Instantaneous frequency estimation based on the robust spectrogram

The robust M-periodogram is defined for the analysis of signals with heavy-tailed distribution noise. In the form of a robust spectrogram (RSPEC) it can be used for the analysis of nonstationary signals. A RSPEC-based instantaneous frequency (IF) estimator, with a time-varying window length, is presented. The optimal choice of the window length can resolve the bias-variance tradeoff in the RSPEC-based IF estimation. However, it depends on the unknown nonlinearity of the IF. The algorithm used is able to provide accuracy close to the one that could be achieved if the IF to be estimated were known in advance. Simulations show good accuracy ability of the adaptive algorithm and good robustness property with respect to rare high-magnitude noise values.