We present a method for sequentially estimating time-varying noise parameters. Noise parameters are sequences of time-varying mean vectors representing the noise power in the log-spectral domain. The proposed sequential Monte Carlo method generates a set of particles in compliance with the prior distribution given by clean speech models. The noise parameters in this model evolve according to random walk functions and the model uses extended Kalman filters to update the weight of each particle as a function of observed noisy speech signals, speech model parameters, and the evolved noise parameters in each particle. Finally, the updated noise parameter is obtained by means of minimum mean square error (MMSE) estimation on these particles. For efficient computations, the residual resampling and Metropolis-Hastings smoothing are used. The proposed sequential estimation method is applied to noisy speech recognition and speech enhancement under strongly time-varying noise conditions. In both scenarios, this method outperforms some alternative methods.