Adaptive local polynomial periodogram for time-varying frequency estimation

The local polynomial periodogram enables one to obtain nonparametric estimates of the instantaneous frequency (IF) and its derivatives. The optimal choice of the window size based on asymptotic formulas for the variance and bias can resolve the bias-variance trade-off usual for nonparametric estimation. However the practical value of such optimal estimator is not large because the optimal window size depends on the unknown smoothness of the IF. The main goal of this paper is to develop an adaptive estimator with a time-varying and data-driven window size which is able to provide a quality close to that which can be achieved if the smoothness of the IF is known in advance. The developed algorithm uses only the formulas for the variance of the estimates. Simulation shows a good tracking ability of the adaptive algorithm.