The Kalman Bucy filter is a well-known observer to estimate the state vector from the incomplete state measurements. However, when the time delay is taken into account, the filter can become ineffective. In this paper, the identification algorithm presented in a previous paper (Anh 2000) is used to improve the Kalman Bucy filter in the presence of time delay. The differential equation of the ob...

Mrstract—The notion is exploded that to build a Kalman–Bucy filter, one needs to know tbe whole structure of the signal generating process. It is shown that the filter is constructible knowing precisely those covariwrces required to construct a Wiener filter, and no more, and that the filter is independent of the particular models of the processes generating these covariances. Performance of th...

In this paper, the Kalman-Bucy filter is designed for an Ito-Volterra process over Ito-Volterra observations that cannot be reduced to the case of a differential observation equation. The Kalman-Bucy filter is then designed for an Ito-Volterra process over discontinuous Ito-Volterra observations. Based on the obtained results, the filtering problem over discrete observations with delays is solv...

The notion is exploded that to build a Kalman-Bucy filter, one needs to know the whole structure of the signal generating process. It is shown that the filter is constructible knowing precisely those covariance~ required to construct a Wiener filter, and no more, and that the filter is independent of the particular models of the processes generating these covariances. Performance of the Kalman-...

This paper is concerned with the filtering problem in continuous-time. Three algorithmic solution approaches for this problem are reviewed: (i) the classical Kalman-Bucy filter which provides an exact solution for the linear Gaussian problem, (ii) the ensemble Kalman-Bucy filter (EnKBF) which is an approximate filter and represents an extension of the Kalman-Bucy filter to nonlinear problems, a...

We study the estimation of change point obtained through a Kalman-Bucy filter for linear systems driven by fractional Brownian motions.

Contraction theory entails a theoretical framework in which convergence of a nonlinear system can be analysed differentially in an appropriate contraction metric. This paper is concerned with utilizing stochastic contraction theory to conclude on exponential convergence of the Unscented Kalman-Bucy Filter. The underlying process and measurement models of interest are Itô-type stochastic differe...

In this paper, we present an application of the stochastic calculusto the problem of modeling electrical networks. The filtering problem have animportant role in the theory of stochastic differential equations(SDEs). In thisarticle, we present an application of the continuous Kalman-Bucy filter for a RLcircuit. The deterministic model of the circuit is replaced by a stochastic model byadding a ...