Thesis - Leigh Moody.pdf - Bad Request - Cranfield University

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Appendix I / Utilities / Quaternions _ _ Expanding, q B A q q q B A B A B A ⎛ Φ ⎜ ⎝ 2 B ⎞ ⎟ ⎠ ⎛ Θ ⎜ ⎝ 2 B ⎞ ⎟ ⎠ ( ) ⎟ ⎜ A ⎟ ⎜ A ⎟ ⎜ A ⋅ ⎟ + ⎜ A 0 : = c ⋅ c c s ⎟ ⋅ s⎜ A ⎟ ⋅ s⎜ A ⎛ Φ ⎜ ⎝ 2 B ⎞ ⎟ ⎠ ⎛ Θ ⎜ ⎝ 2 B ⎞ ⎟ ⎠ 22.10-2 ⎛ Ψ ⎜ ⎝ 2 ⎛ Ψ ⎜ ⎝ 2 B B ⎞ ⎟ ⎠ ⎛ Φ ⎜ ⎝ 2 ⎛ Φ ⎜ ⎝ 2 B ⎞ ⎟ ⎠ ⎛ Θ ⎜ ⎝ 2 B ⎞ ⎟ ⎠ ⎛ Ψ ⎜ ⎝ 2 B Equation 22.10-6 ⎛ Θ ⎜ ⎝ 2 ⎛ Ψ ⎜ ⎝ 2 ( ) ⎟ ⎜ A ⎟ ⎜ A ⎟ ⎜ A ⋅ ⎟ − ⎜ A 1 : = s ⋅ c c c ⎟ ⋅ s⎜ A ⎟ ⋅ s⎜ A ⎛ Φ ⎜ ⎝ 2 B ⎞ ⎟ ⎠ ⎛ Θ ⎜ ⎝ 2 B ⎞ ⎟ ⎠ ⎛ Ψ ⎜ ⎝ 2 ⎞ ⎟ ⎠ B ⎛ Φ ⎜ ⎝ 2 ⎞ ⎟ ⎠ B ⎞ ⎟ ⎠ B Equation 22.10-7 ⎛ Θ ⎜ ⎝ 2 ⎛ Ψ ⎜ ⎝ 2 ( ) ⎟ ⎜ A ⎟ ⎜ A ⎟ ⎜ A ⋅ ⎟ + ⎜ A 2 : = c ⋅ s c s ⎟ ⋅ c⎜ A ⎟ ⋅ s⎜ A ⎛ Φ ⎜ ⎝ 2 B ⎞ ⎟ ⎠ ⎛ Θ ⎜ ⎝ 2 B ⎞ ⎟ ⎠ B ⎛ Ψ ⎜ ⎝ 2 B ⎞ ⎟ ⎠ B ⎛ Φ ⎜ ⎝ 2 ⎞ ⎟ ⎠ B ⎞ ⎟ ⎠ B Equation 22.10-8 ⎛ Θ ⎜ ⎝ 2 ⎛ Ψ ⎜ ⎝ 2 ( ) ⎟ ⎜ A ⎟ ⎜ A ⎟ ⎜ A ⋅ ⎟ − ⎜ A 3 : = c ⋅ c s s ⎟ ⋅ s⎜ A ⎟ ⋅ c⎜ A 22.10.3 Quaternion Product ⎞ ⎟ ⎠ B ⎞ ⎟ ⎠ B ⎞ ⎟ ⎠ B Equation 22.10-9 Q_PRODUCT takes quaternions representing the orientation of frame (B) with respect to frame (B), and frame (C) with respect to (B), and returns the quaternion product representing the transformation from (A) to (C). Q_PRODUCT The product of two quaternions is, B C C ( Q , Q , Q ) A B A Equation 22.10-10 C B C B C B C B C B ( q ( 0 ) ⋅ q ( 0 ) − q • q , q ( 0 ) ⋅ q + q ⋅ q ( 0 ) − q × q ) B Expanding, q C A A B A Q C B ⊗ Q B B A : = A B A B A Equation 22.10-11 C B C B C B C B ( 0 ) : = q ( 0 ) ⋅ q ( 0 ) − q ( 1 ) ⋅ q ( 1 ) − q ( 2 ) ⋅ q ( 2 ) − q ( 3 ) ⋅ q ( 3 ) B A B A B A B A Equation 22.10-12 ⎞ ⎠ ⎞ ⎠ ⎞ ⎠ ⎞ ⎠
Appendix I / Utilities / Quaternions _ _ q q C A C A q C B C B C B C B ( 1 ) : = q ( 0 ) ⋅ q ( 1 ) + q ( 1 ) ⋅ q ( 0 ) + q ( 3 ) ⋅ q ( 2 ) − q ( 2 ) ⋅ q ( 3 ) B A B 22.10-3 A B A B A Equation 22.10-13 C B C B C B C B ( 2 ) : = q ( 0 ) ⋅ q ( 2 ) + q ( 2 ) ⋅ q ( 0 ) − q ( 3 ) ⋅ q ( 1 ) + q ( 1 ) ⋅ q ( 3 ) C A B A B A B A B A Equation 22.10-14 C B C B C B C B ( 3 ) : = q ( 0 ) ⋅ q ( 3 ) + q ( 3 ) ⋅ q ( 0 ) + q ( 2 ) ⋅ q ( 1) − q ( 1) ⋅ q ( 2 ) 22.10.4 Quaternion Normalisation B A B A B A B A Equation 22.10-15 A quaternion of unit magnitude satisfies the normalisation condition: Q 2 : = 1 : = q 2 0 + q • q Equation 22.10-16 Propagating a quaternion over time leads to errors and this condition is no longer satisfied. Q_NORMAL takes in quaternion (Q) and normalises it, returning the corrected quaternion ( C Q). From Equation 22.10-16, Q_NORMAL Q 2 Q ( Q ) ≡ ϕ ( Q ) NORM 2 ( 1 + ξ ) ≅ 1 + ⋅ ξ : = 2 The corrected quaternion is related to the input by, Therefore, 22.10.5 Quaternion Propagation C Q ≅ C ( 1 + ξ ) ⋅ Q Q ≅ 2 ⋅ Q + 2 ( 1 Q ) Equation 22.10-17 Equation 22.10-18 Equation 22.10-19 The orientation of frame (B) with respect to frame (A) can be propagated between time (t) and (t+∆t) using quaternion multiplication,
