USH1720H  Time frequency processor for radar imaging of moving targets  Google Patents
Time frequency processor for radar imaging of moving targets Download PDFInfo
 Publication number
 USH1720H USH1720H US08829263 US82926397A USH1720H US H1720 H USH1720 H US H1720H US 08829263 US08829263 US 08829263 US 82926397 A US82926397 A US 82926397A US H1720 H USH1720 H US H1720H
 Authority
 US
 Grant status
 Grant
 Patent type
 Prior art keywords
 time
 target
 frequency
 radar
 range
 Prior art date
 Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
 Abandoned
Links
Images
Classifications

 G—PHYSICS
 G01—MEASURING; TESTING
 G01S—RADIO DIRECTIONFINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCEDETECTING 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. correcting range migration errors
 G01S13/9035—Particular SAR processing techniques not provided for elsewhere, e.g. squint mode, doppler beamsharpening mode, spotlight mode, bistatic SAR, inverse SAR

 G—PHYSICS
 G01—MEASURING; TESTING
 G01S—RADIO DIRECTIONFINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCEDETECTING 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. correcting range migration errors
 G01S13/9029—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. correcting range migration errors specially adapted for moving target detection
Abstract
Description
The present invention relates to improvements in imaging radar. In particular, the present invention relates to deblurring, feature extraction from, and improving resolution of radar target images using improved methods.
Radar images are widely used in many areas, such as wide area surveillance and remote sensing. Conventional radar systems may transmit electromagnetic waves to a target. The target may consists of a number of points which tend to scatter incumbent radar waves. A radar system may then receive scattered waves from a target. The scattering properties of a target may describe target features. Point scatterers may comprises discontinuities, corners, or cavities in the target. Incident radar waves are diffracted from these scatterers with different timing and different frequency dependencies as described in "High resolution parametric modeling of canonical radar scatterers with application to target identification", R. Carrierre and R. L. Moses, IEEE Trans. Antennas and Prop., 40(1) 1318 (1992) incorporated herein by reference, and "Estimating the timedelay and frequency decay parameter of scattering components using a modified MUSIC algorithm", A. Moghaddar, Y. Ogawa and E. K. Walton, IEEE Trans. Antennas and Prop., 42(10) 14121418 (1994) incorporated herein by reference.
A target return signal may represent the sum of returned signals from scattering points or scatterers in the form of various geometric structures and physical features and properties of a target such as material absorption and reflectivity. A radar processor may reconstruct relative spatial distribution of target scatterers based on reflectivity. The spatial distribution of reflectivity, which may be referred to as a target's radar image may be mapped onto a range and crossrange plane representing its relative location in space. Target range may be represented by straight line distance from radar to target or radar "lineofsight." Target crossrange is the position of a target along a dimension transverse or horizontally perpendicular to a radar's lineofsight.
Increasingly higher resolution radar images are increasingly in demand by radar users. A larger antenna aperture may provide higher cross range resolution. Since range resolution is directly related to bandwidth of a transmitted radar signal, and crossrange resolution is determined by antenna beamwidth, a higher bandwidth, higher frequency signal and larger aperture antenna may normally be required to achieve greater resolutions. To achieve high crossrange resolution without using a large antenna aperture, synthetic array processing is widely employed. Synthetic array radar processing may coherently combine signals obtained from sequences of small apertures to emulate the result of a large aperture.
Synthetic array radar may include both synthetic aperture radar (SAR) and inverse synthetic aperture radar (ISAR). Traditionally, SAR may be associated with a moving radar unit and stationary target; ISAR may be associated with the geometrical inverse in which a target is moving and a radar unit is stationary. For ISAR, the synthetic aperture is formed by coherently combining signals obtained from a single aperture as it observes a rotating target. The rotation of the target emulates the result from a larger circular aperture focusing at the rotation center of the target.
ISAR may use Doppler information to obtain the crossrange resolution. Due to a target's rotation, which can be characterized as a superposition of pitch, roll, and yaw motions, different parts of a target may have slightly different velocities relative to a radar unit and may produce slightly different Doppler frequencies which a radar unit may then receive. Differential Doppler shift of adjacent point scatterers may be measured in the receiver; therefore, the distribution of the target's reflectivity may be characterized by the Doppler spectrum: the distribution of differential Doppler shifts. A conventional Fourier transform method may then be used to generate Doppler spectrum information.
