CA2083906A1 - Phase difference autofocus - Google Patents
Phase difference autofocusInfo
- Publication number
- CA2083906A1 CA2083906A1 CA002083906A CA2083906A CA2083906A1 CA 2083906 A1 CA2083906 A1 CA 2083906A1 CA 002083906 A CA002083906 A CA 002083906A CA 2083906 A CA2083906 A CA 2083906A CA 2083906 A1 CA2083906 A1 CA 2083906A1
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Links
- 238000001228 spectrum Methods 0.000 claims abstract description 65
- 238000000034 method Methods 0.000 claims abstract description 63
- 238000005314 correlation function Methods 0.000 claims abstract description 23
- 230000008569 process Effects 0.000 claims description 6
- 230000004044 response Effects 0.000 claims description 3
- 230000001427 coherent effect Effects 0.000 description 4
- 238000001514 detection method Methods 0.000 description 4
- 230000010354 integration Effects 0.000 description 3
- 101150034533 ATIC gene Proteins 0.000 description 2
- 230000009467 reduction Effects 0.000 description 2
- FBOUIAKEJMZPQG-AWNIVKPZSA-N (1E)-1-(2,4-dichlorophenyl)-4,4-dimethyl-2-(1,2,4-triazol-1-yl)pent-1-en-3-ol Chemical compound C1=NC=NN1/C(C(O)C(C)(C)C)=C/C1=CC=C(Cl)C=C1Cl FBOUIAKEJMZPQG-AWNIVKPZSA-N 0.000 description 1
- 101100204393 Arabidopsis thaliana SUMO2 gene Proteins 0.000 description 1
- 101100311460 Schizosaccharomyces pombe (strain 972 / ATCC 24843) sum2 gene Proteins 0.000 description 1
- 238000003491 array Methods 0.000 description 1
- 101150072047 nei1 gene Proteins 0.000 description 1
- 101150008002 nei2 gene Proteins 0.000 description 1
- 230000010363 phase shift Effects 0.000 description 1
Classifications
-
- 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
-
- 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
- G01S13/9004—SAR image acquisition techniques
- G01S13/9011—SAR image acquisition techniques with frequency domain processing of the SAR signals in azimuth
-
- 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
- G01S13/9004—SAR image acquisition techniques
- G01S13/9019—Auto-focussing of the SAR signals
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- Engineering & Computer Science (AREA)
- Remote Sensing (AREA)
- Radar, Positioning & Navigation (AREA)
- Physics & Mathematics (AREA)
- Electromagnetism (AREA)
- Computer Networks & Wireless Communication (AREA)
- General Physics & Mathematics (AREA)
- Signal Processing (AREA)
- Radar Systems Or Details Thereof (AREA)
Abstract
FAST PHASE DIFFERENCE AUTOFOCUS
ABSTRACT
A phase difference autofocus method that only requires one FFT for estimating a phase error in the entire synthetic array radar data The phase difference autofocus method of the present invention automatically and efficiently estimates phase errors from radar signals, allowing a well focused SAR image to be produced. The present method comprises the following steps. First, each range bin is divided into two subar-rays. Next, the two subarrays are complex-conjugate multiplied together to produce a cross spectrum of the two submaps produced by the subarrays. Then, the phases of each cross spectrum are aligned with an accumulated sum of the cross spectrums from previous processed range bins. The phase aligned cross spectrum is then added to the accumulated cross spectrum sum. All range bins are processed to get a final cross spectrum sum. Next, a single FFT is performed on the final cross spectrum sum to produce the cross correlation function. Then, the cross correlation function is magni-tude-detected. Since the location of the peak of the cross correlation function is propor-tional to the phase error, a phase error estimate is obtained. Finally, the phase error correction signal is produced for the entire synthetic array radar data. Since only one FFT is performed during autofocus processing, the method is relatively fast.
ABSTRACT
A phase difference autofocus method that only requires one FFT for estimating a phase error in the entire synthetic array radar data The phase difference autofocus method of the present invention automatically and efficiently estimates phase errors from radar signals, allowing a well focused SAR image to be produced. The present method comprises the following steps. First, each range bin is divided into two subar-rays. Next, the two subarrays are complex-conjugate multiplied together to produce a cross spectrum of the two submaps produced by the subarrays. Then, the phases of each cross spectrum are aligned with an accumulated sum of the cross spectrums from previous processed range bins. The phase aligned cross spectrum is then added to the accumulated cross spectrum sum. All range bins are processed to get a final cross spectrum sum. Next, a single FFT is performed on the final cross spectrum sum to produce the cross correlation function. Then, the cross correlation function is magni-tude-detected. Since the location of the peak of the cross correlation function is propor-tional to the phase error, a phase error estimate is obtained. Finally, the phase error correction signal is produced for the entire synthetic array radar data. Since only one FFT is performed during autofocus processing, the method is relatively fast.
Description
FAST PHAS~: DIFFERENCE AUTOFOCUS
BACKGROIJND
The present invention relates to synthetic array radar (SAR) signal processing, and more paTticularly, to a phase difference autofocus method for use in such SAR
signal processing.
Many real-time SAR radar products require autofocus methods. In an existing 5 phase difference method developed by the assignee of the present invention, an ~
must be done on many range bin of the image. This method is disclosed in U.S. Patent No. 4,999,635, for "Phase ~ifference Auto~ocusing for Synthetic Aperture Radar Irnaging," assigned to the assignee of the present invention. One disadvantage of this method is the large number of FFTs required to implement it.
By way of introduction, in the basic phase difference method described in the 4,999,635 patent, the relative drift between two subimages is estimated without actually forming the subimages. Subarrays aIe simply mixed and an ~1 filter banlc is formed from a resulting produc~ The FFI filters are then detected to form a phase difference autofocus functionaL The drift ~xy is obtained by finding the location of the 15 peak in the autofocus functional. In order to reduce a staoastical noise in estimating the underlying phase errors, this process of forrning the autofocus functional is repeated over many range bins. The drift ~xy is estimated from the autofocus functional that is integrated over range bins.
The prior art phase difference autofocus method can be summanæd in the 20 following steps. A full array from each range bin is divided into two subarrays X, Y.
