Robust Dynamical Model-based Data Representations and Structuring of Time Series Data for In-sequence Localization
Open Access
- Author:
- Laftchiev, Emil Ivanov
- Graduate Program:
- Electrical Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- November 11, 2014
- Committee Members:
- Constantino Manuel Lagoa, Dissertation Advisor/Co-Advisor
Sean Brennan, Dissertation Advisor/Co-Advisor
Minghui Zhu, Committee Member
John F Doherty, Committee Member
Christopher Rahn, Committee Member - Keywords:
- Data Dimension Reduction
Stochastic Programming
Multi-dimensional Data Representation
In-Sequence Localization - Abstract:
- In the modern era there is an unprecedented ability to actuate via an increasingly cheaper array of actuators, and to sense through a growing, increasingly cheaper, array of sensors. The ability to sense in particular represents both the unique opportunity and the unique challenge of our time. It is an opportunity because through the acquired data, it is possible to glean insight into processes that are still too complex to be modeled correctly, and a challenge because the sheer volume of data generated is often overwhelming. Paradoxically, despite having the capability to collect vast stores of data, we still lack knowledge of how to best analyze and use this data. In fact, multiple review papers have demonstrated that published methods are too application specific and depend too strongly on the data set size to be deployed on the scale necessary to address the problem. Heated debates rage in the scientific literature on how to best reduce the data into meaningful features and how to apply this reduced data to solve real-world problems. This thesis proposes a novel approach to reducing the dimension of data into meaningful features that preserve the information of the data, but also enable the localization of a small, newly collected, set of data in a previously stored data set. The process of identifying a location within a stored data set is termed in-sequence localization and it is particularly important in applications such as vehicle localization, economic forecasting, energy generation mode selection, and stream health monitoring, where stored data can be used to infer the present and future state of a process. To enable the process of in-sequence localization, this thesis proposes to model the data using autoregressive models, such that a small number of model coefficients can be used to represent large subsets of data. Then using these autoregressive models, in-sequence localization is performed by comparing new data with the models and determining model feasibility. Emphasizing the fact that this method is to be used on practical data, the models are determined such that in-sequence localization is robust to the data collection noise typically observed in sensors. This thesis is developed around the application of vehicle localization. This motivating application arises from the need to augment position estimates of the Global Positioning System in the event of emergencies or signal occlusions. We return repeatedly to this application because of its intuitive nature when conveying concepts throughout the thesis. To demonstrate the broad applicability of the methods, data from the applications of economic forecasting, energy generation mode selection, stream health monitoring, and random data is used to demonstrate algorithms throughout the text.