Nonlinear filtering of convex sets of probability distributions
The authors solve a filtering problem for a nonlinear dynamical system whose initial state is specified by a convex set of probability distributions (rather than a single distribution, such as the Gaussian distribution). The system is continuous-time and is observed in discrete time. The convex set of prior densities is defined as the set of (convex) mixtures generated by a given finite set of probability distributions, say \(\Pi\). Galerkin's method is used to solve Kolmogorov's equations for the posterior densities. Their means and variances are expressed by using the elements of \(\Pi\).
scientific article; zbMATH DE number 1790203
scientific article