Constrained expectation maximisation algorithm for estimating ARMA models in state space representation

EURASIP journal on advances in signal processing

article

Galka, Andreas¹  Moontaha, Sidratul²  Siniatchkin, Michael² 

[1]Bundeswehr Technical Centre for Ships and Naval Weapons, Naval Technology and Research (WTD 71)

[2]Institute of Medical Psychology and Medical Sociology, University of Kiel

[3]Digital Health Center, Hasso Plattner Institute, Potsdam University

[4]Clinic for Pediatric and Adolescent Psychiatry and Psychotherapy

关键词: Kalman filtering;    State space modelling;    Expectation maximisation algorithm;   

DOI  :  10.1186/s13634-020-00678-3

来源: SpringerOpen

【 摘 要 】

This paper discusses the fitting of linear state space models to given multivariate time series in the presence of constraints imposed on the four main parameter matrices of these models. Constraints arise partly from the assumption that the models have a block-diagonal structure, with each block corresponding to an ARMA process, that allows the reconstruction of independent source components from linear mixtures, and partly from the need to keep models identifiable. The first stage of parameter fitting is performed by the expectation maximisation (EM) algorithm. Due to the identifiability constraint, a subset of the diagonal elements of the dynamical noise covariance matrix needs to be constrained to fixed values (usually unity). For this kind of constraints, so far, no closed-form update rules were available. We present new update rules for this situation, both for updating the dynamical noise covariance matrix directly and for updating a matrix square-root of this matrix. The practical applicability of the proposed algorithm is demonstrated by a low-dimensional simulation example. The behaviour of the EM algorithm, as observed in this example, illustrates the well-known fact that in practical applications, the EM algorithm should be combined with a different algorithm for numerical optimisation, such as a quasi-Newton algorithm.

【 授权许可】

CC BY