The a/p has its command to provide a particular altitude, airspeed. At the core of this command is PITCH and POWER, yep. I'd be surprised if at disconnect, it lost its recent tracking artifacts. The Pilot is not charged with keeping a three second loop of "last recorded" in his head, as the a/p keeps without a sweat. Frustrating, esteemed Pilots suggest at the beginning to be patient, when all we need is a snapshot of the previous chain of acceptable status points, a normed value and a command, "get us 'here'. A million frames of accelerations? Yes, with random points of data geography such that continued flight can be kept in limits for 5-10 minutes? 5-10 hours? Why not?