Abstract: A speech processing system (30) operates in a noisy environment (20) by performing adaptive prediction between inputs from two sensors positioned to transduce speech from a speaker, such as an accelerometer and a microphone. An adaptive filter (37) such as a finite impulse response (FIR) filter receives a digital accelerometer input signal, adjusts filter coefficients according to an estimation error signal, and provides an enhanced speech signal as an output. The estimation error signal is a difference between a digital microphone input signal and the enhanced speech signal. In one embodiment, the adaptive filter (37) selects a maximum one of a first predicted speech signal based on a relatively-large smoothing parameter and a second predicted speech signal based on a relatively-small smoothing parameter, with which to normalize a predicted signal power. The predicted signal power is then used to adapt the filter coefficients.