The Internet presents a new phenomenon to educators and students in the K-12 environment. It's ease of use and ready access to material provides an overwhelming resource for use in the K-12 classroom. This study looked at content management of Internet resources in the K-12 school environment. Content management is defined as the methods of organizing access to the information available on the Internet allowing the teacher to effectively use resources in a classroom setting. Teachers have managed the material, or content, that they present to students for over a decade. Now that resources available on the Internet are also open to K-12 students, teachers must be aware of the need to manage Internet content, just as they would do for any other content being used in their classroom. This study looked at middle school students in 6th and 7th grades. An experimental design was used to determine if K-12 access to Internet resources provides a higher degree of results when students are presented with managed resources, or when students have open access to Internet resources. Analysis of the results of the study show that there is a significant difference in both the amount and the quality of material that was identified by the group with managed access to Internet content. / Ph. D.

In this thesis we develop a rigorous mathematical framework for analyzing and approximating optimal sensor placement problems for distributed parameter systems and apply these results to PDE problems defined by the convection-diffusion equations. The mathematical problem is formulated as a distributed parameter optimal control problem with integral Riccati equations as constraints. In order to prove existence of the optimal sensor network and to construct a framework in which to develop rigorous numerical integration of the Riccati equations, we develop a theory based on Bochner integrable solutions of the Riccati equations. In particular, we focus on ℐ_p-valued continuous solutions of the Bochner integral Riccati equation. We give new results concerning the smoothing effect achieved by multiplying a general strongly continuous mapping by operators in ℐ_p. These smoothing results are essential to the proofs of the existence of Bochner integrable solutions of the Riccati integral equations. We also establish that multiplication of continuous ℐ_p-valued functions improves convergence properties of strongly continuous approximating mappings and specifically approximating C₀-semigroups. We develop a Galerkin type numerical scheme for approximating the solutions of the integral Riccati equation and prove convergence of the approximating solutions in the ℐ_p-norm. Numerical examples are given to illustrate the theory. / Ph. D.

Scaled test-beds (STBs) are popular tools to develop and physically test algorithms for advanced driving systems, but often lack automotive-grade radars in their sensor suites. To overcome resolution issues when using a radar at small scale, a high-level sensor fusion approach between the radar and automotive-grade LiDAR was proposed. The sensor fusion approach was expected to leverage the higher spatial resolution of the LiDAR effectively. First, multi object radar tracking software (RTS) was developed to track a maneuvering full-scale vehicle using an extended Kalman filter (EKF) and the joint probabilistic data association (JPDA). Second, a 1/5th scaled vehicle performed the same vehicle maneuvers but scaled to approximately 1/5th the distance and speed. When taking the scaling factor into consideration, the RTS' positional error at small scale was, on average, over 5 times higher than in the full-scale trials. Third, LiDAR object sensor tracks were generated for the small-scale trials using a Velodyne PUCK LiDAR, a simplified point cloud clustering algorithm, and a second EKF implementation. Lastly, the radar sensor tracks and LiDAR sensor tracks served as inputs to a high-level track-to-track fuser for the small-scale trials. The fusion software used a third EKF implementation to track fused objects between both sensors and demonstrated a 30% increase in positional accuracy for a majority of the small-scale trials when compared to using just the radar or just the LiDAR to track the vehicle. The proposed track fuser could be used to increase the accuracy of RTS algorithms when operating in small scale and allow STBs to better incorporate automotive radars into their sensor suites. / Master of Science / Research and development platforms, often supported by robust prototypes, are essential for the development, testing, and validation of automated driving functions. Thousands of hours of safety and performance benchmarks must be met before any advanced driver assistance system (ADAS) is considered production-ready. However, full-scale testbeds are expensive to build, labor-intensive to design, and present inherent safety risks while testing. Scaled prototypes, developed to model system design and vehicle behavior in targeted driving scenarios, can minimize these risks and expenses. Scaled testbeds, more specifically, can improve the ease of safety testing future ADAS systems and help visualize test results and system limitations, better than software simulations, to audiences with varying technical backgrounds. However, these testbeds are not without limitation. Although small-scale vehicles may accommodate similar on-board systems to its full-scale counterparts, as the vehicle scales down the resolution from perception sensors decreases, especially from on board radars. With many automated driving functions relying on radar object detection, the scaled vehicle must host radar sensors that function appropriately at scale to support accurate vehicle and system behavior. However, traditional radar technology is known to have limitations when operating in small-scale environments. Sensor fusion, which is the process of merging data from multiple sensors, may offer a potential solution to this issue. Consequently, a sensor fusion approach is presented that augments the angular resolution of radar data in a scaled environment with a commercially available Light Detection and Ranging (LiDAR) system. With this approach, object tracking software designed to operate in full-scaled vehicles with radars can operate more accurately when used in a scaled environment. Using this improvement, small-scale system tests could confidently and quickly be used to identify safety concerns in ADAS functions, leading to a faster and safer product development cycle.

