Method and device for imaging by bistatic synthetic aperture radar

Abstract

Range-compressed data are determined by range-compressing echo data, and are set as first data to be decomposed by first decomposition. Starting from n=1, iteration is performed as follows. nth data to be decomposed are up-sampled. nth decomposition is performed on the up-sampled data. Dependency on slant ranges between a reference point and sub-apertures before and after synthesis is determined. nth azimuth-synthesized data are acquired by performing, according to the dependency on the slant ranges, nth azimuth synthesis on data acquired by the nth decomposition. The nth azimuth-synthesized data are set as (n+1)th data to be decomposed by (n+1)th decomposition. The n is increased by 1. A next iteration is performed until the n reaches a positive integer N greater than 1. A focused image is acquired by performing azimuth focusing on the Nth azimuth-synthesized data by BP.

Claims

1. A method for imaging by Bistatic Synthetic Aperture Radar (BiSAR), comprising: determining range-compressed data by range-compressing echo data, and setting the range-compressed data as first data to be decomposed by first decomposition; starting from n=1, performing an iteration of: up-sampling nth data to be decomposed, performing nth decomposition on the up-sampled data, determining dependency on a slant range between a reference point and a sub-aperture before synthesis and a slant range between the reference point and a sub-aperture after synthesis, acquiring nth azimuth-synthesized data by performing, according to the dependency on the slant ranges, nth azimuth synthesis on data acquired by the nth decomposition, and setting the nth azimuth-synthesized data as (n+1)th data to be decomposed by (n+1)th decomposition; increasing the n by 1, and performing a next iteration until the n reaches an N, the N being a positive integer greater than 1; and acquiring a focused image by performing azimuth focusing on the Nth azimuth-synthesized data by Back Projection (BP), wherein the determining dependency on a slant range between a reference point and a sub-aperture before synthesis and a slant range between the reference point and a sub-aperture after synthesis comprises: for BiSAR with a fixed station, determining a delay from the reference point to the sub-aperture before synthesis and a delay from the reference point to the sub-aperture after synthesis according to the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis, a slant range between the reference point and a receiver, a speed of light, and a coordinate of the reference point, and setting the delays as the dependency on the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis; and/or for azimuth invariant BiSAR, determining the delay from the reference point to the sub-aperture before synthesis and the delay from the reference point to the sub-aperture after synthesis according to the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis and the speed of light, and setting the delays as the dependency on the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis.

2. The method according to claim 1, wherein the determining range-compressed data by range-compressing echo data comprises: for echo data acquired by azimuth invariant BiSAR, acquiring the range-compressed data by performing Fourier Transform (FT) on the echo data and performing Inverse FT (IFT) on a product of data acquired by the FT and a frequency-domain matching filter function; and/or for echo data acquired by BiSAR with a fixed station, acquiring the range-compressed data by performing the FT on the echo data and performing the IFT on a product of data acquired by the FT and data acquired by conjugate FT of satellite transmitted data received by synchronized antennae of a receiver on the ground.

3. The method according to claim 1, wherein the up-sampling nth data to be decomposed comprises: performing Fast Fourier Transform (FFT) on the nth data to be decomposed, and up-sampling data acquired by the FFT by zero padding.

4. The method according to claim 1, wherein the performing nth decomposition on the up-sampled data comprises: acquiring data of sub-apertures of a level 1 and more by performing the nth decomposition on the up-sampled data according to a preset nth level of sub-aperture decomposition, and determining a number of sub-apertures in data of sub-apertures of a level.

5. The method according to claim 1, wherein the acquiring nth azimuth-synthesized data by performing, according to the dependency on the slant ranges, nth azimuth synthesis on data acquired by the nth decomposition comprises: acquiring the nth azimuth-synthesized data by selecting, from data of sub-apertures of a level 1 and more acquired by the nth decomposition according to the dependency on the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis, data of sub-apertures to be synthesized, and performing azimuth synthesis on the selected data of sub-apertures to be synthesized.

6. The method according to claim 1, wherein the acquiring a focused image by performing azimuth focusing on the Nth azimuth-synthesized data by BP comprises: acquiring the focused image by BiSAR by focusing the Nth azimuth-synthesized data via multithreaded time-domain BP imaging.

7. A device for imaging by Bistatic Synthetic Aperture Radar (BiSAR), comprising: a processor; and memory storing instructions executable by the processor, wherein the processor is arranged for: determining range-compressed data by range-compressing echo data, and setting the range-compressed data as first data to be decomposed by first decomposition; starting from n=1, performing an iteration of: up-sampling nth data to be decomposed, performing nth decomposition on the up-sampled data, determining dependency on a slant range between a reference point and a sub-aperture before synthesis and a slant range between the reference point and a sub-aperture after synthesis, acquiring nth azimuth-synthesized data by performing, according to the dependency on the slant ranges, nth azimuth synthesis on data acquired by the nth decomposition, and setting the nth azimuth-synthesized data as (n+1)th data to be decomposed by (n+1)th decomposition; increasing the n by 1, and performing a next iteration until the n reaches an N, the N being a positive integer greater than 1; and acquiring a focused image by performing azimuth focusing on the Nth azimuth-synthesized data by Back Projection (BP), wherein the processor is arranged for: for BiSAR with a fixed station, determining a delay from the reference point to the sub-aperture before synthesis and a delay from the reference point to the sub-aperture after synthesis according to the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis, a slant range between the reference point and a receiver, a speed of light, and a coordinate of the reference point, and setting the delays as the dependency on the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis; and/or for azimuth invariant BiSAR, determining the delay from the reference point to the sub-aperture before synthesis and the delay from the reference point to the sub-aperture after synthesis according to the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis and the speed of light, and setting the delays as the dependency on the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis.

