TY  - JOUR
A1  - Galka, Andreas
A1  - Moontaha, Sidratul
A1  - Siniatchkin, Michael
T1  - Constrained expectation maximisation algorithm for estimating ARMA models in state space representation
T2  - EURASIP journal on advances in signal processing
N2  - 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.
KW  - Kalman filtering
KW  - state space modelling
KW  - expectation maximisation algorithm
Y1  - 2020
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/59906
SN  - 1687-6180
VL  - 2020
IS  - 1
PB  - Springer
CY  - Heidelberg
ER  -