This is a companion paper of Crisan et el [4]. In this article, we study a few classes of solvable models of the stochastic filtering problems with Ornstein-Uhlenbeck noise: Firstly, we study the singular linear filter with OU noise. Secondly, for nonsingular linear filtering with OU noise, we consider the limit to the classical Kalman-Bucy filter as the OU process converges to the Brownian mot...

We extend the Kalman–Bucy filter to the case where both the system and observation processes are driven byfinite dimensional Lévy processes, butwhereas the process driving the system dynamics is square-integrable, that driving the observations is not; however it remains integrable. The main result is that the components of the observation noise that have infinite variance make no contribution t...

We examine the question of determining the "best" linear filter, in an expected squared error sense, for a signal generated by stochastic linear differential equation on a Hilbert space. Our results, which extend the development in Kalman and Bucy (1960), rely heavily on the integration theory for Banach-space-valued functions of Dunford and Schwartz (1958). In order to derive the Kalman-Bucy f...

Kalman-Bucy smoothers are often used to estimate the state variables as a function of time in a system with stochastic dynamics and measurement noise. This is accomplished using an algorithm for which the number of numerical operations grows linearly with the number of time points. All of the randomness in the model is assumed to be Gaussian. Including other available information, for example a...

A respiratory chamber is used for monitoring VO2, VCO2 and RQ in humans, enabling long term (24h) observation under free living conditions. Computation of VO2 and VCO2 is currently done by inversion of a mass balance equation, with no consideration of measurement errors and other uncertainties. In order to improve the accuracy of the results, a new mathematical model is suggested in the present...

Abstract The purpose of this review is to present a comprehensive overview the theory ensemble Kalman–Bucy filtering for continuous-time, linear-Gaussian signal and observation models. We system equations that describe flow individual particles sample covariance mean in continuous-time filtering. consider these their characteristics number popular Kalman variants. Given equations, we study asym...

In this paper, we consider the development of unbiased estimators for ensemble Kalman-Bucy filter (EnKBF). The EnKBF is a continuous-time filtering methodology, which can be viewed as analog famous discrete-time Kalman filter. Our will motivated from recent work (Rhee and Glynn, Oper. Res., 63:1026-1053, 2015) introduces randomization means to produce finite variance estimators. enters through ...