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Physical Sciences and Mathematics Commons™

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2003

Statistics and Probability

Theses and Dissertations

Articles 1 - 5 of 5

Full-Text Articles in Physical Sciences and Mathematics

Generalized Residual Multiple Model Adaptive Estimation Of Parameters And States, Charles D. Ormsby Oct 2003

Generalized Residual Multiple Model Adaptive Estimation Of Parameters And States, Charles D. Ormsby

Theses and Dissertations

This dissertation develops a modification to the standard Multiple Model Adaptive Estimator (MMAE) which allows the use of a new "generalized residual" in the hypothesis conditional probability calculation. The generalized residual is a linear combination of traditional Kalman filter residuals and "post-fit" Kalman filter residuals which are calculated after measurement incorporation. This modified MMAE is termed a Generalized Residual Multiple Model Adaptive Estimator (GRMMAE). The dissertation provides a derivation of the hypothesis conditional probability formula which the GRMMAE uses to calculate probabilities that each elemental filter in the GRMMAE contains the correct parameter value. Through appropriate choice of a single …

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Transient Analysis And Applications Of Markov Reward Processes, Jeffrey A. Sipe Mar 2003

Transient Analysis And Applications Of Markov Reward Processes, Jeffrey A. Sipe

Theses and Dissertations

In this thesis, the problem of computing the cumulative distribution function (cdf) of the random time required for a system to first reach a specified reward threshold when the rate at which the reward accrues is controlled by a continuous time stochastic process is considered. This random time is a type of first passage time for the cumulative reward process. The major contribution of this work is a simplified, analytical expression for the Laplace-Stieltjes Transform of the cdf in one dimension rather than two. The result is obtained using two techniques: i) by converting an existing partial differential equation to …

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Statistical Process Control: An Application In Aircraft Maintenance Management, Bradley A. Beabout Mar 2003

Statistical Process Control: An Application In Aircraft Maintenance Management, Bradley A. Beabout

Theses and Dissertations

Maintenance management at the 135th Airlift Wing, Maryland Air National Guard desires a visualization tool for their maintenance performance metrics. Currently they monitor their metrics via an electronic spreadsheet. They desire a tool that presents the performance information in a graphical manner. This thesis effort focuses on the development of a visualization tool utilizing two of the seven tools offered by Statistical Process Control (SPC). This research demonstrates the application of p-charts and Pareto diagrams in the aircraft maintenance arena. P-charts are used for displaying mission capable (MC) rates and flying scheduling effectiveness (FSE) rates. Pareto diagrams are then used …

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Gaussian Mixture Reduction Of Tracking Multiple Maneuvering Targets In Clutter, Jason L. Williams Mar 2003

Gaussian Mixture Reduction Of Tracking Multiple Maneuvering Targets In Clutter, Jason L. Williams

Theses and Dissertations

The problem of tracking multiple maneuvering targets in clutter naturally leads to a Gaussian mixture representation of the Provability Density Function (PDF) of the target state vector. State-of-the-art Multiple Hypothesis Tracking (MHT) techniques maintain the mean, covariance and probability weight corresponding to each hypothesis, yet they rely on ad hoc merging and pruning rules to control the growth of hypotheses.

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Normal Mixture Models For Gene Cluster Identification In Two Dimensional Microarray Data, Eric Scott Harvey Jan 2003

Normal Mixture Models For Gene Cluster Identification In Two Dimensional Microarray Data, Eric Scott Harvey

Theses and Dissertations

This dissertation focuses on methodology specific to microarray data analyses that organize the data in preliminary steps and proposes a cluster analysis method which improves the interpretability of the cluster results. Cluster analysis of microarray data allows samples with similar gene expression values to be discovered and may serve as a useful diagnostic tool. Since microarray data is inherently noisy, data preprocessing steps including smoothing and filtering are discussed. Comparing the results of different clustering methods is complicated by the arbitrariness of the cluster labels. Methods for re-labeling clusters to assess the agreement between the results of different clustering techniques …

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