Then, the two subarrays are complex-conjugate multiplied together to produce a cross spectrum of the two su~m~ps produced by the subarrays Next, after amplitude weights have been applied, an FPT is performed on the cross spec~um !o produce the complex cross correlation function. One FFT is performed on the subarray complexconjugate product during each lange bin processing. If M denotes the length of the S subarrays, then each range bin process results in M~log2(M) cornplex multiplies. For simplicity-assume an M point ~ is performed. Then, the cross correlation furrction is magnitude-detected. The magnitude-detected cross c~relation function is th~on sum-med across range bins to to produce a summed cross colrelation function. Next, the location, ~xy, of the peak of the summed cross correlation function, which is propor-10 tional to the residual quadratic phase error, is found. Fmally, the center-to-end quad-r~tic phase phase error, ~q, is obtained by multiplying ~xy wi~h a conversion factor.
To summarize, one FFT operation is required to produce ~;FT f~lters for each each range bin. Detected FFT filters are then integrated over r~nge bins. Detection opera-tion is required since those FFT filters can not be coherently added over range bins.
In the cross spectrum derived from the complex-conjugate multiplication step, the predorninate frequency is proportional to the residual quadratic phase error found in the original full array. The cross speclrum is not aYeraged in the prior phase difference method because the initial phase of the predominant frequency is dif~erent for each range bin. The magnitude detection of the cross coIrela~ion function aligns the data '70 before surnmation across range bins in this prior phase difference autofocus method.
Accordingly, a more computationally efficient autofocus method is therefore highly desirable for many existing real-dme SAR radar products. Since ~ l s require extensive computations, a reduction in the number of FFTs substantially reduces the computadon tirne. In real-time systems, mini~uzation of cornputation time is not only 25 desirable but also essential.
SUMMARY OF THE INVENTION
In order to overcome the lirnitadons of exisdng phase difference autofocus methods, and to provide a more computadonally efficient autofocus method, a fast30 phase difference autofocus method has been developed that only requires one ~1 for the entire SAR irnage. The phase difference autofocus method of the present invention automatically and efficiently estirnates and removes phase errors from radar signals, allowing a well focused SAR image to be produced.
The present phase difference autofocus method comprises the following steps.
35 Firs~, a full array from each range bin is divided into two subaIrays. The hvo subar-rays are complex-conjugate multiplied together to p~oduce a cross spectrum of the two sub-maps that would have been produced by the subarrays if compressed. Then, the phases of the cross spectrum are aligned with an accumulated sum of the cross spec-trums from range bins already p~cessed. This is accomplished by complex-conjugate multiplying the accumulated sum of the previous cross spectrums with the current cross spectrum to produce a second order product. All samples from this product are S surmned and the phase is extracted therefrom. A complex phasor having this phase is multiplied with the cuTTent cross spectrum to align the phase thereof. The phase aligned cross spectrum is then added to the accumulated sum of cross spectTums until all range bins are summed~ All range bins are processed to prGduce a final cross spectrum surn.
Snce no FFTs are perforrned prior to this point, the meThod is relatively fast. Next, an 10 arnplitude weighting function is applied to the final cross spectrum sum and an FFT is performed to produce a cross correlation function. Then, the cross correlation function is magnitude-detected. The location of the peak of the cross correlation func~on is proportional to the phase error. The center-to~nd quadratic phase error in the full array is ob~ined by multiplying the location of the pe3k by a conversion factor.
1~
BRIEF DESCRIPTION OF THE DRAWINGS
The various features and advantages of the present invention may be more read-ily understocd with reference to the following detailed description taken in conjunction with the accompanying drawings, wherein like reference numerals designate like struc-'~ tural elements, and in which:
Fig. 1 shows a fast phase difference autofocus method in accordance with thepresent invention;
Figs. 2 and 3 show autofocus functional outputs for a prior art method and the method of Fig. 1, respectively.
DETAILED DESCRlPTION
With reference to the drawing figures, Fig. 1 shows a phase difference autofo-cus method 10 in accordance with the present invention. In contrast to the prior art autofocus method described in the background s~ction, in the present invention, the 30 detection process may be elirninated from range bin processing in the prior art autofo-cus method by computing the proper phase shift for a cross spectrum in each range bin Once the detection process is not needed, then the FFT and the integration operations can be interchanged since they are linear operations, thus eliminating the FFT operation from range bin processing. This substantially reduces the required computational load.
35 This is the essence of the phase difference autofocus meihod 10 of the present in~ren-tion that is depicted in Fig. 1.
More particularly, the fast phase difference method 10 comprises the following steps. First, a cross spec~m is foImed 11 for each ~ange bin. Here, a full array from each range bin is divided into two suba~rays X, Y, such that two subarrays Xn(m) and Yn~m) of length M are formed where n denotes a range bin index and m a sarnple index 5 for each subarray . Then the subarray Xn(m) is complex-conjugated using a conjugator 12 and multiplied with the subarray Yn(m) using a multiplier 13 to produce a cross spectrum rn(m), for l~m~M, of the two sub-maps that would have been produced by the subarrays X, Y if compressed. Next, a phasor that will align the cross spec~um with the accumulated sum of cross spectrums from previously processed range bins is 10 determined. The cross spect~ um rn(m) is complex~onjugated 22 and is multiplied, using a multiplier 23, with the accumulated value SUMn l(m) from t'ne accumulator 27.
Complex sarnples from the resulting product are surnmed in step 24 to form a complex quanti~y Sn. Its magnitude is normalized to unity to form a phasor ej`vn in step 25. A
phasor ei~n is produced to insure coherent integration of rn(m~ over range bins. The 1~ c oss spectrum rn(m) is multiplied with the phasor ei~n using a multiplier 26 to align its phase and then is added to SIJ~Mn l(m) in the accumulator 27 to produce the updated accumulated sum SU~ln(m).
Once cross spectrums are summed over all range bins in 27 to get the final crossspectrum sum, it is processed to produce a cross correlation function using an F~ 1.
70 Since no ~1 is performed prior to this point, the method is relatively fast. The final cross spec~n sum is multiplied 16 with an amplitude weighting func~ion lS and processed by a K-point FFT 17 to produce a complex cross correlation function. Next, the cross correlation function is magnitude-detected 1~. The location ~xy of the peak of the cross correlation function is deterrnined in step 19. The value '~xy is proportional to 25 phase error. Finally, the value ~xy is multiplied 20 by a scale factor ~yM2/(4LK) to produce an estirnates~ center-to-end quadratic phase eIror ~,q.
