在回聲消除系統的應用中，濾波器係數是否能有效的快速更新是相當重要的關 鍵，而收斂的效果也是影響回聲是否能消除乾淨的重要因素。因此向量空間可 適性濾波器被提出，其結合機械學習向量空間的想法，引進可適性演算法中， 達到有效的快速收斂的目標，但其運算複雜度也相對提高。然而為對應到現實 生活中應用，運算複雜度將會是較為重要的考量。因此本篇提出改進的向量空 間可適性濾波器(Improved Vector-space Adaptive Filter)與改進的向量空間仿射 投影符號演算法(Improved Vector-space Affine Projection Sign Algorithm)，藉由 重新設計向量空間以及濾波器係數合成的架構，將運算的矩陣維度降低，並運 用組合演算法的想法，對仿射投影符號演算法與改進的向量空間仿射投影符號 演算法進行組合，達到在任何環境下皆能快速且穩定收斂的目標且比起向量空 間可適性濾波器有著更低的運算複雜度和更好的收斂速度與收斂效果，提升在 現實生活中應用地可行性。

To eliminate acoustic echo, the convergence rate and low residual echo are very important to adaptive echo cancelers. Meanwhile, an affordable computational complexity has to be considered as well. In this paper, we proposed the improved vector space adaptive filter (IVAF)and Improved Vector-space Affine Projection Sign Algorithm (IVAPSA). The proposed can be divided into two phases: offline and online. In the offline phase, IVAF constructs a vector space to incorporate the prior knowledge of adaptive filter coefficients from a wide range of different channel characteristics. Then, in the online phase, the IVAF combines the conventional APSA and IVAPSA algorithms, where IVAPSA computes the filter coefficients based on the vector space obtained in the offline phase. By leveraging the constructed vector space, the proposed IVAF is able to fast converge and achieve a better echo return loss enhancement performance. Moreover, the computational complexity is less than a comparable work.