Asymmetric Gaussian chirplet model and parameter estimation for generalized echo representation

Gaussian Chirplet Model (GCM) is commonly used for signal analysis in many fields including ultrasound, radar, sonar, seismology, and biomedicine. The symmetric envelope of GCM is often inadequate in representing real echo envelopes which are more likely to be asymmetric. In our previous work we introduced the Asymmetric Gaussian Chirplet Model (AGCM) that generalizes the GCM. In this paper, an efficient successive parameter estimation algorithm is proposed utilizing echo envelope and instantaneous phase obtained via analytical signal representation. The initial parameters obtained via successive estimation are fine-tuned with a fast Gauss–Newton algorithm developed for the AGCM to achieve Maximum Likelihood Estimation (MLE) of model parameters. The performance of parameter estimation algorithm is formally verified employing Monte-Carlo simulations and Cramer–Rao Lower Bounds. Parameter estimation is shown to be minimum variance and unbiased for SNR levels 10 dB and higher. Furthermore, AGCM has been tested on real ultrasound echoes measured from planar targets. AGCM provides better echo fits than the GCM due to its more flexible envelope.