On Improved Accuracy Chirp Parameter Estimation Using The DFRFT With Application To SAR-Based Vibrometry
Satish Mandal, Balu Santhanam, Majeed M. Hayat · 2018 52nd Asilomar Conference on Signals, Systems, and Computers · 2018
The estimation of the frequency and chirp rate of a chirp signal in a noisy environment is a fundamental and well-studied problem in signal processing and communications. Its numerous applications include carrier recovery in a communication system, determination of the object position and speed in radar and sonar systems, and many other. Regardless of the application, poor estimation can lead to inaccurate results. In this paper, we attempt to quantify the accuracy of the discrete fractional Fourier transform (DFRFT) approach. We refine prior work to develop analytical expressions for the chirp rate and center frequency parameters. 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 (CRLB) and shown to asymptotically approach the bound. This refined DFRFT approach is then applied to synthetic aperture radar (SAR) 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.