Graphical model driven methods in adaptive system identification

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 2016Identifying and tracking an unknown linear system from observations of its inputs and outputs is a problem at the heart of many different applications. Due to the complexity and rapid variability of modern systems, there is extensive interest in solving the problem with as little data and computation as possible. This thesis introduces the novel approach of reducing problem dimension by exploiting statistical structure on the input. By modeling the input to the system of interest as a graph-structured random process, it is shown that a large parameter identification problem can be reduced into several smaller pieces, making the overall problem considerably simpler. Algorithms that can leverage this property in order to either improve the performance or reduce the computational complexity of the estimation problem are developed. The first of these, termed the graphical expectation-maximization least squares (GEM-LS) algorithm, can utilize the reduced dimensional problems induced by the structure to improve the accuracy of the system identification problem in the low sample regime over conventional methods for linear learning with limited data, including regularized least squares methods. Next, a relaxation of the GEM-LS algorithm termed the relaxed approximate graph structured least squares (RAGS-LS) algorithm is obtained that exploits structure to perform highly efficient estimation. The RAGS-LS algorithm is then recast into a recursive framework termed the relaxed approximate graph structured recursive least squares (RAGSRLS) algorithm, which can be used to track time-varying linear systems with low complexity while achieving tracking performance comparable to much more computationally intensive methods. The performance of the algorithms developed in the thesis in applications such as channel identification, echo cancellation and adaptive equalization demonstrate that the gains admitted by the graph framework are realizable in practice. The methods have wide applicability, and in particular show promise as the estimation and adaptation algorithms for a new breed of fast, accurate underwater acoustic modems. The contributions of the thesis illustrate the power of graphical model structure in simplifying difficult learning problems, even when the target system is not directly structured.The work in this thesis was supported primarily by the Office of Naval Research through an ONR Special Research Award in Ocean Acoustics; and at various times by the National Science Foundation, the WHOI Academic Programs Office and the MIT Presidential Fellowship Program

Environmental model-based time-reversal underwater communications

Advances in underwater acoustic communications require the development of methods to accurately compensate channels that are prone to severe double spreading of time-varying multipath propagation, fading and signal phase variations. Assuming the environmental information as a key issue, this work aims to improve communications performance of single-input-multiple-output transmission systems in such channels through the enhancement of their estimates used for equalization. The acoustic propagation physical parameters of the environment between the source and the receivers are considered in the process. The approach is to mitigate noise e ects in channel identi cation for Passive Time-Reversal (PTR), which is a low complexity probe-based refocusing technique to reduce time spreading and inter-symbol interference. The method Environmental-based PTR (EPTR) is proposed that, inspired by matched eld inversion, inserts physics of acoustic propagation in the channel compensation procedure through ray trace modeling and environmental focalization processing. The focalization is the process of tweaking the environmental parameters to obtain a noise-free numerical model generated channel response that best matches the observed data. The EPTR performance is tested and compared to the pulse-compressed PTR and to the regularized `1-norm PTR. The former is based on classical `2-norm channel estimation and the latter, inspired by compressive sensing, uses weighted `1-norm into the `2-norm estimation problem to obtain improved estimates of sparse channels. Successful experimental results were obtained with the proposed method for signals containing image messages transmitted at 4 kbit/s from a source to a 16-hydrophones vertical array at 890 m range during the UAN'11 experiment conducted o the coast of Trondheim (Norway). The scienti c contributions of this work are (i) the understanding of the process of employing physical modeling and environmental focalization to equalize and retrieve received messages in underwater acoustic communications, thus exploiting the sensitivity of environmental parameters in order to adapt a communications system to the scenario where it is used; and (ii) the presentation of a new PTR-based method that focuses environmental parameters to model suitable noise-free channel responses for equalization and whose real data results were successful for a set of coherent signals collected at sea. The proposed method is a step forward to a better understanding on how to insert physical knowledge of the environment for equalization in digital underwater acoustic communications