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CRANFIELD UNIVERSITY LEIGH MOODY SE
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ABSTRACT When considering advances
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Contents _ _ LIST OF CONTENTS 1 INT
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Contents _ _ 8.2 The Scope of Moder
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Contents _ _ 17.4 Inertial Velocity
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Tables _ _ LIST OF TABLES Table 1-1
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Figures _ _ LIST OF FIGURES Figure
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Figures _ _ Figure 5-1 : Centralise
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Figures _ _ Figure 19-3 : Air Densi
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Acronyms _ _ Acronyms And Abbreviat
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Acronyms _ _ HDOP - NAVSTAR GPS Hor
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Acronyms _ _ RCS - Radar Cross Sect
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Glossary _ _ GLOSSARY A challenge w
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Glossary _ _ 0.1 Predicate Calculus
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Glossary _ _ ]A,B] Real number rang
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Glossary _ _ 0.9 Matrix Operators [
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Glossary _ _ 0.14.2 Special Vectors
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Glossary _ _ P C a , b ≡ XC YC ZC
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Glossary _ _ V ≡ V : = V • V Th
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Glossary _ _ 0.16.4 Matrix Partitio
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Glossary _ _ Only the subset of qua
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Glossary _ _ 0.19 Systeme Internati
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1 Chapter 1 / Introduction _ _ Chap
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Chapter 1 / Introduction _ _ Wherea
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Chapter 1 / Introduction _ _ • Cr
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Chapter 1 / Introduction _ _ genera
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Chapter 1 / Introduction _ _ radar
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Chapter 1 / Introduction _ _ simple
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Chapter 1 / Introduction _ _ optimi
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Chapter 1 / Introduction _ _ 1.3.9
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2 Chapter 2 / Target Modelling _ _
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Chapter 2 / Target Modelling _ _ 2.
