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

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4.1 Through-Wall TOA Estimation 44 dtot = da1 + dw + da2. A minimization method has to be used, because the coordinates of W1 and W2 (Fig. 4.1.1) are unknown and cannot be computed directly. Optimization procedures are based on the minimization of the travel time principle. For example, the travel path must be certain that the travel time between two arbitrary points is minimal [76]. Ryohei Tanaka in [136] introduced a method how to compute true T OA for two layer model (air-ground) used for ground penetrating radar applications. Four roots are computed from derivation of the T OA equaled to zero. Then, the right one is chosen and the true T OA is computed. For three layer model (air-wall-air) Fauzia Ahmad in [6] introduced complex and time consuming method that solves several goniometrical functions for computing true T OA. In order to transform three layer model (air-wall-air) into the less complex two layer model that will not introduce any error in precise T OAAT estimation we introduce one simple trick. Z Antenna Wall 1 Wall 2 Target W di2 W di1 Fig. 4.1.2: Total flight distance does not depend on distance between antenna and wall Wdi. The distance between the antenna and the wall Wdi in Z direction does not play any role in the T OAAT estimation (Fig. 4.1.2). When the distance between antenna and wall changes from Wdi1 to Wdi2, the true flight distance between antenna and target would not be changed. The only one condition has to be fulfilled, the entire wall has to be between the antenna and the target. Now, all the computations can be done with assumption that the rear side of the wall is at the target position and the two layer model (air - wall) can be used. With this simple trick the minimization process for three layer model does not need to be X
4.1 Through-Wall TOA Estimation 45 computed, what leads to much faster computation. Even if the Tanaka has already solved this problem in [136], hereunder, we introduce several improvements and simplifications that speed up computations even more. One have to mention, that antennas can be placed directly on a wall during measurements, and two layer model is directly obtained. However, in this case, the wall is in the antenna’s near field and therefore antenna impulse response in time domain has been significantly changed. Hereby, the reducing of long antenna impulse response influence on measured data by deconvolution, as it is described in Section 2.4.4, is not applicable any more. Therefore, antennas are placed at least 0.5 m from a wall during SAR scanning in practice, Wdi ≥ 0.5 m. The true T OAAT can be computed like summation of both times, the time of flight in the air and the time of flight in the wall: T OAAT (d) = da c + dw vw where da = da1 + da2. The total flight distance dtot is computed as: where dtot = da + dw (4.1.1) (4.1.2) � da = (HZ − Dw) 2 + (HX − d) 2 , dw = � D2 w + d2 (4.1.3) where HX is the distance between the antenna and target in X direction, HZ is the distance between the antenna and target in Z direction (Fig. 4.1.1). The true T OAAT for any antenna position A[xA, zA] and target position T [xT , zT ] that is represented by the image pixel position HX and HZ is required for formatting the image during SAR imaging. After substituting da and dw from (4.1.3) to the (4.1.1), only d will be unknown. In order to estimate d, the minimization process is computed by derivation: dT OAAT (d) = 0 (4.1.4) dd After several simple mathematical operations the fourth order polynomial equation with five coefficients is obtained: where coefficients: co1d 4 + co2d 3 + co3d 2 + co4d + co5 = 0 (4.1.5) co1 =c 2 − v 2 w, co2 = 2HX co3 =H 2 X � v 2 w − c 2� � � 2 2 2 c − vw + c (HZ − Dw) 2 − v 2 wD 2 w co4 =2v 2 wD 2 wHX, co5 = −v 2 wD 2 wH 2 X (4.1.6) The analytical solution of (4.1.5) even with Ferraris or Galois method [139] requires huge number of divisions and square root operations. Therefore, unlike in [136],
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 55 and 56: Chapter 4 Selected Research Methods
Page 57: 4.1 Through-Wall TOA Estimation 43
Page 61 and 62: 4.1 Through-Wall TOA Estimation 47
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
Page 99 and 100: 5.1 Conclusion and Future Work 85 5
Page 101 and 102: 50 100 150 200 250 300 350 400 Z 45
Page 103 and 104: 50 100 150 200 250 300 350 400 Z 45
Page 105 and 106: 50 100 150 200 250 300 350 400 Z 45
Page 107 and 108: 50 100 150 200 250 300 350 400 Z 45
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Z [cm] Z [cm] 50 100 150 200 250 30
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Z [cm] 50 100 150 200 250 300 b) Em
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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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