuth Compression function：
The Data in Azimuth Direction of the obtained echo datas of step S4 and formula (16) are carried out after FFT respectively, are multiplied on frequency domain, Then IFFT is carried out, the two-dimensional time-domain figure after final imaging results, the echo data type Azimuth Compression of the present embodiment is obtained As shown in Figure 6.
One of ordinary skill in the art will be appreciated that embodiment described here is to aid in reader and understands this hair Bright principle, it should be understood that protection scope of the present invention is not limited to such especially statement and embodiment.This area Those of ordinary skill can make according to these technical inspirations disclosed by the invention various does not depart from the other each of essence of the invention Plant specific deformation and combine, these deformations and combination are still within the scope of the present invention.

Claims (4)

1. a kind of double-base synthetic aperture radar numerical distance Doppler imaging method, it is characterised in that comprise the following steps：
S1, data prediction, calculate double-base synthetic aperture radar echo data；Concrete methods of realizing is：Make scene center point Irradiated the moment by beam center, flat pad is fixed, flat pad position is designated as (xT,yT,zT), wherein, xT、yTAnd hTRespectively The x-axis, y-axis and z-axis coordinate of cell site；Receive station location and be designated as (0,0, hR), wherein, 0,0 and hRRespectively the x-axis of receiving station, Y-axis and z-axis coordinate；Receiving station is designated as v with cell site's speed, and is moved along y-axis；Thus, establish to be immediately below receiving station Origin, be highly z-axis, the three-dimensional system of coordinate that velocity attitude is y-axis；
Orientation time arrow is designated as：
Wherein, PRI is pulse recurrence interval, NaCounted for target echo orientation；
It is biradical apart from history and for Rb(t；X, y)=RT(t；x,y)+RR(t；X, y), wherein t is orientation time, RT(t；X, y) and RR(t；X, y) it is respectively cell site and receiving station apart from history：
<mrow> <msub> <mi>R</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>;</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>-</mo> <msub> <mi>x</mi> <mi>T</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mi>y</mi> <mo>+</mo> <mi>v</mi> <mi>t</mi> <mo>-</mo> <msub> <mi>y</mi> <mi>T</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msubsup> <mi>h</mi> <mi>T</mi> <mn>2</mn> </msubsup> </mrow> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>R</mi> <mi>R</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>;</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>-</mo> <msub> <mi>x</mi> <mi>R</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mi>y</mi> <mo>+</mo> <mi>v</mi> <mi>t</mi> <mo>-</mo> <msub> <mi>y</mi> <mi>R</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msubsup> <mi>h</mi> <mi>R</mi> <mn>2</mn> </msubsup> </mrow> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
So as to which the expression formula for obtaining echo data is：
<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>s</mi> <mi>r</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>,</mo> <mi>&amp;tau;</mi> <mo>;</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>A</mi> <mn>0</mn> </msub> <msub> <mi>&amp;omega;</mi> <mi>r</mi> </msub> <mrow> <mo>(</mo> <mi>&amp;tau;</mi> <mo>-</mo> <mfrac> <mrow> <msub> <mi>R</mi> <mi>b</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>;</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> </mrow> <mi>c</mi> </mfrac> <mo>)</mo> </mrow> <msub> <mi>&amp;omega;</mi> <mi>a</mi> </msub> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>t</mi> <mo>-</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> </mrow> <msub> <mi>T</mi> <mi>a</mi> </msub> </mfrac> <mo>)</mo> </mrow> <mi>exp</mi> <mo>&amp;lsqb;</mo> <mo>-</mo> <mi>j</mi> <mn>2</mn> <msub> <mi>&amp;pi;f</mi> <mi>c</mi> </msub> <mfrac> <mrow> <msub> <mi>R</mi> <mi>b</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>;</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> </mrow> <mi>c</mi> </mfrac> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&amp;times;</mo> <mi>exp</mi> <mo>&amp;lsqb;</mo> <msub> <mi>j&amp;pi;K</mi> <mi>r</mi> </msub> <msup> <mrow> <mo>(</mo> <mi>&amp;tau;</mi> <mo>-</mo> <mfrac> <mrow> <msub> <mi>R</mi> <mi>b</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>;</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> </mrow> <mi>c</mi> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
