2023-12-08T10:40:15Zhttps://keep.lib.asu.edu/oai/requestoai:keep.lib.asu.edu:node-1577012021-08-27T02:47:01Zoai_pmh:alloai_pmh:repo_items157701
https://hdl.handle.net/2286/R.I.54949
http://rightsstatements.org/vocab/InC/1.0/
2019
x, 103 pages : color illustrations
Doctoral Dissertation
Academic theses
Text
eng
Jones, Scott, Ph.D
Cochran, Douglas
Berisha, Visar
Bliss, Daniel
Kosut, Oliver
Richmond, Christ
Arizona State University
Partial requirement for: Ph.D., Arizona State University, 2019
Includes bibliographical references (pages 91-94)
Field of study: Electrical engineering
Eigenvalues of the Gram matrix formed from received data frequently appear in sufficient detection statistics for multi-channel detection with Generalized Likelihood Ratio (GLRT) and Bayesian tests. In a frequently presented model for passive radar, in which the null hypothesis is that the channels are independent and contain only complex white Gaussian noise and the alternative hypothesis is that the channels contain a common rank-one signal in the mean, the GLRT statistic is the largest eigenvalue $\lambda_1$ of the Gram matrix formed from data. This Gram matrix has a Wishart distribution. Although exact expressions for the distribution of $\lambda_1$ are known under both hypotheses, numerically calculating values of these distribution functions presents difficulties in cases where the dimension of the data vectors is large. This dissertation presents tractable methods for computing the distribution of $\lambda_1$ under both the null and alternative hypotheses through a technique of expanding known expressions for the distribution of $\lambda_1$ as inner products of orthogonal polynomials. These newly presented expressions for the distribution allow for computation of detection thresholds and receiver operating characteristic curves to arbitrary precision in floating point arithmetic. This represents a significant advancement over the state of the art in a problem that could previously only be addressed by Monte Carlo methods.
Electrical Engineering
Statistics
Applied Mathematics
Multi-channel Detection
Passive Radar
Wishart
Multisensor data fusion
Eigenvalues
Radar--Mathematical models.
Radar
Numerical computation of Wishart eigenvalue distributions for multistatic radar detection