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

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Chapter 3 / Inertial Navigation _ _ ω G C, G : = ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ω ω ZE C, E ZE C, E 0 ⋅ cos λ ⋅ sin λ 3.3-4 d d ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎛ ⎜ ⎜ ⎜ + ⎜ ⎜ ⎜ ⎝ P& − P& XG u P& YG u XG u ⋅ tan λ R d R λd µ d R µ d ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ Equation 3.3-3 The Earth radii at point (d), adjusted for the geodetic height of point (u), used in the conversion of metres into radians are defined in §18.4 and §18.5. The LGA (G) to the Body frame (B) transform is obtained using spline-data in the functions defined in §22.4.1 and §22.4.7. T B G : = ϕ DC E E G G ZG ( ϕLD ( P& & u , P& u , gu ) ) From §19.5, the local gravitational acceleration at point (u) is, G u G d Equation 3.3-4 ( ) ( ) T ZE 2 ZG ω ⋅P ⋅ cosλ ⋅ 0 , − sin λ , cos g = − g + 3 ⋅ λ C, E u d d d Equation 3.3-5 The average angular body rate with respect to LGA over the 800 Hz subframe interval is obtained using the function defined in §22.5.3, ω B G , B ≡ ω B G, B AR B B ( T ( t − ∆ ) , T , ) : = ϕ ∆ G R G R Equation 3.3-6 From the Navigation Equation the accelerometers sense specific acceleration comprising mass attraction and Earth centripetal acceleration components at point (u), f : = A − G : = A − g − ω × ω × r, u r, u u r, u u C, E C, E P r, u Equation 3.3-7 The acceleration of point (u) with respect to the Earth’s centre is obtained by applying the time rate of change operator twice with respect to LGA axes, expanding and combining with Equation 3.3-7, 2 I 2 ( P ) : = ( D + ω ) ( P ) D × r, u G C, G r, u Equation 3.3-8
Chapter 3 / Inertial Navigation _ _ P& & r, u + r, u ( 2 ⋅ ω + ω ) × P& r, u + ω& × Pr, u + ω × ω × Pr, u C, E r, u E, G A 3.3-5 r, u : = C, G C, E C, E Equation 3.3-9 ( 2 ⋅ ωC, E + ωE, G ) × P& r, u + ωC, G × Pr, u g u f : = P& & + & − Equation 3.3-10 Mechanisation of this equation can be performed in the Inertial, Wander Azimuth, LGA or Body frames. When defining sensor inputs the accelerations are required in the Body frame. The linear velocity and acceleration of point (d) is zero with respect to the Earth’s centre, and the angular acceleration of frame (G) with respect to frame (C) can be ignored. Making these approximations and expressing Equation 3.3-10 in terms of cubic spine data, B r, u B G G G G G G ( P& & u + ( 2 ⋅ ωC, E + ωE, G ) × P& u g ) f : = T ⋅ − Expanding the coriolis acceleration components, G G ( 2 ⋅ ω + ω ) u Equation 3.3-11 YG ZG XG YG ZG ( P& ⋅ sin λ − P& ⋅ cos λ ) + P& ⋅ ( P& ⋅ tan λ − P& ) ⎛ ZE 2 ⋅ ω ⎜ C, E ⋅ u d u ⎜ ⎜ ZE XG ⎜ − 2 ⋅ ωC, E ⋅ P& u ⋅ sin λd − ⎜ ⎜ ZE XG ⎝ 2 ⋅ ωC, E ⋅ P& u ⋅ cos λ XG ( P& ) d C, E u + d ⋅ tan λ ⋅ P& : = − ⋅ P& ( ) ( ) ⎟ ⎟⎟⎟⎟⎟⎟ XG 2 YG 2 P& R + P& R u 2 E, G u d G u µ d R u µ d u P& YG u d u ZG u λd R λd R µ d Equation 3.3-12 The angular acceleration of Body axes with respect to LGA is obtained by backward differencing over the sub-frame interval, ω& B G, B ≡ ω& B G, B R B B ( ω − ω ( t − ) ) : = ∆ ⋅ ∆ G, B G, B R Equation 3.3-13 Although this derivation of the IMU inputs from the spline data provides a useful insight into INS processing, in the simulation the sensors inputs are derived from the reference state vector. The orientation of frame (B) with respect to the Alignment frame (A) is derived using the function defined in §22.10.8 for converting direction cosines to quaternions. ⎞ ⎠
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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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Page 85 and 86: 3 Chapter 3 / Sensors _ _ Chapter 3
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Chapter 3 / Sensors / Radar _ _ SN
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Chapter 3 / Sensors / Radar _ _ 3.8
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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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Appendix I / Utilities / Point Mass
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Appendix I / Utilities / Earth, Atm
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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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