Optimal Filtering of a Gaussian Signal in the Presence of Levy Noise

Many engineering applications require extracting a signal from observations corrupted by additive noise, possibly heavy-tailed. We assume that the observation noise is a Levy process, while the signal is Gaussian, and derive a non-linear recursive filter that minimizes the L2 error. A sub-optimal fi...

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Bibliographic Details
Main Authors: Ahn, Hyungsok, Feldman, Raisa E
Format: Report
Language:English
Subjects:
BROWNIAN MOTION
LEVY PROCESSES
LINEAR FILTERING
MATHEMATICAL FILTERS
NOISE REDUCTION
NONLINEAR SYSTEMS
Operations Research
OPTIMIZATION
RECURSIVE FILTERS
SIGNAL PROCESSING
SIGNAL TO NOISE RATIO
STOCHASTIC PROCESSES
SYSTEMS ANALYSIS
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Summary:Many engineering applications require extracting a signal from observations corrupted by additive noise, possibly heavy-tailed. We assume that the observation noise is a Levy process, while the signal is Gaussian, and derive a non-linear recursive filter that minimizes the L2 error. A sub-optimal filter is proposed for numerical purposes, and simulations show that it out performs the existing linear filter.