Uncertainty-Aware Kalman Filtering via Intrusive Polynomial Chaos for Disturbance Estimation

Purnawan, Heri (Department of Electrical Engineering, Universitas Islam Lamongan, Lamongan, Indonesia)
Wakhid, Abdur Rohman (Department of Electrical Engineering, Universitas Islam Lamongan, Lamongan, Indonesia)
Fiddina, Qori Afiata (Department of Information Technology, Telkom University, Surabaya, Indonesia)
Iza, Belgis Ainatul
Sanusi, Tri Muhamad (Department of Electrical Engineering, Universitas Islam Lamongan, Lamongan, Indonesia)
Cahyaningtias, Sari (School of Mathematical and Statistical Sciences, Arizona State University, Arizona, United States)

Zero : Jurnal Sains, Matematika, dan Terapan
Vol 9, No 3 (2025): Zero: Jurnal Sains Matematika dan Terapan

Robust control under parameter uncertainty requires reliable disturbance estimation. This paper proposes an uncertainty-aware method, namely Intrusive Polynomial Chaos-based Kalman Filter (IPC-KF) for systems with probabilistic parameters and measurement noise. The method is evaluated through two numerical case studies and compared with a nominal Kalman filter (KF). Results from 100 realizations, assessed using RMSE and mean variance, show that the IPC-KF achieves estimation accuracy comparable to the nominal KF. For the spring-mass-damper system, the RMSE difference is below , with both methods yielding the same mean variance of . For the F-16 aircraft model, identical RMSE values and a mean variance of are obtained. While IPC-KF captures parameter uncertainty via polynomial chaos, augmenting the state with disturbances does not necessarily improve estimation accuracy. Further studies are needed to assess uncertainty bounds and robustness.