Brief Robust maximum likelihood estimation in the linear model

Authors:
Giuseppe Calafiore;Laurent El Ghaoui
Affiliations:
Dipartimento di Automatica e Informatica, Politecnico di Torino, Cso Duca degli Abruzzi 24, 10129 Torino, Italy;Electrical Engineering and Computer Sciences Department, University of California at Berkeley, USA
Venue:
Automatica (Journal of IFAC)
Year:
2001

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Abstract

This paper addresses the problem of maximum likelihood parameter estimation in linear models affected by Gaussian noise, whose mean and covariance matrix are uncertain. The proposed estimate maximizes a lower bound on the worst-case (with respect to the uncertainty) likelihood of the measured sample, and is computed solving a semidefinite optimization problem (SDP). The problem of linear robust estimation is also studied in the paper, and the statistical and optimality properties of the resulting linear estimator are discussed.