Acoustic Source Separation, Contour Classification, and Trajectory Optimization

Abstract

How can we distinguish individual birds singing in a dawn chorus, and thereby improve measurements of biodiversity to aid conservation efforts? What are the key differences between the walking patterns of an unimpaired individual and a stroke survivor, and how can this inform physical rehabilitation? What is an optimal way to navigate a quadcopter through a complicated environment? This thesis aims to address these questions, and a few others, by linking techniques from optimization, signal processing, and geometry with problems in bioacoustics, biomechanics, and robotics. While the applications are highly interdisciplinary, the methodologies share some fundamental similarities -- all are grounded in physical principles and designed for robust application to real-world datasets. First, in Part 2, we address challenges encountered in acoustic monitoring of wildlife, and develop techniques for separating simultaneous sound sources and finding lower-dimensional structure in birdsong. In Part 3, we draw on geometric principles to study the characteristics of gait kinematics and the mechanisms behind visual perception. Lastly, in Part 4, we design and evaluate algorithms for trajectory optimization of constrained dynamical systems. Overall, we hope this work can be a contribution to both theoretical frontiers and applied sciences.