We are concerned with Bayesian identification and prediction of a nonlinear discrete stochastic process. The fact, that a nonlinear process can be approximated by a piecewise linear function advocates the use of adaptive linear models. We propose a linear regression model within a Rao-Blackwellized particle filter. The parameters of the linear model are adaptively estimated using a finite mixtu...

An adaptive Divided Difference filter for joint estimation of parameters and states of a nonlinear system has been proposed in this work. The adaptive filter is proposed for improved estimation specifically in the situation when knowledge about the process noise statistics is unavailable. The innovation sequence has been employed for adaptation of the unknown process noise covariance. The evolv...

Removing noise from the original medical image is still a challenging research in image processing. This paper presents a new method for speckle noise reduction in Optical coherence Tomography (OCT). Stationary wavelet transform (SWT) is employed to provide effective representation of the noisy coefficients. Nonlinear Anisotropic filtering of the Details coefficients improves the denoising effi...

A new Gaussian mixture filter has been developed, one that uses a re-sampling step in order to limit the covariances of its individual Gaussian components. The new filter has been designed to produce accurate solutions of difficult nonlinear/nonBayesian estimation problems. It uses static multiple-model filter calculations and Extended Kalman Filter (EKF) approximations for each Gaussian mixand...

Median filter is quite effective in recovering the images confounded by salt and pepper noise. It discards outliers (impulses) effectively, but it fails to provide adequate smoothing for images corrupted with non-impulse noise. In this paper, two nonlinear techniques for image filtering, namely, New Filter I and New Filter II are proposed based on a nonlinear high-pass filter algorithm. New Fil...

This paper considers several filtering methods of stochastic nature, based on Monte Carlo drawing, for the sequential data assimilation in nonlinear models. They include some known methods such as the particle filter and the ensemble Kalman filter and some others introduced by the author: the second-order ensemble Kalman filter and the singular extended interpolated filter. The aim is to study ...

The Geometrically Intrinsic Nonlinear Recursive Filter, or GI Filter, is designed to estimate an arbitrary continuous-time Markov diffusion process X subject to nonlinear discrete-time observations. The GI Filter is fundamentally different from the much-used Extended Kalman Filter (EKF), and its secondorder variants, even in the simplest nonlinear case, in that: ¥ It uses a quadratic function o...

A nonlinear filter is proposed for estimating a complex sinusoidal signal and its parameters (frequency, amplitude, and phase) from measurements corrupted by white noise. This filter is derived by applying an extended complex Kalman filter (ECKF) to a nonlinear stochastic system whose state variables are a function of its frequency and a sample of an original signal, and then, proof of the stab...

This paper presents an innovative active power filter design method to simultaneously compensate the current harmonics and reactive power of a nonlinear load. The power filter integrates a passive power filter which is a RL low-pass filter placed in series with the load, and an active power filter which comprises an RL in series with an IGBT based voltage source converter. The filter is assumed...

We use natural gradient (NG) learning neural networks (NNs) for modeling and identifying nonlinear systems with memory. The nonlinear system is comprised of a discrete-time linear filter H followed by a zero-memory nonlinearity g(·). The NN model is composed of a linear adaptive filter Q followed by a two-layer memoryless nonlinear NN. A Kalman filter-based technique and a search-and-converge m...