Through-Wall Imaging With UWB Radar System - KEMT FEI TUKE

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2.5 Radar Imaging Methods Overview 34 current computing techniques. That makes impossible to use inverse problem in real-time for rescue and security applications. 2.5.9 Multiple Signal Classification MUSIC is generally used in signal processing problems and was introduced by Therrien in 1992 [138]. It is the method for estimating individual frequencies of multiple harmonic signals. The use of MUSIC for radar imaging was proposed by Devaney in 2000 [48]. He applied the algorithm to the problem of estimating the locations of a number of point-like scatterers. Detailed description of MUSIC algorithm can be found e.g. in [48, 32, 82]. MUSIC for image processing has been developed for multistatic radar systems. It is the wave equation based method. The basic idea of MUSIC is the formulation of the so called multistatic response matrix which is then used to compute the time reversal matrix whose eigenvalues and eigenvectors are shown to correspond to different point-like targets. The multistatic response matrix is formulated using frequency domain data, which is obtained by applying the Fourier transform to the time domain data. N antennas are centered at the space points Rn, n = 1, 2, ..., N. The positions of the antennas are not necessarily restricted to be in the same plane or regularly spaced. The n-th antenna radiate a scalar field ψn (r, ω) into a half space in which are embedded one or more scatterers (targets). M (M ≤ N) is the number of scatterers and Xm is the location of the m-th target in the space. Born approximation is again considered [54,26]. The waveform radiated by the n-th antenna, scattered by the targets and received by the j-th antenna is given by: ψn (Rj, ω) = M� G (Rj, Xm) τm (ω)G (Xm, Rn) VSn (ω) (2.5.48) m=1 where G (Rj, Xm) and G (Xm, Rn) are the Green’s functions of the Helmholtz equation in the medium in which the targets are embedded in direction from transmitter antenna to the target and from the target to the receiving antenna respectively. τm (ω) represents the strength of the m-th target and VSn (ω) is the voltage applied at the n-th antenna. In this formula, the signal is only considered for a single angular frequency ω. However, the extension for multiple frequencies is obvious. The multistatic response matrix K is defined by: Knj = M� G (Rj, Xm) τm (ω)G (Xm, Rn) . (2.5.49) m=1 The scattered waveform emitted at each antenna is measured by all the antennas,
2.5 Radar Imaging Methods Overview 35 so the elements of the multiple response matrix K can be calculated as: Knj = ψn (Rj, ω) . (2.5.50) VSn (ω) The main idea of MUSIC is to decompose a selfadjoint matrix into two orthogonal subspaces which represent the signal space and the noise space. This method is often called Singular Value Decomposition (SVD) [27]. Since the multistatic response matrix is complex, symmetric but not Hermitian (i.e. it is not selfadjoint), the time reversal matrix T is defined from the multistatic response matrix: T = K ∗ njKnj (2.5.51) where ∗ denotes the complex conjugation. The time reversal matrix has the same range as the multistatic response matrix. Moreover, it is selfadjoint. The time reversal matrix T can be represented as the direct sum of two orthogonal subspaces. The first one is spanned by the eigenvectors of T with respect to non-zero eigenvalues. If noise is present, this subspace is spanned by the eigenvectors with respect to eigenvalues greater than a certain value, which is specified by the noise level. This space is referred to as the signal space. Note that its dimension is equal to the number of the point-like targets. The other subspace, which is spanned by the eigenvectors with respect to zero eigenvalues (or the eigenvalues smaller than a certain value in the case of noisy data), is referred to as the noise subspace. The corresponding eigenvectors are denoted by the eigenvalues: λ1 ≥ λ2 ≥ ... ≥ λM ≥ λM+1 ≥ ... ≥ λN ≥ 0 (2.5.52) of the time-reversal matrix T and vn, n = 1, 2, ..., N are the corresponding eigenvectors. The signal subspace is spanned by v1, ..., vM and the noise subspace is spanned by the remaining eigenvectors. For detection of the target the vector g p is calculated from the vector of the Green’s functions: g p = (G (R1, p) , G (R2, p) , ..., G (RN, p)) ′ . (2.5.53) The point P is at the location of one of the point-like targets if and only if the vector gp is perpendicular to all the eigenvectors vn, n = M +1, ...s, N. In practice, the following pseudo spectrum is usually calculated by: 1 D (P ) = N� |(vn, gp )| 2 . (2.5.54) n=M+1 The point P belongs to the locations of the targets if its pseudo spectrum is very large (theoretically, in the case of exact data, this value will be infinity). Simulated time-reversal imaging with MUSIC considering multiple scattering between the targets is shown in [64] In this case influence of a wall can be taken into account by applying Green’s function considering the wall, what is a real challenge itself.
Page 1 and 2: TECHNICAL UNIVERSITY OF KOˇSICE Fa
Page 3 and 4: Acknowledgement I give a sincere gr
Page 5 and 6: CONTENTS v 3 Goals of Dissertation
Page 7 and 8: LIST OF FIGURES vii List of Figures
Page 9 and 10: LIST OF FIGURES ix 4.4.3 Aquarium f
Page 11 and 12: LIST OF FIGURES xi List of Symbols
Page 13 and 14: LIST OF FIGURES xiii kx - Horizonta
Page 15 and 16: Chapter 1 Introduction 1.1 Motivati
Page 17 and 18: 1.3 Thesis Organization 3 In additi
Page 19 and 20: Chapter 2 State Of The Art 2.1 UWB
Page 21 and 22: 2.2 Through-Wall Radar Basic Model
Page 23 and 24: 2.3 SAR Scanning 9 and shall remain
Page 25 and 26: 2.4 Calibration and Preprocessing 1
Page 27 and 28: 2.4 Calibration and Preprocessing 1
Page 29 and 30: 2.5 Radar Imaging Methods Overview
Page 47: 2.5 Radar Imaging Methods Overview
Page 55 and 56: Chapter 4 Selected Research Methods
Page 57 and 58: 4.1 Through-Wall TOA Estimation 43
Page 71 and 72: 4.2 Measurements of the Wall Parame
Page 81 and 82: 4.3 Highlighting of a Building Cont
Page 91 and 92: 4.4 Measurements of the Practical S
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5.1 Conclusion and Future Work 85 5
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BIBLIOGRAPHY 99 [13] T. W. Barrett,
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BIBLIOGRAPHY 101 [46] G. Derveaux,
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BIBLIOGRAPHY 103 [81] S. Kidera, T.
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BIBLIOGRAPHY 105 [115] J. Sachs, M.
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BIBLIOGRAPHY 107 [150] O. Yilmaz, S
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Through-Wall Imaging With UWB Radar System - KEMT FEI TUKE

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