CN106405514A - Method for simulating synthetic aperture radar echo signal under nonlinear track condition - Google Patents

Abstract

The invention provides a method for simulating a synthetic aperture radar echo signal under a nonlinear track condition. The method includes the steps of 1. setting a set of linear tracks at equal intervals; 2. for each linear track, using an SAR echo signal simulator under a linear track assuming condition to calculate an SAR echo signal; 3. performing Fourier transform on the echo signal of each SAR transmission pulse on each linear track; 4. on each frequency component k, performing interpolation filtering on the SAR echo signal between different linear tracks; and 5. performing inverse Fourier transform on the echo signal of each SAR transmission pulse. The simulation method provided by the invention can realize function upgrading of the SAR echo signal simulator under an ideal linear track condition without any modification of internal codes; limiting conditions for radar parameters are few, and wide applicability is achieved; the calculation efficiency is high; and the simulation method can serve as a unified framework to be used for echo signal simulation of various SAR imaging modes under the non-linear track condition.

Description

The emulation mode of Synthetic Aperture Radar Echo under the conditions of a kind of non-rectilinear flight path

【Technical field】

The invention belongs to synthetic aperture radar and field of signal processing and in particular to Synthetic Aperture Radar Echo imitative True technology, the emulation mode of the Synthetic Aperture Radar Echo under the conditions of particularly a kind of flight path in non-rectilinear.

【Background technology】

Synthetic aperture radar (Synthetic Aperture Radar, SAR) Simulation of Echo Signal device becomes for research SAR As algorithm, checking SAR system scheme etc. have important function.Under the assumed condition of preferable rectilinear path, existing multiple efficient SAR echo signal emulation technology available, such as G.Franceschetti, M.Migliaccio, D.Riccio, and G.Schirinzi,“SARAS:a synthetic aperture radar(SAR)raw signal simulator,”IEEE Transactions on Geoscience and Remote Sensing, public in vol.30, no.1, pp.110 123,1992 The frequency-domain-simulation opened, and A.Khwaja, L.Ferro-Famil, and E.Pottier, " Efficient SAR raw data generation for anisotropic urban scenes based on inverse processing,” Geoscience and Remote Sensing Letters, disclosed in IEEE, vol.6, no.4, pp.757 761,2009. Inverse imaging simulation technology etc..Due to air agitation, carried SAR or unmanned aerial vehicle SAR are usually present driftage, actual radar platform Flight path often be non-rectilinear flight path, cause and SAR imaging caused necessarily to perplex.In order under the conditions of carrying out driftage, SAR becomes As with the method compensating it is proposed that SAR echo signal emulation mode under the conditions of multiple flight path dedicated for non-rectilinear, such as G.Franceschetti,A.Iodice,S.Perna,and D.Riccio,“Efficient Simulation of Airborne SAR Raw Data of Extended Scenes,”IEEE Transactions on Geoscience and Remote Sensing, technology disclosed in vol.44, no.10, pp.2851 2860 etc..

However, there is following technical bottleneck in current SAR Simulation of Echo Signal device.First, under the conditions of non-rectilinear flight path, such as Fruit SAR echo signal emulator want to keep and ideal line flight path under the conditions of similar computational efficiency it is necessary to radar parameter Many restrictions condition, such as low angle of squint, narrow beam, small signal bandwidth or little track deviation etc. are proposed.For modern SAR system, Above-mentioned qualifications are increasingly not being met, and necessarily lead to the computational efficiency of SAR echo signal emulator greatly to decline.The Two, review the SAR echo signal emulator under the conditions of ideal line flight path, computational efficiency is higher, and to radar parameter not There is above-mentioned restriction.However, so far, the efficient SAR echo signal proposing under the assumed condition of preferable rectilinear path is imitated True method can not be used for the non-rectilinear flight path condition that there is driftage.3rd, although in a certain specific non-rectilinear flight path condition Under, the computational efficiency of SAR echo signal emulator still accepts, but the Monte Carlo simulation under the conditions of multiple Different Flight is real Test still very time-consuming.4th, current SAR echo signal emulator is to design for a certain specific SAR imaging pattern to realize 's.For different SAR imaging patterns, need to design different SAR echo signal emulation modes.Apparent if it is possible to Design a kind of SAR echo signal emulation mode being applied to multiple imaging patterns, SAR echo signal emulator will be greatly simplified Complexity.

