  This paper considers the problem of sensorimotor delays in the optimal
control of (smooth) eye movements under uncertainty. Specifically, we consider
delays in the visuo-oculomotor loop and their implications for active
inference. Active inference uses a generalisation of Kalman filtering to
provide Bayes optimal estimates of hidden states and action in generalized
coordinates of motion. Representing hidden states in generalized coordinates
provides a simple way of compensating for both sensory and oculomotor delays.
The efficacy of this scheme is illustrated using neuronal simulations of
pursuit initiation responses, with and without compensation. We then consider
an extension of the gener-ative model to simulate smooth pursuit eye movements
- in which the visuo-oculomotor system believes both the target and its centre
of gaze are attracted to a (hidden) point moving in the visual field. Finally,
the generative model is equipped with a hierarchical structure, so that it can
recognise and remember unseen (occluded) trajectories and emit anticipatory
responses. These simulations speak to a straightforward and neurobiologically
plausible solution to the generic problem of integrating information from
different sources with different temporal delays and the particular
difficulties encountered when a system - like the oculomotor system - tries to
control its environment with delayed signals.