8. The device according to claim 7, wherein the processor is arranged for: for echo data acquired by azimuth invariant BiSAR, acquiring the range-compressed data by performing Fourier Transform (FT) on the echo data and performing Inverse FT (IFT) on a product of data acquired by the FT and a frequency-domain matching filter function; and/or for echo data acquired by BiSAR with a fixed station, acquiring the range-compressed data by performing the FT on the echo data and performing the IFT on a product of data acquired by the FT and data acquired by conjugate FT of satellite transmitted data received by synchronized antennae of a receiver on the ground.

9. The device according to claim 7, wherein the processor is arranged for: performing Fast Fourier Transform (FFT) on the nth data to be decomposed, and up-sampling data acquired by the FFT by zero padding.

10. The device according to claim 7, wherein the processor is arranged for: acquiring data of sub-apertures of a level 1 and more by performing the nth decomposition on the up-sampled data according to a preset nth level of sub-aperture decomposition, and determining a number of sub-apertures in data of sub-apertures of a level.

11. The device according to claim 7, wherein the processor is arranged for: acquiring the nth azimuth-synthesized data by selecting, from data of sub-apertures of a level 1 and more acquired by the nth decomposition according to the dependency on the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis, data of sub-apertures to be synthesized, and performing azimuth synthesis on the selected data of sub-apertures to be synthesized.

12. The device according to claim 7, wherein the processor is arranged for: acquiring the focused image by BiSAR by focusing the Nth azimuth-synthesized data via multithreaded time-domain BP imaging.

13. A non-transitory computer-readable storage medium having stored therein instructions that, when executed by a processor, cause the processor to perform a method for imaging by Bistatic Synthetic Aperture Radar (BiSAR), the method comprising: determining range-compressed data by range-compressing echo data, and setting the range-compressed data as first data to be decomposed by first decomposition; starting from n=1, performing an iteration of: up-sampling nth data to be decomposed, performing nth decomposition on the up-sampled data, determining dependency on a slant range between a reference point and a sub-aperture before synthesis and a slant range between the reference point and a sub-aperture after synthesis, acquiring nth azimuth-synthesized data by performing, according to the dependency on the slant ranges, nth azimuth synthesis on data acquired by the nth decomposition, and setting the nth azimuth-synthesized data as (n+1)th data to be decomposed by (n+1)th decomposition; increasing the n by 1, and performing a next iteration until the n reaches an N, the N being a positive integer greater than 1; and acquiring a focused image by performing azimuth focusing on the Nth azimuth-synthesized data by Back Projection (BP), wherein the determining dependency on a slant range between a reference point and a sub-aperture before synthesis and a slant range between the reference point and a sub-aperture after synthesis comprises: for BiSAR with a fixed station, determining a delay from the reference point to the sub-aperture before synthesis and a delay from the reference point to the sub-aperture after synthesis according to the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis, a slant range between the reference point and a receiver, a speed of light, and a coordinate of the reference point, and setting the delays as the dependency on the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis; and/or for azimuth invariant BiSAR, determining the delay from the reference point to the sub-aperture before synthesis and the delay from the reference point to the sub-aperture after synthesis according to the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis and the speed of light, and setting the delays as the dependency on the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a flowchart of a method for imaging by BiSAR according to an embodiment herein.

(2) FIG. 2 is a diagram of determining dependency on a slant range between a reference point and a sub-aperture before synthesis and a slant range between the reference point and a sub-aperture after synthesis in BiSAR with a fixed station.

(3) FIG. 3 is a diagram of determining dependency on a slant range between a reference point and a sub-aperture before synthesis and a slant range between the reference point and a sub-aperture after synthesis in azimuth invariant BiSAR.

(4) FIG. 4 is a diagram of a structure of a device for imaging by BiSAR according to an embodiment herein.

(5) FIG. 5 is a flowchart of imaging by BiSAR according to an embodiment herein.

(6) FIG. 6 is a result of imaging data measured by BiSAR in BiSAR with a fixed station and enlarged views of targets of highlight.

(7) FIG. 7 is a diagram of a result of imaging data simulating azimuth invariant BiSAR.

DETAILED DESCRIPTION

(8) According to embodiments herein, range-compressed data are determined by range-compressing echo data. The range-compressed data are set as first data to be decomposed by first decomposition. N iterations are performed. Starting from n=1, an iteration is performed as follows. nth data to be decomposed are up-sampled. nth decomposition is performed on the up-sampled data. Dependency on a slant range between a reference point and a sub-aperture before synthesis and a slant range between the reference point and a sub-aperture after synthesis is determined. nth azimuth-synthesized data are acquired by performing, according to the dependency on the slant ranges, nth azimuth synthesis on data acquired by the nth decomposition. The nth azimuth-synthesized data are set as (n+1)th data to be decomposed by (n+1)th decomposition. The n is increased by 1, and a next iteration is performed until the n reaches the N. The N is a positive integer greater than 1. Finally, a focused image is acquired by performing azimuth focusing on the Nth azimuth-synthesized data by BP.

(9) As shown in FIG. 1, a flowchart of a method for imaging by BiSAR according to an embodiment herein includes steps as follows.

