Design of optimum periodic time varying filters for applications in combustion diagnosis of car engines

For adaptive control of modern car engines the combustion process has to be observed. Direct measurement of cylinder pressure is costly and not suitable for implementation. Therefore, the authors approximate the pressure by appropriate filtering of one or more vibration signals that can be measured easily. It has been shown that the pressure signal can be modelled as second order cyclostationary (SOSC) [Konig and Bohme, 1994]. The transfer characteristic between pressure and vibration is time-varying due to the motion of the piston during observation. Therefore, for constant rotation speed the authors assume a linear periodic time-varying model. In this case, pressure and vibration signals are jointly SOCS. Based on this the authors formulate the optimum filter problem for the application. Solutions for this problem are known from the literature. They choose an appropriate one, adapt it to the problem and estimate the filter parameters. A real data experiment demonstrates the quality of this estimation