For SLAM problem [3], building an accurate map leads to an accurate localization. We propose a guaranteed solution using interval methods for nonlinear observation model to work with holnomic robots with no rotation, where the map is proven to converge. Our approach does not require any assumptions with regard to the linearity of the observation model, nor its noise except that it needs to be bounded. We use interval methods to evaluate the domain of a function given the codomain and the function itself. This approach encapsulates all information in the current estimate, therefore, it is not necessary to keep track of all past observations. We will prove the convergence of the approach to the correct map as the robot moves in the environment over time, given that at each time step, at least one old landmark is observed, and the data association problem is assumed a solved problem.
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