Credible uncertainty quantification under noise and system model mismatch

Abstract

State estimators often provide self-assessed uncertainty metrics, such as covariance matrices, whose credibility is critical for downstream tasks. However, these self-assessments can be misleading due to underlying modeling violations such as noise model mismatch (NMM) or system model misspecification (SMM). This work addresses this problem by developing a unified, multimetric framework that integrates noncredibility index (NCI), negative log-likelihood (NLL), and energy score (ES) metrics, featuring an empirical location test (ELT) to detect system model bias and a directional probing technique that uses the metrics’ asymmetric sensitivities to distinguish NMM from SMM. Monte Carlo simulations reveal that the proposed method achieves excellent diagnosis accuracy (80%–100%) and significantly outperforms single-metric diagnosis methods. In addition, the parameter sensitivity and the scalability against the state dimension are analyzed using the same simulated dataset. The effectiveness of the proposed method is further validated on a real-world ultrawideband (UWB) positioning dataset. Finally, the computational complexity of the proposed framework is discussed, providing insights for practical implementation. This framework provides a useful tool for turning patterns of credibility indicators into actionable diagnoses of model deficiencies.