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

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Chapter 4 / Target Tracking _ _ The elements of the fully expanded system noise covariance matrix where (σt) is the rms target acceleration uncertainty, q 11 2 4 ⎛ 2 2 2 3 : = Sσt ⋅ SτC ⋅ ⎜ 1 − ϕ + 2 ⋅ β − 2 ⋅ β + ⋅ β − 4 ⋅ ϕ ⋅ ⎝ 3 12 S 2 t 3 SτC 2 2 ( 1 + ϕ − 2 ⋅ ϕ + 2 ⋅ ϕ ⋅ β − 2 ⋅ β + ) q : = σ ⋅ ⋅ β 22 13 S 2 t 4-18 2 SτC 2 ( 1 − 2 ⋅ ϕ ⋅ β − ) q : = σ ⋅ ⋅ ϕ S 2 t 2 SτC 2 ( −3 + 4 ⋅ ϕ + 2 ⋅ β − ) q : = σ ⋅ ⋅ ϕ 23 S 2 t S C 2 ( 1 − 2 ⋅ ϕ + ) q : = σ ⋅ τ ⋅ ϕ 33 S 2 t S C 2 ( 1 − 2 ⋅ ) q : = σ ⋅ τ ⋅ ϕ When (β) is small these equations tend to the asymptotic form, S A 2 A ( 2 ⋅ σ τ ) Q Q : = ⋅ S t S C A β ⎞ ⎟ ⎠ Equation 4.5-11 Equation 4.5-12 Equation 4.5-13 Equation 4.5-14 Equation 4.5-15 Equation 4.5-16 Equation 4.5-17 The acceleration probability in the Singer model is uniformly distributed between the maximum acceleration limit (± AMAX) with a probability of (± PMAX); the no manoeuvre probability being (P0), S σ 2 t 2 ( 1 + 4 ⋅ P − P ) 3 : = AMAX ⋅ MAX 0 Equation 4.5-18 If the maximum acceleration of a manned jet aircraft is 9 g for short periods during evasion manoeuvres, S σ t : = 5 3 ⋅ A ≈ MAX 80 m / s 2 Equation 4.5-19 A drawback of this model is the apriori selection of maximum acceleration and manoeuvre duration. In the context of the IMM this model is only
Chapter 5 / Missile State Observer _ _ required during transients lasting some 5 s. Whilst the non co-ordinated models here are specified in Cartesian axes, fixed wing target motion is best expressed in a body referenced curvature, torsion and bi-normal (Frenet) axes, Chen [C.7] . Much effort has been expended in this field which is reviewed by Nabaa [N.4] . Singer’s original model was improved by Gholson [G.13] (1977), Moose [M.8&9] (1975-79), Ricker [R.13] (1978) by including randomly switched mean acceleration input with a Gaussian noise residual. k + 1 k 4-19 k k ( U w ) X : = A ⋅ X + Γ ⋅ + k k Equation 4.5-20 Berg [B.8] (1983) added an adaptive mean jerk term to accommodate coordinated target dynamics with constant thrust, drag, lift and zero roll rate, A t −1 C A A ( & A P& t − w ) &P& & t & P& & : = − τ ⋅ + Equation 4.5-21 Song [S.12] (1988) included target dynamics free of Berg’s restrictions, mean jerk being a function of target velocity directed lateral acceleration estimated from its mass, velocity and lift coefficient. Mahapatra [M.6] introduced jerk states, significantly improving velocity and acceleration estimates for an idealised circular trajectory, even when jerk was absent. However, Vergez [V.1] showed that increasing the filter order in general degrades tracking performance compared with the Singer and acceleration models. 4.5.4 Weave Filter Assuming that the target speed and turn rate are constant over the propagation interval, W W iA t A 2 iA iA ( ω ) × P& w & P & : = − + A, TV ⎛ ⎛ 0 , 1 , 0 ⎞ ⎜ ⎜ ⎟ ⎜ ⎜ ⎟ i ⎜ Φ : = exp ⎜ 0 , 0 , 1 ⎟ ⎜ ⎜ ⎟ ⋅ ∆t ⎜ ⎜ ⎟ ⎜ ⎜ ⎟ ⎝ ⎝ 0 , A, TV ⎠ W t W ( ) ⎟ ⎟⎟⎟⎟⎟⎟ iA 2 ω , 0 Equation 4.5-22 ⎞ ⎠ Equation 4.5-23
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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 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 _ _ 6.
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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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