This investigation is concerned with effective state estimation of a system driven by an unknown nonGaussian input with additive white Gaussian noise, and observed by measurements containing feedthrough of the same nonGaussian input and corrupted by additional white Gaussian noise. A Gaussian sum (GS) approach has previously been developed [6-8] which can cope with the non Gaussian nature of the input signal. Due to a serious growing memory problem in this approach, a modified Gaussian sum (MGS) estimation technique is developed that avoids the growing memory problem while providing effective state estimation. Several differences between the MGS and GS algorithms are examined. An MGS adaptive filter is derived for a general system and a modal system, with simulation examples performed using a non Gaussian input signal. The modal system simulation results are compared to those produced from an augmented Kalman filter based on an augmented modal system model assuming a narrowband Gaussian input signal. A necessary condition for effective MGS estimation is derived. Alternate estimation procedures are developed to compensate for situations when this condition is not met. Several configurations are simulated and their performance results are analyzed and compared. Two methods of monitoring and updating key parameters of the MGS filter are developed. Simulation results are analyzed to investigate the performance of these methods. / Ph. D.

Adaptive algorithms for state estimation are currently of tremendous interest. Such estimation techniques have particular military usefulness in automatic gunfire control systems. The conventional Kalman filter, developed by Kalman and Bucy, optimally solves the state estimation problem concerning linear systems with Gaussian disturbance and error processes. The maneuvering target tracking problem generally involves nonlinear system properties as well as non-Gaussian disturbance processes. The study presented here explores several solutions. to this problem. An adaptive state estimator centered about the familiar Kalman filter has been developed for applications in three-dimensional maneuvering target tracking. Target maneuvers are modeled in a general manner by a semi-Markov process. The semi-Markov modeling is based on very intuitively appealing assumptions. Specifically, target maneuvers are randomly selected from a range (possibly infinite) of maneuver commands. The selected command is sustained for a random holding time before another command is selected. Dynamics of the selection and holding process may be stationary or time varying. By incorporating the semi-Markov modeling into a Baysian estimation scheme, an adaptive state estimator can be designed to identify the particular maneuver command influencing the target. The algorithm has the distinct advantages of requiring only one Kalman filter and non-growing computer storage requirements. Several techniques of implementing the adaptive algorithm have been developed. The merits of rectangular and spherical modeling have been explored. Most importantly, the planar discrete level semi-Markov algorithm, originally developed for sonar applications, has been extended to a continuum of levels, as well as extended to three-dimensional tracking. The developed algorithms have been fully evaluated by computer simulations. Emphasis has been placed on computational burden as well as overall tracking performance. Results are presented that show.that the developed estimators largely eliminate severe tracking errors that occur when more simplistic target models are incorporated. / Ph. D.

