This paper presents a novel nonlinear disturbance rejection approach for high precision model-based control of hydraulic robots. While most disturbance rejection approaches make use of observers, we propose a novel adaptive Unscented Kalman Filter to estimate the disturbances in an unbiased minimum-variance sense. The filter is made adaptive such that there is no need to tune the covariance matrix for the disturbance estimation. Furthermore, whereas most model-based control approaches require the linearization of the system dynamics, our method is nonlinear which means that no linearization is required. Through extensive simulations as well as real hardware experiments, we demonstrate that our proposed approach can achieve high precision tracking and can be readily applied to most robotic systems even in the presence of uncertainties and external disturbances. The proposed approach is also compared to existing approaches which demonstrates its superior tracking performance.