In the physical sciences, e.g., meteorology and oceanography, combining measurements with the dynamics of the underlying models is usually referred to as data assimilation. Data assimilation improves the reconstruction of the image fields of interest. Assimilating data with algorithms like the Kalman-Bucy filter (KBf) is challenging due to their computational cost which for two-dimensional (2-D...

This work investigates the problem of state estimation for singular stochastic di®erential systems. A Kalman-Bucy-like ̄lter is proposed, based on a suitable decomposition of the descriptor vector into two components. The ̄rst one is expressed as a function of the observation, and therefore does not need to be estimated, while the second component is described by a regular linear stochastic sys...

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...

We interpret steady linear statistical inverse problems as artificial dynamic systems with white noise and introduce a stochastic differential equation system where the of ending time $T$ naturally plays role squared level. The time-continuous framework then allows us to apply classical methods from data assimilation, namely, Kalman--Bucy filter 3DVAR, analyze their behavior regularization meth...

This paper investigates the problem of controlling a team of Quadrotors that cooperatively transport a common payload. The main contribution of this study is to propose a cooperative control algorithm based on a decentralized algorithm. This strategy is comprised of two main steps: the first one is calculating the basic control vectors for each Quadrotor using Moore–Penrose theory aiming at coo...

Bilateral anterior opercular syndrome and partial Kluver-Bucy syndrome are associated with bilateral middle cerebral artery lesions. The combination of these two syndromes has only been reported in a child with limbic encephalitis. In this case, a 44-year-old woman with bilateral middle cerebral artery infarction, which occurred 2 years prior, could walk independently. However, she showed autom...

In practical situations, we observe the number of claims to an insurance portfolio but not the claim intensity. It is therefore of interest to try to solve the` ltering problem', that is to obtain the best estimate of the claim intensity on the basis of reported claims. In order to use the Kalman-Bucy lter, based on the Cox process incorporating a shot noise process as claim intensity, we need ...