More specifically, the fast phase difference autofocus method 10 perforrns coherent inte;,ration of the subarray second order product (an input to the FFT opera-tion), thus substantially reducing the number of complex multiply operations required 30 during FFTs. Fig. 1 shows that in the present phase difference autofocus method 10, only one ~-1 is perforrned on the surn of phase-aligned cross spectrums in step 17.
This is accomplished by surnming the conjugate products across all range bins and then performing one FFT in step 17. To insure coherent integration over range bins, each conjugate product is multiplied by the complex phasor er~n~ an operation which takes 35 2*M complex multiplies, where M denotes the length of a subarray. Thus, if N
denotes the number of range bins, the prior art phase difference autofocus method would require N*M*log2(M) complex multiplies while the presenl fast phase difference autofocus method 10 requires only N~2~M + M~log2(M). This results in a significant reduction of computational time.
The ~heory behind the phase differencc autofocus method 10 of the pre~ent invention is as follows. Let the phase vanatia~ of ~he nth range bin be denoted by 5 RBn(m) = ~nej2~ + B~m + Cm2) . Then, two subarmys Xn(m) and Yn(m) of length M
are formed: -Xn(m) = RBn(m-L) = 6nei2J~ + B~(m - L) + C(m - L)2) and Yn(m) = RBn(m+L) = ~nei2~ + B~(m + L) + C(m ~ L)2) Corresponding samples from the two subarrays are 2L poin~s apart The subar-mys Xn(m), Yn(m) are then rnultiplied (mixed) after taking the complex conjugate of the first subaIray Xn(m), which results in rn(m) = X'P(m)Y(m) = ~n2ei2~2B~L + 4CLm) Then, rn(m) is summed across range bins and then only one ~1 is performed in step 17. To insure coherent inte~ation, the phasor e3~n is computed and multiplied 1~ with rn(m). The theory behind surnming the cross spectrums over range bins first and performing only one FFT in step 17 is as follows:
For the first range bin, the sum SUMl(m) is initialized with the first conjugateproduct rl(m) and is given by S~ (m) = rl(m) = ~2ei27~(2B-L + 4CLm) For the sec-ond range bin, the complex conjugate product is given by r2(m) = ~22ei2~2B2L + 4CLm) '~0 It is then desired to find the complex phasor ei'Y2 such that r2(m)ei~2 can be coherently added to SU~Il(m). To find such a phasor, the sum S2 is formed which is given by S2 = ~, r2~tm)SUMI(m) mM
= ~ ~22ej2~(2B2L + 4CLm) ~12~j~(2BIL + 4Cl m) m=l ~5 = (6l62)2Mei2~(2BlL-2B2L) If we let ei~ = I S2 1 = ej2~(2BlL - 2B2L) then r2(m)ei~V2 = 622ej2~(2BIL + 4CLm) The terms {r2(m)ei~2}, 1 5 m < M, have the same initial phase and slope as {SUMl(m)}, 1 < m < M, and hence can be adcled coherently, in accordance with theequation SUMl(m) + r2(m)ej`Y2 = ~512ej2~(2BIL + 4CLm) + ~22ej21T(2BIL + 4CLm = (~21 +c~22~l~i47tBlLeis~cLm = SUM2(m) ~ general, for the n-th range bin, the c~mplex conjugate product has the fo~m rn(m) =C5r~2ei2~(2BnL + 4CLm), and a complex quantity Sn is fo~med using the equation Sn = ~, rn8(m)SUM7l(m) m S Then ~Yn is set to the phase of Sn ei~ = l Sn I
and the sum becomes SUMn(m) = SUMn l(m) + rn(m)ei~n = ei4-d~tLej8J~CLm ~
After processing all N range bins, SUMN(m) = ej47~1Lej8~CLm ~ i2 i=l In the phase difference autofocus method 10 of the present invention, the K-point ~1 17 is then performed on {SUMN~m)}, 1 S m < M. The output filters of the~1 17 are detected by the magnitude-detector 18 and the location ~cy of the peak1~ response is determined in step 19. The cen~er-to-end quadratic phase error ~q is then deterrnined by the equation ~Pq = -27~ ~yM2/(4LK) using the multiplier 20.
As shown, the quadratic phase error estimation involves forming two subarrays X, Y from each range bin, processing the complex-conjugate multiply pr~duct {X*Y}, and determining the location of the peak in the cross correlation function. As described 20 in the basic phase difference method disclosed in the 4,999,635 patent, a simultaneous estimation of a quadratic and a cubic phase e~ors involves forming three arrays X, Y, Z fTom each range bin, processing two complex-conjugate-multiply products {X* Z}, {Z* Y) and determining the location of the pealc fIom the two CTOSS correlation functions. The fast phase difference autofocus method of the presenl invention can be 2~ similarly extended to process two complex~onjugate-multiply products {X* Z}, {Z*
Y} for estimating a quadratic and a cubic phase error.
To evaluate the performance of the phase difference autofocus method 10, numerous sets of Advanced Synthetic AITay Radar System (ASARS) spodight mode data were processed offline. For each set of data, the quadratic and cubic phase errors 30 were estimated by applying the fast phase difference autofocus method 10. These results were then compared with the estimates obtained by the basic phase difference autofocus method of the above-cited patent. Table 1 lists the per~nent scene inforrna-tion and the amount of phase errors detected by each metho~ For the majority of the test cases, both the fast phase difference autofocus method 10 and the prior art phase difference autofocus method disclosed in the 4,999,635 patent produced ex~emely well^focused imagery. The agreement of d~e phase e~r estimates was very high. Inmore than half the cases, the qua~atic phase e~r ~s~imates agreed withirl 100 degrees.
Figs. 2 and 3 show the autofocus functional output by ~ach method for scene 5 39 shown in Table 1. The peak response of both functionals is sharp and well-defined, - and the inteIpolated peak loeations yield qua~atic phase estimates which agree within ten (10) degrees. It should be noted that the present phase difference autofocus method 10 has a higher target to clutter ratio than the pnor art phase difference autofocus method. Also, since the fast phase difference autofocus method 10 reduces ~he nurnber 10 of FFTs required for pro essing, it greatly enhances the computational speed.Thus there has been described a new and improved a fast phase difference auto-focus method for use in synthetic array raL~r (SAR) signal processing. It is to be understood that the above-descIibed embodiment is merely illustrative of some of the many specific embodiments which represent applications of the principles of the pre-15 sent invention. Clearly, numerous and other alrangements can be readily devised by those skiUed in the art without departing fr~m the scope of the invention.
