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In this letter, the maximum a posteriori (MAP) framework is introduced to sequentially estimate noise parameters. The estimation is implemented with the first-order vector Taylor series (VTS) approximation to the nonlinear environmental function in the log-spectral domain. The MAP noise estimation provides a mathematical framework, in which several previously published sequential estimation solutions are special cases. Experimental evaluation on the Aurora 2 database shows that the MAP solution can provide consistent performance improvement compared to the recently published ML algorithm, though the performance improvement is limited.