This paper extends a conventional, general framework for online adaptive estimation problems for systems governed by unknown nonlinear ordinary differential equations. The central feature of the theory introduced in this paper represents the unknown function as a member of a reproducing kernel Hilbert space (RKHS) and defines a distributed parameter system (DPS) that governs state estimates and estimates of the unknown function. This paper 1) derives sufficient conditions for the existence and stability of the infinite dimensional online estimation problem, 2) derives existence and stability of finite dimensional approximations of the infinite dimensional approximations, and 3) determines sufficient conditions for the convergence of finite dimensional approximations to the infinite dimensional online estimates. A new condition for persistency of excitation in a RKHS in terms of its evaluation functionals is introduced in the paper that enables proof of convergence of the finite dimensional approximations of the unknown function in the RKHS. This paper studies two particular choices of the RKHS, those that are generated by exponential functions and those that are generated by multiscale kernels defined from a multiresolution analysis.

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Modeling and simulation of vehicles can be improved by using actual road surface data acquired by Road Surface Measurement Systems. Due to inherent properties of the sensors used, the data acquired is often ridden with outliers. This work addresses the issue of identifying and removing outliers by extending the robust outlier rejection algorithm, Random Sampling and Consensus (RANSAC). Specifically, this work modifies the cost function utilized in RANSAC in such a way that it provides a smooth transition for the classification of points as inliers or outliers. The modified RANSAC algorithm is applied to neighborhoods of data points, which are defined as subsets of points that are close to each other based on a distance metric. Based on the outcome of the modified RANSAC algorithm in each neighborhood, a novel measure for determining the likelihood of a point being an outlier, defined in this work as its exogeny, is developed. The algorithm is tested on a simulated road surface dataset. In the future this novel algorithm will also be tested on real-world road surface datasets to evaluate its performance.

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