【Content of the invention】

It is an object of the invention to overcoming the above-mentioned not enough of prior art it is proposed that under the conditions of a kind of flight path in non-rectilinear The emulation mode of Synthetic Aperture Radar Echo, especially a kind of synthetic aperture radar signal simulator is by rectilinear path condition The method carrying out function upgrading to non-rectilinear flight path condition.

In order to achieve the above object, Synthetic Aperture Radar Echo under the conditions of a kind of flight path in non-rectilinear of the present invention Emulation mode, the technical scheme taken is as follows：

Step one：Set one group of equally spaced rectilinear path.Wherein, rectilinear path sample frequency in space should be greater than SAR echo signal Spatial Spectrum bandwidth, that is, require the distance between adjacent rectilinear path should be not more than SAR echo signal spatial domain bands of a spectrum Wide inverse.The number of rectilinear path should spatially cover non-rectilinear flight path enough.

Step 2：It is respectively directed to each rectilinear path, using the SAR echo signal emulation under rectilinear path assumed condition Device calculates SAR echo signal.Wherein, the SAR echo simulation device under rectilinear path assumed condition is taken technology path and reality Existing scheme arbitrarily can select according to basis of reality or demand.

Step 3：Fourier transformation is carried out to the exomonental echo-signal of each SAR on every rectilinear path.Fu Li Leaf transformation will obtain the SAR echo signal on different radar emission signal frequency component k.

Step 4：In each frequency component k, filtering interpolation is carried out between different rectilinear paths to SAR echo signal. Interpolation filter should be chosen according to the standard of general bandpass signal filtering interpolation, wherein, the center frequency of interpolation filter Rate should correspond to the centre frequency of SAR echo signal Spatial Spectrum.

Step 5：To each SAR, exomonental echo-signal carries out inverse Fourier transform.Inverse Fourier transform will be every The exomonental echo-signal of individual SAR switches back to two-dimensional time-domain.

Through above five steps, you can non-rectilinear is obtained by the SAR echo simulation device under rectilinear path assumed condition SAR echo signal under the conditions of flight path.

The emulation mode of the Synthetic Aperture Radar Echo under the conditions of a kind of flight path in non-rectilinear of the present invention, its beneficial effect Fruit is main to be included：

First, the present invention can realize ideal line flight path condition on the premise of internal code is not carried out with any modification Under SAR echo signal emulator function upgrading, be allowed to possess the SAR echo signal emulation energy under the conditions of non-rectilinear flight path Power.

Second, the present invention is few to the restrictive condition of radar parameter, has wide applicability.In wide in range radar stravismus Angle, under conditions of radar beam width, radar signal bandwidth, radar driftage form, the inventive method is respectively provided with validity.

3rd, the inventive method computational efficiency is high.On the one hand, for the emulation under the conditions of single, specific non-rectilinear flight path For experiment, computation complexity mostlys come from step 2, that is, under the conditions of rectilinear path SAR echo signal emulator calculating. It is thus able to the close computational efficiency of SAR echo simulation device under the conditions of holding and ideal line flight path.On the other hand, for many For Monte Carlo simulation under the conditions of secondary, Different Flight, step one to step 3 only need to calculate once, needs repeatedly to calculate Only step 4 and step 5, thus the complexity repeating to test substantially reduces.

4th, because the inventive method is applicable not only to the stripmap SAR of classics, it is also applied for Sliding spotlight SAR, pack Multiple SAR imaging pattern such as SAR, TopSAR, the inventive method can be as a Unified frame, for multiple SAR imaging patterns Simulation of Echo Signal under the conditions of non-rectilinear flight path.

【Brief description】

Fig. 1 is the geometric representation that SAR is imaged on two-dimentional oblique distance plane.

Fig. 2 is that SAR is imaged on three-dimensional geometric representation.

Fig. 3 is the inventive method flow chart.

