A method of detection of signals corrupted by nonstationary random noise via stationarization of the data

Abstract

This paper proposes a method for detecting a signal embedded in nonstationary noise. In most past studies of the signal detection problem, random noise is considered as a stationary stochastic process, since it is mathematically easy to handle. However, the noise observed in practice contains many nonstationary elements with time-varying (evolutionary) statistical properties. In this study, observational noise is modeled as a probability density function with slowly evolving parameters. Then, based on the evolving spectral representation, the nonstationary observation data are transformed to a stationary process. A new method is proposed as follows. It is assumed that nonstationarity remains in the stationarized observation data in the interval containing the signal, due to the effect of the signal. Then the signal is detected by testing for stationarity. In the proposed method, Priestley's evolutionary spectrum is used in the spectral representation of the nonstationary stochastic process, and the method of Okabe and colleagues based on the KM₂O-Langevin equation is used for the stationarity test. The effectiveness of the proposed method is verified by a simulation experiment. © 2007 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 90(8): 29–38, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20302