In understanding circumstances, we human beings direct our attention to appropriate information sources and collect necessary information according to our purpose. The author formalized such an attentional perception process as a sequential experimental design based on an information criterion and described its concrete algorithm. In the present article, the author develops the algorithm with an idea of prediction so as to estimate a time-variant object's state efficiently. The algorithm is to predict the object's state using the internal state transition model and to observe the object with the most informative sensor when the ambiguity of the prediction exceeds a specified limit. The author applies the algorithm to a problem of estimating the position of a moving target with observing it by a camera at times, and investigates its behavior through numerical experiments. The result shows that the system turns the camera's visual field to proper directions at proper times and estimates the target's position with specified accuracy by fewer observations.