Conventional Radar Imaging of Moving Targets
FIG. 1 is a diagram illustrating steppedfrequency inverse synthetic radar imaging of a moving target. The returned signal from moving object 100 can be represented as the integration of the returned signals from its individual scatterers as more fully described in "High Resolution Radar", D. R. Wehner, (2nd edition), Artech House, 1994.
The objective of radar processing may be to estimate the target's reflectivity density function from received baseband signal samples, the socalled frequency signature.
If the moving object 100's range is known exactly and velocity and acceleration of target's motion are constant and known exactly over imaging time duration, then the extraneous phase term of the motion can be exactly removed. Therefore, the reflectivity density function of the target may be obtained simply by taking the inverse Fourier transform of the phase compensated frequency signature. The process of estimating the target's range and removing extraneous phase term may be referred to as focusing or gross translational motion compensation, or, more commonly, aligning radar returns.
An inverse Fourier transform may be used to construct a reflectivity density function for a target. For SAR, motion compensation is facilitated by measuring actual motion of the radar platform. In ISAR, the actual motion can be measured by a rangetracker, or estimated by a motion compensation algorithm which estimates motion parameters and compensates motion with respect to the target's range, velocity, acceleration and other higher order terms. Gross translation techniques however may be inadequate to compensate for radar image blur and distortion due to nonuniform motion and target rotation because the target's velocity, hence the Doppler frequencies returned, may change from pulse to pulse. Motion compensation which would improve resolution beyond that provided by gross methods may be disadvantageous due to processing times involved. Near real time or real time processing of target data to eliminate blur and distortion may not be possible with present motion compensation processing.
ISAR imaging System may use steppedfrequency pulses to generate a wide bandwidth output. The radar unit transmits N burst sequence 101. A typical number of bursts for such a train of bursts may be 512. Each burst in N burst sequence 101 comprises M narrowband pulses 102. A typical number of narrow band pulses may be 64. Within each burst, the center frequency f(m) of each successive narrow band pulse 102 is increased by a constant frequency step Δf. The total bandwidth of a burst in burst sequence 101, i.e., M times the frequency step Δf, determines radar range resolution. The total number of bursts N for a given imaging time duration may determine Doppler or crossrange resolution. The returned pulse is heterodyned and quadrature detected in the radar receiver.
To form a radar image 108 after collecting the returned signals, MbyN complex data are organized into twodimensional arrays which represent unprocessed spatial frequency signatures 104 of moving object 100. Received frequency signatures 104 may be treated as a time history series of moving object 100's reflectivity at each discrete frequency. A radar processor uses frequency signatures as raw data to perform range processing and Doppler processing. Range processing functions and associated time history series acts as a matched filter of the kind used for pulse compression. Such matched filtering removes frequency or phase modulation and resolves range. For steppedfrequency signals, range processing performs an Mpoint inverse discrete Fourier transform (IDFT) 106 for each of the N frequency signatures 104 received. N range profiles 109 representing distribution of target reflectivities in range, each containing M range cells, may be obtained. For each range cell, N range profiles 109 constitute a new time history series, which is sampled at baseband to form N inphase (Ichannel) and N quadraturephase (Qchannel) data sets. The echoes from each burst are used to calculate target range by any known technique. Thereafter, the echoes from the N bursts are aligned in time. In practice, most objects of interest will have plural reflective facets recessed from one another along the line of sight of a radar transmitter: for example, a radar pulse launched at a radially incoming airplane would first reflect from the plane's nose, then separately from each wing, then from the tail. Because the round trip time between the radar emitter and each reflective facet differ, the echoes arrive back at slightly different times. However, this echo pattern will repeat from burst to burst, and these patterns are readily timealignable with one another, much in the same manner that Astronomers align atomic spectra from stars with those known on earth in order to infer red shift.
