A Two-Stage Model for Sequential Engine-Out and Tailpipe Emission Estimation

  • Roland Schmid
  • Johannes BürgerEmail author
  • Jia Chen


This paper presents models for the estimation of vehicular NOx emissions of gasoline-powered vehicles and presents an analysis of the performance based on real driving data. The main contribution is a two-stage model for the sequential estimation of engine-out and tailpipe emissions. This structure allows on-board operation (i.e. the computations can be performed on standard automotive ECUs) and achieves an accurate estimation performance as indicated by a statistical analysis. The estimation of engine-out emissions is based on multiple linear regressions (with a low number of parameters) using training data from driving cycle data. The test data is taken from road measurements to obtain a realistic assessment of the performance of the models under real driving conditions. The accuracy is within 3% for a cumulated error index. For the second model stage, a reduced physical model of the conversion efficiency of a catalytic converter is proposed. This stage is based on physical knowledge about typical conversion behaviour of a three-way catalytic converter. We further provide a comparison with a regression-based model of the second model stage and observe that both approaches are feasible. Both achieve an accuracy within 7% for a cumulated error index. However, the physical model performs better at detecting particular emission events, while regression-based estimation tends to average out these effects.


Emission estimation Regression Modelling of three-way catalytic converters 



Jia Chen is partly supported by Technische Universität München – Institute for Advanced Study, funded by the German Excellence Initiative and the European Union Seventh Framework Program under grant agreement no. 291763.

Compliance with Ethical Standards

Conflict of Interest

The authors declare that they have no conflict of interest.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.BMW AGMunichGermany
  2. 2.Technical University of Munich, Professorship of Environmental Sensing and ModelingMunichGermany

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