Real-Time Signal Processing for Distributed Acoustic Sensing and Acoustic Sensing Systems Under Non-Stationary Noise

Real-time acoustic signal enhancement in non-stationary noise remains challenging, especially for sensing systems that must be causal, low latency, and interpretable. This paper proposes a unified Bayesian-Kalman estimator (UBKE) that analytically fuses a spectral Bayesian MMSE estimator with a temporal Kalman state-space tracker via a variance optimal fusion weight α(k). The UBKE is derived in closed form from a shared probabilistic model, yielding an estimator that adaptively balances spectral and temporal information as noise statistics evolve. We establish theoretical properties including bias-variance behavior, stability conditions, and analytical expressions for output SNR, SNR improvement, and log-spectral distortion. Under typical short-time processing (32 ms frame, 50% overlap), the proposed method operates causally with an algorithmic delay of 16 ms and real-time factors below 0.5 on a modern CPU. Analytical and empirical results show that UBKE achieves up to +9.8 dB ΔSNR and approximately +17% PESQ improvement over a baseline MMSE estimator in highly non-stationary noise, while also reducing log-spectral distortion. Experiments on standard speech corpora with real-world noise confirm that the empirical trends closely follow the analytical predictions, with small mismatch between theoretical and measured gains. The UBKE thus offers an interpretable, low-latency, and quantitatively validated framework for real-time acoustic sensing and speech enhancement, and can serve as a foundation for future hybrid model-driven and learning-augmented systems.