White noise theory of robust nonlinear filtering with correlated state and observation noises

White Noise Theory of Robust Nonlinear Filtering with Correlated State and Observation Noises

In the existing “direct” white noise theory of nonlinear filtering, the state process is still modelled as a Markov process satisfying an It6 stochastic differential equation, while a “finitely additive” white noise is used to model the observation noise. We remove this asymmetry by modelling the state process as the solution of a (stochastic) differential equation with a “finitely additive” wh...

Unscented Filtering from Delayed Observations with Correlated Noises

Robust Filtering for Uncertain Linear Systems with State-Dependent Noise

This paper deals with the problems of robust H2 and H∞ filtering for a class of linear continuous-time systems subject to uncertain constant parameters and both additive and state-dependent noise signals. The uncertain parameters appear affinely in the matrices of the system state-space model and are assumed to belong to a given polytope. Linear matrix inequality approaches are proposed for des...

Towards a general theory of robust nonlinear filtering: selection filters

In this paper we introduce a general framework for edge preserving lters, derived from the powerful class of M-estimators. First, we show that under very general assumptions, any location estimator generates an edge preserving lter if we approximate the estimate by one of the input samples. Based on this premise, we propose the family of S-estimators or Slters, as a selection-type class of lter...

Linear transmitter with correlated noises

A linear transmitter with correlated Gaussian white additive and multiplicative noises and a periodic signal coupled either additively or multiplicatively is considered. The correlations have a weak destructive effect in case of the additive signal and a strong constructive effect in case of the multiplicative one. Analytical results for the linear transmitter with the additive signal agree wit...