Comparison of the approximate solutions of a noisy non-linear system based on Monte Carlo simulation |
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| Authors: | Y. SAWARAGI T. SOEDA T. NAKAMIZO S. OMATU Y. TOMITAS |
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| Affiliation: | 1. Department of Applied Mathematics and Physics , Kyoto University , Kyoto, Japan;2. Department of Information Science and Systems Engineering , Tokushima University , Tokashima, Japan;3. Mechanical Engineering Department , Defense Academy , Yokosuka, Kanagawa, Japan |
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| Abstract: | This paper is concerned with the comparison of the approximate methods in order to evaluate the values of state variables of a noisy nonlinear system by Monte Carlo simulation. The approximate methods considered here are (1) the stochastic linearisation, (2) the first-order approximation and (3) the second-order approximation. It is shown that the order of the accuracies of the covariance based on the approximate equation of Riccati type does not always coincide with the order of the practical error covariance of the original system which is obtained by using Monte Carlo simulation. Therefore the comparison of the accuracies should not be carried out by the solution obtained from the covariance equation but by the practical error covariance of the original system directly. This result is demonstrated with numerical examples. The characteristics of the random numbers which are used for Monte Carlo simulation are examined by various kinds of tests. |
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