An on-board apparatus includes a measuring unit, a filtering unit, a predicting unit, an executing unit, a detecting unit, and an adjusting unit. The measuring unit periodically measures a state of an own vehicle. The filtering unit performs a low-pass filter process on measurement results from the measuring unit. The predicting unit predicts behavior of the own vehicle based on the measurement results on which the low-pass filter process has been performed. The executing unit performs processes based on the behavior of the own vehicle predicted by the predicting unit. The detecting unit detects a traveling environment of the own vehicle. The adjusting unit adjusts a time constant for the low-pass filter process based on the traveling environment detected by the detecting unit.