Fuzzy Bayesian Filter for Sound Environment by Considering Additive Property of Energy Variable and Fuzzy Observation in Decibel Scale

In the measurement and evaluation of actual random signal in a sound environment, the observed data often contain the fuzziness due to several causes. Furthermore, there exists usually a background noise in addition to the objective specific signal, and it is often that the specific signal partly or completely is buried in the background noise. In this paper, a fuzzy Bayesian filter for estimating a 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, after paying attention to the energy variables satisfying the additive property of the specific signal and background noise, by introducing a new type of membership function suitable for the energy variable and the observation in decibel scale, a state estimation method is theoretically derived. The proposed theory is applied to the actual estimation problem of the sound environment, and its usefulness is experimentally verified.