Keywords: noise cancellation, unknown structure, sound environment system, background noise, input estimation, time series signal.

The random signal in a sound environment usually exhibits multifarious and complex characteristics such as a non-Gaussian distribution, non-linearity and non-stationary properties owing to natural, social and, or human factors. Furthermore, the observation data is usually contaminated by the background noise of an arbitrary distribution. In this situation, in order to evaluate the objective system, it is desirable to estimate the waveform fluctuation of the unknown input and output signals of the sound environment system based on the observed noisy data.

Up to now, several state estimation methods for a stochastic environment system have been proposed [1,2]. However, the state estimation algorithms have been explicitly realised by introducing idealised system models such as a linear model, or a simplified system model based on the linear correlation of input and output signals. The actual sound environment systems exhibit non-linear and non-stationary properties and these often contain unknown characteristics. Thus, it is necessary to improve the previous state estimation theory by taking account of the complexity and uncertainty of the actual environment system.

In this study, a complex sound environment system, with unknown structural characteristics is considered. A method for a precise estimation of the input signal for the sound environment system, with unknown structure and a background noise of arbitrary probability distribution, is proposed. More specifically, by adopting the conditional probability density function reflecting the information on linear and non-linear correlation between input and output time series signals as the input-output system characteristics, a method to estimate the waveform fluctuation of the input signal is theoretically derived. The proposed estimation method can be applied to an actual sound environment system with an unknown structure by considering the coefficients of conditional probability density function as unknown parameters and estimating simultaneously these parameters and the input signal. Furthermore, the effectiveness of the proposed theory is confirmed experimentally by applying it to actual data observed in a very complicated sound insulation system, which cannot be evaluated on the basis of internal physical mechanisms.

1

M. Ohta, H. Yamada, "New methodological trials of dynamical state estimation for the noise and vibration environmental system establishment of general theory and its application to urban noise problems", Acustica, 55, 199-212, 1984.

2

A. Ikuta, M. Ohta, "A state estimation method of impulsive signal using digital filter under the existence of external noise and its application to room acoustics", IEICE Trans. Fundamentals, E75-A, 988-995, 1992.

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