Noise PSD Estimation Based on Time–Frequency Signal Presence Probability Sensing for Noncooperative Underwater Acoustic Pulse Signal Enhancement

Accurate noise power spectral density (PSD) estimation is crucial for noncooperative underwater acoustic pulse (UWAP) signal enhancement. In this work, we propose an effective noise PSD estimation method based on the framework of time-recursive averaging algorithms. Unlike conventional methods, where estimating noise spectrum involves a weighted average of past noise estimates and the current observed signal spectrum, the proposed approach does not rely on a time- and single-frequency-dependent weight factor. Instead, it employs a unique time- and multifrequency-dependent weight factor, akin to a time–frequency signal presence probability (SPP). To sense the SPPs of noisy noncooperative UWAP signals without prior information, we define and extract two key time–frequency characteristics of the UWAP signal: the time-dependent energy fluctuation characteristic and the frequency-dependent short-time narrowband characteristic. These characteristics enable us to derive time–frequency SPPs. The proposed method’s superior performance over existing state-of-the-art algorithms is verified through simulations and experiments with sea trial data.