(10) In step 101, range-compressed data are determined by range-compressing echo data. The range-compressed data are set as first data to be decomposed by first decomposition.

(11) The range-compressed data may be determined by range-compressing the echo data via a matching filter according to a mode of imaging by BiSAR as follows.

(12) For echo data acquired by azimuth invariant BiSAR, the range-compressed data may be acquired by performing Fourier Transform (FT) on the echo data and performing Inverse FT (IFT) on a product of data acquired by the FT and a frequency-domain matching filter function.

(13) For echo data acquired by BiSAR with a fixed station, the range-compressed data may be acquired by performing the FT on the echo data and performing the IFT on a product of data acquired by the FT and data acquired by conjugate FT of satellite transmitted data received by synchronized antennae of a receiver on the ground.

(14) Analysis may be performed respectively for azimuth invariant BiSAR and BiSAR with a fixed station, as follows.

(15) For echo data acquired by azimuth invariant BiSAR, range compression may be performed by constructing a frequency-domain matching filter. The spectrum matching filter may be expressed by a formula (1) as follows.

(16) $\begin{array}{cc}\begin{array}{c}{S}_c\left(t,\right)={}_t^{-1}\left\{{}_t\left\{S\left(t,\right)\right\}.Math.\exp \left(j\frac{f^2}{K_r}\right)\right\}\\ =p_r\left[t-\frac{L_R\left(;\stackrel{.fwdarw.}{r}\right)+L_T\left(;\stackrel{.fwdarw.}{r}\right)}{c}\right]\exp \left\{-j4f_{0}L\left(;\stackrel{.fwdarw.}{r}\right)/c\right\}\end{array}& \left(1\right)\end{array}$

(17) may indicate FT. { } may indicate IFT. S.sub.c(t,) may indicate a range-compressed time-domain signal. S(t,) may indicate an acquired radar echo signal. t may indicate a range time. may indicate an azimuth time. f may indicate a range frequency. K.sub.r may indicate a range chirp rate.

(18) $p_r\left[t-\frac{L_R\left(;\stackrel{.fwdarw.}{r}\right)+L_T\left(;\stackrel{.fwdarw.}{r}\right)}{c}\right]$
may indicate a range-compressed range envelope. L.sub.R may indicate a distance from an imaging point {right arrow over (r)} to a receiver. L.sub.T may indicate a distance from the imaging point {right arrow over (r)} to a transmitter. c may indicate the speed of light. f.sub.0 may indicate a carrier frequency of a transmitted signal. L(;{right arrow over (r)}) may indicate a sum of the distance from the imaging point to the receiver and the distance from the imaging point to the transmitter.

(19) For echo data acquired by BiSAR with a fixed station, range compression may be performed by constructing a matching filter according to a pulse signal transmitted by a satellite and received by a direct-wave receiving antenna. The matching filter may be expressed by a formula (2) as follows.

(20) $\begin{array}{cc}\begin{array}{c}{S}_c\left(t,\right)={}_t^{-1}\left\{{}_t\left\{S\left(t,\right)\right\}.Math.{}_t\left\{S_D\left(t,\right)\right\}\right\}\\ =p_r\left[t-\frac{L_R\left(;\stackrel{.fwdarw.}{r}\right)+L_T\left(\stackrel{.fwdarw.}{r}\right)-L_D\left(;{\stackrel{.fwdarw.}{r}}_D\right)}{c}\right]\exp \left\{-j4f_{0}L\left(;\stackrel{.fwdarw.}{r}\right)/c\right\}\end{array}& \left(2\right)\end{array}$

(21) { } may indicate FT. { } may indicate IFT. S.sub.c (t,) may indicate the range-compressed time-domain signal, S(t,) may indicate the acquired radar echo signal. S.sub.D (t,) may indicate the pulse signal transmitted by the satellite and received by the direct-wave receiving antenna. t may indicate the range time. may indicate the azimuth time.

(22) $p_r\left[t-\frac{L_R\left(;\stackrel{.fwdarw.}{r}\right)+L_T\left(;\stackrel{.fwdarw.}{r}\right)}{c}\right]$
may indicate the range-compressed range envelope. L.sub.R may indicate the distance from the imaging point {right arrow over (r)} to the receiver. L.sub.T may indicate the distance from the imaging point {right arrow over (r)} to the transmitter. {right arrow over (r)}.sub.D may indicate a location vector of the direct-wave receiving antenna. L.sub.D(;{right arrow over (r)}.sub.D) may indicate a distance from the direct-wave receiving antenna to the satellite when a satellite signal is transmitted. c may indicate the speed of light. f.sub.0 may indicate the carrier frequency of the transmitted signal. L(;{right arrow over (r)}) may indicate the sum of the distance from the imaging point to the receiver and the distance from the imaging point to the transmitter.

(23) A target in a scene may correspond to a large echo width. After range compression has been performed on the echo data via the matching filter, a range location of a target imaging point may be identified.

(24) In step 102, starting from n=1, an iteration is performed as follows. nth data to be decomposed are up-sampled. nth decomposition is performed on the up-sampled data. Dependency on a slant range between a reference point and a sub-aperture before synthesis and a slant range between the reference point and a sub-aperture after synthesis is determined. nth azimuth-synthesized data are acquired by performing, according to the dependency on the slant ranges, nth azimuth synthesis on data acquired by the nth decomposition. The nth azimuth-synthesized data are set as (n+1)th data to be decomposed by (n+1)th decomposition. The n is increased by 1, and a next iteration is performed until the n reaches an N. The N is a positive integer greater than 1.

