We present the continuous-time particle filter (CTPF) – an extension of the discrete-time particle filter for monitoring continuous-time dynamic systems. Our methods apply to hybrid systems containing both discrete and continuous variables. The dynamics of the discrete state system are governed by a Markov jump process. Observations of the discrete process are intermittent and irregular. Whenev...

A hidden Markov model is called observable if distinct initial laws give rise to distinct laws of the observation process. Observability implies stability of the nonlinear filter when the signal process is tight, but this need not be the case when the signal process is unstable. This paper introduces a stronger notion of uniform observability which guarantees stability of the nonlinear filter i...

An estimation problem is considered for a stochastic parabolic equation with an unknown random coefficient. The additional randomness in the coefficient generalizes a popular estimation problem that has been extensively studied in recent years. The filter estimate of the coefficient is constructed from a finite-dimensional projection of the solution of the equation. Under certain conditions thi...

This paper proposes a distributed secondary voltage control method based on extended state Kalman-Bucy filter (ESKBF) and fast terminal sliding mode (FTSM) for the resilient operation of an islanded microgrid (MG) with inverter-based generations (DGs). To tackle co-existence multiple uncertainties, unified modelling framework is proposed to represent set different types disturbances, including ...

This paper presents the findings of the first stage of a fundamental study of the tilt control problem. A tilting railway vehicle is described via appropriate modelling and a frequency domain analysis illustrates the problems associated with straightforward feedback control. A Kalman-Bucy filter is developed based on 3 inertial measurements (body lateral acceleration, roll and yaw rate) to prov...

A new approach to linear least squares estimation of continuous-time (wide sense) stationary stochastic processes is presented. The basic idea is that the relevant estimates can be expressed not only in terms of the usual (forward) innovation process but also in terms of a backward innovation process. The functions determining the optimal filter as well as the error covariance functions are see...

The Ensemble Kalman filter is a sophisticated and powerful data assimilation method for filtering high dimensional problems arising in fluid mechanics and geophysical sciences. This Monte Carlo method can be interpreted as a mean-field McKean-Vlasov type particle interpretation of the Kalman-Bucy diffusions. In contrast to more conventional particle filters and nonlinear Markov processes these ...