Doppler processing may then be used to take a discrete Fourier transform (DFT) 107 of range profiles 109 comprising time history series representing a frequency signatures 104 and generate an Npoint Doppler spectrum, or Doppler profile 110. By combining Npoint Doppler spectra at M range cells, an MbyN radar image 108 may be formed. Radar image 108 may represent the target's reflectivities mapped onto the rangeDoppler plane.
Conventional ISAR processing may use a Fourier transform to retrieve Doppler spectrum information. In order to use Fourier transform methods properly to generate Doppler spectrum, some restrictions must be applied. Fourier transforms for Doppler processing are adequate only when point scatterers remain in their range cells and their Doppler frequency shifts are constant during the entire observation time. If point scatterers drift through range cells as a result of motion, or associated Doppler frequency shifts are timevarying as a result of motion, a target image constructed therefrom may become blurred. Motion compensation may be used for establishing aligned range and for keeping constant phase changerate for each individual point scatterer.
While a target is moving smoothly, conventional motion compensation may be good enough to produce a clear target image. However, when a target exhibits complex motion, such as fast maneuvering, conventional motion compensation applied to an entire target may not be sufficient to produce an acceptable image for viewing and analysis.
With large motion residues or phase errors, individual scatterers may still drift through their range cells; the associated Doppler spectrum may still be timevarying. Fourier transform methods applied on such time varying data result in a blurred target image. In order to achieve satisfactory results with the application of Fourier methods for motion compensation, Doppler frequency contents data should not change with time. In radar target imaging however, target speeds in both range and crossrange directions may be high and a requirement for time invariance in Doppler frequency contents may be more difficult to meet especially considering higher sampling rates required by higher resolution systems. Such requirements present a distinct disadvantage in radar image processing. A method would be desirable which lifts restrictions for stationary Doppler frequencies while allowing greater resolution of a target image. A method would be desirable which uses other than Fourier transform methods.
Accordingly, an object of the invention is to enhance resolution of radar images, to eliminate smearing of radar images, and to eliminate the necessity of using Fourier methods by applying joint timefrequency transforms to radar imaging to achieve superior image resolution and to extract features of radar targets.
In accordance with these and other objects made apparent hereinafter, the invention concerns performing an N point joint timefrequency transform of the M×N time aligned echo data, rather than a single one. Although this reduces image intensity, because echo energy from the target is spread through a large domain, (time and frequency, rather than just frequency), these images will lack the blurring common in images generated by the conventional approach caused by variations in Doppler echo frequencies from burst to burst. The preferred timefrequency transform is a crossterm reduced WignerVille distribution, such as the TimeFrequency Distribution Series, because of its potentially high resolution.
FIG. 1 is a diagram illustrating steppedfrequency inverse synthetic radar imaging of a moving target.
FIG. 2 is a diagram illustrating use of instantaneous frequency estimation for generating constant Doppler spectrum.
FIG. 3 is a diagram illustrating joint timefrequency transform for generating superior image resolution.
FIG. 4 is a block diagram illustrating inverse synthetic aperture radar using joint timefrequency transforms.
FIG. 5 is an illustration of a radar image of an aircraft with uncompensated phase errors resulting from use of prior art Fourier methods.
FIG. 6 is an illustration of a radar image sequence of an aircraft using joint timefrequency processing.
Timefrequency transforms
In accordance with the present invention, conventional Fourier transform processing is replaced by timefrequency transform processing. Many high resolution timefrequency transform are useful in embodying the method of present invention. Timefrequency transforms include linear transforms, such as the shorttime Fourier transform (STFT) and wavelet transforms, and bilinear transforms such as the WignerVille distribution.
WignerVille distribution transforms have better characteristics for processing timevarying spectrum than the linear transforms and may be used in one embodiment of the present invention. However, WignerVille distribution transforms suffer from crossterm interferences, which significantly interfere with application of bilinear timefrequency transform methods. To reduce the crossterm interference, a WignerVille distribution transform applied to timevarying spectrum in another embodiment can be filtered which while reducing timefrequency resolution also reduces undesirable crossterm interferences. WignerVille distributions with linear lowpass filter are characterized as a Cohen's class transform as described in "TimeFrequency Analysis", L. Cohen, Prentice Hall, 1995 incorporated herein by reference, and the distributions with nonlinear lowpass filter is called the timefrequency distribution series (TFDS) "Decomposition of WignerVille distribution and timefrequency distribution series", S. Qian and D. Chen, IEEE Trans. on Signal Processing, 42(10), 28362842 (1994).
