<p> Jakeman's random walk model with step number fluctuations describes the amplitude
scattered from a rough medium in terms as the coherent summation of (independent)
individual scatterers' contributions. For a population following a birthdeath-
immigration (BDI) model, the resulting statistics are k-distributed and the
multiplicative representation of the amplitude as a Gaussian speckle modulated by
a Gamma radar cross-section (RCS) is recovered. The main objective of the present
thesis is to discuss techniques for the inference of the RCS in local time in order to
facilitate anomaly detection. We first show how the Pearson class of diffusions, which
we derive on the basis of a discrete population model analogous to the BDI, encompasses
this Gamma texture as well as other texture models studied in the literature.
Next we recall how Field & Tough derived, in an Ito calculus framework, the dynamics
and the auto-correlation function of the scattered amplitude from the random
walk model. In particular, they showed how the RCS was observable through the
intensity-weighted squared fluctuations of the phase. Thanks to a discussion of the
sources of discrepancy arising during this process, we derive an analytical expression
for the inference error based on its asymptotic behaviours, together with a condition
to minimize it. Our results are then extended to the Pearson class of diffusions
whose importance for radar clutters is described. Next, we consider an experimental
caveat, namely the presence of an additional white noise. The finite impulse response
Wiener filter enables the design of the optimal filter to retrieve the scattered amplitude
when it lies in superposition with thermal noise, thus enabling the usage of our
inference technique. Finally, we consider weak scattering when a coherent signal lies
in superposition with the aforementioned (strongly) scattered amplitude. Strong and
weak scattering patterns differ regarding the correlation structure of their radial and
angular fluctuations. Investigating these geometric characteristics yields two distinct
procedures to infer the scattering cross-section from the phase and intensity fluctuations
of the weakly scattered amplitude, thus generalizing the results obtained in the
strong scattering case. </p> / Thesis / Doctor of Philosophy (PhD)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/19018 |
| Date | 09 1900 |
| Creators | Fayard, Patrick |
| Contributors | Field, Timothy, Electrical and Computer Engineering |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
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