具機會式排程之綠能卡爾曼濾波法

Abstract

本論文研究一個無線動態系統狀態預估的問題，其中，卡爾曼濾波器經由無線衰減的通道接收感測器所傳送的觀測信號，因為傳送中的觀測信號可能會因為嚴重的通道衰減而被劇烈地減弱，所以我們對於感測器端提出一個基於閾值的機會式排程法使卡爾曼濾波器不會接收到嚴重衰弱的信號。在感測器端完全知道通道狀態信息的假設下，我們首先推導出在使用一個或多個感測器的情形下可以使卡爾曼濾波器穩定的充要條件，該條件說明排程所使用的閾值與動態線性系統矩陣之間的基本限制。接著我們對於間接性通道狀態信息的情況推導出相關的穩定條件，並說明利用通道增益的統計特性可以明顯地提升此條件的穩定性。最後，我們研究機會式排程法的能量效益並且證明利用滿足穩定條件的最大閾值可以達到最大的能量效益。

In this thesis, we study the state estimation problem of a wireless linear dynamic system in which the Kalman filter receives the observation signals transmitted by sensors over wireless fading channels. Since the transmitted observations would be severely weakened while the wireless channels are in deep fade, we propose a threshold-based opportunistic scheduling scheme for the sensors in order to make the signals received by the Kalman filter not fairly weak. Under the assumption of perfect channel state information (CSI) on the sensor side, the stability conditions of Kalman filtering with opportunistically scheduled observations are first derived in the single-sensor and multi-sensor cases, which characterize the fundamental limits between the scheduling threshold and the system matrices of the linear dynamical system. Then we derive the stability conditions for imperfect intermittent CSI on the sensor side and they can be significantly improved by exploiting the statistics of the channel gain. Finally the energy efficiency of the proposed opportunistic scheduling scheme is studied and we show that the maximum energy efficiency can be achieved by utilizing the maximum scheduling threshold which satisfies the stability condition.