本研究提出並實現兩種新的弗德-卡曼濾波階次追蹤（Vold-Kalman Filtering Order Tracking, VKF_OT）方法，分別是 (1) 擴展型角速度與 (2) 適應性角位移VKF_OT技術，以改善原有兩種VKF_OT方法應用於旋轉機械狀態監測與故障診斷時之弱點。論文涵蓋了理論推導、數值模擬與工程應用之實驗驗證三個部份。文中藉由處理三組以不同階次所合成之模擬訊號，對所改良之方法與原先方法進行比較，並針對影響其階次追蹤性能之參數，如權重因子（weighting factor）、程序雜訊相關矩陣（correlation matrix of process noise）及免疫於環境雜訊干擾之影響等分別探討。在實際工程應用上，則以過去實驗室所設計進行之三組實驗量測訊號驗證所發展方法之有效性。研究結果顯示本文所提出之二種演算法皆可同時擷取並分離階次相近或交錯之多軸轉速系統的階次訊號。此外適應性角位移VKF_OT為一基於卡曼濾波器（Kalman Filter），可進行線上（on-line）運算並實現即時（real-time）處理應用之階次追蹤演算法。 The study presents and implements two advanced VKF_OT approaches, i.e. the extended angular-velocity and adaptive angular-displacement VKF_OT techniques, to overcome the deficiencies of two original VKF_OT schemes for condition monitoring and diagnosis of rotary machinery. This thesis comprises the theoretical derivation, numerical implementation, and experimental justification. Comparisons of the improved VKF_OT schemes to the original ones are accomplished through processing three synthetic signals composed of different order/spectral components. Some parameters such as the weighting factor, the correlation matrix of process noise, and unwanted signatures/noise, which influence tracking performance, are investigated in the study. Additionally, three experimentations are designed to justify the effectiveness of applying the developed VKF_OT techniques in practical works. These two proposed schemes can simultaneously extract multiple order/spectral components, and effectively decouple close or crossing orders associated with multi-axial reference rotating speeds. Furthermore, the adaptive angular- displacement VKF_OT scheme based on the Kalman filter can be calculated on-line and implemented as a real-time processing application.