LUNA: Generalizable and Trustworthy State Estimation with Large Language Models

State estimation infers latent states from noisy and partial observations to provide both state estimate and uncertainty quantification (UQ). Classical Kalman-family filters (KFs) heavily depend upon the adopted system transition and observation dynamic models, suffering from low generalization. Pretraning-model based learnable state estimators aim for high generalization, yet with untrustworthy state estimates due to missed UQ. Particularly, offering UQ in LLM-based state estimators is hard due to missing UQ sources. To this end, in this paper, we propose an LLM-based UNcertainty-aware stAte estimation framework, namely \methodname, to offer trustworthy estimates with high generalization. Moreover, \methodname develops three stages to obtain the principled UQ as classic estimators from both observed systems and LLMs. Experiments on six synthetic and real-world benchmarks show that \methodname achieves the lowest RMSE on five benchmarks and the lowest NLL on four under in-domain evaluation, reducing RMSE by 71.8% on average relative to LLMFilter. Under cross-system evaluation, \methodname reduces RMSE by 41.3% on average relative to the best-performing external baseline. The code is available at an anonymous repositoryhttps://anonymous.4open.science/r/LUNA-V1AC.