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Chapter 1 / Introduction
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1.3.9 Appendix C : Transformation Between Frames
Appendix C defines the rotational transformations between the primary
frames whose origins are located at critical geometric points. Euler triplets
and skew-symmetric forms are introduced to describe the relationships
between Euler rotations, direction cosines and quaternions. Nomenclature is
introduced to cope with the transformation between Cartesian, Polar and
UVR co-ordinates with respect to a common frame.
1.3.10 Appendix D : Point Mass Kinematics
The geometry in the previous appendices forms the basis for defining
direction cosine propagation, transformation matrix dynamics, angular rate
and its skew-symmetric form, and their relationship with Euler triplets. The
linear and angular velocity, acceleration and jerk dynamics of a point
moving with respect to an inertial frame are developed.
1.3.11 Appendix E : Earth Geometry
Missile systems often involve terrestrial motion over long distances using
navigation aids requiring a mathematical representation of the ground
beneath. Expressions for earth radius, meridian and polar earth curvature
are derived for a general ellipsoid. The defining characteristics of a number
of commonly used ellipsoids are given, and WGS84 selected to explore the
variation in these radii with latitude.
1.3.12 Appendix F : Atmospheric Characteristics
Expressions for the atmospheric pressure, temperature, and density variation
with geodetic height are given up to 32km together with their relationship
with the speed of sound and Mach number. The variation in these
parameters with respect to the reference-state is provided for use in
trajectory optimisation.
1.3.13 Appendix G : Gravitational Acceleration
Gravity acting at a point above the Earth is defined, and approximations
relating to near-earth operation explored. Its variation with geodetic height
and latitude is expressed in terms of the reference-state for trajectory
optimisation.
1.3.14 Appendix H : Fixed-Gain Filters
This appendix deals with the fixed-gain counterparts of the stochastic filters
used in the target state observer. Historical reviews precede the formulation
of velocity, acceleration and weave filters that arise from the solution to the
associated Ricatti equation. This information complements the presentation
of filter utilities in Appendix J-8 and provides a useful insight into the quasisteady
state performance of stochastic filters. Conceptually, state observers
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