[Studies in Computational Intelligence 481] Artur Babiarz, Robert Bieda, Karol Jędrasiak, Aleksander Nawrat (auth.), Aleksander Nawrat, Zygmunt Kuś (eds.) - Vision Based Systemsfor UAV Applications (2013, Sprin

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Estimation of Solution of Discrete Linear Time-Varying System 317 Namely, its elements are as follows a 11 (n)=sinn a 12 (n)= 1 n 3 +10 a 21 (n)= 1 n 2 +20 a 22 (n)=cosn . Applying the above-mentioned elements of (A(n)) n∈N to (3) and (4) we obtain (5) in the following form a (1) 11 (n) =a 11(n)ã 11 (n)=(a 11 (n)) 2 − 1 = sin 2 n − 1 a (1) 12 (n) =a 11(n)ã 12 (n)=(a 11 (n) − 1) a 12 (n)= sinn − 1 n 3 + 10 a (1) 21 (n) =a 12(n)ã 11 (n)=a 12 (n)((a 11 (n)) + 1)= sinn + 1 n 3 + 10 a (1) 22 (n) =a 12(n)ã 12 (n)=(a 12 (n)) 2 1 = (n 3 + 10) 2 a (2) 11 (n) =a 21(n)ã 21 (n)=(a 21 (n)) 2 = 1 (n 2 + 20) 2 a (2) 12 (n) =a 21(n)ã 22 (n)=a 21 (n)(a 22 (n)+1) = cosn + 1 n 2 + 20 a (2) 21 (n) =a 22(n)ã 21 (n)=(a 22 (n) − 1) a 21 (n)= cosn − 1 n 2 + 20 a (2) 22 (n) =a 22(n)ã 22 (n)=(a 22 (n)) 2 − 1 = cos 2 n − 1 Despite the fact that b(n)= 1 2 s ∑ i, j,k=1 ∣ ∣a (i) ∣ ∣∣ jk (n)+a(i) kj (n) = 1 [∣ ∣ ∣ ∣ ∣ ∣ ∣∣a (1) ∣∣ ∣∣a 11 2 (n)+a(1) 11 (n) (1) ∣∣ ∣∣a + 12 (n)+a(1) 21 (n) (1) ∣∣+ + 21 (n)+a(1) 12 (n) ∣ ∣ ∣ ∣ ∣ ∣ ∣a (1) ∣∣ ∣∣a 22 (n)+a(1) 22 (n) (2) ∣∣ ∣∣a + 11 (n)+a(2) 11 (n) (2) ∣∣+ + 12 (n)+a(2) 21 (n) ∣ ∣ ∣] ∣ ∣a (2) ∣∣ ∣∣a 21 (n)+a(2) 12 (n) (2) ∣∣ + 22 (n)+a(2) 22 (n) = [ 1 ∣∣ sin 2 n − 1 + sin 2 n − 1 ∣ ∣+ 2 ∣ (sinn − 1) 1 n 3 + 10 +(sinn + 1) 1 n 3 + 10∣ + ∣ ∣ ∣ (sinn + 1) 1 n 3 + 10 +(sinn − 1) 1 ∣∣∣∣ n 3 + 10∣ + 1 (n 3 + 10) 2 + 1 ∣∣∣∣ (n 3 + 10) 2 + ∣ 1 ∣(n 2 + 20) 2 + 1 ∣∣∣∣ ∣ (n 2 + 20) 2 + 1 1 ∣∣∣ ∣n 2 (cosn + 1)+ + 20 n 2 + 20 (cosn − 1) +
318 A. Czornik, A. Nawrat, and M. Niezabitowski ∣ 1 1 ∣∣∣ ∣n 2 (cosn − 1)+ + 20 n 2 + 20 (cosn + 1) + ∣ cos 2 n − 1 + cos 2 n − 1 ∣ ] = [ 1 2 ∣ sin 2 n − 1 ∣ ∣ ∣ ∣ ∣ ∣∣∣ sinn ∣∣∣ + 2 2 n 3 + 10∣ + 2 sinn ∣∣∣∣ n 3 + 10∣ + 2 1 ∣∣∣∣ (n 3 + 10) 2 + ∣ 1 ∣∣∣∣ ∣ 2 ∣(n 2 + 20) 2 + 2 cosn ∣∣∣ ∣n 2 + 20∣ + 2 cosn n 2 + 20∣ + 2∣ ∣cos 2 n − 1 ∣ ] = ∣ sin 2 n − 1 ∣ ∣ ∣∣∣ sinn + 2 n 3 + 10∣ + 1 (n 3 + 10) 2 + ∣ 1 ∣∣∣ (n 2 + 20) 2 + 2 cosn n 2 + 20∣ + ∣ cos 2 n − 1 ∣ are more and more smaller but always greater than 1, it implies that for any solution x(n,x 0 ) of system (1) only the upper estimate (7) ‖x(n + 1,x 0 )‖≤‖x 0 ‖ n ∏ p=0 √ (b(p)+1) is valid for all n. The numerical values of the solution and bound are presented in Figure (2) Fig. 2. Our upper estimate and values of norms of matrix products
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Studies in Computational Intelligen
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Aleksander Nawrat · Zygmunt Kuś E
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“In God We Trust, All others we o
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VIII Preface valuable information i
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Contents Part I: Design of Object D
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Contents XIII Technology Developmen
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XVI List of Contributors Adam Czorn
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XVIII List of Contributors Henryk M
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XX List of Contributors Józef Wron
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2 Design of Object Detection, Recog
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4 A. Babiarz et al. 1 Introduction
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6 A. Babiarz et al. The description
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8 A. Babiarz et al. a) b) Fig. 5. T
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10 A. Babiarz et al. o o o “micvo
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12 A. Babiarz et al. a) b) Fig. 7.
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14 A. Babiarz et al. • The camera
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16 A. Babiarz et al. the camera ser
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18 A. Babiarz et al. a) b) Fig. 11.
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20 A. Babiarz et al. patrol point i
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22 A. Babiarz et al. particular ang
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24 A. Babiarz et al. The sample cod