Wherein, A0It is the amplitude of scattering coefficient, ωr() is distance to envelope, ωa() orientation envelope, anaplasia when τ is fast Amount, t is orientation time variable, fcIt is carrier frequency, c is the light velocity, KrIt is distance to frequency modulation rate, TaIt is synthetic aperture time, t0 It is that the beam center of target point (x, y) passes through the moment；
S2, to echo data carry out Range compress；Concrete methods of realizing is：Chirp signals by the use of transmitting are used as reference function Range compress is carried out to echo data, the expression formula of Chirp signals is：
S (τ)=A0wr(τ)exp(jπKrτ2) (4)
Wherein, ωa() be distance to envelope, τ is fast time, KrIt is distance to frequency modulation rate；
It is taken reversely to be conjugated, obtaining expression formula is：
S*(- τ)=A0wr(-τ)exp(-jπKr(-τ)2) (5)
The distance of the obtained echo datas of step S1 is carried out after FFT respectively to data and formula (5), is multiplied on frequency domain, then Carry out IFFT and can be obtained by the echo data after Range compress；
S3, range migration correction function calculated using numerical method, and enter line-spacing using range migration correction function pair echo data From migration correction；Concrete methods of realizing is：
According to the configuration of double-base SAR, obtain biradical distance and formula is：
<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mi>b</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>x</mi> <mi>R</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>y</mi> <mi>R</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>h</mi> <mi>R</mi> </msub> <mo>-</mo> <msub> <mi>h</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <msqrt> <mrow> <msup> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>x</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>y</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>h</mi> <mi>T</mi> </msub> <mo>-</mo> <msub> <mi>h</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
Wherein, (xdc,ydc,hdc) it is aiming spot；
Doppler frequency formula is
<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>f</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msub> <mi>v</mi> <mi>T</mi> </msub> <mo>&amp;CenterDot;</mo> <mo>&amp;lsqb;</mo> <msub> <mi>y</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>y</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mi>&amp;lambda;</mi> <msqrt> <mrow> <msup> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>x</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>x</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>y</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>y</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>h</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>h</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <mfrac> <mrow> <msub> <mi>v</mi> <mi>R</mi> </msub> <mo>&amp;CenterDot;</mo> <mo>&amp;lsqb;</mo> <msub> <mi>y</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>y</mi> <mi>R</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mi>&amp;lambda;</mi> <msqrt> <mrow> <msup> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>x</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>x</mi> <mi>R</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>y</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>y</mi> <mi>R</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>h</mi> <mrow> <mi>d</mi> <mi>c</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>h</mi> <mi>R</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
Wherein, (xdc,ydc,hdc) it is aiming spot, vR、vTThe respectively flying speed of Receiver And Transmitter,TSFor the synthetic aperture time；
Due to the influence of double joint formula, it is impossible to derive RbAnd fdPrecise relation function；Therefore, calculated by numerical method, Described numerical method includes following sub-step：