In yet another embodiment, adaptive timefrequency transforms such as adaptive spectrogram transforms as described in "Signal representation using adaptive normalized Gaussian function", S. Qian and D. Chen, Signal Processing, 36(1) 111 (1994), incorporated herein by reference, and matching pursuit transforms as described in "Matching pursuit with timefrequency dictionaries", S. Mallat and Z. Zhang, IEEE Trans. on Signal Processing, 41(12) 33973415 (1993), incorporated herein by reference, are also high resolution timefrequency decompositions. Such adaptive timefrequency transforms decompose a signal into a family of Gabor elementary functions which may be further characterized as Gaussianmodulated, exponential functions which are very well localized in both the time and the frequency domain and adaptable to match the local behavior of the analyzed signal.
Correction of timevarying Doppler frequency
Fourier processing is based on constant Doppler spectrum associated with a constant target rotation rate. However, in general, the change in target's aspect angle may be nonuniform due to target's nonuniform rotation. Therefore, the Doppler frequencies become timevarying. FIG. 2 is a diagram illustrating use of instantaneous frequency estimation for generating constant Doppler spectrum.
For a single point scatterer, timevarying Doppler frequency 200 may be corrected by estimating the instantaneous frequency distribution 201 with a timefrequency transform. A resulting timedependent phase correction factor 204 can be applied to reshape the Doppler frequency spectrum 202 rendering the Doppler spectrum 203 for the single scatterer timeinvariant. However, for complex targets which consist of many scatterers, phase corrections for these individual scatterers are very complicated.
Replacing Fourier transform with timefrequency transform
Inherent limitations of Fourier transform processing can be overcome by replacing tertiary Fourier transform processing of Doppler spectrum with high resolution timefrequency transform processing. Fourier transform processing may still be useful in early processing of target data and may be present without interfering with timefrequency processing. Because of undesirable effects associated with timevariance in the Doppler spectrum, an efficient method to solve the problem of smeared Fourier spectrum and blurred image the preferred embodiment of the present invention applies a highresolution timefrequency transform to Doppler processing. FIG. 3 is a diagram illustrating joint timefrequency transform for generating superior image resolution.
Timefrequency processing 302 may, in the present invention, be applied to Doppler frequency signature 300 to decompose residual phase errors into instantaneous time slices 303. At each time slice or time instant, Doppler frequency components 304 are fixed. Thus, time relative range cell drift and Doppler frequency shift are eliminated for each scatterer. By examining motion of individual scatterers at successive time instants using high resolution timefrequency transforms there is no scatterer overlapping; therefore, no image blurring occurs. Further details are described in "Radar ambiguity function, timevarying matched filter, and optimum wavelet correlator", V. C. Chen, Optical Engineering, 33(7), 22122217 (1994) incorporated herein by reference, "Reconstruction of inverse synthetic aperture radar image using adaptive timefrequency wavelet transform", V. C. Chen, SPIE Proceedings on Wavelet Applications, 2491, 373386 (1995) incorporated herein by reference, and "Radar rangeDoppler imaging", V. C. Chen, Chapter 10 in "Introduction to Joint TimeFrequency AnalysisMethods and Applications", S. Qian and D. Chen, pp. 214229, Prentice Hall (1996) incorporated herein by reference. Since each scatterer has its own range and its own Doppler shift at each time instant a complete and instantaneous target image can be generated.
By replacing the conventional Fourier transform with a joint timefrequency transform, a 2D rangeDoppler Fourier frame becomes a 3D timerangeDoppler cube. FIG. 4 is a block diagram illustrating inverse synthetic aperture radar using joint timefrequency transforms. Radar receiver 400 inputs raw radar pulse signals so that frequency domain signatures 401 may be obtained. Range Processing 402 may apply a 1 dimensional IDFT to achieve global motion compensation by removing extraneous phase component due to motion. N Range profiles 403 for M range cells may be generated by Range Processing 402. Range Profiles 403 may be input into M Joint TimeFrequency Processors 404. By applying time sampling 405 to the output of Joint TimeFrequency Processors 404 in time, a time sequence of 2D rangeDoppler images can be viewed. Each individual timesampled image frame from ISAR Image Cube 406 provides not only higher resolution but also the temporal information within each frame.
