Outlier-Robust Variational State Estimation of Model-free Process

We develop robust variational state estimation (RoVaS), a data-driven method for estimating the state of a model-free dynamical process from noisy measurements with outliers. We assume no knowledge of the dynamics of the process; hence, we do not have access to the state-transition model. The setting is challenging because outlier detection and dynamics learning are coupled: identifying corrupted measurements requires a model of the dynamics, while learning the dynamics requires knowing which measurements to trust. RoVaS introduces latent corruption indicators alongside the states and infers them jointly under a variational framework. A corruption gate, parameterized to saturate as the measurement magnitude grows, attenuates suspected outliers before they reach the state posterior; this yields a provable outlier-robustness guarantee at inference. On stochastic Lorenz-63 systems and real human motion-capture data, RoVaS degrades gracefully under corruption rates up to 25% and is competitive with a state-transition-model-informed robust filter, despite having no access to the state-transition model.