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

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Chapter 5 / Missile State Observer _ _ bias error characterisation. Simple characterisation should reduce constant or long-term correlated biases to a minimum prior to launch commensurate with the local flexure and noise conditions. 5.3.3 Missile Seeker The RF seeker provides range, range rate, and target angle measurements at 100 Hz with respect to the Missile Body frame. Gimbals with a bandwidth of 80 Hz are pointed using 400 Hz command data. The measurements are provided when the range-to-go is 5 km with a 100 m blind range providing that the target LOS remains in a ± 2° circular beam subject to a ± 30° FoR. 5.4 States and Partitioning The state vector (SOX) comprises target and missile states partitioned as shown in Table 5-1. Being clear in context, the use of the identifier (SO), and the observer kinematic type have been dropped. At this stage sensor error states are not included in the filter – this being an alternative to calibrating the IMU whilst the missile is in the launcher. On-line bias, misalignment and scale factor is made possible due to measurement duality and shaped trajectories. The ideal is a combination of both, characterising the IMU biases before launch which are then fixed, and estimating the IMU scale factors and other sensor errors in-flight. SOXTL Table 5-1 : Missile State Observer States SYMBOL STATE DESCRIPTION SOXM SOXML SOXM SOXMA A P t Target position in Alignment axes A Pt & Target linear velocity in Alignment axes P & Target linear acceleration in Alignment axes A t A P m Missile position in Alignment axes A Pm & Missile linear velocity in Alignment axes P & Missile linear acceleration in Alignment axes A m B QA Orientation of Missile Body to Alignment axes B A, B ω Missile Body frame angular velocity B A, B ω& Missile Body frame angular acceleration Partitioning the state vector, and by implication observer state transition, system noise and covariance matrices, identifies sparseness of the process model. When dealing with matrix partitions the following nomenclature is useful (the symmetric state covariance matrix is used as an example), 5-8
Chapter 5 / Missile State Observer _ _ SO C : = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ SO SO C L C L 0 TLL MTL 5-9 M M M M M SO SO SO C L C L C TML MLL MAL M M M M M SO SO 0 L C L C MLA MAA ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ Equation 5.4-1 Partitioning to 3 and 4-vector level in the case of the target linear partition (and likewise for the missile linear and rotational partitions), SO 5.5 Initialisation ⎛ ⎜ ⎝ ϕ Q DC C TLL : = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ TLL TLL TLL C L C L C PP VP AA M M M M M TLL TLL TLL C L C L C PV VV AV M M M M M TLL TLL TLL C L C L + T T ( X ) , 0 , ( X ) T T SO X : = ⎛ ⎞ ⎜ UL 9 SO MA ⎟ ⎝ ⎠ DC A W DC A A E A ( ϕ ( P ) ) M ϕ ϕ ( P , P& ) , ϕ ( P ) X UL t SO X MA : = C PA VA AA ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ( DE ( X UL t UL t X UL t ) ) Equation 5.4-2 Equation 5.5-1 T M 0 T 3 ⎞ ⎟ ⎠ T Equation 5.5-2 The orientation and angular rate of the missile with respect to the Alignment frame is determined using utility functions and up-linked IMM target data. The launcher rotates slowly whilst tracking long-range targets hence the missile velocity, and its linear and angular accelerations are set to zero. The initial missile covariances must never be underestimated, and if necessary inflated to cope with all possible eventualities. If, as here, IMM data is used to initialise the missile state, the uncertainty in that state must include the pointing error of the launcher and the initial position error of the IMM initialisation source. After re-scaling and expanding the up-linked target state expectations the symmetric state covariance matrix, SO CTLL UL : = C + Equation 5.5-3
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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 _ _ 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 _ _ 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 / 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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