Maximum likelihood parameter estimation of short-time multicomponent signals with nonlinear AM/FM modulation

Parameter estimation for closely spaced or crossing frequency trajectories is a difficult signal processing problem, especially in the presence of both nonlinear amplitude and frequency modulations. In this paper, polynomial models are assumed for the instantaneous frequencies and amplitudes (IF/IA). We suggest two different strategies to process multicomponent signals. In the first one, which is optimal, all model parameters are simultaneously estimated using a maximum likelihood procedure (ML), maximized via a stochastic technique called simulated annealing (SA). In the second strategy, which is suboptimal, the signal is iteratively reconstructed component by component. At each iteration, the IF and IA of one component are estimated using the ML procedure and the SA technique. To evaluate the accuracy of the proposed strategies, Monte Carlo simulations are presented and compared to the derived Cramer-Rao bounds for closely spaced and crossing frequency trajectories. The results show the proposed algorithms perform well compared to existing techniques