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

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Chapter 4 / Target Tracking _ _ S X ˆ + − ⎛ 1 ⎛ = X + ⎜ ∑ ⎜ ⎝ 2 , j ⎝ ˆ : [ K ] ⋅ ⎜ ∆Z − ⋅ ⎜ C ( i , j ) 4-14 ∂ h ⋅ ∂ X ⋅ ∂ X i i j P ⋅ H K : = − T −1 H ⋅ P ⋅ H + R + 2 ⋅ S ( i , j ) : = ⎜ ⋅ C ( m , n ) ⋅ C ( i , j ) − T 2 ⎞ ⎟ ⎠ ⎞ ⎟ ⎟ ⎠ Equation 4.4-25 Equation 4.4-26 ∑ ⎟ ⎛ 2 2 ∂ h ∂ h ⎞ ⋅ ⎜ m, n, j ⎝ ∂ Xi ⋅ ∂ Xm ∂ Xn ⋅ ∂ X ⎠ i, j Equation 4.4-27 The EKF projects the covariance surface linearly along the gradient to the estimated state trajectory. Although the SOF replaces this with parabolic projection, in highly non-linear systems even this can result in deviation from the true covariance. A crude approach is to increase the system noise thereby expanding the uncertainties to ensure that they encompass the true errors at the expense of observability. A promising technique presented by Julier [J.2] propagates defining points on the covariance surface using (f) and re-computes the correct mean and covariance statistics after projection,. Although the method is only accurate to 2 nd order it is shown to improve the 3 rd and 4 th moments that by definition are zero in the SOR. 4.4.4 Converted Measurement Kalman Filter In the Converted Measurement KF (CMKF) the measurements and their uncertainties are converted into the state space before performing the measurement update. Park [P.6] showed that the CMKF is more accurate than the conventional EKF formulation if the bearing error is < 1.5º. Bar- Shalom [B.5] also obtained better results from the CMKF for measurement errors > 0.5º albeit using a de-biasing transformation algorithm. Nearoptimal results for bearing errors up to 10° are possible providing the angular uncertainty is know accurately, Longbin [L.6] and Lerro [L7] . In this application the measurement errors are relatively small, certainly less than 6 mrad, and the technique was not considered. 4.4.5 Modified Gain EKF Universal linearisation implies that (h) can be expressed as, Speyer [S.13] , ( ) X X ˆ X : g Z , ˆ X h ⎛ - ⎞ = ⎛ - − ⎞ ⋅ h ⎜ ⎟ ⎜ ⎟ ∆ ⎝ ⎠ ⎝ ⎠ Equation 4.4-28
Chapter 5 / Missile State Observer _ _ T T ( I − K ⋅ g ) ⋅ C ⋅ ( I − K ⋅ g ) + K ⋅ R K C : = ⋅ 4-15 Equation 4.4-29 The stability of the Modified Gain EKF (MGEKF) and the provision of bias free estimates using bearings only measurements with non-Gaussian characteristics was studied by Song [S.14] . Since the range and range-rate measurements are not in the class of modifiable functions this technique is not suitable for this application. 4.5 IMM Mode Conditioned Filters The dynamics of each filter in an IMM must be distinct, avoiding large injections of system noise making it difficult to distinguish between them, Stepaniak [S.11] . If filters of the same generic type are used their noise levels should differ by a factor of ≈10 so that they operate in distinct frequency bands, particularly when switching between manoeuvring and nonmanoeuvring models, Wheaton [W.2] . Filters with noise adaptation are unsuitable for the IMM application. The following target models were selected (identifying their parameters using the letter in parenthesis): • Constant velocity filter ( V ) • Constant acceleration filter ( A ) • 1 st order Gauss-Markov (Singer) filter ( S ) • Weaving tuned target filter ( W ) At long-range it is assumed that targets travel at constant speed interrupted by short bursts of acceleration. As the range reduces high acceleration avoidance manoeuvres can be expected. Apart from the 1 st order Gauss- Markov (Singer) filter the others use small amounts of system noise. The Singer filter is used to inject omni-directional noise system noise into the IMM to cope with changing target modes when its flight regime is uncertain, rather than target velocity directed noise. The Singer filters expressed in an Earth fixed frame are a poor representation of target dynamics compared with body directed acceleration models and its mode probability should fall once a new flight regime has been established. 4.5.1 Constant Velocity Filter A non co-ordinated velocity model driven by noise in each Cartesian axis, V & P & : = The state transition and system noise matrices for each axis, iA t V w iA Equation 4.5-1
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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 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 / Digital Ma
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Appendix I / Utilities / Matrices _
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Appendix I / Utilities / Quaternion
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