S31, take orientation time taDiscrete point,
Wherein
S32, the biradical distance and R calculated in each synthetic aperture timebi(ta), and with spline interpolation biradical distance and curve It is interpolated toTimes, wherein vRFor receiver movement velocity, FdrFor orientation chirp rate；Similarly, to Doppler frequency Function also does identical interpolation；So as to utilize relationObtainNumerical value homography；
S33, because range-Dopler domain under, orientation frequency isWherein, NaFor side Position, using the numerical value homography obtained in S32, takes Doppler's frequency wherein nearest from each orientation frequency to sampling number Biradical distance corresponding to rate and as the range migration amount under the orientation frequency, so as to obtain range migration correction function；
S34, the echo data after Range compress transformed into range-Dopler domain, utilize the range migration correction obtained in S33 Function, range migration correction is carried out to echo data；
Echo data after S4, generation secondary range compression function and migration of adjusting the distance correction carries out secondary range compression；
Reference target point position corresponding to S5, each range gate of calculating；
S6, using 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 characterised in that Described step S4 concrete methods of realizing is：Because numerical value RD does not use the 2-d spectrum expression formula of error, therefore it can not obtain To secondary range compression function, secondary range compression is carried out to echo data using the Bistatic SAR 2-d spectrum based on MSR；Two Secondary Range compress function expression is：
<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&amp;phi;</mi> <mrow> <mi>s</mi> <mi>r</mi> <mi>c</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>f</mi> <mi>t</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;ap;</mo> <mfrac> <msup> <mi>c</mi> <mn>2</mn> </msup> <mrow> <mn>4</mn> <msub> <mi>k</mi> <mn>2</mn> </msub> </mrow> </mfrac> <mfrac> <mn>2</mn> <msubsup> <mi>f</mi> <mi>c</mi> <mn>3</mn> </msubsup> </mfrac> <msubsup> <mi>f</mi> <mi>t</mi> <mn>2</mn> </msubsup> <mo>+</mo> <mfrac> <mrow> <msup> <mi>c</mi> <mn>3</mn> </msup> <msub> <mi>k</mi> <mn>3</mn> </msub> </mrow> <mrow> <mn>8</mn> <msubsup> <mi>k</mi> <mn>2</mn> <mn>3</mn> </msubsup> </mrow> </mfrac> <mfrac> <mn>6</mn> <msubsup> <mi>f</mi> <mi>c</mi> <mn>3</mn> </msubsup> </mfrac> <msubsup> <mi>f</mi> <mi>t</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mfrac> <msub> <mi>k</mi> <mn>1</mn> </msub> <mi>c</mi> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msub> <mi>f</mi> <mi>c</mi> </msub> </mfrac> <msub> <mi>f</mi> <mi>t</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <mfrac> <mrow> <msup> <mi>c</mi> <mn>4</mn> </msup> <mrow> <mo>(</mo> <mn>9</mn> <msubsup> <mi>k</mi> <mn>3</mn> <mn>2</mn> </msubsup> <mo>-</mo> <mn>4</mn> <msub> <mi>k</mi> <mn>2</mn> </msub> <msub> <mi>k</mi> <mn>4</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mn>64</mn> <msubsup> <mi>k</mi> <mn>2</mn> <mn>5</mn> </msubsup> </mrow> </mfrac> <mfrac> <mn>12</mn> <msubsup> <mi>f</mi> <mi>c</mi> <mn>3</mn> </msubsup> </mfrac> <mrow> <mo>(</mo> <mfrac> <msubsup> <mi>k</mi> <mn>1</mn> <mn>2</mn> </msubsup> <msup> <mi>c</mi> <mn>2</mn> </msup> </mfrac> <msubsup> <mi>f</mi> <mi>t</mi> <mn>2</mn> </msubsup> <mo>+</mo> <mfrac> <mrow> <mn>2</mn> <msub> <mi>k</mi> <mn>1</mn> </msub> </mrow> <mrow> <msub> <mi>f</mi> <mi>c</mi> </msub> <mi>c</mi> </mrow> </mfrac> <msubsup> <mi>f</mi> <mi>t</mi> <mn>3</mn> </msubsup> <mo>+</mo> <mfrac> <mn>1</mn> <msubsup> <mi>f</mi> <mi>c</mi> <mn>2</mn> </msubsup> </mfrac> <msubsup> <mi>f</mi> <mi>t</mi> <mn>4</mn> </msubsup> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
Wherein,
