This paper addresses Blind Source Extraction (BSE) of a stationary Source of Interest (SOI) in dynamic acoustic environments with moving interferers. We build upon a recently proposed Independent Vector Extraction (IVE) mixing model, known as the Constant Mixing Vector (CMV) model, which explicitly accounts for a fixed SOI position while allowing other noise sources to move. To enable the practical deployment of this model, we derive a novel and efficient FastICA-like algorithm. The proposed method is evaluated using both simulated mixtures and real-world recordings and is benchmarked against conventional and block-wise IVE, the Constant Separating Vector (CSV) model, and beamforming. The results show superior interference suppression when the SOI satisfies the CMV assumption. By enforcing a common SOI mixing vector across time intervals, the method mitigates block-wise speaker switching and improves temporal consistency.