An important emerging scientific issue is the real time filtering through observations of noisy turbulent signals for complex systems as well as the statistical accuracy of spatio-temporal discretizations for such systems. These issues are addressed here in detail for the setting with plentiful observations for a scalar field through explicit mathematical test criteria utilizing a recent theory...

In this paper we address sampling and approximation of functions on combinatorial graphs. We develop filtering on graphs by using Schrodinger’s group of operators generated by combinatorial Laplace operator. Then we construct a sampling theory by proving Poincare and Plancherel-Polya-type inequalities for functions on graphs. These results lead to a theory of sparse approximations on graphs and...

A deterministic least squares estimation theory of linear time-invariant systems is presented. It is demonstrated that the well-known Kalman filtering results can be obtained for purely deterministic systems with impulsive noises entering into every measurement. Applying known results from singular optimal control theory, the Kalman filtering results are extended to cases where some or all meas...

Inference for partially observed Markov process models has been a longstanding methodological challenge with many scientific and engineering applications. Iterated filtering algorithms maximize the likelihood function for partially observed Markov process models by solving a recursive sequence of filtering problems. We present new theoretical results pertaining to the convergence of iterated fi...

This paper is a tutorial survey which focuses on some developments introduction in statistical filtering achieved since the of Wiener and Kalman filters for linear gaussian problems. Kalman are reviewed with filters (including reference to their smoothers and predictors) interesting properties and also their fundamental limitations in nonlinear or unknown environments. For nonlinear filtering p...

Within the last two decades a small group of researchers has built a useful, nontrivial theory of nonlinear signal processing around the median-related filters known as rank-order filters, order-statistic filters, weighted median filters, and stack filters. This required significant effort to overcome the bias, both in education and research, toward linear theory, which has been dominant since ...