Estimation et Reconstruction des Signaux Courts à Multicomposantes Modulées à la fois en Amplitude et en Fréquence
Résumé
In this paper, we consider nonstationary signals with nonlinear amplitude and frequency modulation on short time-windows. Motivated by published works [3, 4], where we obtain high performances for monocomponent signals, we propose to extend the approach to multicomponent signals. Both the instantaneous amplitude and frequency were modeled by polynomial functions. The maximization of the likelihood function was achieved using a stochastic optimization technique: the Simulated Annealing. We compare two different strategies. The first one, we simultaneously estimate all model parameters. This is a highly computational strategy. The second one consists in iteratively recontructing the signal component by component. At each iteration, the parameters of only one component are estimated. Monte Carlo simulations are presented and compared to the appropriate Cramer-Rao Bounds. It proves the efficiency of the algorithm. Moreover it underscores the performance to estimate crossing frequency trajectories which is a great challenge related to the low sample number.
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