This study aims to create a prediction model for state-space estimation and to elucidate the required information processing for identifying an external space in prism adaptation. Subjects were 57 healthy students. The subjects were instructed to rapidly perform reaching movements to one of the randomly illuminating light-emitting diode lights. Their movements were measured while wearing prism glasses and after removing that. We provided the following four conditions and control. In target condition, reaching error distance was visually fed back to the subject. In trajectory condition, the trajectory of fingertip movement could be seen, and the final reaching error was not fed back. Two restricted visual feedback conditions were prepared based on a different presentation timing (on-time and late-time conditions). We set up a linear parametric model and an estimation model using Kalman filtering. The goodness of fit between the estimated and observed values in each model was examined using Akaike information criterion (AIC). AIC would be one way to evaluate two models with different number of parameters. In the control, the value of AIC was 179.0 and 154.0 for the linear model and Kalman filtering, respectively, while these values were 173.6 and 161.1 for the target condition, 202.8 and 159.7 for the trajectory condition, 192.7 and 180.8 for the on-time condition, and 206.9 and 174.0 for the late-time condition. Kalman gain in the control was 0.07–0.26. Kalman gain relies on the prior estimation distribution when its value is below 0.5. Kalman gain in the trajectory and late-time conditions was 0.03–0.60 and 0.08–0.95, respectively. The Kalman filter, a state estimation model based on Bayesian theory, expressed the dynamics of the internal model under uncertain feedback information better than the linear parametric model. The probabilistic estimation model can clearly simulate state estimation according to the reliability of the visual feedback.

We present a model for several early stages of the sensorimotor transformations involved in targeted arm movement. In psychophysical experiments, human subjects pointed to the remembered locations of randomly placed targets in three-dimensional space. They made consistent errors in distance, and from these errors stages in the sensorimotor transformation were deduced. When subjects attempted to move the right index finger to a virtual target they consistently undershot the distance of the more distal targets. Other experiments indicated that the error was in the sensorimotor transformation rather than in the perception of distance. The error was most consistent when evaluated using a spherical coordinate system based at the right shoulder, indicating that the neural representation of target parameters is transformed from a retinocentric representation to a shoulder-centered representation. According to the model, the error in distance results from the neural implementation of a linear approximation in the algorithm to transform shoulder-centered target parameters into a set of arm orientations appropriate for placing the finger on the target. The transformation to final arm orientations places visually derived information into a frame of reference where it can readily be combined with kinesthetically derived information about initial arm orientations. The combination of these representations of initial and final arm orientations could give rise to the representation of movement direction recorded in the motor cortex by Georgopoulos and his colleagues. Later stages, such as the transformation from kinematic (position) to dynamic (force) parameters, or to levels of muscle activation, are beyond the scope of the present model.