The objective of this research is to develop time-varying signal processing methods for rapidly varying non-stationary signals based on time-varying autoregressive (TVAR) modeling, and to apply such methods to frequency-modulated (FM) interference rejection in direct-sequence spread spectrum (DSSS) communications. For fast varying non-stationary signal processing, such as the task to reject an FM interference that could chirp over the entire DSSS bandwidth in a symbol interval, an explicit description of the variation is necessary to form a time-varying filter. This is realized using the TVAR model, which is an autoregressive model whose coefficients are time-varying with the variation modeled as a linear combination of a set of known functions of time. In DSSS communications, when the strength of an interference - which could be a hostile jammer or overlaid communication signal - possibly exceeds the inherent spread spectrum processing gain, interference rejection is necessary to secure a usable bit-error-rate. The contributions of this research include: a) revealed the advantageous performance of TVAR model based instantaneous frequency estimation (TVAR-IF), which is expected to change the prevailing opinion that regards TVAR-IF as a poor estimator; b) proposed a time-varying Prony method to improve TVAR-IF at low SNR; c) proposed to use TVAR-IF for time-varying FIR notch filter based FM jammer suppression in DSSS communications; d) developed TVAR model based time-varying optimum filters, including the TVAR based Kalman filter (TVAR-KF) and the TVAR based Wiener filter (TVAR-WF); e) developed a TVAR-WF based formulation of FM interference soft-cancellation in DSSS communications; and f) proposed a TVAR based linear prediction error (TVAR-LPE) filter for soft-cancellation of FM interference in DSSS communications. For the interference rejection problem, our TVAR-IF controlled notch filter yields high processing gain close to that using the known IF and much higher than that using the WVD based IF estimate. Furthermore, unlike the IF based notch filter approaches, the proposed soft-cancellation methods utilize the full spectral information captured by the TVAR model. Our soft-cancellation approaches, including TVAR-WF and TVAR-LPE, maintain at least the DSSS system performance expected when no filtering is used, even under estimated conditions. The latter is in contrast to the notch filter based approaches, which may cause deterioration of overall system performance at low jammer-to-signal ratios. / Ph. D.

A computationally efficient estimation technique is presented for a class of nonlinear systems consisting of memoryless nonlinearities combined with linear dynamic processes. The modeling approach is based on a useful sampled-data method for simulating such systems by adding a system state for each nonlinear element. The nonlinear estimator is next developed along the lines of the Kalman filter, but in contrast to the Extended Kalman Filter (EKF) the present approach does not require the linearization step after each recursive cycle. In addition, it also appears free from the well known divergence problems associated with the EKF. It is demonstrated that this new method is directly applicable to those feedback systems with both major nonlinearities, for example saturating gain blocks, and stochastic disturbances-- an example extremely difficult to handle with EKF techniques. / Master of Science

The simulation and testing of several state tracking techniques over a range of process and measurement noise environments is considered. The problem is placed in the context of tracking a maneuvering vehicle from noisy position data with the vehicle accelerations considered as a random process about which the first and second order statistics are known. The tracking filters under test are the fixed α-β filter, the double α-β filter, the second order Kalman filter, the augmented Kalman filter, and the double Kalman filter. All filters show improved performance as the measurement noise increases and the process noise decreases. The superiority of the Kalman filter over the simpler deterministic digital trackers decreases as the measurement noise increases and the process noise decreases. The double Kalman filter, with the capability of adaptive adjustments of threshold values, indicates the best overall tracking for combined maneuver and non-maneuver tracking. / Master of Science

Autonomous Underwater Vehicles (AUVs) are currently being used for many underwater tasks such as mapping underwater terrain, detection of underwater objects, and assessment of water quality. Possible uses continue to grow as the vehicles become smaller, more agile, and less expensive to operate. However, trade-offs exist between making less expensive, miniature AUVs and the quality at which they perform. One area affected by cost and size is the onboard navigation system. To achieve the challenges of low-cost rate sensors, this thesis examines calibration methods that are suitable for identifying calibration coefficients in low-cost MEMS gyros. A brief introduction to underwater navigation is presented and is followed by the development of a model to describe the operation of a rate gyro. The model uses the integral relationship between angular rate and angular position measurements. A compass and two tilt sensors provide calibrated angular position data against which the three single axis gyros are compared to obtain an error signal describing errors present in the angular rate measurements. A calibration routine that adaptively identifies error parameters in the gyros is developed. Update laws are chosen to recursively apply estimated error parameters to minimize the system error signal. Finally, this calibration method is applied to a simple dead reckoning algorithm in an attempt to measure the improvements calibration provides. / Master of Science

No description available.