Table 1 PHASE DIFFERENCE AUTOFOCUS
Basic Fast Phase Difference Phase Difference Quad.Cubic Quad~Cubic 25 Mission Scene Batch Mode(deg) (de~)Ide ) fde~) 85-106 83Sgl CSPT3-784 376 -820 457 85-107 3351 SS~l-3185 -3~5 -3366 -290 OCF17S 282030 SSPTl-1183-261 -1246 -440 0C~F176392041 SSPll2405 42 2411 15 87SR41 6160 SSPIl552 56 335 -77 87SR41 22184 SSPtll 972 -3031049 -706
BACKGROIJND
The present invention relates to synthetic array radar (SAR) signal processing, and more paTticularly, to a phase difference autofocus method for use in such SAR
signal processing.
Many real-time SAR radar products require autofocus methods. In an existing 5 phase difference method developed by the assignee of the present invention, an ~
must be done on many range bin of the image. This method is disclosed in U.S. Patent No. 4,999,635, for "Phase ~ifference Auto~ocusing for Synthetic Aperture Radar Irnaging," assigned to the assignee of the present invention. One disadvantage of this method is the large number of FFTs required to implement it.
By way of introduction, in the basic phase difference method described in the 4,999,635 patent, the relative drift between two subimages is estimated without actually forming the subimages. Subarrays aIe simply mixed and an ~1 filter banlc is formed from a resulting produc~ The FFI filters are then detected to form a phase difference autofocus functionaL The drift ~xy is obtained by finding the location of the 15 peak in the autofocus functional. In order to reduce a staoastical noise in estimating the underlying phase errors, this process of forrning the autofocus functional is repeated over many range bins. The drift ~xy is estimated from the autofocus functional that is integrated over range bins.
The prior art phase difference autofocus method can be summanæd in the 20 following steps. A full array from each range bin is divided into two subarrays X, Y.
Then, the two subarrays are complex-conjugate multiplied together to produce a cross spectrum of the two su~m~ps produced by the subarrays Next, after amplitude weights have been applied, an FPT is performed on the cross spec~um !o produce the complex cross correlation function. One FFT is performed on the subarray complexconjugate product during each lange bin processing. If M denotes the length of the S subarrays, then each range bin process results in M~log2(M) cornplex multiplies. For simplicity-assume an M point ~ is performed. Then, the cross correlation furrction is magnitude-detected. The magnitude-detected cross c~relation function is th~on sum-med across range bins to to produce a summed cross colrelation function. Next, the location, ~xy, of the peak of the summed cross correlation function, which is propor-10 tional to the residual quadratic phase error, is found. Fmally, the center-to-end quad-r~tic phase phase error, ~q, is obtained by multiplying ~xy wi~h a conversion factor.
To summarize, one FFT operation is required to produce ~;FT f~lters for each each range bin. Detected FFT filters are then integrated over r~nge bins. Detection opera-tion is required since those FFT filters can not be coherently added over range bins.
In the cross spectrum derived from the complex-conjugate multiplication step, the predorninate frequency is proportional to the residual quadratic phase error found in the original full array. The cross speclrum is not aYeraged in the prior phase difference method because the initial phase of the predominant frequency is dif~erent for each range bin. The magnitude detection of the cross coIrela~ion function aligns the data '70 before surnmation across range bins in this prior phase difference autofocus method.
Accordingly, a more computationally efficient autofocus method is therefore highly desirable for many existing real-dme SAR radar products. Since ~ l s require extensive computations, a reduction in the number of FFTs substantially reduces the computadon tirne. In real-time systems, mini~uzation of cornputation time is not only 25 desirable but also essential.
SUMMARY OF THE INVENTION
In order to overcome the lirnitadons of exisdng phase difference autofocus methods, and to provide a more computadonally efficient autofocus method, a fast30 phase difference autofocus method has been developed that only requires one ~1 for the entire SAR irnage. The phase difference autofocus method of the present invention automatically and efficiently estirnates and removes phase errors from radar signals, allowing a well focused SAR image to be produced.
The present phase difference autofocus method comprises the following steps.
35 Firs~, a full array from each range bin is divided into two subaIrays. The hvo subar-rays are complex-conjugate multiplied together to p~oduce a cross spectrum of the two sub-maps that would have been produced by the subarrays if compressed. Then, the phases of the cross spectrum are aligned with an accumulated sum of the cross spec-trums from range bins already p~cessed. This is accomplished by complex-conjugate multiplying the accumulated sum of the previous cross spectrums with the current cross spectrum to produce a second order product. All samples from this product are S surmned and the phase is extracted therefrom. A complex phasor having this phase is multiplied with the cuTTent cross spectrum to align the phase thereof. The phase aligned cross spectrum is then added to the accumulated sum of cross spectTums until all range bins are summed~ All range bins are processed to prGduce a final cross spectrum surn.
Snce no FFTs are perforrned prior to this point, the meThod is relatively fast. Next, an 10 arnplitude weighting function is applied to the final cross spectrum sum and an FFT is performed to produce a cross correlation function. Then, the cross correlation function is magnitude-detected. The location of the peak of the cross correlation func~on is proportional to the phase error. The center-to~nd quadratic phase error in the full array is ob~ined by multiplying the location of the pe3k by a conversion factor.
1~
BRIEF DESCRIPTION OF THE DRAWINGS
The various features and advantages of the present invention may be more read-ily understocd with reference to the following detailed description taken in conjunction with the accompanying drawings, wherein like reference numerals designate like struc-'~ tural elements, and in which:
Fig. 1 shows a fast phase difference autofocus method in accordance with thepresent invention;
Figs. 2 and 3 show autofocus functional outputs for a prior art method and the method of Fig. 1, respectively.
DETAILED DESCRlPTION
With reference to the drawing figures, Fig. 1 shows a phase difference autofo-cus method 10 in accordance with the present invention. In contrast to the prior art autofocus method described in the background s~ction, in the present invention, the 30 detection process may be elirninated from range bin processing in the prior art autofo-cus method by computing the proper phase shift for a cross spectrum in each range bin Once the detection process is not needed, then the FFT and the integration operations can be interchanged since they are linear operations, thus eliminating the FFT operation from range bin processing. This substantially reduces the required computational load.
35 This is the essence of the phase difference autofocus meihod 10 of the present in~ren-tion that is depicted in Fig. 1.
