In recent years, the sequential Monte Carlo method, also referred to as the particle filter has emerged as a powerful methodology for solving the generally difficult nonlinear, non-Gaussian optimal filtering problem. The underlying idea is to use a randomly weighted set of samples to recursively build in time, a point-mass approximation of the true posterior PDF. With this approximation, one can recursively estimate typically intractable posterior expectations of interest. Indeed, the PF can be applied to a very large class of models. Within the last few years, the aforementioned advantages have propelled research on particle filtering and its applications. The subject of this thesis is to the extend the theories and applications of the particle filter. The main contributions of this thesis are described as follows: 1. We consider the optimal filtering problem for a class of partially observed non-Gaussian dynamic state space models. In this class, the process equation consists of a combination of linear and nonlinear states, and the process noise for the nonlinear state update is a mixture of Gaussians. In order to solve this problem, we propose a novel method based on an efficient combination of the approximate conditional mean filter and the sequential importance sampling particle filter.
2. We address the problem of channel equalization and phase noise suppression in orthogonal frequency division multiplexing (OFDM) systems. For OFDM systems, random phase noise introduced by the local oscillator causes two effects: the common phase error (CPE), and the intercarrier interference (ICI). The performance of coherent OFDM systems greatly depends on the ability to accurately estimate the effective dynamic channel i.e., the combined effect of the CPE and the time-varying frequency selective channel. With this in mind, we propose an algorithm that equalizes in the frequency domain, and uses a pilot tone aided particle filter to track/estimate the effective dynamic channel in the time domain. To increase efficiency, we implement the particle filter via a combination of sequential importance sampling, Rao-Blackwellization, and strategies stemming from the auxiliary particle filter. / Thesis / Master of Applied Science (MASc)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/23228 |
| Date | 08 1900 |
| Creators | Yee, Derek |
| Contributors | Reilly, James, Kirubarajan, Thia, Electrical and Computer Engineering |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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