Performance analyses of the stochastic maximum likelihood and the subspace power estimation algorithms

Theoretical relations for the estimation mean and variance are derived for the stochastic maximum likelihood (SML) and subspace power estimation (SPE) algorithms relevant to the estimation of the power of sinusoidal sources in Gaussian white noise. These analyses use perturbation theoretic techniques that generate expressions for the estimation moments that are applicable to finite as well as asymptotic data regimes. Simulation results of these power estimation algorithms are given for relatively harsh parameter scenarios involving combinations of: sparse data; 1/2 Rayleigh source separations; large source dynamic range differences, approximately 60 dB; and weak source SNRs of -5 dB. The simulations show that both algorithms perform comparably well from the relatively sparse to the large data regimes.<>