This paper presents an adaptive filtering algorithm for robot manipulators with respect to uncertainties including unknown plant parameters (e.g. load/tool changes, work piece variations,. ...etc.) when the robot dynamics are excited by random disturbances. Using standard variational arguments, we develop the necessary conditions for optimal identification. Based on these necessary conditions, we propose an algorithm for determining the unknowns and the corresponding estimated states. Kalman filter and an appropriate cost functional whose depending upon the states estimated and expected values form the basis of this algorithm. This algorithm is applied to two degree-of-freedom model of Unimation PUMA/560 Robot to illustrate the convergence of the parameters to its actual values during tracking of its end-effector.