The fully decoupled adaptive filtering problem of nonlinear Volterra system is investigated with the input and output observation data corrupted by noise.Based on the total least mean square technology and the pseudo-linear combination structure of Volterra filter

a total fully decoupled adaptive filtering algorithm is built by using the analysis method of the constrained optimization problem to investigate Volterra filtering process.And the parameter feedback-adjusting model is also built for the convergence analysis of the proposed algorithm.The analysis indicates that the Volterra kernels can evenly converge to the real values by using this algorithm.Simulation results show that the proposed total fully decoupled adaptive filtering algorithm takes on higher robust resistance noise performance and filter precision than the fully decoupled LMS adaptive filtering algorithm

when the input and output observation data are all corrupted by noise.