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

## TL;DR

This paper introduces a new real-time signal processing method that improves acoustic sensing in noisy environments by combining Bayesian and Kalman estimation techniques.

## Contribution

The paper introduces a unified Bayesian–Kalman estimator (UBKE) that analytically fuses spectral and temporal estimation for real-time acoustic signal enhancement.

## Key findings

- UBKE achieves up to +9.8 dB ΔSNR improvement over a baseline MMSE estimator in non-stationary noise.
- The method reduces log-spectral distortion and improves PESQ by approximately +17%.
- UBKE operates with low latency (16 ms delay) and real-time factors below 0.5 on a modern CPU.

## Abstract

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.