Particle filtering for frequency estimation from acoustic time-series in dispersive media

Acoustic signals propagating in the ocean carry information about geometry and environmental parameters within the propagation medium. Accurately retrieving this information leads us to effectively estimate parameters that are of utmost importance in environmental studies, climate monitoring, and defense. This dissertation focuses on the development of sequential Bayesian filtering methods to obtain accurate estimates of instantaneous frequencies using Short Term Fourier Transforms within the acoustic field measured at an array of hydrophones, which can be used in a subsequent step for the estimation of propagation related parameters. We develop a particle filter to estimate these frequencies along with modal amplitudes, variance, model order. In the first part of our work, we consider a Gaussian model for the error in the data measurements, which has been the standard approach in instantaneous frequency estimation to date. We here design a filter that identifies the true structure of the data errors and implement a χ2 model to capture this structure appropriately. We demonstrate both with synthetic and real data that our approach is superior to the conventional method, especially for low Signal-to-Noise-Ratios

On the Probability Distributions of Spectrogram Coefficients for Correlated Gaussian Process

This paper deals with the probability distribution of spectrogram coefficients related to a correlated centered Gaussian process. It is shown that the windowing operation and the presence of correlation between input samples may introduce heteroscedaticity and correlation between the real and imaginary parts of the Short Time Fourier Transform. The impact of this phenomenon on spectrogram distribution is evaluated in terms of deviation from the chi-square distribution. A numerical method to calculate the probability density function of the spectrogramcoefficients is provided and deviation from the chi-square distribution is evaluated using the Kullback- Liebler divergence. This measure of deviation is used to control the validity of a chi-square approximation

On the probability distributions of spectrogram coefficients for correlated gaussian process

International audienceThis paper deals with the probability distribution of spectrogram coefficients related to a correlated centered Gaussian process. It is shown that the windowing operation and the presence of correlation between input samples may introduce heteroscedaticity and correlation between the real and imaginary parts of the Short Time Fourier Transform. The impact of this phenomenon on spectrogram distribution is evaluated in terms of deviation from the chi-square distribution. A numerical method is provided to calculate the probability density function of the spectrogram coefficients and deviation from the chi-square distribution is evaluated using the Kullback-Liebler divergence. This measure of deviation is used to control the validity of a chi-square approximation