Parameter uncertainty in the Kalman--Bucy filter

Journal article

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.

Authors: Allan, A; Cohen, S

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Society for Industrial and Applied Mathematics
• Journal: SIAM Journal on Control and Optimization
• Volume: 57
• Issue: 3
• Pages: 1646–1671
• Publication date: 2019-05-16
• Acceptance date: 2019-04-03
• DOI: 10.1137/18M1167693
• EISSN: 1095-7138
• ISSN: 0363-0129
• Keywords: nonlinear expectation; FFR; optimal control; Kalman--Bucy filter; parameter uncertainty; HJB equation