Statistical signal extraction using stable processes

Abstract

a b s t r a c tThe standard models for statistical signal extraction assume that the signal and noise are generated by linear Gaussian processes. The optimum filter weights for those models are derived using the method of minimum mean square error. In the present work we study the properties of signal extraction models under the assumption that signal/noise are generated by symmetric stable processes. The optimum filter is obtained by the method of minimum dispersion. The performance of the new filter is compared with their Gaussian counterparts by simulation.

Bayesian estimation for target tracking, Part III: Monte Carlo filters

“…Several modifications to the generalized Monte Carlo method can be used to handle heavy‐tailed noise distributions. Instead of using a Gaussian approximation for the predictive and filtering densities, one could use a Levy, α ‐stable or Laplace distribution and replace the nonlinear Gaussian Kalman filter with a Kalman–Levy,27 generalized stable,28 or Laplace filter 29. These filters have a Kalman filter‐like symmetric structure that could readily be used in place of the nonlinear Gaussian Kalman filter in a combination particle filter application.…”

Stable Autoregressive Models and Signal Estimation

“…In the second step, we apply Kalman-Levy filter discussed by Balakrishna and Hareesh (2009) to extract the true signal X n and noise n sequences from the observed signal Y n . This step entails the knowledge of the parameters u , , and values.…”

“…Estimation of signal and noise parameters from an observed signal under heavy tailed assumption is an important problem in this context. Balakrishna and Hareesh (2009) proposed minimum dispersion signal extraction filters for processes with infinite variance. In this article, the signal and noise parameters are assumed to be known.…”

“…An initial estimate of the noise parameters and innovation parameters are estimated using the method of moments. These initial estimates have been used to extract signal and noise from the observed signal by applying Kalman-levy filter discussed by Balakrishna and Hareesh (2009 This article is organized as follows: In Sec. 2, we address stable autoregressive signals estimation problem.…”