The Mathematics of Filtering and Its Applications

The problem of estimating the latent states of a dynamical system from observed data often arises in many branches of physical and social sciences, including image processing, navigation, econometrics, finance and meteorology. Filtering refers to any method for obtaining such state estimates, recursively in time, by combining model predictions with noisy observations. While the solution to the filtering problem for a linear dynamic system is well understood and has been studied extensively since 1960s, the optimal solution to the nonlinear filtering still poses challenging problems in maintaing a complete description of the conditional probability density. A number of suboptimal approximations, mainly based on Bayesian methods, have been proposed for solving the nonlinear filtering problem arising in different fields such as image processing, meteorology and econometrics, each offering an application-specific compromise between estimation accuracy, computational burden and numerical robustness. Because of the diversity of applications, researchers from different fields have developed both methodological and application specific innovations that often remain restricted to their respective fields. The purpose of this special issue on the mathematics of filtering and its applications is to collect experiences in filtering from different fields by including some papers, selected from the homonym workshop held at Brunel University in July 2011, which are representative of different application areas including financial mathematics, robotics and artificial intelligence. We are thankful to the editor Prof. V.J. Rayward-Smith for allocating a special issue dedicated to this topic.