A true stochastic gradient adaptive algorithm for applications using nonlinear actuators

This work considers the practical situation where adaptive systems are subject to a saturation nonlinearity at the output of the adaptive filter. Such is the case in active control of noise and vibration. A new adaptive algorithm is proposed which implements the true stochastic gradient approach to the nonlinear problem. Deterministic nonlinear recursions are derived which model the mean weight and mean square error behaviors. The steady-state behavior is also studied. The practical aspects of nonlinearity estimation and hardware implementation are addressed. It is shown that the new algorithm outperforms the LMS algorithm even for considerable errors in estimating the nonlinearity parameters.