Figure 2. Prediction of the larva’s trajectory from the deflection of the tail.

(a) Parametrization of the displacement of the larva in the horizontal plane. Only 3 parameters are required to describe the trajectory: the axial, lateral and yaw speed. (b) Illustration of the Auto-regressive Model with External Input. Each of the three parameters of trajectory was computed using the tail deflection. Each of the kinematic parameters at time t, K(t) was computed using a linear combination of its past values: and the present and past values of the tail deflection: . See Materials and Methods for details. (c) Examples of four different types of movements showing the true path of the larva (in blue) and that predicted (in red). (i) Tail deflection corresponding to different categories of movement. (ii) The axial speed. (iii) The lateral speed. (iv) Yaw angle. For each case, the observed kinematic parameter is in red, and the predicted in blue. (d) Distribution of the errors between the predicted position and orientation, and those observed, for: (i) change in head orientation; (ii) direction of movement; (iii) amplitude of the tail bout. The results presented in (c) and (d) were taken from the test dataset.