Identification of certain time-varying nonlinear Wiener andHammerstein systems

The problem of identification and tracking of time-varying nonlinear systems is addressed. In particular, the Wiener system that consists of a dynamic time-varying linear part followed by a fixed nonlinearity and the Hammerstein system in which the order of these two blocks is reversed are studied. The extended Kalman filter (EKF) algorithm is applied. It is also shown that this algorithm can be reformulated in terms of a nonlinear minimization problem with a quadratic inequality constraint in order to ensure exponential stability, resulting in the algorithm CEKF. As indicated by means of numerical examples, this latter algorithm is less sensitive to the chosen initialization than the EKF. The proposed algorithms depend on certain second-order statistics that may be unknown in a typical scenario. A method for estimation of these quantities is proposed. It is demonstrated that the suggested algorithms can be successfully applied to the problem of acoustic echo cancelation     

Compensation of the RLS algorithm for output nonlinearities

It is shown how the recursive least squares (RLS) algorithm can be modified to compensate for a priori known errors of linearity in the output measurement. A novel signal model is used for this purpose. Only the nonlinear effects are modeled by an output error model, and much of the output measurements are used directly in the regression vector. The main benefit with this approach is that the advantages of the RLS, like quick initial convergence for infinite impulse response models, can be retained for small linearity errors. At the same time the output nonlinearity is allowed to be noninvertible. This can be important to treat, for example, small deadzones and also to avoid the amplification of additive measurement disturbances. Such amplification can result from inversion of the output nonlinearity. Simulations illustrate the performance of the algorithm