LMS adaptation of an ARMAX model using the optimum scalar data nonlinearity algorithm

The least mean square (LMS) adaptive filter can easily predict an ARMAX model. However, it is known that this filter coefficient converges quite slowly when the input signal is corrupted by white noise. Modified LMS algorithms, in which various quantities in the stochastic gradient estimate are operated upon by memoryless nonlinearities, have been shown to perform better than the LMS algorithm. Using a scalar data nonlinearity in stochastic gradient adaptation, as an equal-eigenvalue covariance structure for the data represents the best situation for stochastic gradient adaptation. Simulation results have clearly shown the significant performance improvement of the optimum scalar data nonlinearity algorithm for ARMAX model prediction in noise conditions.