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

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Appendix C / Axis Transforms _ _ B B A A 16-6 B A [ I 3 − ∆E × ] X X : = ∆T ⋅ X ≡ ⋅ B [ ∆E × ] A ≡ ⎡ 0 ⎢ ⎢ ⎢ B ∆ΨA ⎢ ⎢ ⎢ ⎣ − ∆Θ B A , , , − ∆Ψ 0 ∆Φ B A B A A , , , ∆Θ − ∆Φ 0 Equation 16.2-2 B A B A ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ Equation 16.2-3 Consider a misalignment in the transformation from frame (A) to frame (B), B ~ A B ~ B B A B B [ ] A ~ I 3 − ∆E B × T T : = ∆T ⋅ T : = ⋅ B A B ~ B B ~ A B [ ] ~ B A ~ I 3 + ∆E B × T T : = − ∆T ⋅ T : = ⋅ Equation 16.2-4 Equation 16.2-5 This use of the skew symmetric form using the positive sign is not advised; reversal of the frame identifier is preferred, B A B [ ] ~ B I − ∆E × T T : = ⋅ 16.3 Euler Angles as a Function of Direction Cosines 3 B ~ A Equation 16.2-6 Euler angles are obtained from the transformation matrix direction cosines. B Θ ∈ − π 2 , π 2 , For example, for a YPR Euler triplet where ] [ E B A : = ⎛ ⎜ ⎝ tan −1 ⎛ T ⎜ ⎝ T 8 9 ⎞ ⎟ ⎠ , sin −1 A ⎞ ⎞ ⎟ ⎠ ⎠ ( ) ⎟ −1 − ⎜ 4 T , tan ⎟ 7 ⎛ T ⎜ ⎝ T 1 Equation 16.3-1 The implementation of this equation must accommodate zero pitch and roll angles when defining the arc-tangent function.
Appendix C / Axis Transforms _ _ 16.4 Transformation Between Co-ordinate Systems 16.4.1 Co-ordinate Systems Three types of co-ordinates are defined for dealing with the position of points in E 3 with respect to a frame: Rectangular, Spherical Polar and UVR. Using generic co-ordinates for specifying algorithms is permissible providing that they have been previously defined using the full notation and their scope is clearly identified. Cartesian, Spherical Polar and Radar UVR co-ordinate systems are denoted by (C), (S) and (R) respectively. 16.4.2 Cartesian (Rectangular) Co-ordinates The position of (p) in Rectangular co-ordinates with respect to frame (A) located at (a), XA YA ZA ( x , y , z ) ≡ ( P , P , P ) 16-7 a, b a, b a, b Equation 16.4-1 The position of a point in E 3 is only equal to Rectangular co-ordinates since these are measured in a direction coincident with the unit vectors defining the frame. Rectangular co-ordinates form a vector in its strictest sense, whereas all other co-ordinates are defined in terms of ordered sets (triplets in E 3 ). 16.4.3 Spherical Polar Co-ordinates If frame (B) located at point (p) is rotated through Euler YP angles such that X B passes through point (p) the polar co-ordinates with respect to frame (A), ⎛ ⎜ ⎝ P A b • P A b B B ( P , Θ , Ψ ) , a, b − tan −1 A ⎛ P ⎜ ⎝ P ZA b hA b ⎞ ⎟ ⎠ A , : = tan −1 ⎛ P ⎜ ⎝ P YA b XA b ⎞ ⎞ ⎟ ⎟ ⎟ ⎟ ⎠ ⎠ Equation 16.4-2 The inverse transformation from Spherical Polar to Cartesian co-ordinates, A b ( ) T B B B B B P ⋅ cΨ ⋅ cΘ , P ⋅ sΨ ⋅ cΘ , − P ⋅ s P : = Θ a, b 16.4.4 UVR Co-ordinates A A a, b A A a, b A Equation 16.4-3 The relationship between the position of point (p) in UVR and Rectangular co-ordinates is,
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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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Page 452 and 453: Bibliography _ _ B.13 BABA Y., YAMA
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Page 460 and 461: Bibliography _ _ G.34 GUTMAN P., VE
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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 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
Page 508 and 509: Appendix C / Axis Transforms _ _ B
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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
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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 +
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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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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 / Vectors _
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Appendix I / Utilities / Covariance
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