Maximum likelihood estimation in linear models with a Gaussian model matrix

Ami Wiesel*, Yonica C. Eldar, Amir Beck

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


We consider the problem of estimating an unknown deterministic parameter vector in a linear model with a Gaussian model matrix. We derive the maximum likelihood (ML) estimator for this problem and show that it can be found using a simple line-search over a unimodal function that can be efficiently evaluated. We then discuss the similarity between the ML, the total least squares (TLS), the regularized TLS, and the expected least squares estimators.

Original languageAmerican English
Pages (from-to)292-295
Number of pages4
JournalIEEE Signal Processing Letters
Issue number5
StatePublished - May 2006
Externally publishedYes

Bibliographical note

Funding Information:
Manuscript received September 7, 2005; revised December 5, 2005. This work was supported in part by the Israel Science Foundation and in part by the European Union 6th Framework Program, via the NEWCOM network of excellence. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Brian Sadler.


  • Errors in variables (EIV)
  • Linear models
  • Maximum likelihood (ML) estimation
  • Random model matrix
  • Total least squares (TLS)


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