8Please give only typed answer

Problem 2 [2 points] Tilt correction with accelerometers. Suppose at time t, the estimated orientation of a rigid tract}.F with respect to a xed world frame by gyro integration is a quaternion ti... Let ti, he the sensed linear acceleration from an accelerometer on the rigid body. We assume that there is no external acceleration. Therefore. the sensed linear acceleration corresponds to gravity. Express the angle Q5 between the sensed acceleration and the gra'lritf,r vector 1r = {I}, 1, (if in the world frame using til, and fa. See Figure 1. [Hint 1] The linear acceleration from the accelerometer is in the local coordinates of the rigid body. [Hint 2} To rotate a vector v by a quaternion q, we have fr 2 our; 1 with quatemion multiplication and quaternion inverse. We assume all quatcrnions are with unit length. M Sensed acceleration CU World frame Z Figure 1: Illustration of the SenSed acceleration from an accelerometer in the world frame