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In particular, an alternative framework for terrain estimation based on set\u2010valued or set\u2010membership estimation is proposed, where the goal is to find set\u2010valued estimates (in the form of hyper\u2010rectangles or intervals) of the states and unknown terrain parameters. For this purpose, a state and model interval observer is designed for partially unknown nonlinear systems with bounded noise. By leveraging a combination of nonlinear bounding\/decomposition functions, affine abstractions, and a data\u2010driven function abstraction method (to overestimate the unknown dynamics model from noisy input\u2013output data), the proposed observer is capable of simultaneously estimating the states and learning the unknown dynamics. Further, a tractable sufficient condition is derived for guaranteeing the stability of the designed observer, i.e., such that the sequence of interval estimate widths are uniformly bounded. 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