From a timevarying spectrum point of view, the uncompensated phase error causes the Doppler spectrum to be timevarying. As previously described, processing the timevarying Doppler spectrum using conventional Fourier transform processing, the target image becomes blurred. FIG. 5 is an illustration of a radar image of an aircraft with uncompensated phase errors resulting from use of prior art Fourier methods. In this example, a simulated aircraft with a velocity fluctuation is used. By replacing the Fourier transform with a timefrequency transform, the single image frame 500 is resolved into a stack of its temporal frame elements. For each temporal frame element, its rangeDoppler resolution is higher than the Fourierbased image.
FIG. 6 is an illustration of a radar image of an aircraft using joint timefrequency processing. 600 shows a sequence of timesampled frames from an image sequence constructed using joint timefrequency transform. By using joint timefrequency transform processing, timevarying spectrum can be represented with better clarity. A Fourier based image 500, previously smeared, is resolved into a sequence of timevarying images 601 through 606, which has superior resolution and shows temporal information associated with changing range and Doppler information. In the sequence of frames, Doppler changes from one frame to another can be easily seen, especially for point scatterers smeared in Fourierbased image 500.
Advantage of the timefrequency Doppler processing
If a target has rotating parts, such as a propeller or antenna, the Fourierbased image of such a target may have strong strip lines along the Doppler axis. However, joint timefrequency Doppler processing transforms strip lines into pairs of dots moving with a small displacement up and down along the Doppler axis. Dots from two different frames of a temporal rangeDoppler image sequence provide information about the relative rotation rate of such parts, which may be useful for target identification.
While such additional information may be advantageous, joint timefrequency processing provides slightly less resolution than Fourier methods applied to targets displaying optimum characteristics. Advantages associated with joint timefrequency processing are in direct proportion to magnitude of target movement. Large magnitudes of motion, as previously mentioned, render such targets less susceptible to Fourier processing. In a case where perfect motion compensation for individual scatterers is possible: each scatterer remaining in its range cell with time invariant Doppler frequency, the Fourier transform may achieve a resolution which is better than that possible for the same target using joint timefrequency processing. However, perfect motion compensation is rarely achievable. Joint timefrequency based processing therefore exhibits the following advantages over conventional Fourier transform methods:
(1) Does not limit target point scatterers to the same range cells with constant Doppler shift.
(2) No need for complex, processor resource intensive motion compensation processing for individual point scatterers.
(3) If complex motion compensation has been applied to individual point scatterers with marginal results, joint timefrequency transform processing can still be applied to deblur target image.
(4) Joint timefrequency processing for ISAR imaging is a natural way to process moving targets with nonuniform motion or rotation and is a more efficient than complex motion compensation processing.
(5) Joint timefrequency processing allows radar imaging of multiple targets.
(6) Joint timefrequency processing allows SAR imaging of moving ground targets.
