We consider the filtering problem for linear models where the driving noises may be quite general, non-white and non-Gaussian, and where the observation noise may only be known to belong to a finite family of possible disturbances. Using diffusion approximation methods, we show that a certain nonlinear filter minimizes the asymptotic filter variance. This nonlinear filter is obtained by choosin...

In this paper we first prove, under quite general conditions, that the nonlinear filter and the pair: (signal,filter) are Feller-Markov processes. The state space of the signal is allowed to be non locally compact and the observation function: h can be unbounded. Our proofs in contrast to those of Kunita(1971,1991), Stettner(1989) do not depend upon the uniqueness of the solutions to the filter...

This paper presents a new multi-passive-sensor target tracking algorithm which yields a nonlinear state estimator called Gaussian filter based on deterministic sampling. Firstly, this state estimator employs a deterministic sample selection scheme, where a parametric density function representation of the sample points is employed to approximate the cumulative distribution function of the prior...

Nonlinear adaptive filtering techniques are widely used for the nonlinearities identification in many applications. This paper proposes a new implementation of the third order RLS Volterra filter based on the decomposition of the input vector. Its performances are evaluated in a typical nonlinear system identification application. Different degrees of nonlinearity for the nonlinear system are c...

Some observations and improvements on the conventional Kalman filtering scheme to function properly are presented. The improvements can be achieved using the minimal principle evolutionary programming (EP) technique. A new linearization methodology is presented to obtain the exact linear models of a class of discrete-time nonlinear time-invariant systems at operating states of interest, so that...

The identification of nonlinear and chaotic systems is an important and challenging problem. Neural network models, particularly Recurrent Neural Networks (RNN) trained with suitable algorithms, have received particular attention in the area of nonlinear identification due to their potentialities to approximate any nonlinear behavior. A method of nonlinear identification based on the RNN model ...

A novel method for nonlinear filtering based on a generalized Gaussian cubature approach is shown. Specifically, a new point-based nonlinear filter is developed which is not based on one-dimensional quadrature rules, but rather uses multidimensional cubature rules for Gaussian distributions. The new generalized Gaussian cubature filter is not in general limited to odd-order degrees of accuracy,...

A . Stabilization using filters is intended to model and extract the energy lost to resolved scales due to nonlinearity breaking down resolved scales to unresolved scales. This process is highly nonlinear. We consider nonlinear filters which select eddies for damping (simulating breakdown) based on knowledge of how nonlinearity acts in real flow problems. The particular form of the nonlinear fi...

In this paper we consider the continuous–time nonlinear filtering problem, which has an infinite–dimensional solution in general, as proved by Chaleyat–Maurel and Michel. There are few examples of nonlinear systems for which the optimal filter is finite dimensional, in particular Kalman’s, Beneš’, and Daum’s filters. In the present paper, we construct new classes of scalar nonlinear filtering p...

NONLINEAR EQUALIZATION BASED ON DECISION FEEDBACK EQUALIZER FOR OPTICAL COMMUNICATION SYSTEM by Xiaoqi Han Nonlinear impairments in optical communication systems have become the major performance limiting factor of optical communication systems. The equalizer based on linear filters has limited compensation capability. Therefore, nonlinear models based equalizers are proposed for performance en...