Fig. 4 is to obtain two-dimentional non-rectilinear flight path by the SAR echo signal under the conditions of rectilinear path is carried out with one-dimensional interpolation Under the conditions of SAR echo signal schematic diagram.

Fig. 5 is to obtain three-dimensional non-rectilinear flight path by the SAR echo signal under the conditions of rectilinear path is carried out with two-dimensional interpolation Under the conditions of SAR echo signal schematic diagram.

Fig. 6 is the flight path of the two-dimentional sinusoidal form of stripmap SAR.

Fig. 7 is the phase error between the two-dimensional ribbon there SAR echo signal and theoretical value that the inventive method produces.

Fig. 8 is the flight path of the three-dimensional spiral curve form of stripmap SAR.

Fig. 9 is the phase error between the three-dimensional band SAR echo signal and theoretical value that the inventive method produces.

【Specific embodiment】

Below in conjunction with the accompanying drawings the present invention is further explained.Fig. 1 presents SAR imaging in SAR two dimension oblique distance plane Geometric representation.When we discuss SAR echo signal in two-dimentional oblique distance plane, can hypothesis radar without loss of generality put down Platform bulk motion direction is x-axis direction；Radar site coordinate isScattering center coordinate isRadar Beam position isWherein θ_sqRepresent the angle of squint of radar beam sensing；Scattering center is relative to radar Instantaneous direction beWhereinAs shown in Figure 1；Fig. 2 presents in three-dimensional geometry space The geometric representation of SAR imaging.When we discuss SAR echo signal in three dimensions, still can hypothesis without loss of generality Radar platform bulk motion direction is x-axis direction；Radar site coordinate isScattering center coordinate isRadar beam is oriented toWhereinRepresent respectively Radar beam points to and x, y, z-axis angle；Scattering center relative to the instantaneous direction of radar isWhereinAs shown in Figure 2.

The present invention adopts five steps as shown in Figure 3.

Step one：Set one group of equally spaced rectilinear path.Wherein, rectilinear path sample frequency in space should be greater than SAR echo signal Spatial Spectrum bandwidth, that is, require the distance between adjacent rectilinear path should be not more than SAR echo signal spatial domain bands of a spectrum Wide inverse.The number of rectilinear path should spatially cover non-rectilinear flight path enough.It is specifically divided into following two situations：

The first situation, if we consider driftage problem in SAR two dimension oblique distance plane, now should in SAR two dimension tiltedly One group of rectilinear path is set on anomaly face, as shown in Figure 4.Wherein, the distance between adjacent rectilinear path Δ y^2dFor constant, and should Meet

Wherein,For two-dimensional SAR echo-signal Spatial Spectrum bandwidth, and

Wherein, θ_bwFor radar bearing to beam angle；K=2f_r/ c is corresponding radar emission signal frequency f_r(unit is conspicuous Hereby, Hz) radar emission signal wave number (one, the m that unit is divided for rice^-1), c is propagation velocity of electromagnetic wave.The number of rectilinear path M_yNon-rectilinear flight path should be covered on two-dimensional space enough, and should meet

Wherein,Represent several mathematical operations that round up；The radius changing in the y-axis direction for non-rectilinear flight path；Over-sampling coefficient for rectilinear path space interval；Length for interpolation filter one-dimensional in step 4 Degree.

Second situation, if we consider driftage problem on three dimensions, now should set one on three dimensions Group rectilinear path, as shown in Figure 5.Wherein, the distance between adjacent rectilinear path Δ y^3d,Δz^3dIt is constant, and should meet

Wherein,For D S AR echo-signal Spatial Spectrum bandwidth, and

Wherein, θ_w,y,θ_w,zIt is respectively the beam angle that radar is relative to y-axis, z-axis.Number along the rectilinear path of y-axisNumber along the rectilinear path of z-axisNon-rectilinear flight path should be covered on three dimensions enough, and should meet

Wherein,The radius changing on y-axis, z-axis direction for non-rectilinear flight path； For over-sampling coefficient on y-axis, z-axis direction for the rectilinear path space interval；It is respectively step 4 Middle two-dimensional interpolation wave filter is along the length of y-axis, z-axis.

