*Article* **Unbiased Least-Squares Modelling**

#### **Marta Gatto and Fabio Marcuzzi \***

Department of Mathematics, "Tullio Levi Civita", University of Padova, Via Trieste 63, 35131 Padova, Italy; mgatto@math.unipd.it

**\*** Correspondence: marcuzzi@math.unipd.it

Received: 25 May 2020; Accepted: 11 June 2020; Published: 16 June 2020

**Abstract:** In this paper we analyze the bias in a general linear least-squares parameter estimation problem, when it is caused by deterministic variables that have not been included in the model. We propose a method to substantially reduce this bias, under the hypothesis that some a-priori information on the magnitude of the modelled and unmodelled components of the model is known. We call this method Unbiased Least-Squares (ULS) parameter estimation and present here its essential properties and some numerical results on an applied example.

**Keywords:** parameter estimation; physical modelling; oblique decomposition; least-squares