(25) The nth data to be decomposed may be up-sampled as follows.

(26) FFT may be performed on the nth data to be decomposed. Data acquired by the FFT may be up-sampled by zero padding.

(27) The nth data to be decomposed may be transformed (by FFT) into a range frequency domain. Data acquired by the FFT may be up-sampled by zero padding to increase a sampling rate.

(28) The nth decomposition may be performed on the up-sampled data as follows.

(29) Data of sub-apertures of a level 1 and more may be acquired by performing the nth decomposition on the up-sampled data according to a preset nth level of sub-aperture decomposition. A number of sub-apertures in data of sub-apertures of a level may be determined.

(30) A level of sub-aperture decomposition may be an odd number or an even number. The level of sub-aperture decomposition may be an even number. The number of decompositions may be 4.

(31) The preset level of sub-aperture decomposition may include, but is not limited to, an even number. The number of decompositions may include, but is not limited to, 4.

(32) The dependency on the slant range between the reference point and the sub-aperture of a level may be determined according to a mode of imaging by BiSAR and whether a coordinate of the reference point is required, as follows.

(33) For BiSAR with a fixed station, the coordinate(s) of the reference point may be required. A delay from the reference point to the sub-aperture before synthesis and a delay from the reference point to the sub-aperture after synthesis may be determined according to the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis, a slant range between the reference point and a receiver, a speed of light, and a coordinate of the reference point. The delays may be set as the dependency on the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis.

(34) For azimuth invariant BiSAR, no coordinate of the reference point may be required. The delay from the reference point to the sub-aperture before synthesis and the delay from the reference point to the sub-aperture after synthesis may be determined according to the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis and the speed of light. The delays may be set as the dependency on the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis.

(35) The location of the radar may be determined according to the sub-apertures before and after synthesis. The sub-aperture before synthesis and the sub-aperture after synthesis may indicate different locations of the radar. The slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis may indicate slant ranges from the same reference point to different locations of the radar.

(36) The dependency on the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis may be determined for BiSAR with a fixed station, as shown in FIG. 2, and for azimuth invariant BiSAR, as shown in FIG. 3, respectively, as follows.

(37) As shown in FIG. 2, for echo data acquired by BiSAR with a fixed station, a focal plane may be the ground. A size of a scene on the ground may be WL, with N reference points. The W may indicate a width. The L may indicate a length.

(38) A preset first level of sub-aperture decomposition may be 2. A coordinate of an ith reference point may be S.sub.i(x.sub.i,y.sub.i,z.sub.i). {right arrow over (A)}.sub.1 and {right arrow over (A)}.sub.2 may indicate two sub-apertures to be synthesized. {right arrow over (A)}.sub.0 may indicate a location of a new aperture after synthesis. The {right arrow over (A)}.sub.0 may be selected as a point between the {right arrow over (A)}.sub.1 and the {right arrow over (A)}.sub.2.

(39) A slant range L.sub.iR from the ith reference point S.sub.i to a platform bearing a receiver may be determined. A slant range L.sub.itm from the ith reference point S.sub.i to the first or second sub-aperture before synthesis may be determined. m=1, 2.

(40) A delay from the ith reference point S.sub.i to a sub-aperture before synthesis and from the ith reference point S.sub.i to the receiver may be determined according to the slant range from the ith reference point S.sub.i to the first or second sub-aperture before synthesis and the slant range from the ith reference point S.sub.i to the receiver, as shown by a formula (3).

(41) $\begin{array}{cc}{t}_{\mathrm{im}}=\frac{L_{\mathrm{itm}}+L_{\mathrm{iR}}}{c},m=1,2& \left(3\right)\end{array}$

(42) The t.sub.im may indicate a delay from the ith reference point S.sub.i to a sub-aperture {right arrow over (A)}.sub.m before synthesis and to the receiver. The L.sub.itm may indicate a slant range from the ith reference point S.sub.i to the mth sub-aperture before synthesis. The L.sub.iR may indicate the slant range from the ith reference point S.sub.i to the receiver. The c may indicate the speed of light.

(43) A delay from the ith reference point S.sub.i to the new aperture {right arrow over (A)}.sub.0 after synthesis and to the receiver may be determined by a formula (4).

(44) $\begin{array}{cc}{t}_i=\frac{L_{\mathrm{it}}+L_{\mathrm{iR}}}{c}& \left(4\right)\end{array}$

(45) The t.sub.i may indicate the delay from the ith reference point S.sub.i to the new aperture {right arrow over (A)}.sub.0 after synthesis and to the receiver. The L.sub.it may indicate the slant range from the ith reference point S.sub.i to the new aperture {right arrow over (A)}.sub.0 after synthesis. The L.sub.iR may indicate the slant range from the ith reference point S.sub.i to the receiver. The c may indicate the speed of light.

(46) For a pair of corresponding delays {t.sub.i,t.sub.m}, the delay from the ith reference point S.sub.i to the sub-aperture before synthesis and the delay from the ith reference point to the sub-aperture after synthesis, namely, the dependency on the slant ranges, may be constructed using an interpolating kernel function to indicate projection between an echo delay of the new aperture {right arrow over (A)}.sub.0 after synthesis and an echo delay of a sub-aperture {right arrow over (A)}.sub.m before synthesis, as shown by a formula (5).
I.sub.m(t.sub.i)=t.sub.im,i=1,2, . . . n.sub.r;m=1,2 (5)

(47) The I.sub.m( ) may indicate an interpolating kernel function.

