An Approximate Maximum Likelihood Estimator for Instantaneous Frequency Estimation of Multicomponent Nonstationary Signals

Nonstationary signals are widely observed in various applications. The instantaneous frequency (IF) is an important feature to capture the time-frequency (TF) characteristics of nonstationary signals, so the IF estimation problem has attracted increasing interests in the past three decades. In practice, the signal is usually composed of multiple components, and their IFs may intersect or are closely spaced with each other, which cannot be easily identified from the TF representation (TFR). In this case, the maximum likelihood estimator (MLE), which does not rely on the TFR, is commonly used. However, the MLE cannot deal with signals with time-varying amplitudes and suffers from a large computing load due to the multidimensional search within an indefinite parameter space. To address these problems, we propose an approximate MLE (AMLE). First, the IF is approximated by the Chebyshev interpolation polynomial and represented by several Chebyshev interpolation frequencies which are well bounded between zero and half of the sampling frequency, so that the multidimensional search can be performed within a bounded search space. Then, an approximate maximum likelihood function, which considers both the statistical characteristics of noise and the time-varying characteristics of amplitudes, is derived for amplitude-modulated and frequency-modulated signals. It is proven that the AMLE outperforms the MLE in the computing efficiency and estimation accuracy for nonstationary signals with more complicated IFs and amplitudes. Experimental hydroelectric rotor vibration and radar signals are tested, where the AMLE can accurately find those intersected and closely spaced IFs for their constituent components.