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Chapter 2 / Target Modelling _ _
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Chapter 2 / Target Modelling _ _ t
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Chapter 2 / Target Modelling _ _ P&
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Chapter 2 / Target Modelling _ _ GO
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Chapter 2 / Target Modelling _ _ th
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Chapter 2 / Target Modelling _ _
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Chapter 2 / Target Modelling _ _ VX
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Chapter 2 / Target Modelling _ _ ma
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3 Chapter 3 / Sensors _ _ Chapter 3
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Chapter 3 / Sensors _ _ 3.1 Simulat
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Chapter 3 / Sensors _ _ Table 3-4 :
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Chapter 3 / Sensors _ _ Reference D
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Chapter 3 / Sensors _ _ 3.2-9 s s i
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Chapter 3 / Sensors _ _ 3.2-11 t o
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Chapter 3 / Sensors _ _ Figure 3-5
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Chapter 3 / Sensors _ _ Table 3-7 :
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Chapter 3 / Sensors _ _ IF ϕ LIM
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Chapter 3 / Sensors _ _ The phase e
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Chapter 3 / Sensors _ _ Taking expe
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Chapter 3 / Sensors _ _ Expressing
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Chapter 3 / Sensors _ _ INPUT; AA,
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Chapter 3 / Sensors _ _ The functio
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Chapter 3 / Inertial Navigation _ _
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Chapter 3 / Sensors / Gyroscopes _
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Chapter 3 / Sensors / Accelerometer
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Chapter 3 / Sensors / Barometric Al
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Chapter 3 / Sensors / Barometric Al
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Chapter 3 / Sensors / Radar Altimet
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Chapter 3 / Sensors / Radar _ _ 3.8
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Chapter 3 / Sensors / Radar _ _ LF
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Chapter 3 / Sensors / Radar _ _ ( )
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Chapter 3 / Sensors / Radar _ _ S :
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Chapter 3 / Sensors / Radar _ _ SN
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Chapter 3 / Sensors / Radar _ _ 2
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Chapter 3 / Sensors / Radar _ _ ⎛
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Chapter 3 / Sensors / Seeker _ _ 3.
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Chapter 3 / Sensors / Seeker _ _ 5
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Chapter 3 / Sensors / Seeker _ _
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Chapter 3 / Sensors / Seeker _ _ th
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Chapter 3 / Sensors / Seeker _ _ Th
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Chapter 3 / Sensors / Seeker _ _ Th
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Chapter 3 / Sensors / Fins _ _ 3.10
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Chapter 3 / Sensors / Fins _ _ thro
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Chapter 3 / Sensors / NAVSTAR GPS _
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Chapter 3 / Sensors / Helmet Mounte
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Chapter 3 / Sensors / Helmet Mounte
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Chapter 3 / Sensors / Air Data Syst
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Chapter 4 / Target Tracking _ _ 3.1
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Chapter 4 / Target Tracking _ _ Ine
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Chapter 4 / Target Tracking _ _ ran
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Chapter 5 / Missile State Observer
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5 Chapter 5 / Missile State Observe
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6 Chapter 6 / Missile Guidance _ _
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Chapter 6 / Missile Guidance _ _ 6.
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Chapter 6 / Missile Guidance _ _ As
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Chapter 6 / Missile Guidance _ _
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Chapter 6 / Missile Guidance _ _ CD
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Chapter 6 / Missile Guidance _ _ ge
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Chapter 6 / Missile Guidance _ _ ex
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Chapter 6 / Missile Guidance _ _ &
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Chapter 6 / Missile Guidance _ _ PN
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Chapter 6 / Missile Guidance _ _ ra
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Chapter 6 / Missile Guidance _ _ of
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Chapter 6 / Missile Guidance _ _ NO
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Chapter 6 / Missile Guidance _ _ tr
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Chapter 6 / Missile Guidance _ _ η
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Chapter 6 / Missile Guidance _ _ Au
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Chapter 6 / Missile Guidance _ _ Fo
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Chapter 6 / Missile Guidance _ _ (
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Chapter 6 / Missile Guidance _ _
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Chapter 6 / Missile Guidance _ _ ar
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7 Chapter 7 / Missile Trajectory Op
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Chapter 7 / Missile Trajectory Opti
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8 Chapter 8 / Simulation _ _ Chapte
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Chapter 8 / Simulation _ _ 8.1 The
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Chapter 8 / Simulation _ _ 8.3 The
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Chapter 8 / Simulation _ _ Having p
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Chapter 8 / Simulation _ _ 8.5.1 Gl
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Chapter 8 / Simulation _ _ (1) CONS
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Chapter 8 / Simulation _ _ 8.6.2 Ou
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Chapter 8 / Simulation _ _ The file
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Chapter 8 / Simulation _ _ • The
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Chapter 8 / Simulation _ _ comprehe
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Chapter 8 / Simulation _ _ WIN_RATE
