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A new algorithm for estimating the parameters of multiple wideband polynomial-phase signals (PPSs) in sensor arrays is developed. The spatial high-order instantaneous moments (SHIMs) are first defined using a nonlinear transformation of the array snapshot vectors. Then, the properties of SHIMs of multiple wideband PPSs are employed to obtain recursive estimates of the PPS frequency parameters. The time-frequency properties of SHIMs are then exploited for estimating the source directions-of-arrival (DOAs) using spatial time-frequency distributions (STFDs). The proposed algorithm is shown to have an improved performance compared to the chirp beamformer technique. Since our algorithm is based on multiple one-dimensional searches, it also offers a much simpler implementation avoiding multi-dimensional search, which is needed for other algorithms.