Related papers: On sub-ideal causal smoothing filters

Edge preserving filters preserve the edges and its information while blurring an image. In other words they are used to smooth an image, while reducing the edge blurring effects across the edge like halos, phantom etc. They are nonlinear in…

In this paper we consider the continuous--time nonlinear filtering problem, which has an infinite--dimensional solution in general, as proved by Chaleyat--Maurel and Michel. There are few examples of nonlinear systems for which the optimal…

This paper describes a family of seasonal and non-seasonal time series models that can be viewed as generalisations of additive and multiplicative exponential smoothing models, to model series that grow faster than linear but slower than…

A definition of frequency (cycles per unit-time) based on an approximate reconstruction of the phase-space trajectory of an oscillator from a signal is introduced. It is shown to be invariant under linear filtering, and therefore…

In this paper the issue of filtering and smoothing in continuous discrete time is studied when the state variable evolves in some submanifold of Euclidean space, which may not have the usual Lebesgue measure. Formal expressions for…

This paper is devoted to filtering, smoothing, and prediction of polynomial processes that are partially observed. These problems are known to allow for an explicit solution in the simpler case of linear Gaussian state space models. The key…

We employ the variational formulation and the Euler-Lagrange equations to study the steady-state error in linear non-causal estimators (smoothers). We give a complete description of the steady-state error for inputs that are polynomial in…

Particle filtering is a standard Monte-Carlo approach for a wide range of sequential inference tasks. The key component of a particle filter is a set of particles with importance weights that serve as a proxy of the true posterior…

We consider particle filters with weakly informative observations (or `potentials') relative to the latent state dynamics. The particular focus of this work is on particle filters to approximate time-discretisations of continuous-time…

Singular spectrum analysis is developed as a nonparametric spectral decomposition of a time series. It can be easily extended to the decomposition of multidimensional lattice-like data through the filtering interpretation. In this…

Pathwise predictability of continuous time processes is studied in deterministic setting. We discuss uniform prediction in some weak sense with respect to certain classes of inputs. More precisely, we study possibility of approximation of…

Stochastic sampling techniques are ubiquitous in real-time rendering, where performance constraints force the use of low sample counts, leading to noisy intermediate results. To remove this noise, the post-processing step of temporal and…

In this paper, we propose a new asymptotic expansion approach for nonlinear filtering based on a small parameter in the system noise. This method expresses the filtering distribution as a power series in the noise level, where the…

Causal discovery problems use a set of observations to deduce causality between variables in the real world, typically to answer questions about biological or physical systems. These observations are often recorded at regular time…

In this paper, we study the discrete time filtering problems for linear systems driven by fractional noises. The main difficulty comes from the non-Markovian of the noises. We construct the difference equation of the covariance process…

Time series analysis is used to understand and predict dynamic processes, including evolving demands in business, weather, markets, and biological rhythms. Exponential smoothing is used in all these domains to obtain simple interpretable…

Fractional delay filters are digital filters to delay discrete-time signals by a fraction of the sampling period. Since the delay is fractional, the intersample behavior of the original analog signal becomes crucial. In contrast to the…

We establish an $L_1$-bound between the coefficients of the optimal causal filter applied to the data-generating process and its finite sample approximation. Here, we assume that the data-generating process is a second-order stationary time…

Particle smoothing methods are used for inference of stochastic processes based on noisy observations. Typically, the estimation of the marginal posterior distribution given all observations is cumbersome and computational intensive. In…

This article presents an overview of a theory for performing temporal smoothing on temporal signals in such a way that: (i) temporally smoothed signals at coarser temporal scales are guaranteed to constitute simplifications of corresponding…