Direct estimation of multiple time-varying frequencies of non-stationary signals

Abstract

In this paper, we propose a generalized framework for real-time tracking of multiple time-varying sinusoidal frequencies of a non-stationary signal. The non-stationary signal is modeled as a time-varying autoregressive (TVAR) process. A non-linear state-space model is formed to truly represent the TVAR process, considering the frequencies as state variables. We have defined the observation and its Jacobian by the modified roots of a polynomial formed by the state variables. Numerical derivatives have been substituted by the analytic form of the Jacobian matrix for improved numerical accuracy. A constrained Kalman filter is then applied for real-time tracking of the frequencies. We have compared the statistical performance of the proposed method with four other established methods using Monte-Carlo simulations. The proposed method is found to have superior error performance under different conditions of chirp-rate, resolution, noise variance, and abrupt changes in frequency. Additionally, we have taken the bat echolocation signal, gravitational waves of a binary black hole merger, and supply frequency of a three-phase squirrel cage induction motor as practical examples to demonstrate the applicability and efficacy of the proposed method in real-world scenarios.