A particulate matter deposit amount in a diesel particulate filter (4) provided in an exhaust passage (3) of a diesel engine (1) for a vehicle is estimated on the basis of a pressure loss in the filter (4), which is detected by a differential pressure sensor (12). When the temperature of the differential pressure sensor (12) is not within a predetermined temperature range, estimation of the particulate matter deposit amount based on the pressure loss is restricted, and instead, the particulate matter deposit amount is estimated by accumulating a particulate matter deposit amount per unit time. In so doing, increases in the estimation error outside of the predetermined temperature range are prevented. Moreover, by applying these estimation methods selectively in accordance with the vehicle speed, the precision with which the particulate matter deposit amount is estimated outside of the predetermined temperature range is improved.