Paper Info
Title
Online Maximum-Likelihood Estimation of the Parameters of Partially Observed Diffusion Processes
Abstract
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.
Year
DOI
Venue
2019
10.1109/TAC.2018.2880404
IEEE Transactions on Automatic Control
Keywords
DocType
Volume
Convergence,Parameter estimation,Diffusion processes,Standards,Signal processing algorithms,Maximum likelihood estimation
Journal
64
Issue
ISSN
Citations 
7
0018-9286
1
PageRank 
References 
Authors
0.40
5
2
Name
Order
Citations
PageRank
Simone Carlo Surace110.40
Jean-pascal Pfister215013.64