獨立成份分析(Independent Component Analysis, ICA)模型被廣泛應用於未知訊號源分離(Blind Source Separation, BSS)上，其目標是將麥克風蒐集到的混和訊號中分離出原始訊號。在以往標準的BSS方法中，假設所有來源訊號的統計特性是穩定的，也就是未知訊號的機率密度函數是固定且不會隨時間而改變。然而，在實際應用系統中，來源訊號的統計特性通常是非穩定的，也就是統計特性會隨時間而改變，例如未知訊號可能在某個時間點突然消失或是出現，甚至獨立訊號來源會被另外一個訊號來源所取代，因此對應的未知訊號源的統計特性也要隨著改變；而另外一個非穩定性的議題就是當未知訊號源移動時，其混合係數也會隨著改變，因此過去標準的獨立成份分析演算無法適用及解決這些非穩定的來源訊號分離的問題。
為了解決上述BSS問題，本論文提出了一套新穎的非穩定性訊號分離的演算法，相較於傳統僅使用高階統計量及以資訊理論為主的獨立成份分析模型，此演算法是基於資料的二階統計量，也就是將來源訊號在時間上的關聯性考慮進來，透過高斯程序(Gaussian Process, GP)模型來描述隨著時間改變的混合矩陣係數和具有時間關係的來源訊號的時間結構。高斯程序屬於非參數型的演算法，具有較佳的彈性及計算簡單的優點，能確切的建立起來源訊號的時間結構，最後再透過線上貝氏學習機制，以漸近式的方式來估測模型參數並分離非穩定的來源訊號。實驗中，模擬了許多不同非穩定的條件情境以及多種不同機率分佈的來源訊號，交叉驗證了此方法在不同非穩定的條件情境和來源訊號具有任意機率分佈的假設下都能達到良好的訊號分離的效果。

Blind source separation (BSS) is a procedure of reconstructing the original source signals from mixed signals. The standard BSS methods assume a fixed set of stationary source signals with the fixed distribution functions. In many real-world applications, the source signals are nonstationary and temporally correlated; e.g. source signal may abruptly active or inactive or even the source may be replaced by the other one.
In order to deal with the nonstationary mixing system, we present a new nonstationary BSS algorithm. Different from the high-order statistics ICA algorithm, the proposed nonstationary BSS algorithm is based on the second-order statistics, e.g. we consider temporal structure of the source signals. In this study, we employ Gaussian process (GP) model to characterize the time-varying mixing coefficients and the temporally correlated source signals. We perform an online Bayesian learning procedure for dynamic source separation. A variational Bayesian algorithm is established to estimate the parameters in a noisy mixing process where GP priors are adopted to express the temporally correlated sources and the time-varying mixing matrix. In the experiments, we demonstrate the effectiveness of proposed method in separation of the mixed speech signals in cases of different scenarios.

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