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

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Appendix D / Point Mass Dynamics _ _ Expanding the exponential function as an infinite series, T R I ⎛ ⎞ ( + ∆ ) ⋅ ( ) = + ∑ ⎜ ⋅ ( − [ ω × ] ) ⋅ ∆ ⎟ ⎝ ⎠ ∞ I 1 R n n t t TR t : I 3 I, R t n! 17-6 n : = 1 Equation 17.3-3 Collecting even and odd powers, and expressing them as power series expansions of sine and cosine functions, I 3 − ω −1 I, R ⋅ T I ( t + ∆t ) ⋅ T ( t ) R −2 R 2 [ ω × ] ⋅ sin ( ω ⋅ ∆t ) + ω ⋅ [ ω × ] ⋅ 1 − cos ( ω ⋅ ∆t ) I, R R I I, R R I, R : = I, R Expanding and equating the appropriate direction cosines, T R I I R I ( t + ∆t ) ⋅ T ( t ) − T ( t ) ⋅ T ( t + ∆t ) − 2 ⋅ ω −1 I, R R R [ ω × ] ⋅ sin ( ω ⋅ ∆t ) I, R I R I, R ( ) I, R Equation 17.3-4 : = Equation 17.3-5 The average angular rate of the rotating frame with respect to the reference axes over the time interval (∆t) is therefore, ω R I, R : = R ΛI R I −1 ⋅ sin Λ ⋅ ∆t R ( Λ ) I Equation 17.3-6 ( ( ) ( ) ( ) ( ) ( ) ( ) ) T R I R I R I ∆T 6 − T 8 , ∆T 7 − T 3 , ∆T 2 − T 4 I 17.4 Inertial Velocity Vector R I 2 ⋅ Λ The inertial velocity of point (b) with respect to point (a) is, V I b : = I R R I : = R T& ⋅ P + T ⋅ P& R a, b I R R a, b Substituting for the transformation matrix derivatives, I R Equation 17.3-7 Equation 17.4-1
Appendix D / Point Mass Dynamics _ _ I b I R 17-7 R R R ( Pa, b + ωI, R Pa, b ) V : = T ⋅ & × Equation 17.4-2 Expressing the absolute velocity in terms of its components with respect to the rotating frame, R a, b R a, b R I, R V : = P + ω × & The individual velocity components in the rotating frame (R) are, XR a, b XR a, b YR I, R ZR a, b P R a, b ZR I, R V : = P + ω ⋅ P − ω ⋅ P & YR a, b YR a, b ZR I, R XR a, b XR I, R V : = P + ω ⋅ P − ω ⋅P & ZR a, b ZR a, b XR I, R YR a, b YR I, R V : = P + ω ⋅ P − ω ⋅P & YR a, b ZR a, b XR a, b Equation 17.4-3 Equation 17.4-4 Equation 17.4-5 Equation 17.4-6 Replacing the body rates with the time rate of change of the Euler angles, P& P& P& XR a, b YR a, b ZR a, b + Ψ& R I + Ψ& + Ψ& R I R I ⋅ ⋅ ⋅ ZR R YR R R R YR R ZR R ( P ⋅ sΦ − P ⋅ cΦ ) ⋅ cΘ + Θ& ⋅ ( P ⋅ sΦ + P ⋅ cΦ ) a, b I a, b V I XR a, b : = I I a, b I a, b Equation 17.4-7 XR R R ZR R R XR R R ZR ( P ⋅ cΦ ⋅ cΘ + P ⋅ sΘ ) − Θ& ⋅ P ⋅ sΦ + Φ& ⋅ P a, b I I V YR a, b a, b : = I I a, b I I I a, b Equation 17.4-8 YR R XR R R R XR R R YR ( P ⋅ sΘ − P ⋅ sΦ ⋅ cΘ ) − Θ& ⋅ P ⋅ cΦ + Φ& ⋅ P a, b I a, b V ZR a, b I : = I I a, b I I a, b Equation 17.4-9
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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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Page 474 and 475: Bibliography _ _ S.47 SPEYER J.L.,
Page 476 and 477: Bibliography _ _ V.5 VIAN J.L., MOO
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Page 480 and 481: Appendix A / Geometric Points _ _ 1
Page 482 and 483: Appendix A / Geometric Points _ _ 1
Page 484 and 485: Appendix B / Frames of Reference _
Page 494 and 495: Appendix C / Axis Transforms _ _ 16
Page 496 and 497: Appendix C / Axis Transforms _ _ YP
Page 498 and 499: Appendix C / Axis Transforms _ _ B
Page 500 and 501: Appendix C / Axis Transforms _ _ YB
Page 504 and 505: Appendix C / Axis Transforms _ _ Us
Page 506 and 507: Appendix C / Axis Transforms _ _ No
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Page 514 and 515: Appendix D / Point Mass Dynamics _
Page 526 and 527: Appendix E / Earth Geometry _ _ 18-
Page 528 and 529: Appendix E / Earth Geometry _ _ ELL
Page 530 and 531: Appendix E / Earth Geometry _ _ (dx
Page 532 and 533: Appendix E / Earth Geometry _ _ Int
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Page 536 and 537: Appendix E / Earth Geometry _ _ 19-
Page 538 and 539: Appendix E / Earth Geometry _ _ P S
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Page 542 and 543: Appendix E / Earth Geometry _ _ ∂
Page 544 and 545: Appendix G / Gravity _ _ 20-2
Page 546 and 547: Appendix G / Gravity _ _ g : = g +
Page 548 and 549: Appendix G / Gravity _ _ d −6 2
Page 550 and 551: Appendix G / Gravity _ _ 20-8
Page 552 and 553: Appendix H / Steady State Tracking
Page 562 and 563: Appendix I / Utilities _ _ 22.1-2
Page 564 and 565: Appendix I / Utilities _ _ Cartesia
Page 566 and 567: 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 / Point Mass
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Appendix I / Utilities / Earth, Atm
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Appendix I / Utilities / Digital Ma
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Appendix I / Utilities / Digital Fi
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Appendix I / Utilities / Matrices _
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Appendix I / Utilities / Quaternion
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Appendix I / Utilities / Trigonomet
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Appendix I / Utilities / Covariance
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