Gibbs sampling for time-delay-and amplitude estimation in underwater acoustics

Area of Science:

• Signal Processing
• Underwater Acoustics
• Statistical Inference

Background:

• Multipath arrivals are common in sonar, radar, and communications.
• Accurate extraction of multipath arrivals is crucial for underwater acoustic applications like source localization and geoacoustic inversion.

Purpose of the Study:

• To present a novel method for estimating time delays and amplitudes of multipath arrivals using Maximum a Posteriori (MAP) estimation.
• To address the computational demands of MAP estimation by employing Gibbs sampling.

Main Methods:

• Utilized Gibbs sampling for efficient estimation of posterior probability distributions, bypassing complex analytical calculations.
• The Gibbs sampler estimates time delays, amplitudes, noise variance, and the number of arrivals.
• Performance was evaluated using Monte Carlo simulations.

Main Results:

• The Gibbs sampling method demonstrated performance comparable to analytical MAP estimation.
• The proposed method outperformed the expectation-maximization algorithm for time-delay estimation.
• The approach provides complete posterior distributions, capturing uncertainty more effectively than point estimates.

Conclusions:

• Gibbs sampling offers an efficient and informative approach for multipath arrival estimation in signal processing.
• This method provides a more comprehensive understanding of parameter uncertainty compared to conventional techniques.
• The technique is particularly valuable for complex problems in underwater acoustics and related fields.