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In this paper, we consider improvement of parameter estimation accuracy of multicomponent polynomial-phase signals (mc-PPSs) using the product high-order ambiguity function (PHAF). We propose a fine search method that improves the coarse estimate obtained as the position of maximum PHAF bin. The method is iterative and based on the dichotomous search. It significantly reduces the calculation complexity compared to the oversampling method. The PHAF-based estimates are, however, biased and the bias can be removed using computationally intensive nonlinear least squares (NLS) methods. These methods require initial estimates that are usually obtained from the PHAF. If the initial estimates are provided by the proposed method, the execution time can be significantly reduced.