Abstract
The actual sound environment system exhibits various types of linear and non-linear characteristics, and it often contains uncertainty. Furthermore, the observations in the sound environment are often in the level-quantized form. In this paper, two types of methods for estimating the specific signal for sound envi-ronment systems with uncertainty and the quantized observation are proposed by introducing newly a system model of the conditional probability type and moment statistics of fuzzy events. The effectiveness of the proposed theoretical methods is confirmed by applying them to the actual problem of psychological evalua-tion for the sound environment.
Highlights
The actual sound environment system contains uncertainty and it is often difficult to recognize analytically the internal physical mechanism
A digital filter for estimating the state variables of complex stochastic systems was derived by introducing a nonlinear system model in an expansion series of reflecting various type correlation information from the lower order to the higher order between state variable and observation [1]
The conditional probability density function in the expansion series contains the linear and nonlinear correlations in the expansion coefficients, and these correlations play an important role as the statistical information for the state variable and observation relationship
Summary
The actual sound environment system contains uncertainty and it is often difficult to recognize analytically the internal physical mechanism. In order to evaluate the objective sound environment system, it is desirable to estimate the waveform fluctuation of the specific signal for the system with uncertainty based on the quantized or fuzzy observation data. The actual sound environment systems exhibit complex and unknown system characteristics and often contain uncertainty in the relationship among the state variables and the observation. In this paper, based on the quantized or fuzzy observations, an adaptive method for estimating precisely the specific signal for the sound environment system with uncertainty is theoretically proposed. The proposed estimation method can be applied to an actual complex sound environment system with uncertainty by considering the coefficients of conditional probability distribution as unknown parameters and estimating simultaneously these parameters and the specific signal. The proposed theory is applied to the estimation problem of the psychological evaluation for loudness in sound environment and the effectiveness of the theory is experimentally confirmed
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