As a general rule, in actual noise environments, various kinds of noise factors form the composite noise ambience. This fact, therefore, makes it difficult to estimate the objective noise statistics, especially in the case of non-stationary random noise. This difficulty of estimation arises in every case not only of estimating the mean level, but also of the variance and other higher order moments under the existence of background noise. In reference to random noise, the estimation problem can no longer be solved by employing only the deterministic relationship of the phenomena, like the well-known correction method based upon the sum of the energy. In this case, a new method of statistical estimation should be established. Notwithstanding the strong necessity of practical engineering, apparently no systematical study has been found from such a point of view. Therefore, in this paper, a new trial toward a dynamical method of estimating the objective noise under arbitrary background noise is theoretically discussed for the general case when the random noise fluctuates in an arbitrary distribution form of the non-Gaussian type. The algorithm proposed in this paper agrees on all points with the well-known Kalman filter, as an idealized special case. Furthermore, the validity of this theory is confirmed experimentally by means of observation of actual road traffic noise in Hiroshima city.
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