Abstract-This paper details a hybrid algorithm for estimating the parameters of polynomial-phase signals (PPSs) embedded in additive white Gaussian noise. This algorithm combines the high-order ambiguity function (HAF) and the generalized cubic phase function (GCPF), and is a modification of the hybrid CPF-HAF method. In the proposed algorithm, the HAF is first applied on the original PPS to produce a cubic phase signal, whose parameters are then estimated by the GCPF, instead of the CPF. Numerical examples reveals that the signal-to-noise-ratio (SNR) threshold and mean-squared error (MSE) of the proposed approach are significantly lower than the HAF, and the SNR threshold of the proposed approach is increased by about 4dB with respect to the CPF-HAF, while the MSE is reduced by about 2dB above the threshold. In addition, the proposed approach is extended to the product version in the presence of multicomponent PPSs, where the product version of the CPF-HAF suffers from an identifiability problem.