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

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Appendix C / Axis Transforms _ _ 16.7 Celestial to Satellite LOS Transformations The Euler triplet defining the transform from the Celestial to each of the Satellite LOS frames (TRCTOL) located at the missile receiver point (g), E L C ( i , j ) : = ( i : = [ 1( 1 ) 6 ] ) ∧ ( j : = [ 1( 1 ) 4 ] ) ⎛ ⎜ ⎜ ⎝ 0 , − tan −1 16-10 ⎛ P ⎜ ⎜ ⎝ P ZC g, s hC g, s ( i, j ) ( i, j ) ⎞ ⎟ ⎟ ⎠ , tan ⇒ −1 ⎛ P ⎜ ⎜ ⎝ P YC g, s XC g, s ( ) ( ) ⎟ ⎟ i, j ⎞ ⎞ ⎟ i, j ⎟ ⎠ ⎠ Equation 16.7-1 Index (j) refers to a particular satellite in orbital plane (i). When the roll angle is zero the transformation matrix reduces to, T L C : = ⎡ L L cos ΘC cos ΨC ⎢ ⎢ ⎢ L − sin ΨC ⎢ ⎢ ⎢ L L ⎣ sin ΘC cos ΨC 16.8 Celestial to Earth Transformation , , , cos Θ sin Θ L C cos Ψ L C sin Ψ L C sin Ψ L C L C , , , − sin Θ 0 cos Θ L C L C ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ Equation 16.7-2 Z E rotates clockwise about Z C at 15.041°/hr. At midnight GMT the yaw angle between X C and X E is 30°. The Euler triplet defining the transform from Celestial to Earth axes in terms of the time after midnight (tM), E E C ⎛ π ZE : = ⎜ 0 , 0 , + ωC, E ⋅ tM ⎝ 6 ⎞ ⎟ ⎠ Equation 16.8-1 The transform from the Celestial to Earth frame (TRCTOE) is obtained by substituting these Euler angles into Equation 16.1-4. 16.9 Earth to Alignment Transformation The Earth and Alignment frames are fixed with respect to the Earth. The transform between the two is time invariant and defined by the Euler triplet, E A E ⎛ ⎜ ⎝ π − λ 2 π + µ 2 = r, o , 0 , r, o : The geocentric longitude and latitude at point (o) are, ⎞ ⎟ ⎠ Equation 16.9-1
Appendix C / Axis Transforms _ _ −1 YE XE −1 ZE hE ( µ , λ ) : = ( tan ( P P ) , tan ( P P ) ) r, o r, o 16-11 o o o o Equation 16.9-2 The transform from the Earth to Alignment frame (TRETOA) is obtained by substituting the Euler angles into Equation 16.1-4. Introducing the functional form from LGA to direction cosines for this transform, T A E : = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ − sin λ cos λ A E DC LGA ( µ , ) T : = ϕ λ − sin µ r, o r, o r, o ⋅ cosµ ⋅ cosµ r, o r, o , , , r, o − sin λ cos λ cosµ 16.10 LGA to Earth Position Vector Transformation r, o r, o r, o r, o ⋅ sin µ ⋅ sin µ r, o r, o Equation 16.9-3 , , , 0 cos λ sin λ r, o r, o ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ Equation 16.9-4 The position of a point (p) with respect to Earth axes is determined from its geodetic orientation with respect to the Earth frame, and its altitude along the geodetic vertical through point (d), P E p : = ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ZG ( P + P ) r, d ZG ( P + P ) r, d d, p d, p ⋅ cosµ ⋅ sin µ ⋅ cosλ ⋅ cosλ ( ( ) ) ⎟ ⎟⎟⎟⎟⎟⎟ 2 ZG 1 − e ⋅ P + P ⋅ sin λ r, d p p d, p p p p ⎞ ⎠ Equation 16.10-1 The Earth’s eccentricity (e) and the WGS84 values for the Earth’s semimajor and semi-minor radii (RA and RB) are defined in §18.1. 16.11 Earth to LGA Transformation A review of a number of “exact” and iterative techniques developed by Paul, Heikkinen, Barbee, Borkowski, and Zhu for the inverse transformation from ECEF to LGA axes is provided by Zhu [Z.4] . Although the most accurate of the non-iterative techniques for near-Earth studies is Heikkinen’s method, Olsen’s iterative algorithm taken from [0.7] has been selected and defined in §22.5.4.
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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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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 _ _ INPUT; AA,
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Chapter 3 / Sensors / Radar _ _ 3.8
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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 _ _ 2
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Chapter 3 / Sensors / Radar _ _ ⎛
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Chapter 3 / Sensors / Seeker _ _ 3.
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Chapter 4 / Target Tracking _ _ 3.1
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Chapter 5 / Missile State Observer
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5 Chapter 5 / Missile State Observe
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Chapter 8 / Simulation _ _ (1) CONS
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Chapter 8 / Simulation _ _ WIN_RATE
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Chapter 9 / Performance _ _ 9.1 Air
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Chapter 9 / Performance _ _ 9.3 PN
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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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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
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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
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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 / WGS 84 Tar
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Appendix I / Utilities / Quaternion
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