We present an algorithm for recursive estimation of parameters in a mildly nonlinear model involving incomplete data. In particular, we focus on the time-varying deterministic parameters of additive noise in the nonlinear model. For the nonstationary noise that we encounter in robust speech recognition, different observation data segments correspond to different noise parameter values. Hence, recursive estimation algorithms are more desirable than batch algorithms, since they can be designed to adaptively track the changing noise parameters. One such design based on the iterative stochastic approximation algorithm in the recursive-EM framework is described in this paper. This new algorithm jointly adapts time-varying noise parameters and the auxiliary parameters introduced to linearly approximate the nonlinear model. We present stereo-based robust speech recognition results for the AURORA task, which demonstrate the effectiveness of the new algorithm compared with a more traditional, MMSE noise estimation technique under otherwise identical experimental conditions.