Step 2：It is respectively directed to each rectilinear path, using the SAR echo simulation device meter under rectilinear path assumed condition Calculate SAR echo signal.Wherein, the technology path that the SAR echo simulation device under rectilinear path assumed condition is taken and realization side Case arbitrarily can select according to basis of reality or demand.For example, optional G.Franceschetti, M.Migliaccio, D.Riccio,and G.Schirinzi,“SARAS:a synthetic aperture radar(SAR)raw signal simulator,”IEEE Transactions on Geoscience and Remote Sensing,vol.30,no.1, Pp.110 123, the frequency-domain-simulation disclosed in 1992, or A.Khwaja, L.Ferro-Famil, and E.Pottier, “Efficient SAR raw data generation for anisotropic urban scenes based on inverse processing,”Geoscience and Remote Sensing Letters,IEEE,vol.6,no.4, Pp.757 761, the inverse imaging simulation technology disclosed in 2009, or the SAR echo signal emulation technology of autonomous Design.

Step 3：To each SAR, exomonental echo-signal carries out Fourier transformation.Fourier transformation will obtain not With the SAR echo signal in radar emission signal wavenumber components k.Wherein, k ∈ [2f₀/c-B_r/c,2f₀/c+B_r/ c], f₀And B_rPoint Wei not the centre frequency of radar emission signal and bandwidth.

Step 4：To each radar emission signal wavenumber components k and radar site x coordinate, to SAR echo signal in difference Carry out filtering interpolation between rectilinear path.It is specifically divided into following two situations：

The first situation, if we consider driftage problem in SAR two dimension oblique distance plane, should put down in SAR two dimension oblique distance On face, for each fixing k and x, along y-axis, one-dimensional interpolation is carried out to the SAR echo signal data on different rectilinear paths Filtering, as shown in Figure 4.Interpolation filter should be chosen according to the standard of bandpass signal filtering interpolation.In interpolation filter Frequency of heart should be equal to the centre frequency of two-dimensional SAR echo-signal Spatial SpectrumWherein

For ensureing that emulation signal has a good phase accuracy, choose during interpolation filter it is ensured that its frequency response is two Dimension SAR echo signal Spatial Spectrum frequency band rangeWithin sufficiently flat, and in this frequency band range Outside there is Sidelobe.It should be noted that when SAR is operated in band pattern, θ_sqFor constant value；And work as SAR and be operated in pack During other patterns such as pattern, slip pack, TopSAR, θ_sqValue with radar x coordinate change, the therefore center of interpolation filter Frequency also correspondingly should change with radar x coordinate according to formula (8).

Second situation, if we consider driftage problem in three dimensions, should be solid for each in three dimensions Fixed k and x, carries out two-dimensional interpolation filtering to the SAR echo signal data on different rectilinear paths along y-axis and z-axis, such as Fig. 5 Shown.Two-dimensional interpolation filtering can be carried out one-dimensional filtering interpolation and realize along y-axis, z-axis direction by priority, along y-axis, z-axis direction One-dimensional interpolation filter should be chosen according to the standard of bandpass signal filtering interpolation.In the interpolation filter in y-axis direction Frequency of heart should be equal to the centre frequency of D S AR echo-signal Spatial SpectrumWherein

The centre frequency of the interpolation filter in z-axis direction should be equal to the centre frequency of D S AR echo-signal Spatial SpectrumWherein

For ensureing that emulation signal has a good phase accuracy, choose during interpolation filter it is ensured that its frequency response is three Dimension SAR echo signal Spatial Spectrum frequency band range

Within sufficiently flat, and there is outside spectral range Sidelobe.It should be noted that when SAR is operated in band Pattern,For constant value；And when SAR is operated in other patterns such as beam bunching mode, slip pack, TopSAR,Value will be with The change of radar x coordinate, the therefore centre frequency of interpolation filter also correspondingly should be sat with radar x according to formula (9) and formula (10) Mark change.

Through above four steps, we can obtain non-rectilinear flight path under the conditions of SAR echo signal in orientation time domain Value apart from frequency domain.

