Standard least-squares (LS) methods for pose estimation of objects are sensitive to outliers which can occur due to mismatches. Even a single mismatch can severely distort the estimated pose. This paper describes a least-median of squares (LMedS) approach to estimating pose using point matches. It is both robust (resistant to up to 50% outliers) and efficient (linear in the number of points). The basic algorithm is then extended to improve performance in the presence of two types of noise: 1) type I which perturbs all data values by small amounts (e.g., Gaussian) and 2) type II which can corrupt a few data values by large amounts.