Identification and adaptation of linear look-up table parameters using an efficient recursive least-squares technique

Linear look-up tables are widely used to approximate and characterize complex nonlinear functional relationships between system input and output. However, both the initial calibration and subsequent real-time adaptation of these tables can be time consuming and prone to error as a result of the large number of table parameters typically required to map the system and the uncertainties and noise in the experimental data on which the calibration is based. In this paper, a new method is presented for identifying or adapting the look-up table parameters using a recursive least-squares based approach. The new method differs from standard recursive least squares algorithms because it exploits the structure of the look-up table equations in order to perform the identification process in a way that is highly computationally and memory efficient. The technique can therefore be implemented within the constraints of typical embedded applications. In the present study, the technique is applied to the identification of the volumetric efficiency look-up table commonly used in gasoline engine fueling strategies. The technique is demonstrated on a Ford 2.0L I4 Duratec engine using time-delayed feedback from a sensor in the exhaust manifold in order to adapt the table parameters online.