Adaptive filters for non-linear continuous-time systems based on approximate discretised models

Discrete-time filters based on approximate discretised models for non-linear continuous-time systems are investigated. The discretised models are based on the so-called jump-modelling technique. It is shown that although the discretised models are rather coarse approximations of the underlying continuous-time systems, properly tuned filters can give reasonably accurate state estimates. However, the filter performance is very sensitive with respect to the assumed process noise covariance matrix, which makes filter tuning difficult. As a remedy, two types of adaptive filters are proposed, and their performance improvement due to adaptation is shown. A two-state Van der Pol oscillator is considered as a simulation example