Distributionally Robust Kalman Filtering With Volatility Uncertainty

• 成果类型: Article
• 署名作者: Han, Bingyan
• 署名单位: Hong Kong University of Science & Technology (Guangzhou)
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3522192
• 发表日期: 2025
• 页码: 4000-4007
• 关键词: Kalman filters; Covariance matrices; Filtering; noise; uncertainty; Symmetric matrices; vectors; Target tracking; State-space methods; optimization; Bicausal optimal transport (BCOT); minimax optimization; robust Kalman filtering

摘要

This work presents a distributionally robust Kalman filter to address uncertainties in noise covariance matrices and predicted covariance estimates. We adopt a distributionally robust formulation using bicausal optimal transport to characterize a set of plausible alternative models. The optimization problem is transformed into a convex nonlinear semi-definite programming problem and solved using the trust-region interior point method with the aid of $LDL<^>\top$ decomposition. The empirical outperformance is demonstrated through target tracking and pairs trading.