Kernel-Based Simultaneous Parameter-State Estimation for Continuous-Time Systems

In this note, the problem of jointly estimating the state and the parameters of continuous-time systems is addressed. Making use of suitably designed Volterra integral operators, the proposed estimator does not need the availability of time-derivatives of the measurable signals and the dependence on the unknown initial conditions is removed. As a result, the estimates converge to the true values in arbitrarily short time in a noise-free scenario. In the presence of bounded measurement and process disturbances, the estimation error is shown to be bounded. The numerical implementation aspects are dealt with and extensive simulation results are provides showing the effectiveness of the estimator.