It is well known that when the input variables of the linear regression model are subject to noise contamination, the model parameters can not be estimated uniquely. This, in the statistical literature, is referred to as the identifiability problem of the errors-in-variables models. Further, in linear regression there is an explicit assumption of the existence of a single linear relationship. The statistical properties of the errors-in-variables models under the assumption that the noise variances are either known or that they can be estimated are well documented. In many situations, however, such information is neither available nor obtainable. Although under such circumstances one can not obtain a unique vector of parameters, the space, Ω, of the feasible solutions can be computed. Additionally, assumption of existence of a single linear relationship may be presumptuous as well. A multi-equation model similar to the simultaneous-equations models of econometrics may be more appropriate. The goals of this dissertation are the following: (1) To present analytical techniques or algorithms to reduce the solution space, Ω, when any type of prior information, exact or relative, is available; (2) The data covariance matrix, Σ, can be examined to determine whether or not Ω is bounded. If Ω is not bounded a multi-equation model is more appropriate. The methodology for identifying the subsets of variables within which linear relations can feasibly exist is presented; (3) Ridge regression technique is commonly employed in order to reduce the ills caused by collinearity. This is achieved by perturbing the diagonal elements of Σ. In certain situations, applying ridge regression causes some of the coefficients to change signs. An analytical technique is presented to measure the amount of perturbation required to render such variables ineffective. This information can assist the analyst in variable selection as well as deciding on the appropriate model; (4) For the situations when Ω is bounded, a new weighted regression technique based on the computed upper bounds on the noise variances is presented. This technique will result in identification of a unique estimate of the model parameters.

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Tsang Yuk Fung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 59-62). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Sequential Monte Carlo --- p.5 / Chapter 2.1 --- Recursive Bayesian estimation --- p.7 / Chapter 2.2 --- Bayesian sequential importance sampling --- p.8 / Chapter 2.3 --- Sclcction of iiiipoitance function --- p.10 / Chapter 2.4 --- Particle filter --- p.12 / Chapter 3 --- Target tracking and data association --- p.15 / Chapter 3.1 --- Target tracking and its applications --- p.16 / Chapter 3.2 --- Data association and JPDA method --- p.16 / Chapter 4 --- Particle filter using the acceptance-rejection method --- p.21 / Chapter 4.1 --- Particle Filter using the acceptance-rejection method --- p.22 / Chapter 4.2 --- Modified accoptance-rcjoction algorithm --- p.24 / Chapter 4.3 --- Examples --- p.26 / Chapter 4.3.1 --- Example 1: One dimensional non-linear case --- p.26 / Chapter 4.3.2 --- Example 2: Bearings-only tracking example --- p.27 / Chapter 4.3.3 --- Example 3: Single-target tracking --- p.31 / Chapter 4.3.4 --- Example 4: Multi-target tracking --- p.33 / Chapter 4.4 --- A new importance weight for bearings-only tracking problem --- p.34 / Chapter 5 --- Conclusion --- p.41

"This dissertation documents a study on parameter estimation methods for comprehensive pyrolysis modeling. There are four parts to this work, which are (1) evaluating effects of applying different kinetic models to pyrolysis modeling of fiberglass reinforced polymer composites; (2); evaluation of pyrolysis parameters for fiberglass reinforced polymer composites based on multi-objective optimization; (3) parameter estimation for comprehensive pyrolysis modeling: guidance and critical observations; and (4) engineering guide for estimating material pyrolysis properties for fire modeling. In the first section (Section 1), evaluation work is conducted to determine the effects of applying different kinetic models (KMs), developed based on thermal analysis using TGA data, when used in typical 1D pyrolysis models of fiberglass reinforced polymer (FRP) composites. The study shows that that increasing complexity of KMs to be used in pyrolysis modeling is unnecessary for the FRP samples investigated. Additionally, the findings from this research indicates that the basic assumption of considering thermal decomposition of each computational cell in comprehensive pyrolysis modeling as equivalent to that in a TGA experiment becomes inapplicable at depth and higher heating rates. The second part of this dissertation (Section 2) reports the results from a study conducted to investigate the ability of global, multi-objective and multi-variable optimization methods to estimate material parameters for comprehensive pyrolysis models. The research materials are two fiberglass reinforced polymer (FRP) composites that share the same fiberglass mats but with two different resin systems. One resin system is composed of a single component and the other system is composed of two components (resin and fire retardant additive). The results show that for a well-configured parameter estimation exercise using the optimization method described above, (1) estimated results are within ± 100% of the measurements in general; (2) increasing complexity of the kinetic modeling for a single component system has insignificant effect on estimated values; (3) increasing complexity of the kinetic modeling for a multiple component system with each element having different thermal characteristics has positive effect on estimated values; and (4) parameter estimation using an optimization method with appropriate level of complexity in kinetic model and optimization targets can find estimations that can be considered as effective material property values. The third part of this dissertation (Section 3) proposes a process for conducting parameter estimation for comprehensive pyrolysis models. The work describes the underlying concepts considered in the proposed process and gives discussions of its limitations. Additionally, example cases of parameter estimation exercise are shown to illustrate the application of the parameter estimation process. There are four materials considered in the example cases – thermoplastics (PMMA), corrugated cardboard, fiberglass reinforced polymer composites and plywood. In the last part (Section 4), the actual Guide, a standardized procedure for obtaining material parameters for input into a wide range of pyrolysis models is presented. This is a step-by-step process that provides a brief description of modeling approaches and assumptions; a typical mathematical formulation to identify model parameters in the equations; and methods of estimating the model parameters either by independent measurements or optimization in pair with the model. In the Guide, example cases are given to show how the process can be applied to different types of real-world materials. "

The estimation of the frequency and phase of a complex exponential in additive white Gaussian noise (AWGN) is a fundamental and well-studied problem in signal processing and communications. A variety of approaches to this problem, distinguished primarily by estimation accuracy, computational complexity, and processing latency, have been developed. One class of approaches is based on the Fast Fourier Transform (FFT) due to its connections with the maximum likelihood estimator (MLE) of frequency. This thesis compares several FFT-based approaches to the MLE in terms of their estimation accuracy and computational complexity. While FFT-based frequency estimation tends to be very accurate, the computational complexity of the FFT and the latency associated with performing these computations after the entire signal has been received can be prohibitive in some scenarios. Another class of approaches that addresses some of these shortcomings is based on linear regression of samples of the instantaneous phase of the observation. Linear- regression-based techniques have been shown to be very accurate at moderate to high signal to noise ratios and have the additional benefit of low computational complexity and low latency due to the fact that the processing can be performed as the samples arrive. These techniques, however, typically require the computation of four-quadrant arctangents, which must be approximated to retain low computational complexity. This thesis proposes a new frequency and phase estimator based on simple estimates of the zero-crossing times of the observation. An advantage of this approach is that it does not require arctangent calculations. Simulation results show that the zero-crossing frequency and phase estimator can provide high estimation accuracy, low computational complexity, and low processing latency, making it suitable for real-time applications. Accordingly, this thesis also presents a real-time implementation of the zero-crossing frequency and phase estimator in the context of a time-slotted round-trip carrier synchronization system for distributed beamforming. The experimental results show this approach can outperform a Phase Locked Loop (PLL) implementation of the same distributed beamforming system.

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