Memoirs of the Faculty of Engineering, Yamaguchi University
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Memoirs of the Faculty of Engineering, Yamaguchi University Volume 39 Issue 1
published_at 1988-10
A Posteriori Probability Density of System Described by Fanctional Expansion
汎関数展開可能な系の事後確率密度関数
About This Article
Descriptions
In this paper, we consider a posteriori probability density function of the nonlinear system which is described by the functional expansion and is corrupted by the nongaussian noises of the input and the output. Let us express a posteriori density of the state variables in terms of the Hermite expansion, considering the additivity of the measurement and the input noises, on the bases of Baysian theorem. First, the formula of the rearrangement for the hermite polynominals is derived from its generating function. Then the convolution integrals of Baysian theorem can be analytically calculated by using the orthogonality of the Hermite polynominals. Finally, it is shown from the results of the digital simulation that the validity of this method is confirmed.
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