A numerically efficient implementation of the expectation maximization algorithm for state space models

Wolfgang Mader*, Yannick Linke, Malenka Mader, Linda Sommerlade, Jens Timmer, Bjoern Schelter

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)
5 Downloads (Pure)


Empirical time series are subject to observational noise. Naive approaches that estimate parameters in stochastic models for such time series are likely to fail due to the error-in-variables challenge. State space models (SSM) explicitly include observational noise. Applying the expectation maximization (EM) algorithm together with the Kalman filter constitute a robust iterative procedure to estimate model parameters in the SSM as well as an approach to denoise the signal. The EM algorithm provides maximum likelihood parameter estimates at convergence. The drawback of this approach is its high computational demand. Here, we present an optimized implementation and demonstrate its superior performance to naive algorithms or implementations. (C) 2014 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)222-232
Number of pages11
JournalApplied Mathematics and Computation
Early online date3 Jun 2014
Publication statusPublished - 15 Aug 2014


  • Kalman filter
  • expectation-maximization algorithm
  • parameter estimation
  • state-space model
  • maximum-likelihood
  • systems

Cite this