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Cable driven power transmissions are used in applications such as haptic devices, surgical robots etc. The use of flexible cable based power transmission often causes relative motion between the motor actuator and mechanism joint during operation due to the elasticity of the cable. State-space control methods can be used to improve performance, but may require state estimates. For nonlinear systems, the Unscented Kalman Filter (UKF) provides a computationally efficient way to obtain state estimates. The UKF is applied here to a simulation of a minimially invasive surgical robot, to study the state estimation for a cable driven system with nonlinear dynamics. State estimates from the UKF are compared with the known states available from the simulation. These state estimates are also utilized by two different controllers interacting with the simulation to test the UKF performance under closed loop control. We tested the UKF performance with error perturbations in the system model's cable stiffness parameter.