In a power system, the conventional method for computing participation factors of generators associated with an oscillatory mode involves using linearized system models and element-by-element products of corresponding right and left eigenvectors. Unlike traditional modal analysis methods, this paper proposes a new approach for estimating participation factors from measurements on generator responses under a range of disturbances. This method computes extended participation factors that coincide with accurate model-based participation factors, provided that the measured responses satisfy an ideally symmetric condition. This paper further relaxes the symmetric condition by identifying a coordinate transformation from the original measurement space to an optimal new space for the best symmetry. Consequently, the optimal estimation of participation factors solely from measurements is achieved, and the factors influencing accuracy are discussed. The proposed approach is comprehensively demonstrated using a two-area system and then tested on an NPCC 48-machine power system.