以相關熵為基礎之資料選擇可適性濾波演算法設計

Abstract

在這個大數據的世代，演算法也必須具有資料選擇的能力。然而，傳統的資料選擇策略會使可適性演算法失去追蹤能力，並在有脈衝干擾的環境無法有效的做出資料選擇。主動噪音控制系統中大多數演算法也同樣在脈衝性量測雜訊的干擾下，噪音消除能力會大幅下降。本研究提出了一個基於相關熵的資料選擇策略，利用傳統資料選擇策略中，因為創新資訊量不足而不對資料進行更新的概念，決定臨界值上界。透過梯度上升法最大化相關熵來推導出最佳的核寬度，藉由相關熵當中指數函數的特性結合可變的核寬度調整相關熵對於判斷脈衝干擾的靈敏度，並使用 ROC 曲線法來決定臨界值下界，再者觀察核寬度的變化量提出一個可改善因系統改變造成追蹤性能降低的機制，最後將本論文提出的資料選擇策略運用在主動噪音控制應用中。本研究是使用數值模擬的方式來驗證演算法的性能，並使用三種不同強度的白努力高斯脈衝雜訊測試不同環境下演算法的穩定性，且應用在系統識別架構及主動式噪音控制中。在系統識別的應用中，主要是以正規化均方偏差做為評量指標，且考慮了白高斯輸入、彩色高斯輸入兩種不同的輸入訊號及稀疏通道環境下的模擬；主動式噪音控制中，主要是以平均噪音消除率來做為評量指標，且考慮了白高斯噪音、彩色高斯噪音、複合正弦噪音混和白高斯雜訊三種類型的信號。模擬結果顯示，本論文提出的資料選擇策略相較於傳統的資料選擇，不僅能夠在具有脈衝干擾的情況下僅用 20% 的資料點即能達到與原演算法相同的系統效能，在追蹤速度方面也有顯著的提升，更新率的表現更是能將最大誤差率維持在 0.15 以內。

In the age of big data, algorithms must also be capable of data selection. However, traditional data selective strategies cause the adaptable algorithms to lose tracking capability, and fail to make effective data selection in environments with impulse noise interference. Most of the algorithms in active noise control systems also suffer from a significant degradation in noise cancellation due to the interference of impulsive noises. This study proposes a data selection strategy based on correntropy: by exploiting the concept of not updating data due to insufficient amount of innovative information as seen in the traditional data selection strategy, an upper limit of the threshold value can be determined.The optimal kernel width is derived by maximizing correntropy through the gradient ascent method. The correntropy sensitivity to determine impulse noise can be adjusted by combining the characteristics of the exponential function in correntropy and variable kernel width. Furthermore, the lower threshold can be determined by using the ROC curve method. Additionally, a mechanism that improves the degradation of tracking performance due to system changes is proposed through kernel width variation observation. Lastly, the data selection strategy proposed in this paper is applied to active noise control applications. This study uses numerical simulations to verify the performance of the algorithm, and the stability of the algorithm is tested under three different Bernoulli Gaussian impulsive noise intensity environments. The algorithm is then further applied to system identification and active noise control. In the system identification application, the normalized mean square deviation is used as the main evaluation metric. This application also considers two different input signals, white Gaussian input and color Gaussian input, in the sparse channel environment. Whereas, in active noise control, the average noise ratio is used as the main evaluation metric; and considers three types of signals: white Gaussian noise, color Gaussian noise, and complex sinusoidal noise mixing white Gaussian noise. Simulation results show, by using merely 20% data points under impulsive noise interference, the data selection strategy proposed in this paper achieves the same system performance as the original algorithm. It also significantly improves in terms of tracking speed and maximum error rate maintenance, keeping the latter within 0.15.