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.