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This paper presents a novel sequential estimator for the direction-of-arrival and polynomial coefficients of wideband polynomial-phase signals impinging on a sensor array. Addressing the computational challenges of maximum-likelihood estimation for this problem, we propose a method leveraging random sampling consensus (RANSAC) applied to the time-frequency spatial signatures of sources. Our approach supports multiple sources and higher-order polynomials by employing coherent array processing and sequential approximations of the maximum-likelihood cost function. We also propose a low-complexity variant that estimates source directions via angular domain random sampling. Numerical evaluations demonstrate that the proposed methods achieve Cramér-Rao bounds in challenging multi-source scenarios, including closely spaced time-frequency spatial shelf marks, highlighting their suitability for advanced radar signal processing applications.