Hypothesis Testing Using Spatially Dependent Heavy Tailed Multisensor Data
Abstract
The detection of spatially dependent heavy-tailed signals is considered. While the central limit theorem, and its implication of asymptotic normality of interacting random processes, is useful for the theoretical characterization of a wide variety of signals, sensor data from many applications are characterized by non-Gaussian distributions. A common characteristic in non-Gaussian data is the presence of heavy-tails or fat tails. For such data, the probability density function (p.d.f.) of extreme values decay at a slower-than-exponential rate, implying that extreme events occur with greater probability. When these events are observed simultaneously by several sensors, their observations are also spatially dependent. We develop the theory of detection for such data, obtained through heterogeneous sensors. To validate our theoretical results and proposed algorithms, we collect and analyze the behavior of indoor footstep data using a linear array of seismic sensors. We characterize the inter-sensor dependence using copula theory. We model the heavy-tailed data using the class of alpha-stable distributions. We consider a two-sided test in the Neyman-Pearson framework and present an asymptotic analysis of the generalized likelihood test (GLRT). Both, nested and non-nested models are considered. We also use a likelihood maximization-based copula selection scheme as part of the detection process. With appropriately selected models, our results demonstrate that a high probability of detection can be achieved for false alarm probabilities of the order of 10e-4. These results, using dependent alpha-stable signals, are presented for a two-sensor case.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 2014
- Accession Number
- AD1017299
Entities
People
- Arun Subramanian
Organizations
- Syracuse University