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

Advanced Placement and American Education: A Foucauldian Analysis of the Advanced Placement Program of the College Board

Advanced Placement is a series of courses and tests designed to determine mastery over introductory college material. It has become part of the American educational system. The changing conception of AP was examined using critical theory to determine what led to a view of continual success. The study utilized David Armstrong’s variation of Michel Foucault’s critical theory to construct an analytical framework. Black and Ubbes’ data gathering techniques and Braun and Clark’s data analysis were utilized as the analytical framework. Data included 1135 documents: 641 journal articles, 421 newspaper articles and 82 government documents. The study revealed three historical ruptures correlated to three themes containing subthemes. The first rupture was the Sputnik launch in 1958. Its correlated theme was AP leading to school reform with subthemes of AP as reform for able students and AP’s gaining of acceptance from secondary schools and higher education. The second rupture was the Nation at Risk report published in 1983. Its correlated theme was AP’s shift in emphasis from the exam to the course with the subthemes of AP as a course, a shift in AP’s target population, using AP courses to promote equity, and AP courses modifying curricula. The passage of the No Child Left Behind Act of 2001 was the third rupture. Its correlated theme was AP as a means to narrow the achievement gap with the subthemes of AP as a college preparatory program and the shifting of AP to an open access program. The themes revealed a perception that progressively integrated the program into American education. The AP program changed emphasis from tests to curriculum, and is seen as the nation’s premier academic program to promote reform and prepare students for college. It has become a major source of income for the College Board. In effect, AP has become an agent of privatization, spurring other private entities into competition for government funding. The change and growth of the program over the past 57 years resulted in a deep integration into American education. As such the program remains an intrinsic part of the system and continues to evolve within American education.