On the total least median of squares adjustment for the pattern recognition in point clouds

Abstract

Robust estimation techniques are an important tool in the adjustment of geodetic data, as even a single undetected gross error can render parameters estimates meaningless. In this contribution, the total least median of squares (TLMS) adjustment is investigated. Unlike typical least median of squares (LMS) criterion, which operates on observation errors, the TLMS strategy focuses on equation errors, which is expressed as a linear combination of the observation vector and the columns of the design matrix. TLMS is numerically implemented by the combinatorial strategy, and can speed up by the Monte Carlo acceleration for any large data set. Finally, we demonstrate that the proposed method resists multiple outliers for the pattern recognition in point clouds, even in the presence of cluster and collinear outliers, and the comparison to other methods and the statistical assessment are also presented.