(48) The dependency on the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis may be acquired by interpolation.

(49) There may be m=2 sub-apertures to be synthesized. The value of the m in the formulae (3) and (5) may be adjusted according to a number of sub-apertures to be synthesized. The number of sub-apertures to be synthesized may be determined according to a coefficient of sub-aperture synthesis.

(50) As shown in FIG. 3, for echo data acquired by azimuth invariant BiSAR, A preset first level of sub-aperture decomposition may be 2. {right arrow over (B)}.sub.1 and {right arrow over (B)}.sub.2 may indicate locations of two sub-apertures to be synthesized on a trajectory of a transmitter. {right arrow over (A)}.sub.01 may indicate a location of a new aperture after synthesis. The {right arrow over (A)}.sub.01 may be selected as a point between the {right arrow over (B)}.sub.1 and the {right arrow over (B)}.sub.2 on the trajectory of the transmitter. {right arrow over (A)}.sub.01(x.sub.1,y.sub.1,z.sub.1) may indicate coordinates of the new aperture {right arrow over (A)}.sub.01 after synthesis.

(51) {right arrow over (C)}.sub.1 and {right arrow over (C)}.sub.2 may indicate locations of two sub-apertures to be synthesized on a trajectory of a receiver. {right arrow over (A)}.sub.02 may indicate a location of a new aperture after synthesis. The {right arrow over (A)}.sub.02 may be selected as a point between the {right arrow over (C)}.sub.1 and the {right arrow over (C)}.sub.2 on the trajectory of the receiver. {right arrow over (A)}.sub.02(x.sub.2,y.sub.2,z.sub.2) may indicate coordinates of the new aperture {right arrow over (A)}.sub.02 after synthesis.

(52) A slant range from an ith reference point S.sub.i to the synthesized sub-aperture {right arrow over (A)}.sub.01 on the trajectory of the transmitter may be expressed by a formula (6).
R.sub.it={square root over ((x.sub.ix.sub.1).sup.2+(y.sub.iy.sub.1).sup.2+(z.sub.iz.sub.1).sup.2)} (6)

(53) A slant range from the ith reference point S.sub.i to the synthesized sub-aperture {right arrow over (A)}.sub.02 on the trajectory of the receiver may be expressed by a formula (7).
R.sub.ir={square root over ((x.sub.ix.sub.2).sup.2+(y.sub.iy.sub.2).sup.2+(z.sub.iz.sub.2).sup.2)} (7)

(54) Since y.sub.1=y.sub.2=y, z.sub.1=z.sub.2=z, a sum of the slant range from the ith reference point S.sub.i to the synthesized sub-aperture {right arrow over (A)}.sub.01 and the slant range from the ith reference point to the synthesized sub-aperture {right arrow over (A)}.sub.02 may be expressed by a formula (8).
L.sub.i={square root over ((x.sub.ix.sub.1).sup.2+(y.sub.iy).sup.2+(z.sub.iz).sup.2)}+{square root over ((x.sub.ix.sub.2).sup.2+(y.sub.iy).sup.2+(z.sub.iz).sup.2)} (8)

(55) A slant range from the ith reference point S.sub.i to a sub-aperture before synthesis on the trajectory of the transmitter or the receiver may be expressed by a formula (9).
L.sub.im={square root over ((x.sub.ix.sub.1m).sup.2+(y.sub.iy.sub.m).sup.2+(z.sub.iz).sup.2)}+{square root over ((x.sub.ix.sub.2m).sup.2+(y.sub.iy.sub.m).sup.2+(z.sub.iz).sup.2)}m=1,2 (9)

(56) Since x.sub.1=x.sub.1m, x.sub.2=x.sub.2m, a delay for a signal to transmit between sub-apertures to be synthesized may be acquired according to the transmission slant range of the signal in the formula (9), as shown by a formula (10).

(57) $\begin{array}{cc}{t}_{\mathrm{jm}}=\frac{L_{\mathrm{im}}}{c},m=1,2& \left(10\right)\end{array}$

(58) Since x.sub.1=x.sub.1m, x.sub.2=x.sub.2m, a delay for a signal to transmit between sub-apertures after synthesis may be acquired according to the transmission slant range of the signal in the formula (8), as shown by a formula (11).

(59) $\begin{array}{cc}{t}_j=\frac{L_i}{c}{c}_1={\left(y_i-y_1\right)}^2+{\left(z_i-z_1\right)}^2.c_2={\left(y_2-y_i\right)}^2+{\left(z_i-z_2\right)}^2.c_3=x_1-x_2.& \left(11\right)\end{array}$
A relationship between a range time t.sub.j and a range location x.sub.i of the ith reference point S.sub.i may be acquired according to the formulae (8) through (11), as shown by a formula (12).

(60) $\begin{array}{cc}{x}_i\left(t_j\right)=\frac{-b+\sqrt{b^2-a.Math.d}}{2a}a=c_3^2-{\left(c.Math.t_j\right)}^{2}b=c_3\left[c_1-c_2+a\right]d=c_1^2+c_2^2+a^2-2c_1\left(c_2-a\right)-2c_2\left[c_3^2+{\left(c.Math.t_j\right)}^2\right]& \left(12\right)\end{array}$

(61) Integrating (12) into (10) and (11) may give a relationship between the delay from the ith reference point S.sub.i to the sub-aperture before synthesis and the delay from the ith reference point to the sub-aperture after synthesis. Namely, an analytical delay t.sub.jm(t.sub.j) from a reference point to the sub-aperture before and/or after synthesis may be expressed by a formula (13).
t.sub.m(t.sub.j)=t.sub.jm,j=1,2, . . . n.sub.r;m=1,2 (13)

(62) The analytical delay t.sub.jm(t.sub.j) may be referred to as the dependency on the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis.