More particularly, the fast phase difference method 10 comprises the following steps. First, a cross spec~m is foImed 11 for each ~ange bin. Here, a full array from each range bin is divided into two suba~rays X, Y, such that two subarrays Xn(m) and Yn~m) of length M are formed where n denotes a range bin index and m a sarnple index 5 for each subarray . Then the subarray Xn(m) is complex-conjugated using a conjugator 12 and multiplied with the subarray Yn(m) using a multiplier 13 to produce a cross spectrum rn(m), for l~m~M, of the two sub-maps that would have been produced by the subarrays X, Y if compressed. Next, a phasor that will align the cross spec~um with the accumulated sum of cross spectrums from previously processed range bins is 10 determined. The cross spect~ um rn(m) is complex~onjugated 22 and is multiplied, using a multiplier 23, with the accumulated value SUMn l(m) from t'ne accumulator 27.
Complex sarnples from the resulting product are surnmed in step 24 to form a complex quanti~y Sn. Its magnitude is normalized to unity to form a phasor ej`vn in step 25. A
phasor ei~n is produced to insure coherent integration of rn(m~ over range bins. The 1~ c oss spectrum rn(m) is multiplied with the phasor ei~n using a multiplier 26 to align its phase and then is added to SIJ~Mn l(m) in the accumulator 27 to produce the updated accumulated sum SU~ln(m).
Once cross spectrums are summed over all range bins in 27 to get the final crossspectrum sum, it is processed to produce a cross correlation function using an F~ 1.
70 Since no ~1 is performed prior to this point, the method is relatively fast. The final cross spec~n sum is multiplied 16 with an amplitude weighting func~ion lS and processed by a K-point FFT 17 to produce a complex cross correlation function. Next, the cross correlation function is magnitude-detected 1~. The location ~xy of the peak of the cross correlation function is deterrnined in step 19. The value '~xy is proportional to 25 phase error. Finally, the value ~xy is multiplied 20 by a scale factor ~yM2/(4LK) to produce an estirnates~ center-to-end quadratic phase eIror ~,q.
More specifically, the fast phase difference autofocus method 10 perforrns coherent inte;,ration of the subarray second order product (an input to the FFT opera-tion), thus substantially reducing the number of complex multiply operations required 30 during FFTs. Fig. 1 shows that in the present phase difference autofocus method 10, only one ~-1 is perforrned on the surn of phase-aligned cross spectrums in step 17.
This is accomplished by surnming the conjugate products across all range bins and then performing one FFT in step 17. To insure coherent integration over range bins, each conjugate product is multiplied by the complex phasor er~n~ an operation which takes 35 2*M complex multiplies, where M denotes the length of a subarray. Thus, if N
denotes the number of range bins, the prior art phase difference autofocus method would require N*M*log2(M) complex multiplies while the presenl fast phase difference autofocus method 10 requires only N~2~M + M~log2(M). This results in a significant reduction of computational time.
The ~heory behind the phase differencc autofocus method 10 of the pre~ent invention is as follows. Let the phase vanatia~ of ~he nth range bin be denoted by 5 RBn(m) = ~nej2~ + B~m + Cm2) . Then, two subarmys Xn(m) and Yn(m) of length M
are formed: -Xn(m) = RBn(m-L) = 6nei2J~ + B~(m - L) + C(m - L)2) and Yn(m) = RBn(m+L) = ~nei2~ + B~(m + L) + C(m ~ L)2) Corresponding samples from the two subarrays are 2L poin~s apart The subar-mys Xn(m), Yn(m) are then rnultiplied (mixed) after taking the complex conjugate of the first subaIray Xn(m), which results in rn(m) = X'P(m)Y(m) = ~n2ei2~2B~L + 4CLm) Then, rn(m) is summed across range bins and then only one ~1 is performed in step 17. To insure coherent inte~ation, the phasor e3~n is computed and multiplied 1~ with rn(m). The theory behind surnming the cross spectrums over range bins first and performing only one FFT in step 17 is as follows:
For the first range bin, the sum SUMl(m) is initialized with the first conjugateproduct rl(m) and is given by S~ (m) = rl(m) = ~2ei27~(2B-L + 4CLm) For the sec-ond range bin, the complex conjugate product is given by r2(m) = ~22ei2~2B2L + 4CLm) '~0 It is then desired to find the complex phasor ei'Y2 such that r2(m)ei~2 can be coherently added to SU~Il(m). To find such a phasor, the sum S2 is formed which is given by S2 = ~, r2~tm)SUMI(m) mM
= ~ ~22ej2~(2B2L + 4CLm) ~12~j~(2BIL + 4Cl m) m=l ~5 = (6l62)2Mei2~(2BlL-2B2L) If we let ei~ = I S2 1 = ej2~(2BlL - 2B2L) then r2(m)ei~V2 = 622ej2~(2BIL + 4CLm) The terms {r2(m)ei~2}, 1 5 m < M, have the same initial phase and slope as {SUMl(m)}, 1 < m < M, and hence can be adcled coherently, in accordance with theequation SUMl(m) + r2(m)ej`Y2 = ~512ej2~(2BIL + 4CLm) + ~22ej21T(2BIL + 4CLm = (~21 +c~22~l~i47tBlLeis~cLm = SUM2(m) ~ general, for the n-th range bin, the c~mplex conjugate product has the fo~m rn(m) =C5r~2ei2~(2BnL + 4CLm), and a complex quantity Sn is fo~med using the equation Sn = ~, rn8(m)SUM7l(m) m S Then ~Yn is set to the phase of Sn ei~ = l Sn I
and the sum becomes SUMn(m) = SUMn l(m) + rn(m)ei~n = ei4-d~tLej8J~CLm ~
After processing all N range bins, SUMN(m) = ej47~1Lej8~CLm ~ i2 i=l In the phase difference autofocus method 10 of the present invention, the K-point ~1 17 is then performed on {SUMN~m)}, 1 S m < M. The output filters of the~1 17 are detected by the magnitude-detector 18 and the location ~cy of the peak1~ response is determined in step 19. The cen~er-to-end quadratic phase error ~q is then deterrnined by the equation ~Pq = -27~ ~yM2/(4LK) using the multiplier 20.
