This paper presents the parameter estimation problem for single-phase induction motors (SPIMs) using start-up transient voltage and current measurements available at the motor terminals. This non-instrusive estimation approach relies on a dynamic state-space representation for modeling the SPIM transients, which is augmented by the parameters of interest assumed to be constant quantities during start-up. Extended Kaiman Filtering can be then adopted to estimate the parameter states from the input voltage and output current measurements, by linearizing the state equations of the augmented system. The proposed method has been tested on a realistic SPIM model via numerical simulations. The results demonstrate its effectiveness in estimating those parameters that are more significant for SPIM transient analysis.