The analysis of the periodic components in noise and vibration signals measured on rotating equipment, like car power trains, must more and more be done under rapid changes of an axle, or reference RPM. Normal tracking filters (analog, or digital implementations) have limited resolution in such situations; wavelet methods, even when applied after resampling the data to be proportional to an axle RPM, must compromise between time and frequency resolution. The authors propose the application of nonstationary Kalman filters for the tracking of periodic components in such noise and vibration signals. These filters are designed to track accurately signals with a known structure among noise and signal components of different, ‘unknown’, structure. The tracking characteristics of these filters, i.e., the predicted signal amplitude vs. time values versus exact signal amplitude vs. time values, can be tailored to accurate tracking of harmonics buried in other signal components and noise, even at high rates of change of the reference RPM. A key to the successful construction is the precise knowledge of the structure of the signal to be tracked. For signals that vary with an axle RPM, an accurate estimate of the instantaneous RPM is essential, and procedures to this end will also be presented.