<mrow> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mo>!</mo> </mrow> </mfrac> <mrow> <mo>(</mo> <mfrac> <mrow> <msup> <mo>&amp;part;</mo> <mn>2</mn> </msup> <msub> <mi>R</mi> <mi>R</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msup> <mi>t</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <msup> <mo>&amp;part;</mo> <mn>2</mn> </msup> <msub> <mi>R</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msup> <mi>t</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mo>)</mo> </mrow> <msub> <mo>|</mo> <mrow> <mi>t</mi> <mo>=</mo> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <mfrac> <mrow> <msubsup> <mi>v</mi> <mi>R</mi> <mn>2</mn> </msubsup> <msup> <mi>cos</mi> <mn>2</mn> </msup> <msub> <mi>&amp;theta;</mi> <mi>R</mi> </msub> </mrow> <msub> <mi>R</mi> <mrow> <mi>R</mi> <mi>c</mi> </mrow> </msub> </mfrac> <mo>+</mo> <mfrac> <mrow> <msubsup> <mi>v</mi> <mi>T</mi> <mn>2</mn> </msubsup> <msup> <mi>cos</mi> <mn>2</mn> </msup> <msub> <mi>&amp;theta;</mi> <mi>T</mi> </msub> </mrow> <msub> <mi>R</mi> <mrow> <mi>T</mi> <mi>c</mi> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>k</mi> <mn>3</mn> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>3</mn> <mo>!</mo> </mrow> </mfrac> <mrow> <mo>(</mo> <mfrac> <mrow> <msup> <mo>&amp;part;</mo> <mn>3</mn> </msup> <msub> <mi>R</mi> <mi>R</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msup> <mi>t</mi> <mn>3</mn> </msup> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <msup> <mo>&amp;part;</mo> <mn>3</mn> </msup> <msub> <mi>R</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msup> <mi>t</mi> <mn>3</mn> </msup> </mrow> </mfrac> <mo>)</mo> </mrow> <msub> <mo>|</mo> <mrow> <mi>t</mi> <mo>=</mo> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> <mrow> <mo>(</mo> <mfrac> <mrow> <mn>3</mn> <msubsup> <mi>v</mi> <mi>R</mi> <mn>3</mn> </msubsup> <msup> <mi>cos</mi> <mn>2</mn> </msup> <msub> <mi>&amp;theta;</mi> <mi>R</mi> </msub> <msub> <mi>sin&amp;theta;</mi> <mi>R</mi> </msub> </mrow> <msubsup> <mi>R</mi> <mrow> <mi>R</mi> <mi>c</mi> </mrow> <mn>2</mn> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mrow> <mn>3</mn> <msubsup> <mi>v</mi> <mi>T</mi> <mn>3</mn> </msubsup> <msup> <mi>cos</mi> <mn>2</mn> </msup> <msub> <mi>&amp;theta;</mi> <mi>T</mi> </msub> <msub> <mi>sin&amp;theta;</mi> <mi>T</mi> </msub> </mrow> <msubsup> <mi>R</mi> <mrow> <mi>T</mi> <mi>c</mi> </mrow> <mn>2</mn> </msubsup> </mfrac> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>k</mi> <mn>4</mn> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>4</mn> <mo>!</mo> </mrow> </mfrac> <mrow> <mo>(</mo> <mfrac> <mrow> <msup> <mo>&amp;part;</mo> <mn>4</mn> </msup> <msub> <mi>R</mi> <mi>R</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msup> <mi>t</mi> <mn>4</mn> </msup> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <msup> <mo>&amp;part;</mo> <mn>4</mn> </msup> <msub> <mi>R</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msup> <mi>t</mi> <mn>4</mn> </msup> </mrow> </mfrac> <mo>)</mo> </mrow> <msub> <mo>|</mo> <mrow> <mi>t</mi> <mo>=</mo> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mn>24</mn> </mfrac> <mo>&amp;lsqb;</mo> <mfrac> <mrow> <mn>3</mn> <msubsup> <mi>v</mi> <mi>R</mi> <mn>4</mn> </msubsup> <msup> <mi>cos</mi> <mn>2</mn> </msup> <msub> <mi>&amp;theta;</mi> <mi>R</mi> </msub> <mrow> <mo>(</mo> <mn>4</mn> <msup> <mi>sin</mi> <mn>2</mn> </msup> <msub> <mi>&amp;theta;</mi> <mi>R</mi> </msub> <mo>-</mo> <msup> <mi>cos</mi> <mn>2</mn> </msup> <msub> <mi>&amp;theta;</mi> <mi>R</mi> </msub> <mo>)</mo> </mrow> </mrow> <msubsup> <mi>R</mi> <mrow> <mi>R</mi> <mi>c</mi> </mrow> <mn>3</mn> </msubsup> </mfrac> <mo>+</mo> <mfrac> <mrow> <mn>3</mn> <msubsup> <mi>v</mi> <mi>T</mi> <mn>4</mn> </msubsup> <msup> <mi>cos</mi> <mn>2</mn> </msup> <msub> <mi>&amp;theta;</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <mn>4</mn> <msup> <mi>sin</mi> <mn>2</mn> </msup> <msub> <mi>&amp;theta;</mi> <mi>T</mi> </msub> <mo>-</mo> <msup> <mi>cos</mi> <mn>2</mn> </msup> <msub> <mi>&amp;theta;</mi> <mi>T</mi> </msub> <mo>)</mo> </mrow> </mrow> <msubsup> <mi>R</mi> <mrow> <mi>T</mi> <mi>c</mi> </mrow> <mn>3</mn> </msubsup> </mfrac> <mo>&amp;rsqb;</mo> </mrow>
Then using be calculated as below to echo data carry out secondary range compression：
<mrow> <msub> <mi>S</mi> <mrow> <mi>s</mi> <mi>r</mi> <mi>c</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>f</mi> <mi>&amp;tau;</mi> </msub> <mo>,</mo> <msub> <mi>f</mi> <mi>t</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>S</mi> <mrow> <mi>r</mi> <mi>c</mi> <mi>m</mi> <mi>c</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>f</mi> <mi>&amp;tau;</mi> </msub> <mo>,</mo> <msub> <mi>f</mi> <mi>t</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mi>j</mi> <mn>2</mn> <msub> <mi>&amp;pi;&amp;phi;</mi> <mrow> <mi>s</mi> <mi>r</mi> <mi>c</mi> </mrow> </msub> <mo>(</mo> <msub> <mi>f</mi> <mi>t</mi> </msub> <mo>)</mo> <mfrac> <msubsup> <mi>f</mi> <mi>&amp;tau;</mi> <mn>2</mn> </msubsup> <mi>c</mi> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