Step 5：On each fixing radar x coordinate, to each SAR, exomonental echo-signal is carried out in inverse Fu Leaf transformation.Inverse Fourier transform will switch back to fast time-domain exomonental for each SAR echo-signal.

Fig. 6 to Fig. 7 applies the experiment obtained by the inventive method when being and considering driftage problem in SAR two dimension oblique distance plane Result.In emulation experiment, setting SAR is operated in band pattern, and the nominal resolving power of distance and bearing is 0.5m, and radar emission is believed Number carrier frequency 6GHz, bandwidth 300MHz；Setting radar beam is oriented toCorresponding radar antenna stravismus Angle θ_sq=0.1rad, Azimuth beam width θ_bw=0.05rad, antenna radiation pattern Wherein α represents target and deviates the angle that radar beam main lobe points to；Setting radar track For two-dimentional sine curve as shown in Figure 6；Setting target be positioned atScattering center.Upper Under the conditions of stating parameter setting, step one of the present invention sets one group of equally spaced rectilinear pathWherein adjacent straight line displacement Δ y^2d=2.0m, flight path bar numberIn step 2 of the present invention, using time domain SAR echo signal emulation mode, according to SAR echo signal Mathematical Modeling Definition calculate the SAR echo signal under the conditions of each rectilinear path.In step 4 of the present invention, weighted using Hamming window, Block the Sinc function that length is 11 as the baseband portion of interpolation kernel function.The two-dimensional ribbon there that contrast the inventive method produces Phase error between SAR echo signal and theoretical value, obtains result as shown in Figure 7.Experimental result shows, the inventive method Highly consistent between produced signal and theoretical value, the maximum of phase error is 3 × 10^-3Rad, the experimental verification present invention The validity of method.

Fig. 8 to Fig. 9 is the experimental result applied when considering driftage problem on three dimensions obtained by the inventive method.Imitative In true experiment, setting SAR is operated in band pattern, and the nominal resolving power of distance and bearing is 0.5m, radar emission signal carrier frequency 6GHz, bandwidth 300MHz；Setting radar beam points toAntenna radiation patternWherein α represents target and deviates the angle that radar beam main lobe points to；Setting radar trackFor three-dimensional vortical form as shown in Figure 8；Setting target is position InScattering center.Under above-mentioned parameter imposes a condition, in step of the present invention One group of equally spaced rectilinear path is set in one Wherein adjacent straight line displacement Δ y^3d=0.3923m, Δ z^3d=0.2310m, flight path bar numberAt this In bright step 2, using time domain SAR echo signal emulation mode, the definition according to SAR echo signal Mathematical Modeling calculates each SAR echo signal under the conditions of bar rectilinear path.In step 4 of the present invention, using Hamming window weighting, block length for 7 × 7 Sinc function as interpolation kernel function baseband portion.Still high between signal and theoretical value produced by application the inventive method Degree is consistent, and phase error shown in Fig. 9 again show the validity of the inventive method.

Claims (4)

1. the emulation mode of the Synthetic Aperture Radar Echo under the conditions of a kind of flight path in non-rectilinear, step is as follows：

Step one：Set one group of equally spaced rectilinear path；Wherein, rectilinear path sample frequency in space should be greater than SAR Echo-signal Spatial Spectrum bandwidth, that is, require the distance between adjacent rectilinear path should be not more than SAR echo signal Spatial Spectrum bandwidth Inverse；The number of rectilinear path should spatially cover non-rectilinear flight path enough；

Step 2：It is respectively directed to each rectilinear path, using the SAR echo signal emulator meter under rectilinear path assumed condition Calculate SAR echo signal；Wherein, the technology path that the SAR echo simulation device under rectilinear path assumed condition is taken and realization side Case arbitrarily can select according to basis of reality or demand；

Step 3：Fourier transformation is carried out to the exomonental echo-signal of each SAR on every rectilinear path；Fourier becomes Change commanders the SAR echo signal obtaining on different radar emission signal frequency component k；

Step 4：In each frequency component k, filtering interpolation is carried out between different rectilinear paths to SAR echo signal；Interpolation Wave filter should be chosen according to the standard of general bandpass signal filtering interpolation, and wherein, the centre frequency of interpolation filter should The centre frequency of corresponding SAR echo signal Spatial Spectrum；

Step 5：To each SAR, exomonental echo-signal carries out inverse Fourier transform；Inverse Fourier transform will be each The exomonental echo-signal of SAR switches back to two-dimensional time-domain；

Through above five steps, you can non-rectilinear flight path is obtained by the SAR echo simulation device under rectilinear path assumed condition Under the conditions of SAR echo signal.

