This paper investigates the problems of partially scanned, and outlier contaminated tree point clouds for estimation of diameter at breast height (DBH). We study algebraic, geometric, as well as RANSAC, Hough Transform (HT), and robust regression methods for circle fitting and their potential to estimate DBH. We show that classical methods are highly sensitive to the outliers and noise, and unreliable when the data are incomplete to produce a circular arc. We develop an algorithm using a robust statistical approach for circle fitting that estimates precise, unbiased, and robust DBH. One experiment shows that when the ground truth DBH is 38.1cm, the estimates for the existing methods are 40.1cm, 41.6cm, 41.5cm and 42.4cm for an algebraic, a geometric, RANSAC and HT, respectively. Whereas our robust method was able to avoid the influence of outliers for fitting a robust circle and provides the most accurate DBH estimate of 38.3cm.