M´ ethodologies d’Estimation et de D´ etection Robuste en Conditions Non-Standards Pour le Traitement d’Antenne, l’Imagerie et le Radar Jean-Philippe Ovarlez 1 , 2 1 SONDRA, CentraleSup´ elec, France 2 French Aerospace Lab, ONERA DEMR/TSI, France Joint works with F. Pascal, P. Forster, G. Ginolhac, M. Mahot, J. Frontera-Pons, A. Breloy, G. Vasile, and many others eme ´ Ecole d’´ 12 ` Et´ e de Peyresq en Traitement du Signal et des Images 25 juin au 01 juillet 2017 12 ` eme ´ Ecole d’´ Jean-Philippe Ovarlez Et´ e de Peyresq
General Introduction Background on Radar, Array Processing, ... Background on Signal Processing Motivations for more robust detection schemes General Introduction Motivations: Almost all algorithms and systems analysis for detection, estimation and classification rely on Covariance-Based methods Air and Ground Surveillance Radar Detection, Space-Time Adaptive Processing Synthetic Aperture Radar, Ground Moving Target Indicator Advance Communications Interferometry, Classification of Ground Adaptive Beamforming SAR Change Detection, SAR Classification Spectral Analysis Hyperspectral Detection and Classification Signal Intelligence MIMO MIMO Radar Spectral Analysis Tracking Superresolution Localization of Sources ELINT, COMINT Undersea Surveillance Detection, Space-Time Adaptive Processing Synthetic Aperture Sonar, Localization of Sources Change Detection Tracking 2 1/68 Almost all algorithms and systems analysis for detection, 12 ` eme ´ Ecole d’´ Jean-Philippe Ovarlez Et´ e de Peyresq
General Introduction Background on Radar, Array Processing, ... Background on Signal Processing Motivations for more robust detection schemes General Introduction Survey on • General statistical non-Gaussian modeling (spherically, elliptically random processes), • Robust covariance matrix estimation schemes (MLE, M -estimators), • Robust detection schemes (Adaptive Normalized matched Filter). 3 Main Parts • Part A: Background on Statistical Radar Processing and Motivations, • Part B: Recent Methodologies on Robust Estimation and Detection in non-Gaussian Environment, • Part C: Applications and Results in Radar, STAP and Array Processing, SAR Imaging, Hyperspectral Imaging. 2/68 12 ` eme ´ Ecole d’´ Jean-Philippe Ovarlez Et´ e de Peyresq
General Introduction Background on Radar, Array Processing, ... Background on Signal Processing Motivations for more robust detection schemes Contents Part A: Background on Radar, Array Processing, SAR and Hyperspectral Imaging Part B: Robust Detection and Estimation Schemes Part C: Applications and Results in Radar, STAP and Array Processing, SAR Imaging, Hyperspectral Imaging 3/68 12 ` eme ´ Ecole d’´ Jean-Philippe Ovarlez Et´ e de Peyresq
General Introduction Background on Radar, Array Processing, ... Background on Signal Processing Motivations for more robust detection schemes Part A Background on Radar, Array Processing, SAR and Hyperspectral Imaging 4/68 12 ` eme ´ Ecole d’´ Jean-Philippe Ovarlez Et´ e de Peyresq
General Introduction Background on Radar, Array Processing, ... Background on Signal Processing Motivations for more robust detection schemes Part A: Contents 1 General Introduction 2 Background on Radar, Array Processing, SAR and Hyperspectral Imaging Radar Background Array Processing - Space Time Adaptive Processing (STAP) SAR Image Processing Hyperspectral Image Processing 3 Background on Signal Processing Some Background on Detection Theory Examples 4 Motivations for more robust detection schemes 5/68 12 ` eme ´ Ecole d’´ Jean-Philippe Ovarlez Et´ e de Peyresq
General Introduction Background on Radar, Array Processing, ... Background on Signal Processing Motivations for more robust detection schemes Outline 1 General Introduction 2 Background on Radar, Array Processing, SAR and Hyperspectral Imaging Radar Background Array Processing - Space Time Adaptive Processing (STAP) SAR Image Processing Hyperspectral Image Processing 3 Background on Signal Processing Some Background on Detection Theory Examples 4 Motivations for more robust detection schemes 6/68 12 ` eme ´ Ecole d’´ Jean-Philippe Ovarlez Et´ e de Peyresq
General Introduction Radar Background Background on Radar, Array Processing, ... Array Processing - Space Time Adaptive Processing (STAP) Background on Signal Processing SAR Image Processing Motivations for more robust detection schemes Hyperspectral Image Processing Introduction RADAR = RAdio Detection And Ranging • emits and receives electromagnetic waves, • detects targets, • estimates target parameters (range, radial velocity, angles of presentation, acceleration, amplitude (related to Radar Cross Section), etc.) • images, recognizes, classifies, 7/68 12 ` eme ´ Ecole d’´ Jean-Philippe Ovarlez Et´ e de Peyresq
