State estimation for sound environment system by using Bayesian filter based on fuzzy observation

The specific signal in a sound environment is measured in decibel scale and often contains the fuzziness due to several causes. Furthermore, there exists usually a background noise in addition to the specific signal. In this study, a Bayesian filter for estimating the specific signal, based on the observed data containing the fuzziness and the effects of a background noise with non-Gaussian type, is proposed. More specifically, the energy variables satisfying the additive property of the specific signal and background noise are first considered. Next, after introducing an expansion expression of the probability density function based on a log-normal distribution and a new type of membership function, which are suitable for the nonlinear relationship between the energy variable and the measurement in decibel scale, by applying probability measure of fuzzy events, a state estimation method is theoretically derived. The proposed theory is applied to the actual observation data in a sound environment, and its usefulness is experimentally confirmed.