Acoustic-Dynamical Data Assimilation For Capturing Environmental Uncertainty

The ocean is a complicated hydro-dynamic system, showing various forms of dy-namic processes exist, such as internal waves, eddies, and fronts. These processes and their inter-coupling and interactions with the seabed make the ocean environment highly variable in time and space, which contributes to the so-called environmental uncertainty. There is a close connection between the ocean environmental uncertainty and sonar signal processing. First, environmental uncertainty cause the sound pressure field showing uncer-tainty and variability in space and time, which can then severely affect the performance of sonar signal processing. For example, the main technique for passive source localiza-tion, matched-field processing (MFP), is concerned with exploiting the combination of the acoustic propagation physics in an ocean waveguide and the observation data; its perfor-mance is rather sensitive to the environmental uncertainty. If the available environmental information is not sufficiently accurate, MFP would break down even if the signal-to-noise ratio is high. Thus, a major research direction for underwater acoustics today is to quan-tify the effects of a variety of physical processes on the acoustic propagation, capture the environmental uncertainty, and reduce the impact of the environmental uncertainty on the performance of a sonar system.Environmental parameters can be directly measured by the instruments. However, carrying out a large area and long-term observation with sufficient temporal and spatial sampling is unrealistic given limited in situ measurement resources and capabilities. Da-ta assimilation by assimilating instant observed data of different natures to oceanograph-ic dynamical system, provides a deterministic description of the dynamic process, which is consistent with the observation data on the relevant scales. As such, it is becoming a common technique for integrated marine environmental monitoring. Because the acoustic propagation contains a wealth of distribution information of the ocean temperature and flow field, the acoustic data provides a new effective data source for data assimilation; in the meantime, acoustic-dynamical data assimilation renders a new technical framework for capturing environmental uncertainty.Targeting at the impact of the environmental uncertainty on the performance of sonar systems, this thesis focuses on both ocean environmental and acoustic field prediction the-ory and methods research in the framework of the acoustic-dynamical data assimilation. The approach here learned from the Harvard Ocean Prediction System (HOPS) and the Adaptive Rapid Environmental Assessment, and aims to render a train of thoughts for obtaining both sensitive and robust ocean observing information through dynamical mod-eling, dynamical measurements, quantification and fusion, as well as the combination of model and data in the context of real ocean applications. On one hand, acoustic-dynamical data assimilation melds high-resolution environmental measurements and acoustic mea-surements, and models the dynamical system on a relatively small scale required by the acoustic propagation modeling. On the other hand, the acoustic measurement model can be built according to specific system applications, and then coupled to data assimilation results to analyze the error and acoustic measurement performance, which can be used for optimizing the resource deployment of an environmental observational network.Following the basic framework of the acoustic-dynamical data assimilation, this the-sis has conducted research on the following subjects:oceanographic dynamical modeling, data assimilation algorithm, acoustic measurement modeling, and optimum deployment algorithm for mobile observational systems. The main results can be summarized in three aspects.1. A modified Garrett-Munk model for the internal wave with the scale on the or-der of100m is introduced as an oceanographic dynamical model based on measurement data from specific shallow water sites relevant to internal wave modeling. The evolution characteristics of sound speed under internal wave perturbations, which is closely related to acoustic measuring process, are then discussed. In the meantime, the implementation framework, function principles, and application methods of the HOPS for large-scale o-cean environmental prediction are described in detail. The prediction results of the HOPS, using the Massachusetts Bay area as an example site, are presented. HOPS prediction re-sults can be used as the initialization and boundary conditions for the acoustic-dynamical data assimilation system.2. A general framework of the acoustic-dynamical data assimilation is presented, which includes a local sound speed measurement model, an oceanographic dynamical model, a local acoustic pressure measurement model, and an acoustic propagation model. Based on the general framework, three algorithms are developed to estimate the uncertain-ty of sound speed field:the traditional variational approach, the ensemble Kalman filter (EnKF), and the unscented Kalman filter (UKF). For the traditional variational approach, a linear internal wave model is included, and the sound speed is estimated by minimizing the mean square errors of those four models, called the cost function. This method can be applied to nonlinear systems with internal wave disturbances. However, it requires to search for each dimension of the unknown parameters in the possible distribution space, which would result in very high computational complexity for a high dimensional param-eter set. In order to reduce the computational load in data assimilation, the sound speed perturbations are described by the empirical orthogonal functions (EOF), and the general framework of the acoustic-dynamical data assimilation is modeled as a state-space mod-el following the concept of sequential filtering. However, it is difficult to directly derive an explicit, time-varying EOF state equation from an oceanographic dynamical model. Instead, auto-regressive analysis method is introduced here to obtain high-order state evo-lution model of the EOF coefficients based on the oceanographic dynamical model or the sound speed measurements. Compared with the traditional first-order state evolution mod-el, the estimated results of EnKF and UKF based on the high-order state evolution model show better performance.3. The optimum deployment algorithm for mobile observational systems is conduct-ed for three specific application modes:reducing sound speed field prediction uncertain-ty, reducing acoustic field prediction uncertainty, and improving target localization. The main idea is to create the corresponding objective function, and then minimize the objec- tive function to get the Autonomous Underwater Vehicle path through some very efficient shortest path algorithms. For the first application mode, the objective function is the poste-rior sound speed field uncertainty, which is calculated through the Kalman filter based on the estimated results of the data assimilation implementation. For the second application mode, the objective function is the posterior acoustic field prediction uncertainty. Here, we need to describe the propagation of both environmental and sound speed uncertainty to acoustic field uncertainty. Considering the need for online processing, a linear approxima-tion method is applied to calculate the variance of sound transmission loss, which is defined as the acoustic field prediction uncertainty. For the third application mode, the Cramer-Rao Bound in the Bayesian framework is used to establish acoustic measurement error and cou-pling model, and the uncertainty of environmental parameters strongly coupled with source range is defined as the objective function. The effectiveness of the optimum deployment al-gorithm for different application modes are analyzed via simulations in a realistic shallow water environment selected from the Shelf Break PRIMER experiment.Finally, experimental data from the SW06Experiment in2006and the Qiandao-Lake experiment in2011are processed to validate some of the theoretical developments. Ex-perimental data processing results have verified the feasibility and effectiveness of the acoustic-dynamical data assimilation for capturing environmental uncertainty. The opti-mum deployment algorithm for mobile observational systems based on reducing sound speed field prediction uncertainty is also validated using the output data from the HOPS running for the region of the Massachusetts Bay.