2. the emulation side of the Synthetic Aperture Radar Echo under the conditions of a kind of flight path in non-rectilinear according to claim 1 Method it is characterised in that：In described step one, the number of rectilinear path should spatially cover non-rectilinear flight path enough, concrete point For following two situations：

The first situation, if we consider driftage problem in SAR two dimension oblique distance plane, now should put down in SAR two dimension oblique distance One group of rectilinear path is set on face, wherein, the distance between adjacent rectilinear path Δ y^2dFor constant, and should meet

${\mathrm{\Δy}}^{2d}\≤1/B_y^{2d}---\left(1\right)$

Wherein,For two-dimensional SAR echo-signal Spatial Spectrum bandwidth, and

$B_y^{2d}=\left\{\begin{array}{cc}2ksin\left({\mathrm{\θ}}_{bw}\right)sin\left(\right|{\mathrm{\θ}}_{sq}\left|\right),& \left|{\mathrm{\θ}}_{sq}\right|\≥{\mathrm{\θ}}_{bw}/2\\ k(1-\cos (\left|{\mathrm{\θ}}_{sq}\right|+{\mathrm{\θ}}_{bw}/2)),& \left|{\mathrm{\θ}}_{sq}\right|\≤{\mathrm{\θ}}_{bw}/2\end{array}\right.---\left(2\right)$

Wherein, θ_bwFor radar bearing to beam angle；K=2f_r/ c is corresponding radar emission signal frequency f_rRadar emission signal Wave number, c is propagation velocity of electromagnetic wave；Number M of rectilinear path_yNon-rectilinear flight path should be covered on two-dimensional space enough, and should Meet

Wherein,Represent several mathematical operations that round up；The radius changing in the y-axis direction for non-rectilinear flight path；Over-sampling coefficient for rectilinear path space interval；Length for interpolation filter one-dimensional in step 4 Degree；

Second situation, if we consider driftage problem on three dimensions, now should set on three dimensions one group straight Line flight path, wherein, the distance between adjacent rectilinear path Δ y^3d,Δz^3dIt is constant, and should meet

${\mathrm{\Δy}}^{3d}\≤1/B_y^{3d};{\mathrm{\Δz}}^{3d}\≤1/B_z^{3d}---\left(4\right)$

Wherein,For D S AR echo-signal Spatial Spectrum bandwidth, and

$B_y^{3d}=\left\{\begin{array}{cc}2ksin\left({\mathrm{\θ}}_{w,y}\right)sin\left(\right|{\mathrm{\θ}}_{0,y}\left|\right),& \left|{\mathrm{\θ}}_{0,y}\right|\≥{\mathrm{\θ}}_{w,y}/2\\ k(1-\cos (\left|{\mathrm{\θ}}_{0,y}\right|+{\mathrm{\θ}}_{w,y}/2)),& \left|{\mathrm{\θ}}_{0,y}\right|\≤{\mathrm{\θ}}_{w,y}/2\end{array}\right.---\left(5\right)$

$B_z^{3d}=\left\{\begin{array}{cc}2ksin\left({\mathrm{\θ}}_{w,z}\right)sin\left(\right|{\mathrm{\θ}}_{0,z}\left|\right),& \left|{\mathrm{\θ}}_{0,z}\right|\≥{\mathrm{\θ}}_{w,z}/2\\ k(1-\cos (\left|{\mathrm{\θ}}_{0,z}\right|+{\mathrm{\θ}}_{w,z}/2)),& \left|{\mathrm{\θ}}_{0,z}\right|\≤{\mathrm{\θ}}_{w,z}/2\end{array}\right.---\left(6\right)$

Wherein, θ_w,y,θ_w,zIt is respectively the beam angle that radar is relative to y-axis, z-axis；Number along the rectilinear path of y-axisAlong z The number of the rectilinear path of axleNon-rectilinear flight path should be covered on three dimensions enough, and should meet

Wherein,The radius changing on y-axis, z-axis direction for non-rectilinear flight path； For over-sampling coefficient on y-axis, z-axis direction for the rectilinear path space interval；It is respectively step 4 Middle two-dimensional interpolation wave filter is along the length of y-axis, z-axis.

