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

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Chapter 4 / Target Tracking _ _ ) ) + + + ) ( µ , X , C ) : = ( µ , X , C ) 4.9 IMM Filter Propagation and Update i i i 4-24 i i i Equation 4.8-4 Each filter is propagated to the next measurement reference time. When processing (m) measurements in parallel the filter weights evolve according to an m-dimensional Gaussian distribution. The i’th filter weight being, µ + i exp ⎛ ⎜ − ⎝ ⋅ 0. 5 ⋅ µ + i : = i T i T −1 i ( Z − Z ( X ) ) ⋅ ( H ⋅ C ⋅ H + R ) ⋅ ( Z − Z ( X ) ) m i T ( 2 ⋅ π ) ⋅ det ( H ⋅ C ⋅ H + R ) ⎞ ⎟ ⎠ Equation 4.9-1 EKF linearisation is usually improved by serially processing each measurement. The maximum likelihood function is then constructed from the individual measurement probability densities, ⎛ ⎜ m + + µ i : = ⎜ µ i ⋅ ∏ k : = 1 ⎜ ⎝ ⎛ ⎜ ⎜ ⎝ ⎛ 1 ⎜ ⋅ exp ⎜ − σ ⎜ ⎝ i ( Z − Z ( X ) ) 2 ⋅ σ 2 2 ⎞ ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎠ ⎞ ⎟ ⎟ ⎟ ⎠ 0. 98 0. 02 Equation 4.9-2 The measurement uncertainty is represented by (σ). The ( ) m − 2 ⋅ π scaling is omitted as the normalisation process ensures that the weights sum to 1. 4.10 IMM Filter Combination The weighted sum of the IMM states and covariances before and after measurement updates is required to determine the new information for the missile state observer, IMM C − : = N ∑ i : = 1 µ − i IMM ⋅ ⎛ ⎜ ⎝ X − C − i − − ( µ ⋅ X ) = N ∑ i : = 1 i i : + Equation 4.10-1 − − − − ( X − X ) ⋅ ( X − X ) i IMM i IMM T ⎞ ⎟ ⎠ Equation 4.10-2
Chapter 5 / Missile State Observer _ _ The filter weights used are those prior to update by the measurement likelihood function. The 2 nd term accounts for the each filters deviation from the weighted mean. The weighted sum of the filter states and covariances after the measurement updates, IMM C + : = N ∑ i : = 1 µ + i IMM ⋅ ⎛ ⎜ ⎝ X + C + i 4-25 + + ( µ ⋅ X ) = N ∑ i : = 1 i i : + Equation 4.10-3 + + + + ( X − X ) ⋅ ( X − X ) i IMM i IMM T ⎞ ⎟ ⎠ Equation 4.10-4 As well as up-linking missile measurements, the IMM target state and covariance (upper triangular partition) data, measurement reference time and filter probabilities are transmitted to the missile, the later providing a target manoeuvre indicator. 4.11 Target Tracking Simulator The target-tracking simulator shown in Figure 4-7 contains the embedded target and sensor simulators. Initialisation and characterisation of the tracking function is performed in the normal fashion, although there is no dedicated default data for the tracking simulator. The target simulator is automatically activated inside the integration loop, providing the radar (sensor) with reference data. The tracking simulator is isolated by setting the program termination time to be less than the missile launch time (TIMEND < TLAUNCH). Either the radar or HMS sensors must be activated to obtain reference or corrupted measurement data. The selection of a single tracking filter, or the IMM, propagation and measurement update is controlled by IMM_CONTROL according to the bit pattern of IMM_TP: • Velocity filter VEL_FILTER ( bit 1 ) • Acceleration filter ACC_FILTER ( bit 2 ) • 1 st order Markov filter MK1_FILTER ( bit 3 ) • Weave filter MK2_FILTER ( bit 4 ) If a single tracking filter is selected IMM fusion is by-passed. When a combination of tracking filters are activated the IMM processes are automatically applied. The target observer states and covariances from a single filter or the IMM are processed to determine the parameters and expectations listed in §22.3 and §22.13 respectively.
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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 _ _
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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 _ _ 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 _ _ 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 _ _ 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 / 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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