An Explanation of the Expectation Maximization Algorithm

The expectation maximization (EM) algorithm computes maximum like-lihood estimates of unknown parameters in probabilistic models involvinglatent variables. More pragmatically speaking, the EM algorithm is an iter-ative method that alternates between computing a conditional expectationand solving a maximization problem, hence the name expectation maxi-mization. We will in this work derive the EM algorithm and show that itprovides a maximum likelihood estimate. The aim of the work is to showhow the EM algorithm can be used in the context of dynamic systems andwe will provide a worked example showing how the EM algorithm can beused to solve a simple system identification problem