We propose the study of robustness measures for signal detection in non-stationary
noise using differential geometric tools in conjunction with empirical distribution analysis.
Our approach shows that the gradient can be viewed as a random variable and
therefore used to generate sample densities allowing one to draw conclusions regarding
the robustness. As an example, one can apply the geometric methodology to the
detection of time varying deterministic signals in imperfectly known dependent nonstationary
Gaussian noise. We also compare stationary to non-stationary noise and
prove that robustness is barely reduced by admitting non-stationarity. In addition,
we show that robustness decreases with larger sample sizes, but there is a convergence
in this decrease for sample sizes greater than 14.
We then move on to compare the effect on robustness for signal detection between
non-Gaussian tail effects and residual dependency. The work focuses on robustness
as applied to tail effects for the noise distribution, affecting discrete-time detection of
signals in independent non-stationary noise. This approach makes use of the extension
to the generalized Gaussian case allowing the comparison in robustness between the
Gaussian and Laplacian PDF. The obtained results are contrasted with the influence
of dependency on robustness for a fixed tail category and draws consequences on residual dependency versus tail uncertainty.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/4732 |
| Date | 25 April 2007 |
| Creators | Raux, Guillaume Julien |
| Contributors | Halverson, Don |
| Publisher | Texas A&M University |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | 1540691 bytes, electronic, application/pdf, born digital |
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