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 timederivatives 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 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.

The derivative estimation problem is addressed in this paper by using Volterra integral operators which allow to obtain the estimates of the time-derivatives with fast convergence rate. A deadbeat state observer is used to provide the estimates of the derivatives with a given fixed-time convergence. The estimation bias caused by modeling error is characterized herein as well as the ISS property of the estimation error with respect to the measurement perturbation. A number of numerical examples are carried out to show the effectiveness of the proposed differentiator also including comparisons with some existing methods.

Abstract-This paper presents a novel framework for the problem of target localization based on the range information collected by a single mobile agent. The proposed methodology exploits the algebra of Volterra integral operators to annihilate the influence of initial conditions on the transient phase, thus achieving a deadbeat performance. The robustness properties against additive measurement perturbations are analyzed and the bias caused by the time-discretization is characterized as well. Extensive simulation results and comparisons are provided showing the effectiveness of the proposed technique in coping with both stationary and drifting targets.