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This paper investigates the computationally efficient parameter estimation of polynomial phase signals embedded in noise. Many authors have previously proposed multilinear analysis methods which operate on uniformly spaced samples of the signal. Such methods include the higher-order ambiguity functions (HAFs), the Polynomial Wigner-Ville distributions (PWVDs) and the higher-order phase (HP) functions. This paper investigates the use of multilinear methods which operate on nonuniformly spaced signal samples. It is seen that the relaxation of the requirement to use uniformly spaced samples in the analysis can lead to significant performance improvements. A theoretical analysis and simulations are presented in support of these claims.