STATISTICAL METHODS FOR ADVANCED ECONOMETRIC MODELS WITH APPLICATIONS TO VEHICLE HOLDING AND SPEED QUANTILES DISTRIBUTION

This dissertation proposes statistical methods to formulate, estimate and apply complex transportation models. Two main problems are part of the analyses conducted and presented in this dissertation. The first method solves an econometric problem and is concerned with the joint estimation of models that contain both discrete and continuous decision variables. The use of ordered models along with a regression is proposed and their effectiveness is evaluated with respect to unordered models. Procedure to calculate and optimize the log-likelihood functions of both discrete-continuous approaches are derived, and difficulties associated with the estimation of unordered models explained. Numerical approximation methods based on the Genz algortithm are implemented in order to solve the multidimensional integral associated with the unordered modeling structure. The problems deriving from the lack of smoothness of the probit model around the maximum of the log-likelihood function, which makes the optimization and the calculation of standard deviations very difficult, are carefully analyzed. A methodology to perform out-of-sample validation in the context of a joint model is proposed. Comprehensive numerical experiments have been conducted on both simulated and real data. In particular, the discrete-continuous models are estimated and applied to vehicle ownership and use models on data extracted from the 2009 National Household Travel Survey. The second part of this work offers a comprehensive statistical analysis of free-flow speed distribution; the method is applied to data collected on a sample of roads in Italy. A linear mixed model that includes speed quantiles in its predictors is estimated. Results show that there is no road effect in the analysis of free-flow speeds, which is particularly important for model transferability. A very general framework to predict random effects with few observations and incomplete access to model covariates is formulated and applied to predict the distribution of free-flow speed quantiles. The speed distribution of most road sections is successfully predicted; jack-knife estimates are calculated and used to explain why some sections are poorly predicted. Eventually, this work contributes to the literature in transportation modeling by proposing econometric model formulations for discrete-continuous variables, more efficient methods for the calculation of multivariate normal probabilities, and random effects models for free-flow speed estimation that takes into account the survey design. All methods are rigorously validated on both real and simulated data.

Optical Wireless Communication for Mobile Platforms

The past few decades have witnessed the widespread adaptation of wireless devices such as cellular phones and Wifi-connected laptops, and demand for wireless communication is expected to continue to increase. Though radio frequency (RF) communication has traditionally dominated in this application space, recent decades have seen an increasing interest in the use of optical wireless (OW) communication to supplement RF communications. In contrast to RF communication technology, OW systems offer the use of largely unregulated electromagnetic spectrum and large bandwidths for communication. They also offer the potential to be highly secure against jamming and eavesdropping. Interest in OW has become especially keen in light of the maturation of light-emitting diode (LED) technology. This maturation, and the consequent emerging ubiquity of LED technology in lighting systems, has motivated the exploration of LEDs for wireless communication purposes in a wide variety of applications. Recent interest in this field has largely focused on the potential for indoor local area networks (LANs) to be realized with increasingly common LED-based lighting systems. We envision the use of LED-based OW to serve as a supplement to RF technology in communication between mobile platforms, which may include automobiles, robots, or unmanned aerial vehicles (UAVs). OW technology may be especially useful in what are known as RF-denied environments, in which RF communication may be prohibited or undesirable. The use of OW in these settings presents major challenges. In contrast to many RF systems, OWsystems that operate at ranges beyond a few meters typically require relatively precise alignment. For example, some laser-based optical wireless communication systems require alignment precision to within small fractions of a degree. This level of alignment precision can be difficult to maintain between mobile platforms. Additionally, the use of OW systems in outdoor settings presents the challenge of interference from ambient light, which can be much brighter than any LED transmitter. This thesis addresses these challenges to the use of LED-based communication between mobile platforms. We propose and analyze a dual-link LED-based system that uses one link with a wide transmission beam and relaxed alignment constraints to support a more narrow, precisely aligned, higher-data-rate link. The use of an optical link with relaxed alignment constraints to support the alignment of a more precisely aligned link motivates our exploration of a panoramic imaging receiver for estimating the range and bearing of neighboring nodes. The precision of such a system is analyzed and an experimental system is realized. Finally, we present an experimental prototype of a self-aligning LED-based link.