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As a first step to Antarctic blue whale (ABW) monitoring using passive acoustics, a method based on the stochastic matched filter (SMF) is proposed. Derived from the matched filter (MF), this filter-based denoising method enhances stochastic signals embedded in an additive colored noise by maximizing its output signal to noise ratio (SNR). These assumptions are well adapted to the passive detection of ABW calls where emitted signals are modified by the unknown impulse response of the propagation channel. A filter bank is computed and stored offline based on a priori knowledge of the signal second order statistics and simulated colored sea-noise. Then, the detection relies on online background noise and SNR estimation, realized using time-frequency analysis. The SMF output is cross-correlated with the signal's reference (SMF + MF). Its performances are assessed on an ccean bottom seismometer-recorded ground truth dataset of 845 ABW calls, where the location of the whale is known. This dataset provides great SNR variations in diverse soundscapes. The SMF + MF performances are compared to the commonly used MF and to the Z-detector (a sub-space detector for ABW calls). Mostly, the benefits of the use of the SMF + MF are revealed on low signal to noise observations: in comparison to the MF with identical detection threshold, the false alarm rate drastically decreases while the detection rate stays high. Compared to the Z-detector, it allows the extension of the detection range of ≃ 30 km in presence of ship noise with equivalent false discovery rate. [ABSTRACT FROM AUTHOR]