An amount of deposition of intramural PM in a particulate filter is estimated with a high degree of accuracy. A controller obtains, as a correlation between a reference value of an intramural PM deposition amount and an oxygen storage capacity of the catalyst, a change over time of an oxygen storage capacity of the catalyst according to a change of a filter PM deposition amount in a period of time from a point in time at which the filter PM deposition amount is substantially zero to a point in time at which the oxygen storage capacity of the catalyst, which becomes larger according to an increase of the filter PM deposition amount, reaches a maximum value. Further, the controller estimates a current intramural PM deposition amount based on a current oxygen storage capacity of the catalyst and the correlation.