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Description
Power spectral analysis is a fundamental aspect of signal processing used in the detection and \\estimation of various signal features. Signals spaced closely in frequency are problematic and lead analysts to miss crucial details surrounding the data. The Capon and Bartlett methods are non-parametric filterbank approaches to power spectrum estimation. The Capon algorithm is known as the "adaptive" approach to power spectrum estimation because its filter impulse responses are adapted to fit the characteristics of the data. The Bartlett method is known as the "conventional" approach to power spectrum estimation (PSE) and has a fixed deterministic filter. Both techniques rely on the Sample Covariance Matrix (SCM). The first objective of this project is to analyze the origins and characteristics of the Capon and Bartlett methods to understand their abilities to resolve signals closely spaced in frequency. Taking into consideration the Capon and Bartlett's reliance on the SCM, there is a novelty in combining these two algorithms using their cross-coherence. The second objective of this project is to analyze the performance of the Capon-Bartlett Cross Spectra. This study will involve Matlab simulations of known test cases and comparisons with approximate theoretical predictions.
ContributorsYoshiyama, Cassidy (Author) / Richmond, Christ (Thesis director) / Bliss, Daniel (Committee member) / Electrical Engineering Program (Contributor, Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
Radar systems seek to detect targets in some search space (e.g. volume of airspace, or area on the ground surface) by actively illuminating the environment with radio waves. This illumination yields a return from targets of interest as well as highly reflective terrain features that perhaps are not of interest (called clutter). Data adaptive algorithms are therefore employed to provide robust detection of targets against a background of clutter and other forms of interference. The adaptive matched filter (AMF) is an effective, well-established detection statistic whose exact probability density function (PDF) is known under prevalent radar system model assumptions. Variations of this approach, however, lead to tests whose PDFs remain unknown or incalculable. This project will study the effectiveness of saddlepoint methods applied to approximate the known pdf of the clairvoyant matched filter, using MATLAB to complete the numerical calculations. Specifically, the approximation was used to compute tail probabilities for a range of thresholds, as well as compute the threshold and probability of detection for a specific desired probability of false alarm. This was compared to the same values computed using the known exact PDF of the filter, with the comparison demonstrating high levels of accuracy for the saddlepoint approximation. The results are encouraging, and justify further study of the approximation as applied to more strained or complicated scenarios.
ContributorsRhoades, Rachel (Author) / Richmond, Christ (Thesis director) / Cochran, Douglas (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Electrical Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05