Payri, F., Guardiola, C., Blanco-Rodriguez, D., Mazer, A. et al., "Methodology for Design and Calibration of a Drift Compensation Method for Fuel-To-Air Ratio Estimation," SAE Technical Paper 2012-01-0717, 2012, doi:10.4271/2012-01-0717.
Observers can be used for combining different information sources, as fast models with slow but accurate sensors. For that, a Kalman filter can be used for identifying the bias and cancelling its variation during time. However, normal calibration procedure is iterative and ad-hoc and this does not get optimal results. Furthermore, the lack of enough accurate references make difficult to estimate the best tuning, and more if the calibration pretends to be an online procedure. For solving this, the paper presents a novel calibration method for Kalman filter based on a Monte Carlo analysis, simulating real conditions by means of statistical distributions. This makes possible to create actual references for estimating error metrics of the observer output. A previous sensitivity study is presented for understanding the performance of the algorithm under different conditions. And finally, adequacy of the proposed method is demonstrated for the relative fuel-to-air ratio estimate λ-₁ obtained from the secondary output of an exhaust NOx sensor installed in a turbocharged diesel engine.