Parameter Uncertainty in the Kalman--Bucy Filter

Allan, Andrew L.; Cohen, Samuel N.

Abstract

In standard treatments of stochastic filtering one first has to estimate the parameters of the model. Simply running the filter without considering the reliability of this estimate does not take into account this additional source of statistical uncertainty. We propose an approach to address this problem when working with the continuous time Kalman--Bucy filter, by making evaluations via a nonlinear expectation. We show how our approach may be reformulated as an optimal control problem, and proceed to analyze the corresponding value function. In particular we present a novel uniqueness result for the associated Hamilton--Jacobi--Bellman equation.

Citation

Allan, A. L., & Cohen, S. N. (2019). Parameter Uncertainty in the Kalman--Bucy Filter. SIAM Journal on Control and Optimization, 57(3), 1646-1671. https://doi.org/10.1137/18m1167693

• Journal Article Type: Article
• Acceptance Date: Apr 3, 2019
• Online Publication Date: May 16, 2019
• Publication Date: 2019
• Deposit Date: Jan 24, 2023
• Publicly Available Date: Jan 26, 2023
• Journal: SIAM Journal on Control and Optimization
• Print ISSN: 0363-0129
• Electronic ISSN: 1095-7138
• Publisher: Society for Industrial and Applied Mathematics
• Peer Reviewed: Peer Reviewed
• Volume: 57
• Issue: 3
• Pages: 1646-1671
• DOI: https://doi.org/10.1137/18m1167693