This paper proposes three steps of improvements for identification of the nonlinear dynamic system, which exploits the concept of a state-space based time domain Volterra model. The first step is combining the forward and backward estimator in the original Volterra model; the second step is reformulating the Volterra model into a state-space model so that the Kalman Smoother (KS) adaptive filter can be used to estimate the kernel coefficients; the third step is optimization of KS parameters using evolutionary computing algorithms such as particle swarm optimization (PSO), genetic algorithm (GA) and artificial bee colony (ABC). The applicability of the proposed methods is tested in three simulated data and one experimental data. The results show that Volterra model with PSO-KS is preferable for fast identification process, while ABC-KS method is preferable for accurate identification process. However, in some cases, as the iteration number increases the result of PSO-KS method is comparable with ABC-KS method. © 2015 Elsevier B.V. All rights reserved.