Quasi-maximum-likelihood estimator of polynomial phase signals

A novel approach for the parameter estimation of the polynomial phase signals (PPS) based on the short-time Fourier transform (STFT) is proposed. Estimator accuracy is significantly higher compared to the high-order ambiguity function (HAF), product HAF, and similar the non-linear transforms based strategies. The proposed approach is more efficient than the maximum likelihood (ML) estimator for the high-order PPS. One-dimensional search is performed over a set of window widths in the STFT, whereas in the case of ML estimators, it has been done over the space of phase parameters. The proposed estimator is implemented in several steps: the instantaneous frequency (IF) estimation using the STFT for various window widths; a polynomial regression from the IF estimate producing a coarse signal coefficients estimate; refinement procedure, producing fine coefficients estimates; determination of the optimal window width in the STFT. The proposed technique is extended for the non-parametric estimation with a 2D search over a set of polynomial orders and window widths. Good estimation results are achieved up to the SNR threshold of about SNR=0 dB for the parametric case and SNR=2 dB for the non-parametric case.