Optimal estimation of nonlinear and linear parameters in general linear models

Supratim Saha, University of Rhode Island


This dissertation primarily concerns maximum likelihood (ML) estimation of linear and nonlinear parameters in some class of general linear models (GLMs). We deal with problems which are directly expressible in GLM as well as the ones in which some manipulation is required to obtain a GLM. It is well known that the joint ML estimation of the linear and nonlinear parameters in a GLM leads to a multidimensional grid search. As closed form solutions do not exist, iterative techniques have been the only resort to avoid a multidimensional grid search. However iterative techniques are not guaranteed to converge. As a result our aim has been to develop non-iterative ML estimators. Fortunately there exists a theorem to obtain the global maximum of a multidimensional function, if the global maximum is unique. However the closed form solution requires an evaluation of a multidimensional integral. We use the concept of Monte Carlo importance sampling to evaluate this multidimensional integral with modest computational burden. ^ We apply the technique for obtaining ML estimates of frequencies of multiple sinusoids in additive white Gaussian noise (AWGN). It has been shown via simulations that the technique achieves the Cramer Rao Lower Bound (CRLB) upto as low SNRs as the direct ML method. Thereafter we applied the technique for the important practical problem of direction of arrival (DOA) estimation of multiple narrowband plane waves and compared our results to that of EM algorithm which is another implementation of the ML method. ^ We have shown that the technique is not only restricted to estimation problems. It can also be used for choice of parameters to optimize certain cost functions. The problem of linear sparse array design comes under this category. ^ After discussing examples of GLMs with one unknown parameter vector we extend the technique to estimation of parameters of GLMs having more than one parameterizing vector in the transformation matrix. ^ Finally we state the conditions to be satisfied by the GLMs in order to apply the proposed method efficiently. ^

Subject Area

Engineering, Electronics and Electrical

Recommended Citation

Supratim Saha, "Optimal estimation of nonlinear and linear parameters in general linear models" (2001). Dissertations and Master's Theses (Campus Access). Paper AAI3025579.