3. double-base synthetic aperture radar numerical distance Doppler imaging method according to claim 2, it is characterised in that Described step S5 concrete methods of realizing is：
Location of pixels in the geographical coordinate of known scene center point and its image, if distance is to space-variant in space-variant and height In the case of the same, only with the position for solving the target as scene center point height, then it is used to construct orientation Reference function；Specific derivation method is as follows：
Some known corresponding coordinate of pixel (i, j) is (xi,j,yi,j), wherein (i, j) is respectively image middle-range descriscent and side Position is to position；Its distance to consecutive points be respectively (xi-1,j,yi-1,j) and (xi+1,j,yi+1,j), first, from beam model：
<mrow> <mfrac> <mrow> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> </mrow> <mrow> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> </mrow> <mrow> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> </mrow> </mfrac> <mo>=</mo> <msub> <mi>tan&amp;theta;</mi> <mi>c</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>
For near point, it can obtain
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>R</mi> <mo>-</mo> <msub> <mi>&amp;Delta;R</mi> <mi>i</mi> </msub> <mo>=</mo> <msqrt> <mrow> <msubsup> <mi>x</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>y</mi> <mi>R</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msubsup> <mi>H</mi> <mi>R</mi> <mn>2</mn> </msubsup> </mrow> </msqrt> <mo>+</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>x</mi> <mi>T</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>y</mi> <mi>T</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msubsup> <mi>H</mi> <mi>T</mi> <mn>2</mn> </msubsup> </mrow> </msqrt> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>)</mo> </mrow> <msub> <mi>tan&amp;theta;</mi> <mi>c</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>
Wherein, θcFor reception antenna Horizontal oblique visual angle, R- Δs RiFor i-th of range gate biradical distance and；Finally draw：
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mo>-</mo> <mi>b</mi> <mo>&amp;PlusMinus;</mo> <msqrt> <mrow> <msup> <mi>b</mi> <mn>2</mn> </msup> <mo>-</mo> <mn>4</mn> <mi>a</mi> <mi>c</mi> </mrow> </msqrt> </mrow> <mrow> <mn>2</mn> <mi>a</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>)</mo> </mrow> <msub> <mi>tan&amp;theta;</mi> <mi>c</mi> </msub> <mo>+</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>
Wherein,
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>a</mi> <mo>=</mo> <mn>4</mn> <msup> <mrow> <mo>(</mo> <mi>R</mi> <mo>-</mo> <msub> <mi>&amp;Delta;R</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <msup> <mi>tan</mi> <mn>2</mn> </msup> <msub> <mi>&amp;theta;</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mn>4</mn> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>T</mi> </msub> <mo>+</mo> <mo>(</mo> <mrow> <msub> <mi>y</mi> <mi>T</mi> </msub> <mo>-</mo> <msub> <mi>y</mi> <mi>R</mi> </msub> </mrow> <mo>)</mo> <msub> <mi>tan&amp;theta;</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>b</mi> <mo>=</mo> <mn>8</mn> <msub> <mi>tan&amp;theta;</mi> <mi>c</mi> </msub> <msup> <mrow> <mo>(</mo> <mi>R</mi> <mo>-</mo> <msub> <mi>&amp;Delta;R</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <msub> <mi>tan&amp;theta;</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>y</mi> <mi>R</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <mn>4</mn> <mo>&amp;lsqb;</mo> <msub> <mi>C</mi> <mn>0</mn> </msub> <mo>-</mo> <mn>2</mn> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>T</mi> </msub> <mo>-</mo> <msub> <mi>y</mi> <mi>R</mi> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <msub> <mi>tan&amp;theta;</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>&amp;lsqb;</mo> <msub> <mi>x</mi> <mi>T</mi> </msub> <mo>+</mo> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>T</mi> </msub> <mo>-</mo> <msub> <mi>y</mi> <mi>R</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