Parameter estimation of coupled polynomial phase and sinusoidal FM signals

This paper considers parameter estimation of a new coupled mixture of polynomial phase signal (PPS) and sinusoidal frequency modulated (FM) signal, recently introduced for industrial systems such as linear electromagnatic encoders. Compared with both conventional PPS-only and independent mixture models, the coupled mixture one captures the coupling between the sinusoidal FM frequency and the PPS parameters induced by structural system configurations. In this paper, we are particularly interested in estimating phase parameters of the coupled mixture signal at low signal-to-noise ratios (SNRs). Specifically, we propose a three-stage approach consisting of instantaneous frequency (IF) extraction (e.g., the short-time Fourier transform) and refining steps that reduce the bias introduced by the IF estimation and the mean-squared errors (MSEs) up to the Cramér-Rao bound (CRB). The proposed method is numerically compared with an existing phase-based approach as well as corresponding CRBs in terms of the empirical MSE. The results show that, compared with the phase-based approach, the proposed method can significantly lower the SNR threshold. The convergence of the measured MSEs from the initial stage to the latter refining stages is also numerically evaluated.