Performance-computation tradeoffs in detection and estimation
Detection and estimation problems involve challenging tasks that often demand real-time, accurate results. Algorithms able to produce highly accurate results are often computationally expensive or inefficient. Naturally, we need to tailor algorithms to the specific needs of problems to optimally trade off between computation and accuracy. To explore this ever-present tradeoff, this dissertation describes three distinct problems in detection and estimation and our contribution to the decision-making process for choosing the best algorithms for solving these problems. First, we look at tradeoffs involved in designing a low-cost, camera-based autonomous gait acquisition and analysis system for inspecting gait impairments in mice. Specifically, we give a detailed description of our detection and classification algorithms for gait-event detection and gait-parameter extraction. Using the videos acquired in a live-animal study, we validate the performance of our system for assessing recovery in a mouse model of Parkinson's disease. Next, we analyze the tradeoffs involved in designing a modified data association algorithm for tracking multiple objects using measurements of uncertain origins, such as radar detection with false alarms and missed detection. Specifically, we explore the performance of the distance-weighting probabilistic data association approach in conjunction with the loopy-sum product algorithm and, using simulation data, we analyze its performance in terms of tracking accuracy and computation against other state-of-the-art data association methods for tracking multiple targets in clutter. Finally, to address the ill-conditioning of linear minimum mean square error estimation, we develop four approximate Wiener filter formulas that do not directly involve the inverse of the observation covariance matrix. Using real data, we evaluate the performance-complexity tradeoff for our approximated filters. The common underlying theme that connects our solutions to these distinct problems is that our decisions for selecting various parameters in each solution are based on the performance-computation tradeoff. Throughout this dissertation, we employ various methods to handle this tradeoff, such as receiver operating characteristics analysis and line-search procedure. Our analysis is beneficial for choosing the best algorithm to optimally trade off between performance and computation.
Includes bibliographical references.