互關訊息於非線性估計之探討

Abstract

對於一般非線性估計問題，我們自互關訊息 (mutual entropy)發展一上 限 (upper bound) 於相關性係數 (correlation coefficient)，此一上 限依據非線性轉換 (nonlinear transformation)，而經由此轉換之後， 進而產生相互高斯 (jointly Gaussian) 訊號。我們也探討了最小均方估 計誤差 (minimum mean-squared estimation error) 和互關訊息的關係 。此外，當給定一相關性係數時，我們可以很容易地產生 ergodic 和相 互高斯訊號，所以可經由電腦來模擬。 For a general estimation problem, we develop an upper bound on the correlation coefficients in terms of the mutual entropy. This upper bound may be reached by means of a nonlinear trans- formation, after transformation, the processes are jointly Gaussian. The relationship between the minimum mean-squared error and the mutual entropy is discussed. Moreover, given a correl- ation coefficient, ergodic and jointly Gaussian signals can be generated easily, so that the simulation can be done by mputer.