Distributed multivariate regression with unknown noise covariance in the presence of outliers: an MDL approach

Abstract

We consider the problem of estimating the coefficients in a multivariable linear model by means of a wireless sensor network which may be affected by anomalous measurements. The noise covariance matrices at the different sensors are assumed unknown. Treating outlying samples, and their support, as additional nuisance parameters, the Maximum Likelihood estimate is investigated, with the number of outliers being estimated according to the Minimum Description Length principle. A distributed implementation based on iterative consensus techniques is then proposed, and it is shown effective for managing outliers in the data.