1998 — 2003 |
Mikulevicius, Remigijus (co-PI) [⬀] Tartakovsky, Alexander Rozovsky, Boris [⬀] |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
Stochastic Partial Differential Equations With Applications to Nonlinear Filtering @ University of Southern California
9802423 Rozovskii Each time an outfielder tracks and catches a fly ball, he intuitively solves a problem of target tracking. That problem has stymied engineers, mathematicians, and computer scientists for years. Two great mathematicians, American, Norbert Wiener and Russian, Andrey Kolmogorov, first approached the problem during World War II. Rather than catching fly balls, Kolmogorov and Wiener were trying, in the days before computers, to develop mathematical algorithms that would help to track enemy aircraft by radar. The research started by Kolmogorov and Wiener has developed into a thriving area of applied mathematics known as Filtering Theory. Filtering, estimation of a signal or an image from noisy data, is the basic component of the data assimilation in target tracking. It is of central importance in navigation, image and signal processing, control theory, automatic tracking systems and other areas of engineering and science. This research is a joint collaborative effort between researchers at the Institute of Mathematics and Informatics, Vilnius, Lithuania, and researchers at the University of Southern California. The project is devoted to applications of stochastic partial differential equations to nonlinear filtering. The focus of the research is twofold: (1) Cauchy- boundary problems for parabolic partial differential equations arising in nonlinear filtering of stochastic processes evolving under some constraints; and (2) nonlinear filtering with distributed observation and applications to tracking of low-observable targets in images. The research will also consider the numerical aspects of nonlinear filtering. It is expected that relatively simple nonlinear filtering algorithms which are not too demanding in computational and memory requirements for on-line implementation and yet are nearly optimal from a statistical viewpoint will be developed for a wide variety of applications. The applications include air traffic control, human-computer interfaces based on motion- capture, and advanced optical and magnetic registration systems.
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0.915 |
2008 — 2013 |
Tartakovsky, Alexander |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
Collaborative Research: Optimal Changepoint Detection and Identification Algorithms With Applications @ University of Southern California
Changepoint problems deal with detecting anomalies or more generally changes in patterns. In the sequential setting, as long as the behavior of observations is consistent with the ``normal state," one is content to let the process continue. If the state changes, then one is interested in detecting that a change is in effect, usually as quickly as possible. Any detection policy may give rise to false alarms and attempting to avoid false alarms too strenuously will lead to a long delay between the time of occurrence of the change and its detection. The gist of the changepoint problem is to produce a detection policy that minimizes the average detection delay subject to a bound on the false alarm rate.
While the quickest changepoint detection problem has been studied for over fifty years, there has been remarkably little prior work on theoretical extensions to general stochastic models that go beyond independent and identically distributed observations in the pre- and post-change modes, and to the distributed sensor setting. The goal of this project is to investigate the properties of known changepoint detection procedures and to develop novel procedures for change detection and classification under general system models that are relevant in practical applications, as well as to provide an analytical framework to predict their performance. The usefulness of the theoretical advances will be demonstrated through two key application areas: (a) the rapid detection of intrusions and disruptions in computer networks, and (b) the efficient monitoring of critical infrastructures. In both cases, the distributions of the noisy observations change, and this change occurs at an a priori unknown point in time. Also, in both cases, the detection should be performed in a timely manner, while keeping the false alarm rate at an acceptable level. Our results will be validated using simulations as well as real data (to the extent possible).
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0.915 |
2010 — 2013 |
Ghanem, Roger [⬀] Tartakovsky, Alexander |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
Stochastic Prediction For the Design and Management of Interacting Complex Systems @ University of Southern California
This research considers systems that combine social networks and sensor networks with complicated interactions involving hierarchical structure. To design and analyze such complex distributed systems, information-theoretical methods will be combined with advanced Bayesian and non-Bayesian statistical techniques such as spatiotemporal nonlinear estimation and prediction, advanced changepoint detection and estimation methods, and multihypothesis decision-making strategies. Advanced data fusion methods at different levels will be proposed and tested. Distributed networks will be modeled by quite general coupled fractional hidden Markov models adapted to allow for nonlinear prediction and detection-classification. The spaces in which estimation, prediction, and classification are performed may be both metric and symbolic, thus allowing for the effective incorporation of sensor (metric) and social (symbolic) networks as a part of a large-scale distributed system.
Design of complex multi-level hierarchical systems, including systems that search for patterns to identify developing or immediate threats, is vitally important for various areas, including national security, environmental monitoring, SmartGrid and other critical infrastructures. This research will develop novel approaches for automated efficient fusion of information from multiple sources or/and from multiple levels of hierarchy of complex systems that will enable these systems to achieve high accuracy in detection of changes in trends, prediction, and recognition. Probabilistic modeling of networks will be coupled with novel approaches to event pattern recognition, change detection and information integration/fusion in complex, multisource-multisensor distributed heterogeneous systems. Both mathematical formulations and solution algorithms will be developed.
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0.915 |
2012 — 2015 |
Tartakovsky, Alexander |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
Collaborative Research: Atd: Advanced Quickest Multidecision Change Detection-Classification Methods For Threat Assessment in Distributed Sensing Systems @ University of Southern California
The overarching goal of this project is to develop the next generation of mathematical and statistical algorithms and methodologies in sensor systems for the detection of chemical and biological materials based on advanced quickest change detection and classification methods. To this end, the next generation of the quickest joint change detection and classification methods will be developed that are optimal or nearly optimal in a variety of scenarios. Specifically, a general theory of multidecision quickest change detection and classification for non-i.i.d. stochastic models will be developed. Developing this general theory requires novel probabilistic methods for both designing effective quickest change detection-classification strategies as well as analyzing their performance. Furthermore, the general theory will be extended to the distributed sensor setting. In particular, novel techniques for adaptive sampling at the sensors will be explored, change process detection methods will be developed for settings where the change might occur at different times at the various sensors, and techniques for controlling the sensing process to make it energy-efficient will be designed.
It is expected that the proposed theoretical advances in change detection and classification will have a strong practical impact on future systems that are built for the purposes of detecting and predicting chemical, biological and related threats using large sensor networks. Conversely the engineering insights gained from working on this important problem will lead to significant developments in the underlying statistical theory of quickest change detection and classification. Advances in this theory couldpotentially have an impact on a broad spectrum of applications from qualitycontrol engineering to econometrics.
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0.915 |