A method is presented for estimating an unknown parameter of a distributed parameter system which depends on the system state. The system considered is modelled by a class of non-linear partial differential equations of a parabolic type. Noisy observations are assumed to be taken through an arbitrary number of sensors allocated on the spatial region. First, the explicit form of the stationary solution of the state equation is discussed. Second, use is made of the maximum likelihood approach to obtain the optimal estimate of the unknown parameter. Consistency properties w.p.1 of the optimal estimate obtained are also shown. Finally, results of digital simulation experiments are included to support the theoretical aspects.