This paper is dedicated to Dr. Roberto Temple. The topic, outliers in system identification, was initially started with a discussion with Roberto in the early 2000. The first part of the paper summaries the approach, optimization with few violated constrains for linear bounded error parameter estimation, that was appeared in IEEE Trans. on Automatic Control. The topic was revisited by a new approach, system identification in the presence of outliers and radome noise by compressed sensing, is summarized in the second part of the paper which was appeared in Automatica.