Applications of interval methods to parameter set estimation from bounded-error data
Parameter estimation plays an important role in numerous engineering areas such as function estimation, system identification for the design of control systems, pattern recognition systems, equalization of communication channels, and artificial neural networks. In each of these applications, parametric models are used to either emulate an unknown system, perform a specific task within the system, or mitigate anomalies caused by uncertainty. Conventional estimation methods are often used to compute the parameters so that the mean-squared error between the model output and the desired response is minimized. A robust approach to the estimation problem is possible when the error between the parametric model and the desired response is bounded. This approach, called parameter set estimation, seeks to find the feasible set of parameters consistent with all observed data and error bounds. Often, the structure of the feasible set is too complicated for an exact description. Therefore, set-membership methods based on simple structures, such as ellipsoids and axis-aligned orthotopes (boxes), are used to bound the feasible set. This dissertation presents a novel recursive method for computing axis-aligned orthotopic bounds on the set of feasible parameters for bounded-error problems using rigorous interval methods. Algorithms for both linear and nonlinear estimation problems are presented and the benefits of the approach are demonstrated via computer simulated engineering applications. An additional by-product of this research is a constructive algorithm for generating radial basis function neural networks that meet a priori error bounds on the training data.
Richard William Kelnhofer,
"Applications of interval methods to parameter set estimation from bounded-error data"
(January 1, 1997).
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