Data-driven Kalman filter for linear continuous-time parametric uncertain systems with non-uniformly sampled data

This paper develops one Kalman filtering technique for parametric uncertain continuous-time linear systems with non-uniformly sampled data. The considered problem is challenging in sense that normal Kalman filter is not applicable due to the unknown parameter in the system dynamics and the unknown parameter cannot be identified directly due to the lack of good state estimates. Based on a new discretization scheme addressing the known parameter and the non-uniformly sampled data, an algorithm based on Kalman filtering theory is proposed to estimate the uncertain parameter and states simultaneously, whose main idea is to merge the parameter estimation and state filtering in the same loop, that is to say, with the help of discrete-time model obtained, the estimated states are used to estimate the parameter and the estimated parameter is fed into the state estimation. One typical numerical example is given to illustrate the feasibility and effectiveness of the proposed algorithm.