Proportional myoelectric control of powered prostheses requires the estimation of a time-varying control signal from the patient's myoelectric signal. Since the myoelectric signal is a zero-mean stochastic process, a nonlinearity is a necessary element of the estimator. Typically, a full-wave rectifier is used for this nonlinearity, followed by a low-pass filter to complete the estimation of the control signal. In this work, it is proposed to use a logarithmic nonlinearity, followed by a linear minimum mean-square error estimator. The logarithmic nonlinearity maps the myoelectric signal into an additive control signal-plus-noise domain in which the Kalman filter is employed to estimate the control signal. The theoretical performance of this estimator is obtained and verified by experiments.