Method and apparatus for estimating nitrogen oxides out of an engine

A system comprising:

• a fuel module configured to, based on a crankshaft angle of an engine, generate a first value indicative of (i) an amount of fuel burned in a cylinder of the engine, or (ii) a change in the amount of fuel burned in the cylinder;
• a heat release module configured to, based on the first value, determine an amount of heat released during a combustion event of the cylinder;
• a pressure module configured to, based on the amount of heat released, estimate a pressure in the cylinder;
• a temperature module configured to, based on the pressure, estimate a temperature in the cylinder;
• a concentration module configured to, based on the pressure or the temperature, estimate nitrogen oxide concentration levels in the cylinder;
• an output module configured to, based on the nitrogen oxide concentration levels, estimate an amount of nitrogen oxides out of the cylinder;
• and
• a control module configured to, based on the amount of nitrogen oxides out of the cylinder, control operation of the engine or an exhaust system of the engine.