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DSTO–TN–0640Glossary, Conventions, and Constantsα Latitude of a point in the ECEF frame.ω Longitude of a point in the ECEF frame.Aircraft’s own axes x, y, z.Aircraft’s own axes as vec<strong>to</strong>rs in ECEF x, y, z.Earth’s elliptical cross-section This is defined by the following numbers:Semi-major: a = 6,378,137 m; semi-minor: b = 6,356,752.3142 m.ECEF Earth-Centred, Earth-Fixed Frame. A rotating frame fixed <strong>to</strong> Earth; the globalframe of this report within which all computations are done.ECEF Cartesian Axes X, Y, Z.Three Euler rotations act on a set of orthonormal vec<strong>to</strong>rs x 0 , y 0 , z 0 <strong>to</strong> give, in order,x 1 , y 1 , z 1 , then x 2 , y 2 , z 2 , and finally x 3 , y 3 , z 3 .GPS Global Positioning Satellite System.Local Geographic Frame A frame based at our current position, usually on or nearEarth’s surface. Two common choices for its axes are:NED North-East-Down set of axes.ENU East-North-Up set of axes.n A unit vec<strong>to</strong>r pointing along an axis of rotation. A column when used with matrices,and a row when used with quaternions. This might seem potentially confusing, butthere’s no ambiguity in practice; on the contrary, <strong>to</strong> continually write n and n t (thetranspose) just <strong>to</strong> emphasise a column or row would be tedious.North, East, Down axes N, E, D.North, East, Down axes as vec<strong>to</strong>rs in ECEF N, E, D.Rotation matrix R n (θ) rotates by angle θ around unit vec<strong>to</strong>r n using the right-handconvention.Rotation quaternion Q n (θ) rotates by angle θ around unit vec<strong>to</strong>r n using the righthandconvention.r A←BPosition of point A relative <strong>to</strong> point B; i.e., a vec<strong>to</strong>r pointing from B <strong>to</strong> A.SLERP Spherical Linear Interpolation. Used for interpolating orientations using quaternions.WGS-84 World Geodetic System 1984 standard for maps. This standard defines theoblate spheroid typically used <strong>to</strong> model Earth’s shape, as used in this report.ix