This article is concerned with the identification of unknown parameters for a proposed non-linear time-variant, multivnriable model, that is observed in an additive statistically known white Gaussian noisy environment. The estimation problem is investigated by partitioning the system into subsequent sub-systems to yield a computationally more pragmatical solution. An optimal predictor-corrector maximum-likelihood state estimator and a stochastic hill-climbing procedure are delineated for solving the identification problem. Two particular applications are furnished to illustrate the suggested technique. In the first application, the approach presented is carried out to determine the inertia constant and damping coefficient of a synchronous machine in an unsteady operation, The second application is devoted to tho evaluation of the moments of inertia for a rigid body rotating about its principal axes and subject to external random disturbances and control torques. It is highlighted for the two preceding applications that, though the equations of motion are non-linear in the unknown quantities and/or tho state variables, the solutions obtained via partitioning are expressible in a linear form.