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1、Time frequency analysis based techniques for radar signal processing,Igor Djurovi,LJubia Stankovi,Milo DakoviElectrical Engineering Department,University of MontenegroThayananthan Thayaparan,Department of Defense,Canada,Background,From 2003,the Research Center for Signals and Systems,from the Univer
2、sity of Montenegro(head of the centerp Prof.Stankovi)has been engagged in several projects related to the radar signal processing and application of the time-frequency analysis techniques in this field.Projects were funded by Department of defense Canada and we collaborated with Dr Thayanathan Thaya
3、paran.,Topics of projects,We analyzed multiple topics:HF radar imaging in clutter environment based on the TF analysis and decomposition techniques.Modeling radar images.Analysis and removal of micro-Doppler effects in ISAR images.Focusing and reducing motion caused effects in SAR and ISAR images.Hi
4、gh-resolution radar systems.Noise waveform radar systems.SAR imaging of ships and other vessels.,My topics,I were engaged in two main subtopics:Removing and analysis of micro-Doppler effect from radar images;Focusing and reducing motion caused effects in SAR and ISAR images.In this presentation thre
5、e issues are highlighted:Decomposition of radar signals by using the TF representations with application to radar imaging in clutter environment(this technique is proposed by Dr Milo Dakovi).Model of helicopter target developed in analysis of micro-Doppler effect.Focusing and reducing motion caused
6、effects in SAR and ISAR images.,I.PARAMETER ESTIMATION BY USING DECOMPOSITION OF SIGNALS IN TIME-FREQUENCY DOMAIN WITH APPLICATION TO RADAR SIGNALS,Wigner distribution(WD),Bilinear TF representationHighly concentrated in the TF planeIdeal representation of the linear FM signalsDrawbacks:cross-termso
7、ver-samplingPseudo-Wigner distribution(PWD)window along coordinatecross-terms reducing for components located in different time intervals,Wigner and pseudo-Wigner TFD,Signal with 6 components.Auto-terms denoted with ai,cross-terms cij.PWD reduces some cross-terms.Cross-terms caused by signals that a
8、ppear in the same instant could not be removed.,S-method,Based on the short-time Fourier transform(STFT)Special cases:P()=1the PWD with window function w()w*(-)P()=()the spectrogramSuitable selection of the window P()width reduces cross-terms with the same quality of the auto-terms as in the WD,S-me
9、thod,Signal with 6 short componentsSTFT with rectangular windowS-method eliminates cross terms on different frequenciesCross-term causes by signal on the same frequency remains.,S-method-discrete realization,It can be realized in recursive manner.Rectangular window of width 2L+1 is used.Initial step
10、 in calculation is the spectrogram for L=0.,S-method for L=0,1,.,N/2,Signal parameters estimation,Estimation of signal amplitudeInstantaneous frequency estimationSignal detection for high noise environmentEstimating number of componentsAnalysis of components in multicomponent signals,Decomposition o
11、f multicomponent signals,The inverse of the WD can be calculated by eigendecomposition of appropriate matrix obtained from the WD.S-method of multicomponent signal can be equal to sum of the WD of components.Eigenvalue decomposition of matrix obtained by using the S-method produces the eigenvectors
12、that represent normalized signal components.Eigenvalues contain information on energy of components.,Discrete WD is defined as:,Inversion of the WD,Inverse FT produces:,Now we can form matrix R with elements:,Eigenvector decomposition,Eigenvector decomposition of R gives:,where n are eigenvalues whi
13、le un are eigenvectors.,Matrix obtained based on the WD is:,From this conclusions it follows that:Matrix R has one non-zero eigenvalue 1 Eigenvector u1 is proportional to analyzed signalReconstructed signal is:,S-method decomposition,S-method could be equal to the sum of WDs of signal components.,Ma
14、trix R is now:,Eigenvectors of R are proportional to signal components under condition that signal components are linearly independent and that we have no multiple eigenvalues.,Example:Decomposition of signal with multiple components,TFR of eigenvectors for the S-method decomposition,Problems in dec
15、omposition,n=(n1+n2)/2 and m=(n1-n2)/2 can introduce non-integer index(to avoid it,the TFR is oversampled).For very close components in the TF plane it is not possible to select L in the WD that the S-method is equal to sum of WDs.ThenAnalyzed component can be contained in several eigenvectors.Eigen
16、vectors are orthogonal and it is possible to sum their TFRs.We need some criterion for selection of eigenvectors(or eigenvalues).,Detection of deterministic signal,Signal+Noise,Noise,Fourier transform and TFR,TF signal detector,TFR of signal s(n)is S(n,k).Assume that signal s(n)has deterministic com
17、ponent x(n),with slowly varying amplitude and IF.Form set of paths in the TF plane=(n):|(n)-(n-1)|D.Calculate sum of S(n,k)values along the paths from P and calculate maximum.Obtained maximum is compared with threshold value and based on this comparison we are making decision about existence of dete
