O. Besson et P. Stoica, Nonlinear least-squares approach to frequency estimation and detection forsinusoidal signals with arbitrary envelope, DIGIT SIG P, 9(1), 1999, pp. 45-56
In this paper, we consider the problem of estimating the frequency of a sin
usoidal signal whose amplitude could be either constant or time-varying. We
present a nonlinear least-squares (NLS) approach when the envelope is time
-varying. It is shown that the NLS criterion can be explicitly minimized wi
th respect to the signal amplitude and envelope values, leaving out a perio
dogram-like function whose peak location gives the frequency estimate. This
result is a significant generalization of a similar result on the NLS freq
uency estimation for a sinusoidal signal with constant amplitude. A statist
ical analysis shows that the NLS frequency estimator is asymptotically stat
istically efficient. The problem of detecting amplitude time variations is
next addressed. A statistical test is formulated, based on the statistics o
f the difference between two frequency estimates. The test is computational
ly efficient and yields as a by-product consistent frequency estimates unde
r either hypothesis (i.e., constant or time-varying amplitude). Numerical e
xamples are included to show the performance both in terms of estimation an
d detection. (C) 1999 Academic Press.