This study describes an online target sound extraction (TSE) process, derived from the iterative batch algorithm using the similarity-and-independence-aware beamformer (SIBF), to achieve both latency reduction and extraction accuracy maintenance. The SIBF is a linear method that estimates the target more accurately compared with a reference, an approximate magnitude spectrogram of the target. Evidently, deriving the online algorithm from the iterative batch algorithm reduces the latency of the SIBF; however, this process presents two challenges: 1) the derivation may degrade the accuracy, and 2) the conventional post-process, meant for scaling the estimated target, may increase the accuracy gap between the two algorithms. To maintain the best possible accuracy, herein, an approach that minimizes this gap during post-processing is adopted, and a novel scaling method based on the single-channel Wiener filter (SWF-based scaling) is proposed. To improve the accuracy further, the time-frequency-varying variance generalized Gaussian (TV GG) distribution is employed as a source model to represent the joint probability between the target and reference. Thus, experiments using the CHiME-3 dataset confirm that 1) the online algorithm reduces latency; 2) SWF-based scaling eliminates the gap between the two algorithms while improving the accuracy; 3) TV GG model achieves the best accuracy when it corresponds to the Laplacian model; and 4) our online SIBF outperforms the conventional linear TSE, including the minimum mean square error beamformer. These findings can contribute to the fields of beamforming and blind source separation.