not yet reached a predetermined amount in step s 22 exhaust gas flow rate qexh is read in step s 23 it is determined whether or not read exhaust gas flow rate qexh has reached a predetermined value i e whether or not the exhaust gas flow rate is sufficient this determination aims at recognizing that a differential pressure suitable for measurement is generated between the inlet and outlet of diesel particulate filter 12 if the answer in step s 23 is affirmative the control proceeds to step s 24 if the answer in step s 23 is negative the control returns in step s 24 count value c is increased by 1 count value c is initially set to 0 and is increased by one every time ash estimation amount ash is estimated in the manner described above count value c is maintained even after stoppage of engine 1 in step s 25 filter differential pressure u03b4pdpf and mileage d are read mileage d is set to 0 at the time of shipping of a vehicle or latest replacement of diesel particulate filter 12 and is calculated by accumulation of vehicle speed vsp d u03c3 vsp u00d7 u03b4t where u03b4t is a calculation cycle in step s 26 ash accumulation amount ash is estimated based on read filter differential pressure u03b4pdpf and exhaust gas flow rate qexh estimation of ash is performed by reference to a map fig4 wherein ash is assigned to u03b4pdpf and qexh by this map ash is estimated to be a larger value as filter differential pressure u03b4pdpf becomes larger under constant exhaust gas flow.