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Recognition and Location of Objects
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48 P. Demski et al. Fig. 1. Automat
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50 P. Demski et al. E-Grip firing m
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52 P. Demski et al. 4 Automatic Tar
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54 P. Demski et al. implementing su
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Object Tracking for Rapid Camera Mo
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Object Tracking in a Picture during
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94 Construction of Image Acquisitio
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96 G. Bieszczad et al. effectivenes
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98 G. Bieszczad et al. such a way t
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100 G. Bieszczad et al. Table 1. No
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102 G. Bieszczad et al. Fig. 7. Pri
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104 G. Bieszczad et al. Fig. 10. Re
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106 G. Bieszczad et al. Fig. 13. Ti
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108 G. Bieszczad et al. Fig. 16. Op
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110 G. Bieszczad et al. has to make
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112 G. Bieszczad et al. MTF functio
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114 G. Bieszczad et al. [11] Krupi
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116 D. Bereska et al. Presented in
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118 D. Bereska et al. Fig. 2. Image
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120 D. Bereska et al. Fig. 4. Ortho
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Omnidirectional Video Acquisition D
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Part III Design of Vision Based Con
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Vision System for Group of Mobile R
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A Distributed Control Group of Mobi
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178 D. Bereska et al. The aim of th
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180 D. Bereska et al. 3 Control Alg
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182 D. Bereska et al. Fig. 5. Schem
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184 D. Bereska et al. 4.1 Mechanica
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186 D. Bereska et al. 4.1.3 Open-Lo
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188 D. Bereska et al. Fig. 16. Comp
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Probabilistic Approach to Planning
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206 Practical Applications of Class
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208 M. Mellado and K. Skrzypczyk an
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210 M. Mellado and K. Skrzypczyk a
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212 M. Mellado and K. Skrzypczyk wh
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214 M. Mellado and K. Skrzypczyk Fi
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216 M. Mellado and K. Skrzypczyk 6
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Prototyping the Autonomous Flight A
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Feature Extraction and HMM-Based Cl
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248 K. Daniec et al. In this articl
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250 K. Daniec et al. Fig. 2. Applic
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252 K. Daniec et al. by the ability
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254 K. Daniec et al. The idea of us
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Selection of Individual Gait Featur
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[Studies in Computational Intelligence 481] Artur Babiarz, Robert Bieda, Karol Jędrasiak, Aleksander Nawrat (auth.), Aleksander Nawrat, Zygmunt Kuś (eds.) - Vision Based Systemsfor UAV Applications (2013, Sprin

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