(20 pts.) Some of the work I do involves estimating the position of an unmanned underwater vehicle at a particular time. The Kalman Filter can be used to do this. We do this by letting xt be the state at time t where xt = ut yt zt ut yt zt , ut is the East position of the vehicle at time t, yt is the North position at time t, zt is the down position at time t, ut is the East velocity at time t, and so on. The state equation for the motion of the vehicle is