Strong consistency results for a class of nonlinear approximate maximu
m likelihood algorithms for robust system identification are developed
, where the system is assumed to be of the ARMAX form. The analysis us
es the Martingale results, and strong consistency is shown to hold und
er a new assumption, representing a generalization of the strictly pos
itive-real condition. Arguments are also given for using Huber's nonli
nearity, in order to reduce the influence of outliers in practice.