Considering the TKalman–Bucy Filter (KBF) from an engineering point of view it is always important to know in advance, before KBF implementation, which variables are practically "good" and which are "bad" observable and how long it will take to estimate all of them in the presence of measurement noise to some appropriate (not necessarily theoretically optimal) level. This article presents an ap...

The use a€ exponential weighting of data (favoring more recent data) is considered for continuous-time and discrete-time Kalman-Bucy filters. Quantitative consideration is given to matters such as the computation, stability and statianarity of filters designed with data weighting. The problem of divergence or data saturation is explored, and the use of exponential weighting is compared with oth...

We investigate the information theoretic properties of KalmanBucy filters in continuous time, developing notions of information supply, storage and dissipation. By introducing a concept of energy, we develop a physical analogy in which the unobservable signal describes a statistical mechanical system interacting with a heat bath. The abstract ‘universe’ comprising the signal and the heat bath o...

We investigate the information theoretic properties of KalmanBucy filters in continuous time, developing notions of information supply, storage and dissipation. Introducing a concept of energy, we develop a physical analogy in which the unobserved signal describes a statistical mechanical system interacting with a heat bath. The abstract ‘universe’ comprising the signal and the heat bath obeys ...

Increased patronage of railways in the UK in the past 20 years has put demands on rolling stock to operate at peak availability with reduced time available for maintenance. One possible tool to enable this is the use of real time fault detection and diagnosis on board railway vehicles to detect faulty components and provide information about the current running condition of the system. This pap...

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 ...

In this paper, the optimal filtering problem for linear systems with state and observation delays is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate, error variance, and various error covariances. As a result, the optimal estimate equation similar to the traditional Kalman-Bucy one is derived; however, the resulting system of equations ...

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...