18、rministic signal in the mixture.,Problems in TF detector realization,Decreasing of number of paths in We propose strategy for decreasing the number of paths in P that decreases search complexity but it increases probability of error in detection.Considered paths are only those that are on the local
19、maximum of the TFRDetection thresholdProportional to noise variance(noise variance estimation is required step).Threshold depends on the used TFR.Threshold depends on the“false alarm”probability.For a given TFR and“false alarm”probability detector threshold can be efficiently determined using statis
20、tical techniques.,Radar signals,Radar signals are non-stationary and TFR can produce very favorable results for this signal type.Algorithm for decomposition has been applied for separating useful signal(radar targets return)from noise and clutter.The proposed algorithm has been tested on simulated a
21、nd experimentally obtained signals.It has been shown that the TFR decomposition gives very accurate results even for high noise environment.,Model of radar signals,We derived analytical model of radar signal reflected from the moving target.Radar emits sequence of M linear frequency modulated signal
22、s.Reflected signal is delayed for 2d/c with respect to emitted signal.Frequency shift is proportional to target velocity.Based on the derived model we analyzed resolution of radar system in estimation of position and distance of targets.Radar clutter is also modeled.,Experimental data,High frequency
23、 surface wave radar(HFSWR)is used in experiments.Target was King Air 200 above the sea on small altitude(emphatic radar clutter)Operating frequency:5.672 MHzBandwidth:125 kHzPulse repetition frequency:9.17762 HzNumber of pulses:256Coherent integration time:27.89 s Number of positions:69Total experim
24、ent duration:33 min.The main source of clutter were signals reflected from sea surface.,Decomposition of experimental data:Algorithm,Calculate the STFT of oversampled radar signal.Calculate S-method for a given L.Form matrix R.Perform eigendecomposition of RCalculate TFR of eigenvectors and decide i
25、f it is signal caused by target or by clutter(or noise).If radar target is not detected repeat step 2 with smaller L.TFR of target is obtained as a sum of TFRs of eigenvectors that correspond to the detected target components.,Selection of Eigenvectors,Criterion based on the concentration measure:S-
26、method of the eigenvectorS-method of target is cross-term freeClutter signal has emphatic cross-termsCross-terms have oscillatory natureCriterion based on amplitude of target signal:Signal reflected from target has slowly varying amplitudeBased on the experimental data we concluded that clutter comp
27、onents have fast varying amplitude,Example 1:Constant target velocity,Example 1:TFR of eigenvectors,Example 2:Target with nonstationary motion,Example 2:TFR of eigenvectors,12,11,10,9,8,7,6,5,4,3,2,1,Example 3:Nonstationary motion with small velocity,Example 3:TFR of eigenvectors,Example of Signal D
28、etectionExperimental data,SNR=-8 dB,Conclusion,It is developed theoretical model of decomposition of multicomponent signal to separate signal components.The algorithm for decomposition has been applied to simulated and real signals.Noise influence to decomposition has been analyzed.Method for detect
29、ion of deterministic signals in heavy noise based on the TFR has been developed.,Published Papers on this Topic,LJ.Stankovi,T.Thayaparan,M.Dakovi,Signal Decomposition by Using the S-method With Application to the Analysis of HF Radar Signals in Sea-Clutter,IEEE Trans.on Signal Processing,Vol.54,No.1
30、1,Nov.2006.LJubisa Stankovic,Thayananthan Thayaparan,Milos Dakovic,“Algorithm for signal decomposition by using the S-method”,13th EUSIPCO Conference,Antalya,Turkey.,II.SEPARATION OF MICRO-DOPPLER EFFECT AND STATIONARY BODY FOR HELICOPTER SIGNALS BY USING THE SPECTROGRAM AND L-STATISTICS,Model of he
31、licopter signal,Modeled effects(model of UH-1D Iroquois):Main body fuselage(stationary reflector points)Main rotorMain rotor flashesTail rotor flashes,Signal is sampled with Dt=1/48000s and considered within interval of 400ms.Rigid body is modeled as sinusoidal components at:-10.3kHz,-2.5kHz,2.3kHz
32、and 2.7kHz.In addition components at 0.4kHz are modulated time tones added to the data tape.,Model of moving parts,Main rotor:Flashes:,AROT=19kHz,TROT=175ms,TTAIL=35.8ms,Filters for flashes,hFL_M(t)and hFL_T(t)are impulse responses of filters with frequency responses:,Simulated signal,Fourier transf
33、orm,Spectrogram and L-statistics,Separation of the m-D effect and stationary body influence will be performed by using the spectrogram:For a given frequency w spectrogram samples are sorted from the smallest toward the bigger:S(n)(w)S(n+1)(w)where S(n)(w)STFT(t,w),for a given w.,Spectrogram,smallest
