In the sound environment related to the mutual effects on physical phenomenon and human response, most of the actual observed data show a complex fluctuation pattern differing from a standard Gaussian distribution, and furthermore, these often contain the fuzziness due to the existence of confidence limitation in measuring instruments, permissible error in experimental data, and the variety of human response to phenomena. 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. Therefore, the fluctuation waveform of the specific signal must be momentarily estimated as precisely as possible, based on the observed data contaminated by the background noise, in order to evaluate the sound environment. In this study, a nonlinear 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 with unknown parameter, which is suitable for the energy variable and the observation in decibel scale, a state estimation method is theoretically derived. In the proposed estimation algorithm, the parameter of the membership function is estimated simultaneously with the specific signal based on the fuzzy observation data. The proposed theory is applied to the actual observation data in a sound environment, and its usefulness is experimentally verified.
