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Maximum Likelihood Estimation of Gaussian Models with Missing Data - Eight Equivalent Formulations and Applications to System Identification

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  • Visitor Seminars
When Nov 03, 2011
from 02:00 PM to 03:00 PM
Where Tesla Room 53-125, Engineering IV Building
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Dr. Anders Hansson
Linköping University, Sweden



In this talk we derive the maximum likelihood problem for missing data from a Gaussian model. We present in total eight different equivalent formulations of the resulting optimization problem, four out of which are nonlinear least squares formulations. Among these formulations are also formulations based on the expectation-maximization algorithm. Expressions for the derivatives needed in order to solve the optimization problem are presented. We also present numerical comparisons for two of the formulations for an ARMAX model. We will discuss input models for missing input data and make comparisons with the case when the missing inputs are modeled as parameters. Finally, we will discuss the reason for bias in popular suboptimal schemes.


Anders Hansson was born in Trelleborg, Sweden, in 1964. He received the Master of Science degree in Electrical Engineering in 1989, the Degree of Licentiate of Engineering in Automatic Control in 1991, and the PhD in Automatic Control in 1995, all from Lund University, Lund, Sweden. In 1989, 1992, and 1995 he spent three months at Landis & Gyr AG, Switzerland. During the academic year 1992-1993 he spent six months at Imperial College in London, UK. From 1989 until 1995 he was a Teaching Assistant at the Department of Automatic Control, Lund Institute of Technology. From 1995 until 1997 he was a postdoctoral student, and from 1997 until 1998 a research associate at the Information Systems Lab, Department of Electrical Engineering, Stanford University. In 1998 he was appointed assistant professor and in 2000 associate professor (docent) at S3-Automatic Control, Royal Institute of Technology, Stockholm, Sweden. In 2001 he was appointed associate professor at the Division of Automatic Control, Linköping University. From 2006 he is full professor at the same department.

Anders Hansson is a senior member of the IEEE. During 2006-2007 he was an associate editor of the IEEE Transactions on Automatic Control. He is also a member of the EUCA Council from 2009, and of Technical Committee on Systems with Uncertainty of the IEEE Control Systems Society from 2009.

His research interests are within the fields of optimal control, stochastic control, linear systems, signal processing, fuzzy logic, applications of control, image processing, and telecommunications. He got the SAAB-Scania Research Award in 1992.

For more information contact Prof. Lieven Vandenberghe (


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