A noise cancellation by use of wide-sense digital filter based on the expanded expression of inverse Gaussian distribution - hierarchical algorithm and its field experiments under wind-induced noise

摘要

In this paper, from the theoretical viewpoint of analyzing the stochastic systems, the new statistical methodologies for actual random fluctuations have been proposed based on the inverse Gaussian distribution function. By considering the flexibility of the inverse Gaussian distribution function, the orthogonally expanded expression of the probability function is first derived by use of the Schmit's orthogonalization technique, whose expansion coefficients reflect hierarchically the lower and higher order statistics of phenomena. Next, by expanding Bayes' theorem hierarchaically, a computer-aided algorithm for estimating the unknown state of energy stochastic systems under random measurement noise is newly established. Finally, the effectiveness of theoretical results has been experimentally confirmed by applying it to the actual data under wind-induced noise.