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In this paper, the Pisarenko and MUSIC methods based on quadratic form transform are proposed for the first time to the parameters estimation of nonstationary multi-chirp signals embedded in colored noise. Compared with general approaches, the methods here have many notable virtues such as reduced computational complexity and working in low SNR almost without any prior information about colored noise. All of these virtues make the methods applicable in engineering. Simulation results justify the viability and correctness of the new methods.