value Z(t) by which the calculated value X(t) can be offset to provide the estimated value Xa(t) for soot loading is represented by the equation: Z(t)=Z(t???1)+G*[E(t???1)???Z(t???1)] where G is a factor corresponding to reliability of soot loading data between time t=0 and time t=T, and the estimated value Xa(t) for soot loading of the subject filter is represented by the equation Xa(t)=X(t)???Z