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...

Efficient processing of nonstationary signals requires time-varying approach. An interesting research area within this approach is time-varying filtering. Since there is a certain amount of freedom in the definition of timevarying spectra, several definitions and solutions for the time-varying filtering have been proposed so far. Here we will consider the Wigner distribution based time-varying ...

Suppose that the signal X to be estimated is a diffusion process in a random medium W and the signal is correlated with the observation noise. We study the historical filtering problem concerned with estimating the signal path up until the current time based upon the back observations. Using Dirichlet form theory, we introduce a filtering model for general rough signal X and establish a multipl...

In this paper we provide explicit formulæ to compute bilinear pairings in compressed form, and indicate families of curves where particularly generalised versions of the Eta and Ate pairings due to Zhao et al. are especially efficient. With the new formulæ it is possible to entirely avoid F pk arithmetic during pairing computation on elliptic curves over Fp with even embedding degree k. Using o...

Filtering denotes any method whereby an agent updates its belief state—its knowledge of the state of the world—from a sequence of actions and observations. In logical filtering, the belief state is a logical formula describing the possible world states. Efficient algorithms for logical filtering bear important implications on reasoning tasks such as planning and diagnosis. In this paper, we wil...

Let Fλ be the space of tensor densities on R n of degree λ (or, equivalently, of conformal densities of degree −λn) considered as a module over the Lie algebra o(p+1, q+1). We classify o(p+1, q+1)-invariant bilinear differential operators from Fλ ⊗ Fμ to Fν . The classification of linear o(p + 1, q + 1)invariant differential operators from Fλ to Fμ already known in the literature (see [6, 9]) i...