Look-up tables are commonly used in the automotive field for handling operating point variations. However, constant maps cannot cope with systems variations and ageing. Methods, such as Kalman filter or Extended Kalman filter for non-linear cases, can be used for table adaptation providing an optimal solution to the problem. But these methods are computationally intensive, making difficult to implement them on commercial engine control units. The current paper proposes a learning method for online updating of look-up tables or maps. This algorithm uses precalculated membership functions based on a standard Kalman filter observer for weighting the adaptation. The main contribution of the method is the derivation of a steady-state Kalman filter observer that lowers the calculation burden and simplifies the implementation against the standard Kalman filter implementation that requires higher computational cost. As far as table is updated online while engine runs, this allows correcting drift errors and the unit-to-unit dispersion. The method is illustrated for mapping engine variables such as λ-1 and NOx in a Diesel engine by using an adaptive look-up table, and its characteristics make it suitable for implementing in commercial engine electronic control units for online purposes. © 2012 Elsevier Ltd.
Guardiola, C., Pla, B., Blanco-Rodriguez, D., & Cabrera, P. (2013). A learning algorithm concept for updating look-up tables for automotive applications. Mathematical and Computer Modelling, 57(7–8), 1979–1989. https://doi.org/10.1016/j.mcm.2012.02.001