A second-order adaptive Volterra filter with rapid convergence

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An algorithm for updating the linear and quadratic weights of a second-order Volterra filter (SVF) is proposed. This algorithm uses a fast Kalman filter algorithm to calculate the Kalman gain vector used in updating the linear and quadratic weights of the SVF. The convergence of the algorithm for the quadratic weights is established. A simulation is then performed in which a fast Kalman filter implementation of an SVF is compared to an LMS implementation in a system identification problem. The fast Kalman filter implementation is shown to converge to the unknown system parameters considerably faster than the LMS implementation.