(63) The dependency on the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis may be acquired using an analytical expression.

(64) There may be m=2 sub-apertures to be synthesized. The value of the m in the formulae (9), (10), and (13) may be adjusted according to a number of sub-apertures to be synthesized. The number of sub-apertures to be synthesized may be determined according to a coefficient of sub-aperture synthesis.

(65) The nth azimuth-synthesized data may be acquired by performing, according to the dependency on the slant ranges, the nth azimuth synthesis on the data acquired by the nth decomposition as follows.

(66) The nth azimuth-synthesized data may be acquired by selecting, from data of sub-apertures of a level 1 and more acquired by the nth decomposition according to the dependency on the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis, data of sub-apertures to be synthesized, and performing azimuth synthesis on the selected data of sub-apertures to be synthesized.

(67) The dependency on the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis may be determined by determining dependency of the range location of the reference point on the range time. There is no change to a length of range data.

(68) Azimuth synthesis may be implemented respectively for BiSAR with a fixed station and for azimuth invariant BiSAR as follows.

(69) For BiSAR with a fixed station, FFT may be performed on the range-compressed data acquired In step 101 by range-compressing the echo data. Data acquired by the FFT may be up-sampled by zero padding. A sub-aperture to be synthesized may be selected according to a coefficient of sub-aperture synthesis same as a level of sub-aperture decomposition. Data from the synthesized new aperture {right arrow over (A)}.sub.0 to the sub-aperture {right arrow over (A)}.sub.1 before synthesis may be acquired according to the dependency I.sub.m(t) on the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis, as shown by a formula (14).
S.sub.c(I.sub.1(t),)exp{j2f.sub.0(I.sub.1(t)t)} (14)

(70) Data from the new aperture after synthesis to the sub-aperture {right arrow over (A)}.sub.0 before synthesis may be expressed by a formula (15).
S.sub.c(I.sub.2(t),)exp{j2f.sub.0(I.sub.2(t)t)} (15)

(71) The azimuth-synthesized data, i.e., the data of the new aperture {right arrow over (A)}.sub.0 after synthesis, may be acquired by coherent accumulation of the data of the two apertures {right arrow over (A)}.sub.1 and {right arrow over (A)}.sub.2 before synthesis. That is, the azimuth-synthesized data may be acquired by azimuth-synthesizing the data of the sub-apertures to be synthesized, by coherently accumulating the formulae (14) and (15), as shown by formula (16).

(72) 0$\begin{array}{cc}S1\left(t,\right)=\underset{i=1}{\overset{2}{.Math.}}{S}_c\left(I_m\left(t\right),\right)\exp \left\{-j2f_0\left(I_m\left(t\right)-t\right)\right\}& \left(16\right)\end{array}$

(73) The S1(t,) may indicate a signal of the azimuth-synthesized data. The f.sub.0 may indicate a carrier frequency.

(74) A preset first level of sub-aperture decomposition may be 2. Data of sub-apertures of two levels may be acquired by performing the first decomposition on the data acquired by up-sampling the range-compressed data. A number of sub-apertures in data of sub-apertures of a level may be determined. The coefficient of sub-aperture synthesis may be identical to the level of sub-aperture decomposition. One sub-aperture may be selected respectively from the data of sub-apertures of the two levels. A new aperture may be acquired by synthesizing the selected sub-apertures. The azimuth-synthesized data may be acquired by azimuth-synthesizing data of the selected sub-apertures according to the formula (16) and the determined dependency on the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis.

(75) For azimuth invariant BiSAR, FFT may be performed on the range-compressed data acquired In step 101 by range-compressing the echo data. Data acquired by the FFT may be up-sampled by zero padding. A sub-aperture to be synthesized may be selected according to the coefficient of sub-aperture synthesis and the level of sub-aperture decomposition. Data from the synthesized new aperture {right arrow over (A)}.sub.01 on the trajectory of the transmitter to the sub-aperture {right arrow over (B)}.sub.1 before synthesis may be acquired according to the dependency I.sub.m(t) on the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis, as shown by a formula (17).
S.sub.c(t.sub.1(t),)exp{j2f.sub.0(t.sub.1(t)t)} (17)

(76) Data from the new aperture {right arrow over (A)}.sub.01 after synthesis on the trajectory of the transmitter to the sub-aperture {right arrow over (B)}.sub.2 before synthesis may be expressed by a formula (18).
S.sub.c(t.sub.2(t),)exp{j2f.sub.0(t.sub.2(t)t)} (18)

(77) The azimuth-synthesized data, i.e., the data of the new aperture {right arrow over (A)}.sub.01 after synthesis, may be acquired by coherent accumulation of the data of the two apertures {right arrow over (B)}.sub.1 and {right arrow over (B)}.sub.2 before synthesis. That is, the azimuth-synthesized data may be acquired by azimuth-synthesizing the data of the sub-apertures to be synthesized, by coherently accumulating the formulae (17) and (18), as shown by a formula (19).

