Detection of Signals in Nonstationary Noise via Kalman Filter-Based Stationarization Approach 263 Detection of Signals in Nonstationary Noise via Kalman Filter-Based Stationarization Approach

Needless to say, the signal detection is one of the most important problems in the signal processing area for a long time, and a great deal of investigations has been done up to the present time. Most of the conventional approaches are based on the (binary) hypothesis-testing, and treat the corrupting (additive) noise as a stationary random process because stationary process is rather easy to handle andmoreover its (invariant) statistical parameters can be readily calculated under the ergodic hypothesis. However, it will be no doubt that the actual random noise such as environmental noise is considered to be nonstationary because its statistical properties are not always unchanged but vary according to underlying physical circumstances. Thus the problem of detecting signals in nonstationary random noise is the more important. For such problem, several interesting methods have been proposed. For example, Haykin (1996) and Haykin & Bhattacharya (1997) treat this problem and proposed a method named the modular learning strategy which incorporates such three fundamental blocks as timefrequency analysis, feature extraction and pattern classification. Also, Haykin & Thomson (1998) proposed an adaptive detector based on learning for the detection of the target signal buried in nonstationary background noises. Philosophically different from their method, the authors have proposed an approach to the signal detection in nonstationary random noise, a new method of stationarization of the observation noise. The key of the approach is to convert the nonstationary random noise to a stationary one, and this procedure was named as stationarization of the observation data. In Ijima, Okui & Ohsumi (2005) and Ijima, Ohsumi & Okui (2006), the signal detection is performed by testing the stationarized observation data whether there is some non-stationarized portion or not, based on the KM2O-Langevin equation (which is the AR model with timevarying coefficients). If there exists such a portion in the data, the existence of a signal is decided. Related to the signal detection, the stationarization approach is also used in Ijima,