Self-paced learning for instantaneous frequencies estimation in heavy noise environments

Abstract

Estimating instantaneous frequencies (IFs) overlap in both time and frequency domains is desired in time-frequency (TF) analysis. In this paper, a simple method, called IFs estimation based on self-paced learning (IFsESPL) algorithm, is proposed to separate overlapped components of multi-component (MC) non-stationary signals in TF plane, and simultaneously estimate IFs. The proposed IFsESPL algorithm first detects TF ridge points from a TF representation, and then the TF ridge points are used to construct training dataset of self-paced learning (SPL). In the following, minimization of particular objective function of SPL yields iteratively selecting and classifying the samples in training dataset into clusters. Each cluster is corresponding to one component of a MC signal and hence component separation is achieved. In addition, together with the partitioning of the training dataset, the IF of each component is estimated by a predefined parameterized model. IFsESPL incorporates SPL regime into TF ridge points regrouping to sequentially include ridge points into IFs estimation from easy to hard, which not only can separate crossed components in TF plane, but also can prevent interference of noise and outliers. The effectiveness of the proposed method is verified through analytical results and numerical examples.