Sensor Planning for Bayesian Nonparametric Target Modeling

Bayesian nonparametric models, such as the Gaussian process and the Dirichlet process, have been extensively applied for target kinematics modeling in various applications including environmental monitoring, traffic planning, endangered species tracking, dynamic scene analysis, autonomous robot navigation, and human motion modeling. As shown by these successful applications, Bayesian nonparametric models are able to adjust their complexities adaptively from data as necessary, and are resistant to overfitting or underfitting. However, most existing works assume that the sensor measurements used to learn the Bayesian nonparametric target kinematics models are obtained a priori or that the target kinematics can be measured by the sensor at any given time throughout the task. Little work has been done for controlling the sensor with bounded field of view to obtain measurements of mobile targets that are most informative for reducing the uncertainty of the Bayesian nonparametric models. To present the systematic sensor planning approach to leaning Bayesian nonparametric models, the Gaussian process target kinematics model is introduced at first, which is capable of describing time-invariant spatial phenomena, such as ocean currents, temperature distributions and wind velocity fields. The Dirichlet process-Gaussian process target kinematics model is subsequently discussed for modeling mixture of mobile targets, such as pedestrian motion patterns.

Novel information theoretic functions are developed for these introduced Bayesian nonparametric target kinematics models to represent the expected utility of measurements as a function of sensor control inputs and random environmental variables. A Gaussian process expected Kullback Leibler divergence is developed as the expectation of the KL divergence between the current (prior) and posterior Gaussian process target kinematics models with respect to the future measurements. Then, this approach is extended to develop a new information value function that can be used to estimate target kinematics described by a Dirichlet process-Gaussian process mixture model. A theorem is proposed that shows the novel information theoretic functions are bounded. Based on this theorem, efficient estimators of the new information theoretic functions are designed, which are proved to be unbiased with the variance of the resultant approximation error decreasing linearly as the number of samples increases. Computational complexities for optimizing the novel information theoretic functions under sensor dynamics constraints are studied, and are proved to be NP-hard. A cumulative lower bound is then proposed to reduce the computational complexity to polynomial time.

Three sensor planning algorithms are developed according to the assumptions on the target kinematics and the sensor dynamics. For problems where the control space of the sensor is discrete, a greedy algorithm is proposed. The efficiency of the greedy algorithm is demonstrated by a numerical experiment with data of ocean currents obtained by moored buoys. A sweep line algorithm is developed for applications where the sensor control space is continuous and unconstrained. Synthetic simulations as well as physical experiments with ground robots and a surveillance camera are conducted to evaluate the performance of the sweep line algorithm. Moreover, a lexicographic algorithm is designed based on the cumulative lower bound of the novel information theoretic functions, for the scenario where the sensor dynamics are constrained. Numerical experiments with real data collected from indoor pedestrians by a commercial pan-tilt camera are performed to examine the lexicographic algorithm. Results from both the numerical simulations and the physical experiments show that the three sensor planning algorithms proposed in this dissertation based on the novel information theoretic functions are superior at learning the target kinematics with

little or no prior knowledge

Cost of wind energy: comparing distant wind resources to local resources in the midwestern United States.

The best wind sites in the United States are often located far from electricity demand centers and lack transmission access. Local sites that have lower quality wind resources but do not require as much power transmission capacity are an alternative to distant wind resources. In this paper, we explore the trade-offs between developing new wind generation at local sites and installing wind farms at remote sites. We first examine the general relationship between the high capital costs required for local wind development and the relatively lower capital costs required to install a wind farm capable of generating the same electrical output at a remote site,with the results representing the maximum amount an investor should be willing to pay for transmission access. We suggest that this analysis can be used as a first step in comparing potential wind resources to meet a state renewable portfolio standard (RPS). To illustrate, we compare the cost of local wind (∼50 km from the load) to the cost of distant wind requiring new transmission (∼550-750 km from the load) to meet the Illinois RPS. We find that local, lower capacity factor wind sites are the lowest cost option for meeting the Illinois RPS if new long distance transmission is required to access distant, higher capacity factor wind resources. If higher capacity wind sites can be connected to the existing grid at minimal cost, in many cases they will have lower costs.

Low-loss directional cloaks without superluminal velocity or magnetic response.

The possibility of making an optically large (many wavelengths in diameter) object appear invisible has been a subject of many recent studies. Exact invisibility scenarios for large (relative to the wavelength) objects involve (meta)materials with superluminal phase velocity [refractive index (RI) less than unity] and/or magnetic response. We introduce a new approximation applicable to certain device geometries in the eikonal limit: piecewise-uniform scaling of the RI. This transformation preserves the ray trajectories but leads to a uniform phase delay. We show how to take advantage of phase delays to achieve a limited (directional and wavelength-dependent) form of invisibility that does not require loss-ridden (meta)materials with superluminal phase velocities.

Dust in the wind: How climate variables and volcanic dust affect rates of tooth wear in Central American howling monkeys.

OBJECTIVES: Two factors have been considered important contributors to tooth wear: dietary abrasives in plant foods themselves and mineral particles adhering to ingested food. Each factor limits the functional life of teeth. Cross-population studies of wear rates in a single species living in different habitats may point to the relative contributions of each factor. MATERIALS AND METHODS: We examine macroscopic dental wear in populations of Alouatta palliata (Gray, 1849) from Costa Rica (115 specimens), Panama (19), and Nicaragua (56). The sites differ in mean annual precipitation, with the Panamanian sites receiving more than twice the precipitation of those in Costa Rica or Nicaragua (∼3,500 mm vs. ∼1,500 mm). Additionally, many of the Nicaraguan specimens were collected downwind of active plinian volcanoes. Molar wear is expressed as the ratio of exposed dentin area to tooth area; premolar wear was scored using a ranking system. RESULTS: Despite substantial variation in environmental variables and the added presence of ash in some environments, molar wear rates do not differ significantly among the populations. Premolar wear, however, is greater in individuals collected downwind from active volcanoes compared with those living in environments that did not experience ash-fall. DISCUSSION: Volcanic ash seems to be an important contributor to anterior tooth wear but less so in molar wear. That wear is not found uniformly across the tooth row may be related to malformation in the premolars due to fluorosis. A surge of fluoride accompanying the volcanic ash may differentially affect the premolars as the molars fully mineralize early in the life of Alouatta.