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Time-varying systems in turn pose additional hurdles as such models must be continuously updated to accommodate changes in their underlying behavior. In this paper, we introduce a novel grid-based filter designed to inherently deal with the continuous learning problem. Specifically, Bayesian-grounded procedures are employed to both recursively predict observations and incrementally build a suitable non-parametric, probabilistic model of the indirectly observed phenomenon. Moreover, we also present a one-shot learning, memory-based implementation of the proposed filter, a shallow weightless neural network which is able to efficiently store and retrieve associative inputoutput pairs. 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