# Parameter estimation of mixture of damped sinusoids

What are the most known methods (algorithms) for the parameter estimation of the superimposed (mixture) of damped (complex) sinusoids?

The noiseless signal model (with $P$ sinusoids) is as follows:

$$x(t) = \sum_{i=1}^P A_i e^{s_it}$$

• $A_i=a_i e^{j\phi_i}$ is a complex amplitude.
• $s_i=\alpha_i + j \omega_i$, where $\alpha_i <0$: damping factor and $\omega_i$: angular frequency.

The most known methods I know are used for such parameter estimation are Pisarenko, Prony, Matrix Pencil, ESPRIT, MUSIC. Nonetheless, I'm not sure if all can be used for this model or if some are only used for particular cases (for e.g. undamped sinusoids) or if there are any specific cases or conditions where we can use one but not the other.

Are there any good references summarizing the different estimation algorithms for this model, and giving the main differences, advantages and disadvantages?