ABSTRACT

An https://www.w3.org/1998/Math/MathML"> ℋ ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429352850/bcdb6ac0-dd9f-41e6-a56b-f915f2a28a62/content/equ_993.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> -norm bounded LS (NBLS) algorithm for robust parameter estimation of linear-regression models in a deterministic framework is proposed in this chapter by extending some results of https://www.w3.org/1998/Math/MathML"> ℋ ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429352850/bcdb6ac0-dd9f-41e6-a56b-f915f2a28a62/content/equ_993.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> filtering theory. By definition, the proposed algorithm guarantees estimates with the smallest possible estimation error energy over all possible modeling errors of fixed energy, and therefore is robust. As a result of the underlying https://www.w3.org/1998/Math/MathML"> ℋ ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429352850/bcdb6ac0-dd9f-41e6-a56b-f915f2a28a62/content/equ_993.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> performance criterion, the NBLS estimator is conservative. This leads to active and accelerated parameter estimation. In general, variance estimates may be misleading when computed over a finite amount of data. In such cases, non-asymptotic deterministic formulae such as those given in this chapter provide valid bounds. These formulae are also useful for the exercise of error quantification to be treated in Chapter 5.