The need for increasingly accurate and fast Phasor Measurement Units (PMUs), especially for active distribution systems monitoring, requires to achieve challenging trade-offs between measurement uncertainty and responsiveness. This is particularly important for protection-oriented (i.e., P Class) PMUs. In order to improve estimation accuracy with no need to prolong the data record size and the related delays, this paper presents a Taylor Kalman Filter (TKF) enhanced with a preliminary stage able to whiten possible narrowband disturbances over short observation intervals. The use of dynamic estimators such as the TKF is motivated by the need to track possible sudden amplitude or phase changes of voltage or current AC waveforms, which are likely to occur in smart grids. However, while a basic TKF is very sensitive to disturbances different from white noise, the proposed whitening-technique is able to greatly improve the estimation accuracy of synchrophasor amplitude, phase, frequency and Rate of Change of Frequency (ROCOF) under the influence of harmonics and amplitude or phase step changes even over one-cycle observation intervals, with just a minor performance degradation in the other P Class testing conditions reported in the IEEE/IEC Standard 60255-118-1:2018.