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In this paper, we propose an original strategy for estimating and reconstructing monocomponent signals having a high nonstationarity and long-time duration. We locally apply to short-time duration intervals the strategy developed in our previous work about nonstationary short-time signals. This paper describes a nonsequential time segmentation that provides segments whose lengths are suitable for modeling both the instantaneous amplitude and frequency locally with low-order polynomials. Parameter estimation is done independently for each segment by maximizing the likelihood function by means of the simulated annealing technique. The signal is then reconstructed by merging the estimated segments. The strategy proposed is sufficiently flexible for estimating a large variety of nonstationarity and specifically applicable to high-order polynomial phase signals. The estimation of a high-order model is not necessary. The error propagation phenomenon occurring with the known approach, the higher ambiguity function (HAF)-based method, is avoided. The proposed strategy is evaluated using Monte Carlo noise simulations and compared with the Cramer-Rao bounds (CRBs). The signal of a songbird is used as a real example of its applicability.