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A Practical Trial of Dynamical State Estimation for Non-Gaussian Random Variable with Amplitude Limitation and Its Application to the Reverberation Time Measurement
Noboru NAKASAKO Mitsuo OHTA Yasuo MITANI
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 1993/09/25
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
nonlinear saturation function, Bayes' theorem, digital filter, non-Gaussian distribution, reverberation time measurement,
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Most of actual environmental systems show a complicated fluctuation pattern of non-Gaussian type, owing to various kinds of factors. In the actual measurement, the fluctuation of random signal is usually contaminated by an external noise. Furthermore, it is very often that the reliable observation value can be obtained only within a definite fluctuating amplitude domain, because many of measuring equipments have their proper dynamic range and original random wave form is unreliable at the end of amplitude fluctuation. It becomes very important to establish a new signal detection method applicable to such an actual situation. This paper newly describes a dynamical state estimation algorithm for a successive observation contaminated by the external noise of an arbitrary distribution type, when the observation value is measured through a finite dynamic range of measurement. On the basis of the Bayes' theorem, this method is derived in the form of a wide sense digital filter, which is applicable to the non-Gaussian properties of the fluctuations, the actual observation in a finite amplitude domain and the existence of external noise. Differing from the well-known Kalman's filter and its improvement, the proposed state estimation method is newly derived especially by paying our attention to the statistical information on the observation value behind the saturation function instead of that on the resultant noisy observation. Finally, the proposed method is experimentally confirmed too by applying it to the actual problem for a reverberation time measurement from saturated noisy observations in room acoustics.