State-estimation and cooperative control with uncertain time

State estimation and control typically depend on the implicit assumption that actuation and measurement occur at known points in time. This assumption is predicated on sufficiently precise timekeeping afforded by engineered clocks. Biological control systems do not have access to quartz-crystal technology and yet animals perform behaviors that engineered systems cannot. Here, we examine the problem of state estimation using imprecisely timed measurements, with known temporal statistics. We consider the case that there are two controllers, each with its own imperfect clock, performing a cooperative task-formulated in a leader-follower paradigm. In our problem, the follower estimates the state of the leader's noisy clock along with other state variables. An example of a complex cooperative leader-follower task is ballroom dancing.