MULTISCALE IDENTIFICATION OF REAL SINUSOIDS IN NOISE

We consider the problem of the identification of the real sinusoids in white Gaussian noise. Since the maximum likelihood function is ill-conditioned and possesses numerous local maxima, we propose a different cost function that preserves statistical efficiency. It allows to reparametrise the problem and to consider a whole set of different parametrizations that correspond to different time scales. To each such parametrization one associates in a trivial fashion an initial point. By change of scale, this point is transformed into an initial estimate of the parameters of interest. One then selects the parametrization with lowest initial cost. This procedure already attains the standard Cramer-Rao bound when the difficulty is to resolve two closely spaced sinusoids. Any further processing, such as fusion of the different scales or iterative optimization, is thus useless. We consider situations with SNRs below 10 dB and frequency separations not resolvable by the basic periodogram.