Claims (11)
Priority Applications (1)
Application Number  Priority Date  Filing Date  Title 

US08829263 USH1720H (en)  19970331  19970331  Time frequency processor for radar imaging of moving targets 
Applications Claiming Priority (1)
Application Number  Priority Date  Filing Date  Title 

US08829263 USH1720H (en)  19970331  19970331  Time frequency processor for radar imaging of moving targets 
Publications (1)
Publication Number  Publication Date 

USH1720H true USH1720H (en)  19980407 
Family
ID=25254008
Family Applications (1)
Application Number  Title  Priority Date  Filing Date 

US08829263 Abandoned USH1720H (en)  19970331  19970331  Time frequency processor for radar imaging of moving targets 
Country Status (1)
Country  Link 

US (1)  USH1720H (en) 
Cited By (19)
Publication number  Priority date  Publication date  Assignee  Title 

US6014099A (en) *  19981109  20000111  The United States Of America As Represented By The Secretary Of The Army  Isar method to analyze radar cross sections 
US6255981B1 (en) *  19990804  20010703  Raytheon Company  Method for range alignment and rotation correction of a high resolution image in an inverse synthetic aperture radar system 
US6332116B1 (en) *  20000419  20011218  National Instruments Corporation  System and method for analyzing signals of rotating machines 
US6356227B1 (en) *  19990916  20020312  Honeywell International, Inc.  Smearing compensation apparatus for a radar system 
US6384766B1 (en) *  19970618  20020507  Totalförsvarets Forskningsinstitut  Method to generate a threedimensional image of a ground area using a SAR radar 
US6453273B1 (en)  20000419  20020917  National Instruments Corporation  System for analyzing signals generated by rotating machines 
US6466156B1 (en) *  19990226  20021015  Totalforsvarets Forskningsinstitut  Method of detecting objects that change with time by means of a SAR radar 
US6469662B2 (en) *  19961017  20021022  Celsiustech Electronics Ab  Procedure for the elimination of interference in a radar unit of the FMCW type 
US6810341B2 (en)  20000419  20041026  National Instruments Corporation  Time varying harmonic analysis including determination of order components 
US20060066475A1 (en) *  20040127  20060330  Saab Ab  Method for reducing angular blur in radar pictures 
US7030808B1 (en) *  20040305  20060418  The United States Of America As Represented By The Secretary Of The Air Force  Nonlinear target recognition 
US20060109162A1 (en) *  20041123  20060525  Krikorian Kapriel V  Technique for enhanced quality high resolution 2D imaging of ground moving targets 
US20090292475A1 (en) *  20070525  20091126  Aftab Alam  TimeSpace Varying Spectra for Seismic Processing 
WO2010066458A1 (en) *  20081212  20100617  Astyx Gmbh  Imaging radar sensor having digital beam forming and synthetic magnification of the antenna aperture 
US20100245167A1 (en) *  20090325  20100930  Honeywell International Inc.  Systems and methods for gaussian decomposition of weather radar data for communication 
WO2011101225A1 (en) *  20100216  20110825  Astyx Gmbh  Device and method for measuring distance and speed 
US8044846B1 (en) *  20071129  20111025  Lockheed Martin Corporation  Method for deblurring radar rangedoppler images 
CN102608600A (en) *  20120409  20120725  西安电子科技大学  FPGA (fieldprogrammable gate array)based step frequency image splicing implementation method 
US8305256B1 (en) *  20100209  20121106  Lockheed Martin Corporation  Radar with PRF alteration on receive 
Cited By (24)
Publication number  Priority date  Publication date  Assignee  Title 

US6469662B2 (en) *  19961017  20021022  Celsiustech Electronics Ab  Procedure for the elimination of interference in a radar unit of the FMCW type 
US6384766B1 (en) *  19970618  20020507  Totalförsvarets Forskningsinstitut  Method to generate a threedimensional image of a ground area using a SAR radar 
US6014099A (en) *  19981109  20000111  The United States Of America As Represented By The Secretary Of The Army  Isar method to analyze radar cross sections 
US6466156B1 (en) *  19990226  20021015  Totalforsvarets Forskningsinstitut  Method of detecting objects that change with time by means of a SAR radar 
US6255981B1 (en) *  19990804  20010703  Raytheon Company  Method for range alignment and rotation correction of a high resolution image in an inverse synthetic aperture radar system 
US6356227B1 (en) *  19990916  20020312  Honeywell International, Inc.  Smearing compensation apparatus for a radar system 
US6332116B1 (en) *  20000419  20011218  National Instruments Corporation  System and method for analyzing signals of rotating machines 