General Introduction Radar Background Background on Radar, Array Processing, ... Array Processing - Space Time Adaptive Processing (STAP) Background on Signal Processing SAR Image Processing Motivations for more robust detection schemes Hyperspectral Image Processing Range Measurement Electromagnetic wave propagates with speed light c . The two-way propagation delay up to the distance D is τ = 2 D c • Radar emitted signal: s e ( t ) = u ( t ) exp ( 2 i π f 0 t ) where f 0 is the carrier frequency, and u ( . ) the baseband signal, • Radar received signal: s r ( t ) = α s e ( t − τ ) + b ( t ) where α is the backscattering amplitude of the target and b ( . ) is an additive noise. � � t − 2 D s r ( t ) = α s e + b ( t ) . c 8/68 12 ` eme ´ Ecole d’´ Jean-Philippe Ovarlez Et´ e de Peyresq
General Introduction Radar Background Background on Radar, Array Processing, ... Array Processing - Space Time Adaptive Processing (STAP) Background on Signal Processing SAR Image Processing Motivations for more robust detection schemes Hyperspectral Image Processing Velocity Measurement Let us consider an illuminated moving target located for time t at range D ( t ) = D 0 + v t where v is the radial target velocity. If τ ( t ) is the two-way delay of the received signal at time t , the signal has been reflected at time t − τ ( t ) / 2 and the range D ( t ) has to verify the following equation: � � t − τ ( t ) c τ ( t ) = 2 D . 2 We obtain τ ( t ) = 2 D 0 + v t and the model relative to signal return is: c + v � c − v � c + v t − 2 D 0 s r ( t ) = α s e + b ( t ) . c + v The moving target is characterized in the signal return by a time-shift-compression/dilation of the emitted signal: action of Affine Group 9/68 12 ` eme ´ Ecole d’´ Jean-Philippe Ovarlez Et´ e de Peyresq
General Introduction Radar Background Background on Radar, Array Processing, ... Array Processing - Space Time Adaptive Processing (STAP) Background on Signal Processing SAR Image Processing Motivations for more robust detection schemes Hyperspectral Image Processing Velocity Measurement Under the so-called narrow-band assumptions: • f 0 >> B , where B is the bandwidth of baseband signal u ( . ) , • v << c , then � c − v � c + v t − 2 D 0 s r ( t ) = α s e + b ( t ) , c + v � � � � t − 2 D 0 − 2 i π 2 v = α exp ( i φ ) u exp ( 2 i π f 0 t ) exp c f 0 t + b ( t ) . c � � t − 2 D 0 s r ( t ) = α ′ s e exp (− 2 i π f d t ) + b ( t ) . c where | α ′ | = | α | and where f d = 2 v c f 0 is called the Doppler frequency corresponding to moving target. The moving target is so characterized in the signal return by a time-shift/frequency shift of the emitted signal: action of Heisenberg Group 10/68 12 ` eme ´ Ecole d’´ Jean-Philippe Ovarlez Et´ e de Peyresq
General Introduction Radar Background Background on Radar, Array Processing, ... Array Processing - Space Time Adaptive Processing (STAP) Background on Signal Processing SAR Image Processing Motivations for more robust detection schemes Hyperspectral Image Processing Doppler Effect 11/68 12 ` eme ´ Ecole d’´ Jean-Philippe Ovarlez Et´ e de Peyresq
General Introduction Radar Background Background on Radar, Array Processing, ... Array Processing - Space Time Adaptive Processing (STAP) Background on Signal Processing SAR Image Processing Motivations for more robust detection schemes Hyperspectral Image Processing Doppler Effect 12/68 12 ` eme ´ Ecole d’´ Jean-Philippe Ovarlez Et´ e de Peyresq
General Introduction Radar Background Background on Radar, Array Processing, ... Array Processing - Space Time Adaptive Processing (STAP) Background on Signal Processing SAR Image Processing Motivations for more robust detection schemes Hyperspectral Image Processing Ambiguity function and distance criterion One of the most important problem arising in radar theory is to separate targets in range and Doppler spaces. A L 2 ( R ) distance R between two signals X and Y can be defined: � + ∞ R 2 = | X ( t ) − Y ( t ) | 2 dt . − ∞ Minimizing this distance leads to maximize the inner product between X and Y : � + ∞ X ( t ) Y ∗ ( t ) dt . − ∞ According to the physical transformation of X , we obtain the so-called Ambiguity functions [Woodward, 1953, Kelly and Wishner, 1965]: � + ∞ X ( t ) X ∗ ( t − τ ) e − 2 i π ν t dt , • Example: Y ( t ) = X ( t − τ ) e 2 i π ν t : A ( τ, ν ) = − ∞ � + ∞ � � X ( t ) X ∗ � � 1 a − 1 t − b ) a − 1 t − b ) 1 • Example: Y ( t ) = √ a X : A ( a , b ) = √ a dt . − ∞ 13/68 12 ` eme ´ Ecole d’´ Jean-Philippe Ovarlez Et´ e de Peyresq
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