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Chapter 8 / Simulation _ _ for this
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Chapter 8 / Simulation _ _ with the
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Chapter 8 / Simulation _ _ Figure 8
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Chapter 8 / Simulation _ _ Table 8-
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Chapter 8 / Simulation _ _ 8.8 Disc
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9 Chapter 9 / Performance _ _ Chapt
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Chapter 9 / Performance _ _ 9.1 Air
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Chapter 9 / Performance _ _ XM ( >
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Chapter 9 / Performance _ _ 9.3 PN
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Chapter 9 / Performance _ _ The eff
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Chapter 9 / Performance _ _ VXMVOM
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Chapter 9 / Performance _ _ VXMVOM
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Chapter 9 / Performance _ _ 9.4 CLO
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Chapter 9 / Performance _ _ AR_BOM
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Chapter 9 / Performance Chapter 9 /
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Initially the position error falls
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values of CN are not always a relia
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crude initialisation introduces err
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9.5.3 Singer Filter Tuning The Sing
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9.6.2 CLOS Study The CLOS study sho
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Chapter 10 / Conclusions _ _ 10-2
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Chapter 10 / Conclusions _ _ 10.3 T
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Chapter 10 / Conclusions _ _ 10.7 M
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Chapter 11 / Future Research _ _ 11
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Chapter 11 / Future Research _ _
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Chapter 11 / Future Research _ _ To
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References _ _ B.4 BAZARAA M.S., SH
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References _ _ F.1 FOX J.E., “A C
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References _ _ H.5 #HULL D.G., RADK
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References _ _ L.2 LOOZE D.P., HSU
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References _ _ N.4 NABAA N., BISHOP
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References _ _ R.3 RUSNACK I., “O
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References _ _ S.15 SINGER R.A.,
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References _ _ Y.2 YUAN P., CHERN J
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Bibliography _ _ B.13 BABA Y., YAMA
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Bibliography _ _ B.40 BECKER J.C.,
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Bibliography _ _ C.33 CORTINA E., O
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Bibliography _ _ E.8 ERSHOV A.A.,
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Bibliography _ _ G.34 GUTMAN P., VE
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Bibliography _ _ H.35 HUSSAIN A.M.,
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Bibliography _ _ K.14 KATZIR S., CL
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Bibliography _ _ L.19 LEFAS C.C,
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Bibliography _ _ M.16 MAYNE D.Q., P
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Bibliography _ _ P.1 PAINTER J.H.,
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Bibliography _ _ R.32 RONG LI X., Z
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Bibliography _ _ S.47 SPEYER J.L.,
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Bibliography _ _ V.5 VIAN J.L., MOO
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Bibliography _ _ W.29 WATSON G.A.,
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Appendix A / Geometric Points _ _ 1
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Appendix A / Geometric Points _ _ 1
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Appendix B / Frames of Reference _
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Appendix C / Axis Transforms _ _ 16
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Appendix C / Axis Transforms _ _ YP
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Appendix C / Axis Transforms _ _ B
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Appendix C / Axis Transforms _ _ YB
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Appendix C / Axis Transforms _ _ Us
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Appendix C / Axis Transforms _ _ No
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Appendix C / Axis Transforms _ _ B
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Appendix C / Axis Transforms _ _
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Appendix D / Point Mass Dynamics _
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Appendix E / Earth Geometry _ _ 18-
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Appendix E / Earth Geometry _ _ ELL
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Appendix E / Earth Geometry _ _ (dx
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Appendix E / Earth Geometry _ _ Int
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Appendix E / Earth Geometry _ _ 18.
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Appendix E / Earth Geometry _ _ 19-
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Appendix E / Earth Geometry _ _ P S
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Appendix E / Earth Geometry _ _ 19.
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Appendix E / Earth Geometry _ _ ∂
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Appendix G / Gravity _ _ 20-2
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Appendix G / Gravity _ _ g : = g +
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Appendix G / Gravity _ _ d −6 2
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Appendix G / Gravity _ _ 20-8
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Appendix H / Steady State Tracking
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Appendix I / Utilities _ _ 22.1-2
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Appendix I / Utilities _ _ Cartesia
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Appendix I / Utilities _ _ Matrix P
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Appendix I / Utilities _ _ 22.1-8
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Appendix I / Utilities / General Ut
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Appendix I / Utilities / WGS 84 Tar
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Appendix I / Utilities / Axis Trans
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Page 664 and 665: Appendix I / Utilities / Trigonomet
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Page 676 and 677: Appendix I / Utilities / Covariance
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