石油工学のパラメーター決定問題に対する回帰解析および誤差評価方法

(第3報) パラメーター決定方法に関するいくつかの考察

抄録

The simplicity and versatility of the Kalman sequential filter has establish it as a fundamental tool in the analysis and solution of linear estimation problems. Petroleum engineers recently recognized it as a potential tool for regression analysis and applied it to non-linear problems. However numerical experience has shown that the Kalman filter algorithm is sensitive to computer round-off and that numeric accuracy sometimes degrades to the point where the results cease to be meaningful. In order to avoid this trouble, Potter proposed to decompose the covariance matrix into a square root covariance matrix.
In this paper, the Potter's linear algorithm is applied to two non-linear problems, one of which is non-recurrence type and the other is recurrence type. The linearization of the non-linear functions proposed in this paper appears to be proper to the respective type mathematical models. In addition, two other methods for parameter determination are tested in this paper, which are suitable to mathematical problems with discontinuous functions.