Online Maximum-Likelihood Estimation of the Parameters of Partially Observed Diffusion Processes

Surace, Simone Carlo; Pfister, Jean-Pascal (2019). Online Maximum-Likelihood Estimation of the Parameters of Partially Observed Diffusion Processes. IEEE transactions on automatic control, 64(7), pp. 2814-2829. IEEE 10.1109/TAC.2018.2880404

Text Surace2019Online Max.pdf - Published Version Restricted to registered users only Available under License Publisher holds Copyright. Download (1MB) | Request a copy

We revisit the problem of estimating the parameters of a partially observed diffusion process, consisting of a hidden state process and an observed process, with a continuous time parameter. The estimation is to be done online, i.e., the parameter estimate should be updated recursively based on the observation filtration. We provide a theoretical analysis of the stochastic gradient ascent algorithm on the incomplete-data log-likelihood. The convergence of the algorithm is proved under suitable conditions regarding the ergodicity of the process consisting of state filter, and tangent filter. Additionally, our parameter estimation is shown numerically to have the potential of improving suboptimal filters, and can be applied even when the system is not identifiable due to parameter redundancies. Online parameter estimation is a challenging problem that is ubiquitous in fields such as robotics, neuroscience, or finance in order to design adaptive filters and optimal controllers for unknown or changing systems. Despite this, theoretical analysis of convergence is currently lacking for most of these algorithms. This paper sheds new light on the theory of convergence in continuous time.

Interest & Impact

Downloads

2 since deposited on 12 Dec 2019
0 in the past 12 months

Citations

5 Citations in Web of Science ®
6 Citations in Scopus

Search

in Google Scholar™

Services

Actions (login required)

Edit item

Actions (login required)

Edit item