By Farrell, Jay
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2 steps through the derivation of eqns. 7). 6 asks the user to derive formulas related to eqns. 7) that are useful in subsequent derivations. 2 Earth Gravity Model The gravity vector varies as a function of position due to the gravitational attraction being a function of geocentric radius, the centripetal acceleration being a function of latitude and radius, and the non-uniform Earth mass distribution. 1. 3. 001931851353 sin2 (φ) . 0066943800229 sin2 (φ) The vector [ζg , −ηg , δg ] represents local perturbations in the gravity vector relative to the ellipsoidal normal vector.
2. 7 27 Platform Frame This book will only discuss applications where the sensors are rigidly attached to the vehicle. For inertial navigation, such systems are referred to as strap-down systems. Although the sensor platform is rigidly attached to the vehicle, for various reasons the origin of the platform frame may be oﬀset or rotated with respect to the origin of the body frame. The origin of the platform coordinate frame is at an arbitrary point on the platform. The platform frame axes are deﬁned to be mutually orthogonal and righthanded, but their speciﬁc directions are application dependent.
REFERENCE FRAME TRANSFORMATIONS 35 Convergence to centimeter accuracy requires 25 iterations. , from a previous measurement) is available. Various alternative approximate and closed form solutions exist in the literature [24, 66, 68, 76, 117]. 4 Reference Frame Transformations This section presents methods for transforming points and vectors between rectangular coordinate systems. The axes of each coordinate system are assumed to be right-handed and orthogonal. Three dimensions are used throughout the discussion; however, the discussion is equally valid for Rn .
Aided Navigation by Farrell, Jay