Strong consistency of nonlinear recursive algorithms of estimation of the parameters of linear difference equations (Q1177623)

This paper deals with adaptive parameter estimation for linear difference equations with known order. The authors give sufficient conditions for the a.s. convergence of estimates provided by a stochastic gradient algorithm with a gain which is a nonlinear transformation of the residual from the estimate. Once the system is written as \(y_ n=c^ T x_ n+\xi_ n\) the algorithm is written as \(c_ n=c_{n-1}+\gamma_ n\hat x_ n\varphi(\varepsilon_ n)\) where \(\hat x_ n\) is the state estimate and the residual \(\varepsilon_ n=y_ n-\hat x^ T_ n c_{n-1}\).