As shown, the quadratic phase error estimation involves forming two subarrays X, Y from each range bin, processing the complex-conjugate multiply pr~duct {X*Y}, and determining the location of the peak in the cross correlation function. As described 20 in the basic phase difference method disclosed in the 4,999,635 patent, a simultaneous estimation of a quadratic and a cubic phase e~ors involves forming three arrays X, Y, Z fTom each range bin, processing two complex-conjugate-multiply products {X* Z}, {Z* Y) and determining the location of the pealc fIom the two CTOSS correlation functions. The fast phase difference autofocus method of the presenl invention can be 2~ similarly extended to process two complex~onjugate-multiply products {X* Z}, {Z*
Y} for estimating a quadratic and a cubic phase error.
To evaluate the performance of the phase difference autofocus method 10, numerous sets of Advanced Synthetic AITay Radar System (ASARS) spodight mode data were processed offline. For each set of data, the quadratic and cubic phase errors 30 were estimated by applying the fast phase difference autofocus method 10. These results were then compared with the estimates obtained by the basic phase difference autofocus method of the above-cited patent. Table 1 lists the per~nent scene inforrna-tion and the amount of phase errors detected by each metho~ For the majority of the test cases, both the fast phase difference autofocus method 10 and the prior art phase difference autofocus method disclosed in the 4,999,635 patent produced ex~emely well^focused imagery. The agreement of d~e phase e~r estimates was very high. Inmore than half the cases, the qua~atic phase e~r ~s~imates agreed withirl 100 degrees.
Figs. 2 and 3 show the autofocus functional output by ~ach method for scene 5 39 shown in Table 1. The peak response of both functionals is sharp and well-defined, - and the inteIpolated peak loeations yield qua~atic phase estimates which agree within ten (10) degrees. It should be noted that the present phase difference autofocus method 10 has a higher target to clutter ratio than the pnor art phase difference autofocus method. Also, since the fast phase difference autofocus method 10 reduces ~he nurnber 10 of FFTs required for pro essing, it greatly enhances the computational speed.Thus there has been described a new and improved a fast phase difference auto-focus method for use in synthetic array raL~r (SAR) signal processing. It is to be understood that the above-descIibed embodiment is merely illustrative of some of the many specific embodiments which represent applications of the principles of the pre-15 sent invention. Clearly, numerous and other alrangements can be readily devised by those skiUed in the art without departing fr~m the scope of the invention.
Table 1 PHASE DIFFERENCE AUTOFOCUS
Basic Fast Phase Difference Phase Difference Quad.Cubic Quad~Cubic 25 Mission Scene Batch Mode(deg) (de~)Ide ) fde~) 85-106 83Sgl CSPT3-784 376 -820 457 85-107 3351 SS~l-3185 -3~5 -3366 -290 OCF17S 282030 SSPTl-1183-261 -1246 -440 0C~F176392041 SSPll2405 42 2411 15 87SR41 6160 SSPIl552 56 335 -77 87SR41 22184 SSPtll 972 -3031049 -706
Claims (7)
1. A fast phase difference autofocus method for removing phase errors from synthetic array radar signals, said method comprising the steps of:
dividing each range bin of the synthetic array radar data into two subarrays;
complex-conjugate multiplying the the two subarrays together to produce a cross spectrum;
determining a complex phasor for the cross spectrum to align its phase so that the cross spectrum can be coherently added to the accumulated sum of cross spectrums from previously processed range bins;
multiplying the cross spectrum with the complex phasor and adding it to the accumulated sum of cross spectrums from previously processed range bins;
repeating the process over all range bins to form the final cross spectrum sum from all range bins;
applying an amplitude weighting function to the final cross spectrum sum;
performing an FFT to the amplitude-weighted cross spectrum sum to produce a cross correlation function;
magnitude-detecting the cross correlation function and determining a peak location of the cross correlation function;
multiplying the peak location by a scale factor to compute a center-to-end phase error estimate; and generating a phase error correction signal and removing the phase error from the synthetic array radar data by multiplying them with the phase error correction signal.
dividing each range bin of the synthetic array radar data into two subarrays;
complex-conjugate multiplying the the two subarrays together to produce a cross spectrum;
determining a complex phasor for the cross spectrum to align its phase so that the cross spectrum can be coherently added to the accumulated sum of cross spectrums from previously processed range bins;
multiplying the cross spectrum with the complex phasor and adding it to the accumulated sum of cross spectrums from previously processed range bins;
repeating the process over all range bins to form the final cross spectrum sum from all range bins;
applying an amplitude weighting function to the final cross spectrum sum;
performing an FFT to the amplitude-weighted cross spectrum sum to produce a cross correlation function;
magnitude-detecting the cross correlation function and determining a peak location of the cross correlation function;
multiplying the peak location by a scale factor to compute a center-to-end phase error estimate; and generating a phase error correction signal and removing the phase error from the synthetic array radar data by multiplying them with the phase error correction signal.
2. The method of Claim 1 wherein the step of the determining the complex phasor to align the phase of the cross spectrum comprises the steps of:
complex-conjugate multiplying the current cross spectrum and a previously accumulated sum of cross spectrums to produce a second order cross spectrum product;
summing all terms of the second order cross spectrum product to form a complex sample; and extracting the phase of the complex sample.
complex-conjugate multiplying the current cross spectrum and a previously accumulated sum of cross spectrums to produce a second order cross spectrum product;
summing all terms of the second order cross spectrum product to form a complex sample; and extracting the phase of the complex sample.
3. The method of Claim 2 which further comprises the step of delaying the previously accumulated sum of cross spectrums prior to complex-conjugate multiplying it with the current cross spectrum.
4. A phase difference autofocus method for removing phase errors from synthetic array radar data, said method comprising the steps of:
dividing a full array of each range bin in the synthetic array radar data into two subarrays;
complex-conjugate multiplying the the two subarrays together to produce a cross spectrum;
aligning the phases of a current cross spectrum with a presently accumulated cross spectrum sum;
adding the current phase aligned cross spectrum to the previously accumulated cross spectrum sum to update the cross spectrum sum;
whereby when all range bins have been processed, a final cross spectrum sum is produced;
applying an amplitude weighting function to the final cross spectrum sum;
performing an FFT on the amplitude-weighted cross spectrum sum to produce a cross correlation function;
magnitude-detecting the cross correlation function to detect a peak location of the cross correlation function;
multiplying the filter location of the peak by a scale factor to compute a center-to-end phase error estimate; and generating a phase correction signal using the phase error estimate and removing the phase error from the synthetic array radar data by multiplying them with the phase correction signal.
dividing a full array of each range bin in the synthetic array radar data into two subarrays;
complex-conjugate multiplying the the two subarrays together to produce a cross spectrum;
aligning the phases of a current cross spectrum with a presently accumulated cross spectrum sum;
adding the current phase aligned cross spectrum to the previously accumulated cross spectrum sum to update the cross spectrum sum;
whereby when all range bins have been processed, a final cross spectrum sum is produced;
applying an amplitude weighting function to the final cross spectrum sum;
performing an FFT on the amplitude-weighted cross spectrum sum to produce a cross correlation function;
magnitude-detecting the cross correlation function to detect a peak location of the cross correlation function;
multiplying the filter location of the peak by a scale factor to compute a center-to-end phase error estimate; and generating a phase correction signal using the phase error estimate and removing the phase error from the synthetic array radar data by multiplying them with the phase correction signal.