34、 samples(average of smallest samples for a given frequency)used for detection of stationary patterns.,region used for detection of tail blades(stationary patterns are removed),detection of effects associated with main blades,detection of stationary patterns,detection of tail blades,detection of main
35、 blades,stationary signal pattern,main rotor flashes,tail rotor flashes,rotating blades,Separation requires additional processing in time domain and pattern recognition tools currently under investigation.,Characteristics of the algorithm,Current setup with proposed algorithm parameters and for give
36、n example works accurate for SNR10dB.Two ingredients of the algorithm:spectrogram(common and its implementation could be assumed to be fast)sorting of samples(fast sorting procedures such as quicksort or insertion sort should be employed).There is a room for improvement of the algorithm in terms of
37、accuracy and adaptivity but all kind of optimization requires training on real data.Proposed example is simulated according to:S.L.Marple:Special time-frequency analysis of helicopter Doppler radar data,in Time-Frequency Signal Analysis and Processing,ed.B.Boashash,Elsevier 2004.,Published Paper on
38、this Topic,LJ.Stankovi,T.Thayaparan,I.Djurovi:Time-frequency representation based approach for separation of target rigid body and micro-Doppler effects in ISAR imaging,IEEE Transactions on Aerospace and Electronics,accepted for publication.,III.IMPROVING RADAR IMAGES FOR SAR AND ISAR SYSTEMS,Introd
39、uction,ISAR(Inverse Synthetic Aperture Radar)images are commonly obtained by a 2D Fourier transform of the dechirped reflected signal.Longer time interval gives better image resolution.Target points with high velocity changes within the considered time interval are blurred.By using time-frequency an
40、alysis methods sharpness of ISAR images can be improved without reducing resolution.,ISAR model,Analytic CW Radar Signal Model,Consider radar signal model in the form of series of M chirps:,Each chirp is a linear frequency modulated signal:,ISAR imaging,The ISAR image P(m,n)is obtained by 2D DFT,Dem
41、odulated filtered received signal component is of the form,Fourier transform of the Doppler part,Consider Doppler part of the received signal:,and its Fourier transform:,where w(t)is window defining the considered Coherent Intergration Time(CIT).,Denote Fourier transform of the window w(t)by W(),Tim
42、e varying distance,Taylor expansion of the time varying distance,reduces Fourier transform to,with spreading factor,SAR Model,SAR Model,SAR model is similar to the ISAR with difference that it is assumed that radar is moving and that target is non-moving.Motion of target causes spreading of componen
43、ts but also dislocation from the proper position.We will demonstrate technique for SAR imaging based on the polynomial FT with couple comments and simulations for ISAR images.,PFT some basic informations,The polynomial FT(PFT)is introduced several times in science.Detailed statistical study has been
44、 provided by Katkovnik.It is defined as:For polynomial phase signal:the PFT is ideally concentrated on w=a1,ai=ai,i=2,.,k.,PFT-Introduction,Since the PFT can be calculationally demanding we will consider the PFT of the second order:We assume that the second-order nonlinearity is enough for compensat
45、ing motion caused effects but also we propose the order adaptive PFT form in the case that we need to increase the PFT order.,Notation,Set of received chirps will be denoted as:s0(t,m).Standard radar image obtained by the 2D FT is:,where,SAR imaging algorithm,For each mLet r(t,m)=s0(t,m)andI=1 and.W
46、hile radar return r(t,m)contains significant energyCalculate SI(wt,m)=R(wt,m)for(wt,m)representing well-focused component(target)and SI(wt,m)=0 otherwise.Non-focused components are updated as:R(wt,m)SI(wt,m)-R(wt,m).Then we calculate:Set II+1.For aL(for various chirp rates from set L)Calculate:Endfo
47、r,1,2,3,SAR Imaging algorithm,Estimate the chirp-rate of the radar return:EndwhileEndforRadar image is calculated as:,Comments on the algorithm,A technique for determination of chirp returns with significant energy has been developed.This technique works accurately for images with small noise and fo
48、r some noise environments.Chirps with small energy are not processed since it is assumed that they have not moving components.Technique for determination of well-focused components has been developed.When we cannot detect highly concentrated component we can use the third order PFT to get better con
49、centration:,Comments on the algorithm,Set of chirp rates L can be selected based on information of maximal velocity and acceleration of targets.Chirp-rates in the set could be non-equidistantly spaced.This technique does not solve problem of displacement radar targets from proper position due to mot
50、ion caused effects.For handling this problem some classical techniques for motion estimation from video-signals processing are commonly used.The PFT imaging does not require the estimation of chirp rates for each frame since it can be assumed that the chirp rates varies very slowly.,Examples,We cons
