By Farrell, Jay
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Additional info for Aided Navigation
6 Body Frame In navigation applications, the objective is to determine the position and velocity of a vehicle based on measurements from various sensors attached to a platform on the vehicle. This motivates the deﬁnition of vehicle and instrument frames-of-reference and their associated coordinate systems. The body frame is rigidly attached to the vehicle of interest, usually at a ﬁxed point such as the center of gravity. Picking the center of gravity as the location of the body frame origin simpliﬁes the derivation of the kinematic equations  and is usually convenient for control system design.
4. 10: Deﬁnition of the coordinates of a point P with respect to two frames-of-reference φ1 and φ2 . question of interest is how to calculate [v2 ]1 based on the available information. Let I2 , J2 , K2 represent the unit vectors along the φ2 axes. As discussed relative to eqn. 14), vectors vI , vJ , and vK deﬁned as ⎡ ⎡ ⎡ ⎤ ⎤ ⎤ I1 · I2 I 1 · J2 I1 · K2 vI = ⎣ J1 · I2 ⎦ , vJ = ⎣ J1 · J2 ⎦ , and vK = ⎣ J1 · K2 ⎦ K1 · I2 K 1 · J2 K1 · K2 represent the unit vectors in the direction of the φ2 coordinate axes that are resolved in the φ1 reference frame.
The purpose of this chapter is to deﬁne the various frames and the methods for transforming the coordinates of points and representation of vectors between frames. Before proceeding to the main body of the chapter, the next paragraph steps through the measurements and computations of a strapdown inertial navigation system (INS). The goals of this brief introduction are to deﬁne notation and to illustrate how the diﬀerent frames-of-reference come into play in navigation applications. 1: High level block diagram of an inertial navigation system.
Aided Navigation by Farrell, Jay