5. A phase difference autofocus method that removes phase errors from synthetic army radar data, said method comprising the steps of:
dividing a full array from each range bin of the synthetic array radar data into two subarrays Xn(m), Yn(m) of length M;
complex-conjugate multiplying the the two subarrays together to produce a cross spectrum rn(m);
computing a phasor e?n by complex-conjugate multiplying the cross spectrum rn(m) with the presently accumulated sum SUMn-1(m), adding all terms of the resulting product, and then extracting its phase ?n to form the phasor e?n;
integrating the phase aligned cross spectrum rn(m)ej?n across all range bins to produce a cross spectrum sum comprising a summed value SUMn(m) = SUMn-1(m) +
rn(m)ej?n, applying an amplitude weighting function to the cross spectrum sum SUMN(m);
performing an FFT to the amplitude-weighted cross spectrum sum to produce a cross correlation function;
magnitude-detecting the cross correlation function to determine the location ?xy of the peak response therein;
computing a quadratic phase error estimate .PHI.q = -2.pi.?xyM2/(4LK);
generating a phase error correction signal ej.PHI.q(m/M)2,-M<m<M; and removing the phase error from the synthetic array radar data by multiplying them with the phase error correction signal.
dividing a full array from each range bin of the synthetic array radar data into two subarrays Xn(m), Yn(m) of length M;
complex-conjugate multiplying the the two subarrays together to produce a cross spectrum rn(m);
computing a phasor e?n by complex-conjugate multiplying the cross spectrum rn(m) with the presently accumulated sum SUMn-1(m), adding all terms of the resulting product, and then extracting its phase ?n to form the phasor e?n;
integrating the phase aligned cross spectrum rn(m)ej?n across all range bins to produce a cross spectrum sum comprising a summed value SUMn(m) = SUMn-1(m) +
rn(m)ej?n, applying an amplitude weighting function to the cross spectrum sum SUMN(m);
performing an FFT to the amplitude-weighted cross spectrum sum to produce a cross correlation function;
magnitude-detecting the cross correlation function to determine the location ?xy of the peak response therein;
computing a quadratic phase error estimate .PHI.q = -2.pi.?xyM2/(4LK);
generating a phase error correction signal ej.PHI.q(m/M)2,-M<m<M; and removing the phase error from the synthetic array radar data by multiplying them with the phase error correction signal.
6. The method of Claim 5 wherein:
the two subarrays each have length M and are given by Xn(m) = RBn(m-L) = .sigma.nej2.pi.(A? + B?(m - L)+C(m - L)2) and Yn(m) = RBn(m+L) = .sigma.ej2.pi.(A? + B?(m + L) + C(m + L)2);
the cross spectrum is given by rn(m) = X*(m)*Y(m) = .sigma.nej2.pi.(2BnL + 4CLm);
the phasor ej?n is given by ej?n = , where Sn = ?rn*(m)SUMn-1(m);
SUMN(m) = ; and the center-to-end quadratic phase .PHI.q is given by the equation .PHI.q = -2.pi.?xyM2/(4LK).
the two subarrays each have length M and are given by Xn(m) = RBn(m-L) = .sigma.nej2.pi.(A? + B?(m - L)+C(m - L)2) and Yn(m) = RBn(m+L) = .sigma.ej2.pi.(A? + B?(m + L) + C(m + L)2);
the cross spectrum is given by rn(m) = X*(m)*Y(m) = .sigma.nej2.pi.(2BnL + 4CLm);
the phasor ej?n is given by ej?n = , where Sn = ?rn*(m)SUMn-1(m);
SUMN(m) = ; and the center-to-end quadratic phase .PHI.q is given by the equation .PHI.q = -2.pi.?xyM2/(4LK).
7. A phase difference autofocus method that removes phase errors from synthetic array radar data, said method comprising the steps of:
dividing each range bin of the synthetic array radar data into two subarrays;
producing a cross spectrum of the two subarrays;
aligning the phases of each cross spectrum with an accumulated sum of cross spectrums;
adding the phase aligned cross spectrum to the accumulated cross spectrum sum;
processing all range bins to compute a final cross spectrum sum;
applying an amplitude weighting function to the final cross spectrum sum;
performing an FFT on the amplitude weighted cross spectrum sum to produce a cross correlation function;
magnitude-detecting the cross correlation function;
computing a phase error estimate;
producing a phase error correction signal; and removing the phase error from synthetic array radar data by multiplying them with the phase correction signal.
dividing each range bin of the synthetic array radar data into two subarrays;
producing a cross spectrum of the two subarrays;
aligning the phases of each cross spectrum with an accumulated sum of cross spectrums;
adding the phase aligned cross spectrum to the accumulated cross spectrum sum;
processing all range bins to compute a final cross spectrum sum;
applying an amplitude weighting function to the final cross spectrum sum;
performing an FFT on the amplitude weighted cross spectrum sum to produce a cross correlation function;
magnitude-detecting the cross correlation function;
computing a phase error estimate;
producing a phase error correction signal; and removing the phase error from synthetic array radar data by multiplying them with the phase correction signal.