(78) $\begin{array}{cc}S2\left(t,\right)=\underset{i=1}{\overset{2}{.Math.}}{S}_c\left(t_m\left(t\right),\right)\exp \left\{-j2f_0\left(t_m\left(t\right)-t\right)\right\}& \left(19\right)\end{array}$

(79) The S.sub.2(t,) may indicate a signal of the azimuth-synthesized data. The f.sub.0 may indicate the carrier frequency.

(80) Azimuth-synthesized data may be acquired by azimuth-synthesizing the data of the sub-apertures to be synthesized on the trajectory of the receiver using a formula same as that used to acquire the azimuth-synthesized data by azimuth-synthesizing the data of the sub-apertures to be synthesized on the trajectory of the transmitter, which will not be repeated here.

(81) A preset first level of sub-aperture decomposition may be 2. Data of sub-apertures of two levels may be acquired by performing the first decomposition on the data acquired by up-sampling the range-compressed data. A number of sub-apertures in data of sub-apertures of a level may be determined. The coefficient of sub-aperture synthesis may be identical to the level of sub-aperture decomposition. One sub-aperture may be selected respectively from the data of sub-apertures of the two levels. A new aperture may be acquired by synthesizing the selected sub-apertures. The azimuth-synthesized data may be acquired by azimuth-synthesizing data of the selected sub-apertures according to the formula (19) and the determined dependency on the slant range between the reference point and a sub-aperture of a level.

(82) Described in the step are but one decomposition and one synthesis. In general there may be more decomposition. Additional decomposition and synthesis may be done likewise, and thus will not be elaborated.

(83) In step 103, a focused image is acquired by performing azimuth focusing on the Nth azimuth-synthesized data by BP.

(84) The focused image may be acquired by performing azimuth focusing on the Nth azimuth-synthesized data by BP as follows. The focused image may be acquired by BiSAR by focusing the Nth azimuth-synthesized data via multithreaded time-domain BP imaging.

(85) With conventional BP imaging, a focused image may be implemented by BiSAR by range-compressing echo data and performing azimuth focusing on the range-compressed data, which may be time consuming. With an embodiment herein, first data to be decomposed may be acquired by range-compressing echo data. Then, N iterations of decomposition and azimuth synthesis may be performed. The Nth azimuth-synthesized data may be acquired by azimuth synthesizing data of sub-apertures of a level acquired by the Nth decomposition, and azimuth focusing may be performed on the Nth azimuth-synthesized data, such that fast focusing may be implemented to acquire a BiSAR image.

(86) As shown in FIG. 4, to implement the method according to an embodiment herein, a device for imaging by BiSAR according to an embodiment herein includes a range-compressing module 41, an azimuth-synthesizing module 42, and an azimuth-focusing module 43.

(87) The range-compressing module 41 is arranged for: determining range-compressed data by range-compressing echo data, and setting the range-compressed data as first data to be decomposed by first decomposition.

(88) The azimuth-synthesizing module 42 is arranged for: starting from n=1, performing an iteration of: up-sampling nth data to be decomposed, performing nth decomposition on the up-sampled data, determining dependency on a slant range between a reference point and a sub-aperture before synthesis and a slant range between the reference point and a sub-aperture after synthesis, acquiring nth azimuth-synthesized data by performing, according to the dependency on the slant ranges, nth azimuth synthesis on data acquired by the nth decomposition, and setting the nth azimuth-synthesized data as (n+1)th data to be decomposed by (n+1)th decomposition; increasing the n by 1, and performing a next iteration until the n reaches an N.

(89) The azimuth-focusing module 43 is arranged for: acquiring a focused image by performing azimuth focusing on the Nth azimuth-synthesized data by BP.

(90) The range-compressing module 41 may be arranged for: for echo data acquired by azimuth invariant BiSAR, acquiring the range-compressed data by performing FT on the echo data and performing IFT on a product of data acquired by the FT and a frequency-domain matching filter function. The range-compressing module may be arranged for: for echo data acquired by BiSAR with a fixed station, acquiring the range-compressed data by performing the FT on the echo data and performing the IFT on a product of data acquired by the FT and data acquired by conjugate FT of satellite transmitted data received by synchronized antennae of a receiver on the ground.

(91) The azimuth-synthesizing module 42 may be arranged for: performing FFT on the nth data to be decomposed, and up-sampling data acquired by the FFT by zero padding. The azimuth-synthesizing module may be arranged for: acquiring data of sub-apertures of a level 1 and more by performing the nth decomposition on the up-sampled data according to a preset nth level of sub-aperture decomposition, and determining a number of sub-apertures in data of sub-apertures of a level.

(92) The preset level of sub-aperture decomposition may include, but is not limited to, an even number. The number of decompositions may include, but is not limited to, 4.

(93) The azimuth-synthesizing module 42 may be arranged for: for BiSAR with a fixed station, determining a delay from the reference point to the sub-aperture before synthesis and a delay from the reference point to the sub-aperture after synthesis according to the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis, a slant range between the reference point and a receiver, a speed of light, and a coordinate of the reference point, and setting the delays as the dependency on the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis. The azimuth-synthesizing module may be arranged for: for azimuth invariant BiSAR, determining the delay from the reference point to the sub-aperture before synthesis and the delay from the reference point to the sub-aperture after synthesis according to the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis and the speed of light, and setting the delays as the dependency on the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis.

(94) The location of the radar may be determined according to the sub-apertures before and after synthesis. The sub-aperture before synthesis and the sub-aperture after synthesis may indicate different locations of the radar. The slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis may indicate slant ranges from the same reference point to different locations of the radar.

