Stochastic filtering theory

Introduction to Stochastic Filtering Theory

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Stochastic Vorticity and Associated Filtering Theory

The focus of this work is on a two-dimensional stochastic vorticity equation for an incompressible homogeneous viscous fluid. We consider a signed measure-valued stochastic partial differential equation for a vorticity process based on the Skorohod–Ito evolution of a system of N randomly moving point vortices. A nonlinear filtering problem associated with the evolution of the vorticity is consi...

Stochastic Calculus, Filtering, and Stochastic Control

Stochastic Filtering via Reweighted-`1

Many modern signal processing applications can be stated in terms of performing inference on sparse signals that have significant dependencies between those signals. Consider the task of recovering signals xn ∈ R from incomplete and noisy linear measurements yn = Φnxn + n, where Φn ∈ RM×N is the potentially timevarying measurement matrix, n is the measurement noise, and n ∈ K is an index (e.g.,...

Higher-Degree Stochastic Integration Filtering

We obtain a class of higher-degree stochastic integration filters (SIF) for nonlinear filtering applications. SIF are based on stochastic spherical-radial integration rules that achieve asymptotically exact evaluations of Gaussian weighted multivariate integrals found in nonlinear Bayesian filtering. The superiority of the proposed scheme is demonstrated by comparing the performance of the prop...