Mass based methods and systems for estimating soot load in a filter of an after-treatment system for exhaust stream are provided. The after-treatment system can comprise a sensor, a filter, and a processor configured to estimate soot load in the filter based on a mass based multi-layer model. An example system includes a virtual sensor comprising an estimator for providing information corresponding to a filter outlet NO2 concentration. An example method includes the steps of providing the mass based multi-layer model, passing the exhaust stream through the filter, and using the sensor to monitor a condition of the exhaust stream. The example method further includes the steps of calculating a total regeneration rate based on the multi-layer model by solving a second-order ordinary differential equation with a plurality of parameters using an analytical approach, and estimating the soot load based on the calculated total regeneration rate.