Credible Uncertainty Quantification under Noise and System Model Mismatch

View PDF HTML (experimental)

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 like noise model mismatch (NMM) or system model misspecification (SMM). This letter addresses this problem by developing a unified, multi-metric 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. The effectiveness of the proposed method is further validated on a real-world UWB positioning dataset. This framework provides a practical tool for turning patterns of credibility indicators into actionable diagnoses of model deficiencies.

Comments: This manuscript has been submitted to IEEE Transactions on Instrumentation and Measurement

Subjects:

Signal Processing (eess.SP); Information Theory (cs.IT)

Cite as: arXiv:2509.03311 [eess.SP]

(or arXiv:2509.03311v5 [eess.SP] for this version)

https://doi.org/10.48550/arXiv.2509.03311

arXiv-issued DOI via DataCite

Submission history

From: Penggao Yan [view email] [v1] Wed, 3 Sep 2025 13:42:05 UTC (244 KB) [v2] Tue, 30 Sep 2025 08:26:49 UTC (1,110 KB) [v3] Mon, 17 Nov 2025 08:26:56 UTC (1,109 KB) [v4] Thu, 20 Nov 2025 11:58:06 UTC (1,109 KB) [v5] Wed, 1 Apr 2026 12:10:50 UTC (1,802 KB)