The estimation accuracy of the instantaneous angular speed ( IAS) signal is easily affected by the encoder’ s error, which affects its fault detection results. Because of such problems, a local polynomial differential estimation method was proposed to estimate the IAS signal. First, the local polynomial differential was used to suppress the sawtooth noise generated by the encoder subdivision errors and the signal discontinuity caused by the estimation errors, so high-precision acquisition of the IAS signal was achieved, and finally, the accurately estimated IAS signal was used to extract the sun gear fault characteristics by local synchronous fitting technique. Through experiments and simulations, it is shown that the local polynomial differential estimation proposed in this paper can effectively suppress the IAS signal noise caused by encoder errors, improve the signal to noise ratio of the IAS signal, and combine local synchronous fitting to effectively extract the features of the sun gear tooth surface spalling fault.