Analysis of Hydroacoustical Time Series by State Space Modelling

This talk deals with predictive time-domain modelling of time series, either univariate or multivariate. The aim is to identify and reconstruct independent source components from the time series. For this purpose, a special class of linear state space models is employed, which describes the individual source components by autoregressive moving-average (ARMA) processes. As a useful result of ARMA modelling, parametric estimates of the power spectra of the source components can be obtained. In a simulation study, it is demonstrated that also components generated by nonlinear processes can be separated by linear state space modelling, using Kalman filtering and smoothing. Furthermore, comparison with algorithms from Independent Component Analysis (ICA) shows that ICA fails to distinguish correlations due to mixing from correlations due to finite data set size, leading to distorted estimates. Parameter estimation is performed by numerical maximisation of the logarithmic likelihood, using the Expectation Maximisation (EM) algorithm and other algorithms for optimisation. The implementation of the EM algorithm for state space modelling under constraints is discussed in detail, and some new results are presented. Finally, results for applying state space modelling to several hydroacoustic time series are presented, including components of the underwater signature of ships and vocalisations of marine mammals. Special emphasis is given to phenomena typical of ship components, such as frequency combs and Doppler effects.