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| US07/799,514 US5184134A (en) | 1991-11-27 | 1991-11-27 | Fast phase difference autofocus |
| US799,514 | 1991-11-27 |
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| CA2083906A1 true CA2083906A1 (en) | 1993-05-28 |
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| CA002083906A Abandoned CA2083906A1 (en) | 1991-11-27 | 1992-11-26 | Phase difference autofocus |
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| US (1) | US5184134A (en) |
| EP (1) | EP0544280B1 (en) |
| JP (1) | JPH05249238A (en) |
| KR (1) | KR960011786B1 (en) |
| AU (1) | AU648940B2 (en) |
| CA (1) | CA2083906A1 (en) |
| DE (1) | DE69221703T2 (en) |
| ES (1) | ES2106813T3 (en) |
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| DE4122592C1 (en) * | 1991-07-08 | 1993-01-28 | Deutsche Forschungsanstalt Fuer Luft- Und Raumfahrt Ev, 5300 Bonn, De | |
| US5546084A (en) * | 1992-07-17 | 1996-08-13 | Trw Inc. | Synthetic aperture radar clutter reduction system |
| US5854602A (en) * | 1997-04-28 | 1998-12-29 | Erim International, Inc. | Subaperture high-order autofocus using reverse phase |
| JP3696379B2 (en) * | 1997-08-22 | 2005-09-14 | 株式会社アドバンテスト | Multi-input amplitude / phase measurement method and apparatus |
| KR19990042860A (en) * | 1997-11-28 | 1999-06-15 | 구광시 | Production method of polyester |
| US6037892A (en) * | 1998-05-28 | 2000-03-14 | Multispec Corporation | Method for automatic focusing of radar or sonar imaging systems using high-order measurements |
| US7061992B2 (en) * | 2000-01-18 | 2006-06-13 | National Researc Council Of Canada | Parallel correlator architecture |
| AU2002300531B2 (en) * | 2001-08-15 | 2007-01-18 | Raytheon Company | Combining signal images in accordance with signal-to-noise ratios |
| US6670907B2 (en) * | 2002-01-30 | 2003-12-30 | Raytheon Company | Efficient phase correction scheme for range migration algorithm |
| US6661369B1 (en) * | 2002-05-31 | 2003-12-09 | Raytheon Company | Focusing SAR images formed by RMA with arbitrary orientation |
| US7126524B2 (en) * | 2004-08-04 | 2006-10-24 | Raytheon Company | Motion compensation for convolutional SAR algorithms |
| US7145496B2 (en) * | 2004-11-23 | 2006-12-05 | Raytheon Company | Autofocus method based on successive parameter adjustments for contrast optimization |
| US7145498B2 (en) * | 2004-11-23 | 2006-12-05 | Raytheon Company | Efficient autofocus method for swath SAR |
| JP4541120B2 (en) * | 2004-12-09 | 2010-09-08 | 三菱電機株式会社 | Radar equipment |
| JP4541189B2 (en) * | 2005-03-02 | 2010-09-08 | 三菱電機株式会社 | Radar equipment |
| US7391357B1 (en) * | 2005-03-25 | 2008-06-24 | Sandia Corporation | Correction of motion measurement errors beyond the range resolution of a synthetic aperture radar |
| WO2008021374A2 (en) * | 2006-08-15 | 2008-02-21 | General Dynamics Advanced Information Systems, Inc | Methods for two-dimensional autofocus in high resolution radar systems |
| US20080297405A1 (en) * | 2007-04-06 | 2008-12-04 | Morrison Jr Robert L | Synthetic Aperture focusing techniques |
| EP2171896A4 (en) * | 2007-06-29 | 2012-06-06 | Thomson Licensing | Apparatus and method for removing common phase error in a dvb-t/h receiver |
| CN101690060B (en) * | 2007-06-29 | 2012-09-26 | 汤姆逊许可公司 | Apparatus and method for removing common phase error in a dvb-t/h receiver |
| CN104730520B (en) * | 2015-03-27 | 2017-05-10 | 电子科技大学 | Circumference SAR back projection self-focusing method based on subaperture synthesis |
| DE102016218643A1 (en) * | 2016-09-28 | 2018-03-29 | Robert Bosch Gmbh | Method for evaluating radar radiation and radar apparatus |
| CN108387875A (en) * | 2018-03-01 | 2018-08-10 | 南京理工大学 | Time-division MIMO radar phase error antidote based on Two-dimensional FFT |
| DE102018123334A1 (en) * | 2018-09-21 | 2020-03-26 | Gottfried Wilhelm Leibniz Universität Hannover | Method for determining a change in position of an object |
| CN110187317B (en) * | 2019-06-17 | 2021-01-05 | 北京无线电测量研究所 | FMCW signal nonlinear error compensation method, device and storage medium |
| US11209524B2 (en) * | 2019-09-30 | 2021-12-28 | Veoneer Us, Inc. | Detection system and method for characterizing targets |
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| US4219811A (en) * | 1975-02-07 | 1980-08-26 | Hughes Aircraft Company | Synthetic array autofocus system |
| US4771287A (en) * | 1983-06-23 | 1988-09-13 | Westinghouse Electric Corp. | Method of correcting for errors in radar imaging |
| GB8700973D0 (en) * | 1987-01-17 | 1987-07-08 | Scicon Ltd | Aperture synthesis |
| US5043734A (en) * | 1988-12-22 | 1991-08-27 | Hughes Aircraft Company | Discrete autofocus for ultra-high resolution synthetic aperture radar |
| US4924229A (en) * | 1989-09-14 | 1990-05-08 | The United States Of America As Represented By The United States Department Of Energy | Phase correction system for automatic focusing of synthetic aperture radar |
| US4999635A (en) * | 1990-03-29 | 1991-03-12 | Hughes Aircraft Company | Phase difference auto focusing for synthetic aperture radar imaging |
| US5021789A (en) * | 1990-07-02 | 1991-06-04 | The United States Of America As Represented By The Secretary Of The Air Force | Real-time high resolution autofocus system in digital radar signal processors |
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- 1991-11-27 US US07/799,514 patent/US5184134A/en not_active Expired - Lifetime
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1992
- 1992-11-26 ES ES92120181T patent/ES2106813T3/en not_active Expired - Lifetime
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- 1992-11-26 CA CA002083906A patent/CA2083906A1/en not_active Abandoned
- 1992-11-27 JP JP4319082A patent/JPH05249238A/en active Pending
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| AU2974392A (en) | 1993-06-03 |
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| EP0544280A1 (en) | 1993-06-02 |
| AU648940B2 (en) | 1994-05-05 |
| US5184134A (en) | 1993-02-02 |
| KR930010563A (en) | 1993-06-22 |
| KR960011786B1 (en) | 1996-08-30 |
| EP0544280B1 (en) | 1997-08-20 |
| ES2106813T3 (en) | 1997-11-16 |
| JPH05249238A (en) | 1993-09-28 |
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