State--space models provide a flexible framework for analyzing dynamical systems, yet they often rely on Gaussian assumptions that fail to capture heavy-tailed or outlier-prone measurement noise. We propose a robust estimation scheme for linear state--space models subject to compound-Gaussian noise, as encountered for instance in radio interferometry affected by radio-frequency interference (RFI). The method relies on a Stochastic Approximation Expectation--Maximization (SAEM) algorithm in which the standard E-step is replaced by Monte Carlo sampling of the latent states and noise texture through closed-form Gibbs updates, enabling tractable inference despite the heavy-tailed likelihood. Numerical experiments show that the proposed method significantly improves reconstruction fidelity and robustness to RFI, outperforming a Gaussian EM algorithm and even an oracle RTS smoother. These results highlight the benefits of heavy-tailed state--space modeling and SAEM-based inference in interference-dominated imaging scenarios.

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