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We introduce a framework for inference in general state-space hidden Markovmodels (HMMs) under likelihood misspecification. In particular, we leverage theloss-theoretic perspective of Generalized Bayesian Inference (GBI) to definegeneralised filtering recursions in HMMs, that can tackle the problem ofinference under model misspecification. In doing so, we arrive at principledprocedures for robust inference against observation contamination by utilisingthe $\beta$-divergence. Operationalising the proposed framework is madepossible via sequential Monte Carlo methods (SMC), where most standard particlemethods, and their associated convergence results, are readily adapted to thenew setting. We apply our approach to object tracking and Gaussian processregression problems, and observe improved performance over both standardfiltering algorithms and other robust filters.

Generalized Bayesian Filtering via Sequential Monte Carlo