On Improved Accuracy Chirp Parameter Estimation using the DFRFT with Application to SAR-based Vibrometry

The Discrete Fractional Fourier Transform (DFRFT) has in recent years, become a useful tool for multicomponent chirp signal analysis. Chirp signals are transformed into spectral peaks in the chirp rate versus center frequency representation, whose coordinates are related to the underlying chirp parameters via a computed empirical peak to parameter mapping incorporated into the Santhanam-Peacock algorithm. In this thesis, we attempt to quantify the accuracy of the DFRFT approach by first studying the discretization error sources that arise from the transitioning of the continuous FRFT to DFRFT. Then, we refine prior work by Ishwor Bhatta to develop analytical expressions for the chirp rate and center frequency parameters instead of the empirical mapping approach. We further study the extensions of this refined DFRFT approach using zero padding, spectral peak interpolation, and chirp-z-transform based zooming. The performance of the refined estimators is compared versus the Cramer-Rao lower bound and shown to asymptotically approach the bound. This refined DFRFT approach is then applied to Synthetic Aperture Radar Vibrometry data from several vibrating targets and the estimated acceleration information and vibration frequencies are shown to be very close to the corresponding ground-truth accelerometer measurements