Quasi-maximum likelihood-based estimator of the hyperbolic frequency modulated signals

The quasi-maximum likelihood (QML) algorithm has been extended to estimate the phase parameters and the instantaneous frequency (IF) of the hyperbolic frequency modulated (HFM) signals. The Nelder-Mead simplex algorithm (NMSA) is adopted for a fine estimation. The obtained accuracy is excellent with the estimates achieving the Cramer-Rao lower bound (CRLB) above the signal-to-noise (SNR) threshold of 0 dB. The proposed technique is capable of functioning with signals that are sampled below the requirements of the sampling theorem, which is particularly important for HFM signals. Additionally, there are no limitations for signals with monotonic IF and/or group delay (GD) functions.