Acoustic-scene-related parameters such as relative transfer functions (RTFs) and power spectral densities (PSDs) of the target source, late reverberation and ambient noise are essential for microphone array signal processing and are challenging to estimate. Existing methods typically only estimate a subset of the parameters by assuming the other parameters are known. This can lead to unmatched scenarios and reduced estimation performance on the parameters of interest. Moreover, many methods process time frames independently, despite they share common information such as the same RTF. In this work, we consider a noisy scenario by modelling the noise component as a spatially homogeneous sound field with a time-invariant spatial coherence matrix and time-varying PSD. We first modify an existing alternating least squares (ALS) method to obtain more accurate estimates using a single time frame. Then, we extend the method to use multiple time frames that share the same RTF. Furthermore, we propose more robust constraints on the PSDs to avoid large estimation errors. We compare our proposed methods to the state-of-the-art simultaneously confirmatory factor analysis (SCFA) method, a joint maximum likelihood estimation (JMLE) method and an existing ALS-based method. The experimental results in terms of estimation accuracy, noise reduction performance, predicted speech quality, and predicted speech intelligibility demonstrate that our proposed methods achieve similar performance compared to the state-of-the-art SCFA method, which outperforms the existing ALS method in all scenarios and outperforms the JMLE method particularly in low SNR scenarios. Moreover, our proposed methods have significantly lower computational complexity than SCFA.
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