US6453273B1 (en)  20000419  20020917  National Instruments Corporation  System for analyzing signals generated by rotating machines 
US6477472B2 (en)  20000419  20021105  National Instruments Corporation  Analyzing signals generated by rotating machines using an order mask to select desired order components of the signals 
US6810341B2 (en)  20000419  20041026  National Instruments Corporation  Time varying harmonic analysis including determination of order components 
US7236125B2 (en) *  20040127  20070626  Saab Ab  Method for reducing angular blur in radar pictures 
US20060066475A1 (en) *  20040127  20060330  Saab Ab  Method for reducing angular blur in radar pictures 
US7030808B1 (en) *  20040305  20060418  The United States Of America As Represented By The Secretary Of The Air Force  Nonlinear target recognition 
US7106243B2 (en) *  20041123  20060912  Raytheon Company  Technique for enhanced quality high resolution 2D imaging of ground moving targets 
US20060109162A1 (en) *  20041123  20060525  Krikorian Kapriel V  Technique for enhanced quality high resolution 2D imaging of ground moving targets 
US20090292475A1 (en) *  20070525  20091126  Aftab Alam  TimeSpace Varying Spectra for Seismic Processing 
US8185316B2 (en)  20070525  20120522  Prime Geoscience Corporation  Timespace varying spectra for seismic processing 
US8044846B1 (en) *  20071129  20111025  Lockheed Martin Corporation  Method for deblurring radar rangedoppler images 
WO2010066458A1 (en) *  20081212  20100617  Astyx Gmbh  Imaging radar sensor having digital beam forming and synthetic magnification of the antenna aperture 
US20100245167A1 (en) *  20090325  20100930  Honeywell International Inc.  Systems and methods for gaussian decomposition of weather radar data for communication 
US8144048B2 (en) *  20090325  20120327  Honeywell International Inc.  Systems and methods for gaussian decomposition of weather radar data for communication 
US8305256B1 (en) *  20100209  20121106  Lockheed Martin Corporation  Radar with PRF alteration on receive 
WO2011101225A1 (en) *  20100216  20110825  Astyx Gmbh  Device and method for measuring distance and speed 
CN102608600A (en) *  20120409  20120725  西安电子科技大学  FPGA (fieldprogrammable gate array)based step frequency image splicing implementation method 
Similar Documents
Publication  Publication Date  Title 

Moreira et al.  Airborne SAR processing of highly squinted data using a chirp scaling approach with integrated motion compensation  
Wang et al.  Global range alignment for ISAR  
Moreira et al.  Extended chirp scaling algorithm for airand spaceborne SAR data processing in stripmap and ScanSAR imaging modes  
Fornaro  Trajectory deviations in airborne SAR: Analysis and compensation  
Barbarossa et al.  Spacetimefrequency processing of synthetic aperture radar signals  
Romeiser et al.  Numerical study on the alongtrack interferometric radar imaging mechanism of oceanic surface currents  
Madsen  Estimating the Doppler centroid of SAR data  
Desai et al.  Convolution backprojection image reconstruction for spotlight mode synthetic aperture radar  
US4450444A (en)  Stepped frequency radar target imaging  
Hasselmann et al.  Theory of synthetic aperture radar ocean imaging: A MARSEN view  
Bamler et al.  Accuracy of differential shift estimation by correlation and splitbandwidth interferometry for wideband and deltak SAR systems  
Berizzi et al.  Autofocusing of inverse synthetic aperture radar images using contrast optimization  
Gough et al.  Imaging algorithms for a stripmap synthetic aperture sonar: Minimizing the effects of aperture errors and aperture undersampling  
Rigling et al.  Polar format algorithm for bistatic SAR  
US6222933B1 (en)  Method of processing spotlight SAR raw data  
Cantalloube et al.  Airborne Xband SAR imaging with 10 cm resolution: Technical challenge and preliminary results  
Ender et al.  New aspects of bistatic SAR: Processing and experiments  
Oliver et al.  Understanding synthetic aperture radar images  
Gough et al.  Unified framework for modern synthetic aperture imaging algorithms  
Lanari et al.  Spotlight SAR data focusing based on a twostep processing approach  
Brenner et al.  Demonstration of advanced reconnaissance techniques with the airborne SAR/GMTI sensor PAMIR  
Jao  Theory of synthetic aperture radar imaging of a moving target  
US5818383A (en)  Interferometric moving vehicle imaging apparatus and method  
US20050237236A1 (en)  Method and apparatus for performing bistatic radar functions  
Zhu et al.  Ground moving targets imaging algorithm for synthetic aperture radar 