Recursive nonlinear system identification by a stochastic gradient algorithm: stability, performance, and model nonlinearity considerations

A parameter estimation problem in a class of nonlinear systems is considered where the input-output relation of a nonlinear system is approximated by a polynomial model (e.g., a Volterra series). A least mean squares (LMS) type algorithm is utilized for the recursive estimation of the polynomial coefficients, and its resulting mean square error (MSE) convergence properties are investigated. Conditions for the algorithm stability (in the mean square sense) are established, steady-state MSE bounds are obtained, and the convergence rate is discussed. In addition, modeling accuracy versus steady-state performance is examined; it is found that an increase of the modeling accuracy may result in a deterioration of the asymptotic performance, that is, yielding a larger steady-state MSE. Linear system identification is studied as a special case.