Exhaust after treatment systems for internal combustion engine powered vehicles are provided. One system includes logic in the form of one or more routines implemented by one or more of the system's components for determining the quantity of NO2 present in the exhaust that exits an oxidation catalyst, such as a diesel oxidation catalyst (DOC), without the use of an NO2 sensor. Results from such a determination may then be used to estimate the amount of soot present in the particulate filter. This estimated value of soot present in the particulate filter can then be subsequently used to determine when the particulate filter should be actively regenerated.