Robust Parameter Estimation
An ℋ ∞ -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 ℋ ∞ 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 ℋ ∞ 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.