Radar hedef görüntüleme ve sınıflandırma için seyrek doğrusal öngörü modelleri

RADAR, which is the abbreviation for Radio Detection and Ranging, is used for many applications including fire control, air traffic control, meteorology, target searching, detecting and tracking. Radar transmits pulses or burst to search for targets. Scattered signals from the target are processed by the radar receiver to extract information about the target such as range, velocity, image of target. The most important radar application is the imaging. Imaging radars can provide range profile and radar image in addition to target's velocity. Resolution, which is the key point of imaging radar, is the problem for conventional radar because high resolution is succeeded with wide bandwidth and angular width. While wide bandwidth can be achieved by using stepped frequency or linear frequency modulated signal, wide angular width is obtained by increasing the dimension of antenna which is not desired or possible in real life application. Instead of huge antenna, synthetic aperture concept that is obtained by relative motion of target and radar is introduced. Synthetic Aperture Radar (SAR) and Inverse Synthetic Aperture Radar (ISAR) are based on the synthetic aperture concept. Range profile and radar image are reconstructed by processing the backscattered signals which are collected in frequency and frequency-aspect domain, respectively. Fourier Transform based method is the most common method to reconstruct range profile and radar image. 1-D IFFT of frequency domain data gives the range profile and scattering centers are estimated from the peaks of range profile. Uniformity in spatial frequency domain is required to construct focused radar image but collected data are uniformly sampled in frequency aspect domain. Polar to Cartesian transform is used to convert frequency aspect data to spatial frequency data with uniform sampling. After employing polar reformatting, 2-D IFFT of data constructs focused radar image. Computational cost of this method is very low. In spite of this advantage, the achieved resolution is limited. Spectral estimation methods are another method to generate high resolution range profile and radar image. Multiple Signal Classification (MUSIC) and Autoregressive (AR) model algorithms are the most popular spectral estimation methods. The idea behind the Multiple Signal Classification algorithm is the decomposition of correlation matrix into signal and noise subspaces. Correlation matrix is computed from averaging over the number of snapshots. However, only one snapshot is available in radar application. Spatial smoothing method is used to compute correlation matrix. MUSIC algorithm with spatial smoothing process provides high resolution although it decreases the effective bandwidth. Success of this algorithm is not enough to find the location of scatterers if backscattered data are limited or have low signal to noise ratio (SNR). AR model which is based on the forward and backward linear prediction improves the resolution in range and cross range direction. Radar profile and radar image are obtained by AR model power spectrum. The simplest way to estimate AR model coefficients is to minimize the l-2 norm of the error between predicted and observed signal. Spurious peaks and sidelobes might appear in the range profile and radar image depending on the AR model order. Sidelobes can be suppressed by Singular Value Decomposition (SVD) truncation. The drawback of this method is that number of scatterers should be known or estimated. Backscattered data can be represented as linear combination of small number of elements from overcomplete dictionary which consists of elementary signals. The idea behind the sparsity is to find the smallest subset of dictionary which represents the observed signal. Most of entries in signal representation vector/matrix should be zero to represent backscattered signal with less atoms. Radar image which is based on sparse signal representation provides high resolution in both range and cross range direction without predicting the number of scatterers. Sparse representations can be computed by three-different minimization problem which are Basis Pursuit Denoising (BPDN), Basis Pursuit Denoising with Penalty term and Least Absolute Shrinkage and Selection Parameter (LASSO). Basis Pursuit Denoising algorithm minimizes the sum of the absolute value of coefficients of the sparse representation vector/matrix subject to the residual sum of squares being less than the constant. BPDN with penalty terms is the unconstraint formulation of BPDN. Sparse coefficients are obtained by the l-2 norm minimization of residual by penalizing l-1 norm of the coefficients of the sparse representation vector/matrix. LASSO minimizes residual sum of squares while sum of the absolute value of coefficients of the sparse representation vector/matrix is smaller than constant threshold. Solution of BPDN with penalty term, BPDN and LASSO minimization problems take a lot of time. Orthogonal Matching Pursuit (OMP) algorithm is another method to generate sparse representations of the range profile and radar image. This method requires short time to find the sparse solution. High resolution radar image and range profile can be achieved by using these methods. In this thesis, radar imaging based on sparse AR modeling is proposed. Tickhonov regularization is another way to solve the ill-posed equation system by introducing smoothness and sparsity. If l-2 norm of the AR model coefficients are penalized, smoother solution is produced. The inclusion of l-0 norm penalty function produces sparse solution. In this work, backscattered signals are modeled by AR model algorithm and sparse AR model coefficients are calculated. Sparse AR model coefficients are computed from BPDN, BPDN with penalty term and LASSO. Spurious peaks and side lobes are suppressed in the resulting radar image. Especially, proposed sparse AR model approaches yield better result than the other spectral estimation methods in case of the low SNR and narrowband data. Although all scatterers and location of them are found correctly in radar image based sparse representation, classification success of these methods is the worst one. As a result, radar imaging based on sparse representation is a good candidate for imaging if data are collected at wide bandwidth and angular width. Classification results of methods except sparse radar image representation are very close to each other under the wide bandwidth and aspect angle case. For the limited data case, classification of radar images based sparse AR model methods yields best result among all the methods which are explained in the thesis. Classification results of MUSIC algorithm is in the second place. This result is expected since sparse AR model methods are more successful than MUSIC algorithm to find the scatterers and location of them. As a conclusion, 1-D and 2-D sparse AR model are proposed and these models are applied on the radar data to reconstruct range profile and radar image. Sidelobes are suppressed in the generated range profile and radar image. In addition to that, this method is more successful than MUSIC algorithm to find the scatterers for the limited data case. Classification success will be enhanced if range profile and radar image are generated by using proposed method.