New adaptive modeling algorithms utilizing the dynamics of multidegree-of-freedom system

We propose a new adaptive modeling algorithm, nonlinear multidegree-of-freedom (NLMDF). The underlying idea is to assimilate the adaptive modeling process of iteration for the optimal solution to a particle's movement on the mean-square error (MSE) surface geometry, which is imagined to be located in the gravitational field. The new algorithm is derived by incorporating a viscous damping force in the particle movement differential equation. A new variable step size least mean square (LMS) algorithm-new variable step LMS (NVLMS)-is derived from the NLMDF algorithm by choosing specific value for the damping parameter in the NLMDF recursion. The simulation results show a faster rate of convergence for the new algorithms as compared with the damping force LMS (DFLMS) algorithm and the LMS algorithm with a white or colored noise input signal.