The Epistemic Support-Point Filter (ESPF): A Bounded Possibilistic Framework for Ordinal State Estimation

Abstract: Traditional state estimation methods rely on probabilistic assumptions that often collapse epistemic uncertainty into scalar beliefs, risking overconfidence in sparse or adversarial sensing environments. We introduce the Epistemic Support-Point Filter (ESPF), a novel non-Bayesian filtering framework fully grounded in possibility theory and epistemic humility. ESPF redefines the evolution of belief over state space using compatibility-weighted support updates, surprisalaware pruning, and adaptive dispersion via sparse grid quadrature. Unlike conventional filters, ESPF does not seek a posterior distribution, but rather maintains a structured region of plausibility or non-rejection, updated using ordinal logic rather than integration. For multi-model inference, we employ the Choquet integral to fuse competing hypotheses based on a dynamic epistemic capacity function, generalizing classical winner-take-all strategies. The result is an inference engine capable of dynamically contracting or expanding belief support in direct response to information structure, without requiring prior statistical calibration. This work presents a foundational shift in how inference, evidence, and ignorance are reconciled, supporting robust estimation where priors are unavailable, misleading, or epistemically unjustified.