A novel sensor placement criterion is proposed for structural health monitoring after five influencing criteria are critically reviewed. The objective of the proposed criterion is to achieve best identification of modal frequencies and mode shapes through almost unbiased estimation of modal coordinates. The proposed criterion derived by the Representative Least Squares method depends on both the characteristics and the actual loading situations of a structure. It selects sensor positions with the best subspace approximation of the vibration responses from the linear space spanned by the mode shapes. Furthermore, the connection between the Effective Independence and the approximate Representative Least Squares estimator is obtained through matrix perturbation analysis. It is found that the Effective Independence is a step-by-step approximation to that of the Representative Least Squares criterion.