Stability of optimal filter higher-order derivatives

Conference item

In many scenarios, a state-space model depends on a parameter which needs to be inferred from data. Using stochastic gradient search and the optimal filter (first-order) derivative, the parameter can be estimated online. To analyze the asymptotic behavior of online methods for parameter estimation in non-linear state-space models, it is necessary to establish results on the existence and stability of the optimal filter higher-order derivatives. The existence and stability properties of these derivatives are studied here. We show that the optimal filter higher-order derivatives exist and forget initial conditions exponentially fast. We also show that the optimal filter higher-order derivatives are geometrically ergodic. The obtained results hold under (relatively) mild conditions and apply to state-space models met in practice.

Authors: Tadić, VZB; Doucet, A

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: IEEE
• Host title: 2019 IEEE 58th Conference on Decision and Control (CDC)
• Pages: 1644-1649
• Publication date: 2020-03-12
• Acceptance date: 2019-09-12
• Event title: 2019 IEEE 58th Conference on Decision and Control (CDC)
• Event location: Nice, France
• Event website: https://cdc2019.ieeecss.org/
• Event start date: 2019-12-11
• Event end date: 2019-12-13
• DOI: 10.1109/CDC40024.2019.9029771
• EISSN: 2576-2370
• ISSN: 0743-1546
• EISBN: 9781728113982
• ISBN: 9781728113999
• Language: English
• Keywords: FFR; optimal filter higher-order derivatives; state-space models; log-likelihood; geometric ergodicity; optimal filter; forgetting of initial conditions