Next-generation quickest detection
Abstract
This proposal aims to develop state of the art geometric probabilistic optimization techniques to address the substantial danger posed by space weather threats (in particular, the threat caused by cosmic rays, solar flames, and solar particles) to critical U.S. Army defense systems, including, but not limited to, GPS systems and electrical power grids, both of which rely on the highest standards of modern satellite communication. The following quickest detection/change-point framework to consider space weather effects is proposed. Consider a clear sky (or clear space) that may be modeled as standard Brownian motion without drift. Assume that at some random, unobservable time, cosmic rays start (invisibly) appearing, the latter modelled as Brownian motion with drift. The task is to detect the Brownian motion with drift as soon as possible while simultaneously minimizing the false alarm probability, the detection delay, as well as the length of time that the satellites are shielded. Upon detection, the satellites are to be covered with a shield to protect them from potential enormous destruction from cosmic rays. The above mathematical framework can be accordingly rephrased as an optimal stopping/free boundary problem. The inherent difficulty, however, lies is the fact that the value function cannot be computed in optimal stopping problems in higher dimensions. Peskir (J. Convex Analysis, 2012) formulated and explained a duality principle for the Legendre transform that yields the shortest path between the graphs of functions and embodies the underlying Nash equilibrium. The critical limitation is that the Legendre transform has only been established in one dimension. Extensions to two and higher dimensional settings represent a formidable challenge that requires novel ideas and techniques that will go far beyond the current state of the art. With the above application as its inspiration, I propose to (i) introduce and explore geometry of geodesics associated with the important classes of Markov processes in one dimension, (ii) extend these methods and results to two and higher dimensional settings, (iii) establish duality principles and explain their geometry, (iv) examine connections between these results and establish links with optimal detection of hidden targets and (v) utilize geometry of geodesics in solutions to these problems. Current systems in place designed to protect satellites from the harmful effects of cosmic rays do not employ the most advanced optimal detection techniques, which can lead to satellites being shut down for longer periods of time than necessary. Successful optimal detection algorithms for the detection of cosmic rays would be of enormous benefit to society. All citizens would be beneficiaries of this project s success. This is because the proposal s aim to achieve optimal high-dimensional detection would afford superior protection of our electrical power grids, failures of which could potentially halt the delivery of key U.S. Army services.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 14, 2019
- Source ID
- W911NF1810319
Entities
People
- Philip Ernst
Organizations
- Army Contracting Command
- Rice University
- United States Army