Estimating the parameters of sinusoids and decaying sinusoids in noise

摘要

Picture a low earth orbit satellite hurtling around the earth in an 800 km orbit. At this altitude, the satellite travels about 7.5 km every second, and any signals between it and an earth terminal experience significant Doppler shifts. These frequency offsets must be estimated and removed at the earth terminal to enable successful communications with the satellite. As in this example, the estimation of the parameters of a sinusoid plays a fundamental role in a variety of applications ranging from seismology to radar and biological signals. Therefore, this problem has received, and continues to receive, significant attention in the literature. In power delivery systems, the estimation of the supply frequency is required for the monitoring of the system quality and the detection of faults [1], [2]. In nuclear magnetic resonance spectroscopy (NMRS), on the other hand, the signal is modelled as a sum of decaying complex exponentials whose frequencies and decay factors must be estimated [3].