廣義靜止訊號積分之最小變異估測器

Abstract

本篇論文提出一個以卡門濾波器為基礎的遞迴演算法來有效率地實現最小變異估測器。藉由數位取樣所得到的點，來估計一個廣義靜止訊號的積分值。從均方的觀點來看，當取樣的點數趨近到無限多點的時候，估測的最小變異誤差值也會跟者收斂到零。而隨機積分對於陳述線性運算子方面，像摺合積分(出現在當一個隨機訊號通過一個線性系統時候) ，是很重要的應用。因此我們可以把我們的演算法延伸套用到一個輸入廣義靜止訊號的線性非時變系統的結果輸出。

In this thesis, we propose a recursive algorithm based on Kalman Filter to implement efficiently the minimum variance estimator of the integration of WSS random signal by the discrete-time samples. As the number of samples trends to infinity, the minimum mean square errors will converge to zero in mean square sense. Stochastic integrals are important in applications for representing linear operator such as convolution, which arises when random processes are passed through linear systems. Thus, we can extend our results to the output of a linear time-invariant system with WSS random signal input.