(95) The azimuth-synthesizing module 42 may be arranged for: acquiring the nth azimuth-synthesized data by selecting, from data of sub-apertures of a level 1 and more acquired by the nth decomposition according to the dependency on the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis, data of sub-apertures to be synthesized, and performing azimuth synthesis on the selected data of sub-apertures to be synthesized.

(96) The azimuth-focusing module 43 may be arranged for: acquiring the focused image by BiSAR by focusing the Nth azimuth-synthesized data via multithreaded time-domain BP imaging.

(97) Each of the range-compressing module 41, the azimuth-synthesizing module 42, and the azimuth-focusing module 43 may be implemented by at least one of a Central Processing Unit (CPU), a Micro Processing Unit (MPU), a Digital Signal Processor (DSP), a FieldProgrammable Gate Array (FPGA), etc., in the device for imaging by BiSAR.

(98) Those skilled in the art may understand that all or part of the steps of the method may be completed by instructing a related hardware through a program. The program may be stored in a transitory or non-transitory computer-readable storage medium. The computer-readable storage medium may be Read-Only Memory (ROM), a magnetic disk, a CD, and/or the like. All or part of the steps in an aforementioned embodiment may be implemented using one or more Integrated Circuits. A unit or module in an aforementioned embodiment may be implemented in form of hardware or a software functional module. The present disclosure is not limited to any specific combination of hardware and software.

(99) According to an embodiment herein, a device for imaging by BiSAR includes a processor and memory storing instructions executable by the processor for performing the method for imaging by BiSAR.

(100) According to an embodiment herein, a non-transitory computer-readable storage medium has stored therein instructions that, when executed by a processor, cause the processor to perform the method for imaging by BiSAR.

(101) The present disclosure is further elaborated below with reference to embodiments.

(102) As shown in FIG. 5, a flowchart of imaging by BiSAR according to an embodiment herein may include steps as follows.

(103) In step 1, range-compressed data may be determined by range-compressing echo data via a matching filter corresponding to a mode of imaging by BiSAR. The range-compressed data may be set as first data to be decomposed by first decomposition.

(104) In step 2, it may be determined whether a coordinate of a reference point is required according to the mode of imaging by BiSAR. The flow may go to step 3 if the coordinate of the reference point is required. Otherwise, the flow may go to step 4.

(105) In step 3, for BiSAR with a fixed station, the coordinate of the reference point may be set. Data of sub-apertures of a level 1 and more may be acquired by decomposing the up-sampled nth data to be decomposed according to a preset nth level of sub-aperture decomposition. A number of sub-apertures in data of sub-apertures of a level may be determined. Sub-apertures to be synthesized may be selected respectively from the decomposed data of sub-apertures of the level 1 and more according to a coefficient of sub-aperture synthesis same as a level of sub-aperture decomposition. A location of a synthesized new aperture may be determined according to locations of the sub-apertures to be synthesized. Dependency on a slant range between the reference point and a sub-aperture before synthesis and a slant range between the reference point and a sub-aperture after synthesis may be acquired by range interpolation. The flow may then go to step 5.

(106) In step 4, for azimuth invariant BiSAR, the data of sub-apertures of the level 1 and more may be acquired by decomposing the up-sampled nth data to be decomposed according to the preset nth level of sub-aperture decomposition. The number of sub-apertures in the data of sub-apertures of a level may be determined. The sub-apertures to be synthesized may be selected respectively from the decomposed data of sub-apertures of the level 1 and more according to the coefficient of sub-aperture synthesis same as the level of sub-aperture decomposition. The location of the synthesized new aperture may be determined according to the locations of the sub-apertures to be synthesized. The dependency on the slant range between the reference point and the sub-aperture before synthesis and the slant range between the reference point and the sub-aperture after synthesis may be acquired by range projection. The flow may then go to step 5.

(107) In step 5, FFT may be performed on the nth data to be decomposed. Data acquired by the FFT may be up-sampled by zero padding.

(108) In step 6, the nth azimuth-synthesized data may be acquired by azimuth synthesizing data acquired by the nth decomposition according to the dependency on the slant ranges determined in step 3 or 4. The nth azimuth-synthesized data may be set as the (n+1)th data to be decomposed by the (n+1)th decomposition.

(109) In step 7, it may be determined whether sub-aperture decomposition has ended. That is, it may be determined whether the n is equal to the N. The N may be a preset number of decompositions. The flow may go to step 8 if the sub-aperture decomposition has ended. Otherwise, the flow may go to step 3 or 4.

(110) In step 8, an accurate focused image may be acquired by BiSAR by performing azimuth focusing on the Nth azimuth-synthesized data by BP.

(111) FIG. 6 is a diagram of a focusing result in imaging data measured by spaceborne-ground BiSAR with a fixed station. The diagram includes views a, b, and c. Enlarged views of typical areas A and B in view a are displayed. The area A may include a playground and vegetation. The area B may include buildings. It may be seen that the imaging by BiSAR may render good focusing.

(112) FIG. 7 is a diagram of a focusing result in imaging data simulating azimuth invariant BiSAR. The diagram includes views e and f. The view e shows an image acquired by focusing with a conventional BP algorithm. The view f shows an image acquired by focusing with the present disclosure. It may be seen that the view f may render fair focusing comparable to that rendered by the view e.

(113) What described are merely embodiments of the present disclosure, and are not intended to limit the scope of the present disclosure. Any modification, equivalent replacement, improvement, and/or the like made within the spirit and principle of the present disclosure should be included in the scope of the present disclosure.