By Farrell, Jay
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702 m. 0478571082 rad. 3. 358] m. 4. The transformation from [x, y, z]e to geodetic coordinates is more involved, but is important in GPS applications where the ECEF rectangular coordinates are directly determined from range measurements and the CHAPTER 2. REFERENCE FRAMES 34 geodetic coordinates are often desired. Longitude can be found explicitly from eqns. 10) as λ = arctan2(y, x). Solution for h and φ can be computed by iteration as follows : 1. Initialization: Let h = 0 = a RN p = x2 + y 2 .
REFERENCE FRAMES 22 mean sea level. By deﬁnition the gravity vector is everywhere perpendicular to the geoid. For analytic tractability the Earth’s geoid is usually approximated by a reference ellipsoid that is produced by rotating an ellipse around its semi-minor axis. 2 depicts an ellipse that has much greater ﬂatness than the that of the Earth, but the ellipse is useful for making a few important points. Most importantly, the normal to the ellipse, when extended towards the interior of the ellipse does not intersect the center of the Earth.
8, where φ denotes latitude, λ denotes longitude, and h denotes altitude above the reference ellipsoid. Latitude is the angle in the meridian plane from the equatorial plane to the ellipsoidal normal N . Note that the extension of the normal towards the interior of the ellipsoid will not intersect the center of the Earth except in special cases such as φ = 0 or ±90◦ . 1. Longitude is the angle in the equatorial plane from the prime meridian to the projection of the point of interest onto the equatorial plane.
Aided Navigation by Farrell, Jay