>tan&amp;theta;</mi> <mi>c</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>c</mi> <mo>=</mo> <mn>4</mn> <msup> <mrow> <mo>(</mo> <mi>R</mi> <mo>-</mo> <msub> <mi>&amp;Delta;R</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>{</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <msub> <mi>tan&amp;theta;</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>y</mi> <mi>R</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msubsup> <mi>H</mi> <mi>R</mi> <mn>2</mn> </msubsup> <mo>}</mo> <mo>-</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <mn>2</mn> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>T</mi> </msub> <mo>-</mo> <msub> <mi>y</mi> <mi>R</mi> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>tan&amp;theta;</mi> <mi>c</mi> </msub> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>C</mi> <mn>0</mn> </msub> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>C</mi> <mn>0</mn> </msub> <mo>=</mo> <msubsup> <mi>x</mi> <mi>T</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>y</mi> <mi>T</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>H</mi> <mi>T</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>y</mi> <mi>R</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>H</mi> <mi>R</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msup> <mrow> <mo>(</mo> <mi>R</mi> <mo>-</mo> <msub> <mi>&amp;Delta;R</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow>
So as to can just derive the reference target point position (x of orientation zero moment different distance door under antenna angle of squinti, yi, 0) (i=1,2 ..., Nr), wherein NrIt is distance to sampling number.
4. double-base synthetic aperture radar numerical distance Doppler imaging method according to claim 3, it is characterised 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 of the different distance door obtained in S5 Put (xi,yi, 0) (i=1,2 ..., Nr), obtain Azimuth Compression reference function：
<mrow> <mi>S</mi> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>A</mi> <mn>0</mn> </msub> <msub> <mi>w</mi> <mi>a</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mi>exp</mi> <mo>&amp;lsqb;</mo> <mi>j</mi> <mn>2</mn> <mi>&amp;pi;</mi> <mfrac> <mrow> <msub> <mi>R</mi> <mrow> <mi>b</mi> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>a</mi> </msub> <mo>)</mo> </mrow> </mrow> <mi>&amp;lambda;</mi> </mfrac> <mo>&amp;rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow>
Wherein, waFor orientation window function, taFor the orientation time, λ is pulse signal wavelength, Rbi(ta) it is orientation taMoment Biradical distance and：
<mrow> <msub> <mi>R</mi> <mrow> <mi>b</mi> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>x</mi> <mi>R</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>y</mi> <mi>R</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>h</mi> <mi>R</mi> </msub> <mo>-</mo> <msub> <mi>h</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>+</mo> <msqrt> <mrow> <msup> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>x</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>y</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>h</mi> <mi>T</mi> </msub> <mo>-</mo> <msub> <mi>h</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mrow>
Wherein, (xi,yi,hi) be each range gate reference point locations；
Take the reverse conjugation of reference function, as Azimuth Compression function：
<mrow> <msup> <mi>S</mi> <mo>*</mo> </msup> <mrow> <mo>(</mo> <mo>-</mo> <msub> <mi>t</mi> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>A</mi> <mn>0</mn> </msub> <msub> <mi>w</mi> <mi>a</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mi>exp</mi> <mo>&amp;lsqb;</mo> <mo>-</mo> <mi>j</mi> <mn>2</mn> <mi>&amp;pi;</mi> <mfrac> <mrow> <msub> <mi>R</mi> <mrow> <mi>b</mi> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <mo>-</mo> <msub> <mi>t</mi> <mi>a</mi> </msub> <mo>)</mo> </mrow> </mrow> <mi>&amp;lambda;</mi> </mfrac> <mo>&amp;rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>16</mn> <mo>)</mo> </mrow> </mrow>
The Data in Azimuth Direction of the obtained echo datas of step S4 and formula (16) are carried out after FFT respectively, are multiplied on frequency domain, then IFFT is carried out, final imaging results are obtained.
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