A stochastic approximation technique has been developed for optimal state estimation in a class of systems modelled by the generalized Itô-Doob non-linear stochastic integral equation, the observation process is assumed to be available as a non-linear transformation of the state process with additive measurement errors. The theory of martingales in general, and the innovations approach in particular, have boon employed to yield conceptually simpler solution models with explicit expressions for operational implementation. Stochastic approximation techniques are utilized for numerical computation of innovations processes, and consequently the system state of non-linear dynamical systems. A comparative study of the computational results demonstrates the fact that stochastic approximation may turn out to be superior to other existing methods, in particular, the extended Kalman technique and the invariant imbedding approach, for certain optimal estimation problems. Having observed that the principal obstacle in implementation of the filter algorithm for non-linear systems rests in computation of the associated gain function, an adaptive scheme for improvement has been proposed, based on the innovations property of the filter. Some problems resulting from this study have also been mentioned for further investigation. It is envisaged that the algorithm will find application in some problems in engineering and also yield more compact bases for optimal design and control of other complex phenomena.