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 ...

The Kalman filter formula, given by the linear recursive algorithm, is usually used for estimation of the time-varying parameter model. The filtering formula, introduced by Kalman (1960) and Kalman and Bucy (1961), requires the initial state variable. The obtained state estimates are influenced by the initial value when the initial variance is not too large. To avoid the choice of the initial s...

In this article we consider the linear filtering problem in continuous-time. We develop and apply multilevel Monte Carlo (MLMC) strategies for ensemble Kalman-Bucy filters (EnKBFs). These can be viewed as approximations of conditional McKean-Vlasov-type diffusion processes. They are also interpreted continuous-time analogue \textit{ensemble Kalman filter}, which has proven to successful due its...

the error of inertial navigation systems increase versus time, therefore for achieving higher accuracy specially in long time navigations we have to use an aiding system. global positioning system is the best aiding system in this case. in this paper we first simulate a gps and ins; then simulate tightly integration and finally review adaptation method of kalman filtering a fuzzy adaptive kalma...

Preface These lecture notes are concerned with state estimation problem of linear and particularly nonlinear discrete and continuous-discrete stochastic systems. State estimation has a great variety of applications including The general solution of the state estimation problem is based on the Bayesian recursive relations and the Fokker-Planck equation which generate conditional probability dens...