3. the emulation side of the Synthetic Aperture Radar Echo under the conditions of a kind of flight path in non-rectilinear according to claim 1 Method it is characterised in that：Frequency component k ∈ [2f described in step 3 kind₀/c-B_r/c,2f₀/c+B_r/ c], f₀And B_rIt is respectively radar The centre frequency of transmission signal and bandwidth.

4. the emulation side of the Synthetic Aperture Radar Echo under the conditions of a kind of flight path in non-rectilinear according to claim 1 Method it is characterised in that：Described step 4 is specifically divided into following two situations：

The first situation, if we SAR two dimension oblique distance plane on consider driftage problem, should SAR two dimension oblique distance plane on, For each fixing k and x, along y-axis, one-dimensional filtering interpolation is carried out to the SAR echo signal data on different rectilinear paths, Interpolation filter should be chosen according to the standard of bandpass signal filtering interpolation；The centre frequency of interpolation filter should be equal to two dimension The centre frequency of SAR echo signal Spatial SpectrumWherein

$k_{c,y}^{2d}=k{\mathrm{cos\θ}}_{sq}---\left(8\right)$

For ensureing that emulating signal has good phase accuracy, chooses during interpolation filter it is ensured that its frequency response is in two dimension SAR echo signal Spatial Spectrum frequency band rangeWithin sufficiently flat, and this frequency band range it There is outward Sidelobe；It should be noted that when SAR is operated in band pattern, θ_sqFor constant value；And work as SAR and be operated in pack mould During other patterns such as formula, slip pack, TopSAR, θ_sqValue with radar x coordinate change, therefore interpolation filter center frequency Rate also correspondingly should change with radar x coordinate according to formula (8)；

Second situation, if we consider driftage problem in three dimensions, should fix for each in three dimensions K and x, carries out two-dimensional interpolation filtering to the SAR echo signal data on different rectilinear paths along y-axis and z-axis；Two-dimensional interpolation is filtered Ripple can be carried out one-dimensional filtering interpolation and realize along y-axis, z-axis direction by priority, along the one-dimensional interpolation filter of y-axis, z-axis direction Should be chosen according to the standard of bandpass signal filtering interpolation；The centre frequency of the interpolation filter in y-axis direction should be equal to three-dimensional The centre frequency of SAR echo signal Spatial SpectrumWherein

$k_{c,y}^{3d}=k{\mathrm{cos\θ}}_{0,y}---\left(9\right)$

The centre frequency of the interpolation filter in z-axis direction should be equal to the centre frequency of D S AR echo-signal Spatial SpectrumWherein

$k_{c,z}^{3d}=k{\mathrm{cos\θ}}_{0,z}---\left(10\right)$

For ensureing that emulating signal has good phase accuracy, chooses during interpolation filter it is ensured that its frequency response is in three-dimensional SAR echo signal Spatial Spectrum frequency band range

$\left\{(k_y,k_z)\right|k_y\∈\[k_{c,y}^{3d}-\frac{B_y^{3d}}{2},k_{c,y}^{3d}+\frac{B_y^{3d}}{2}\],k_z\∈\[k_{c,z}^{3d}-\frac{B_z^{3d}}{2},k_{c,z}^{3d}+\frac{B_z^{3d}}{2}\]\}---\left(11\right)$

Within sufficiently flat, and there is outside spectral range Sidelobe；It should be noted that when SAR is operated in band pattern,For constant value；And when SAR is operated in other patterns such as beam bunching mode, slip pack, TopSAR,Value will be with radar x The centre frequency of changes in coordinates, therefore interpolation filter also correspondingly should change with radar x coordinate according to formula (9) and formula (10).