The estimation of the instantaneous amplitudes of sum of sinusoids with unknown frequencies and phases: The martingale approach

The martingale optimality principle is used to estimate the positive time-varying amplitudes that appear in the sum of sinusoids models. A closed form expression is obtained for the estimates of the time-varying amplitudes. These estimates are then embedded into the observation equation and nonlinear optimization methods are used to find the unknown frequencies. Given are examples and comparisons to existing methods.

► Estimation of the parameters of sum of sinusoids.
► The martingale optimality principle is used.
► The nonparametric problem has been transformed into parametric one.