I have a system with a motor, some masses, damping and springs. One of the masses is loaded with an unknown external force F. I want to estimate the force F using data of the motor (mainly current). There are some unknown disturbances, like temperature and friction in the system. Can this be done or are there better ways to estimate the unknown force? There will be no feedback loop. The available data will look be a time series of the current acting on the motor.
First, start with a precise mathematical description of your system. Second, analyze it observability. If the system is observable, of course you can estimate the (augmented) state vector (along with the load as an unknown parameter). In practice, there are always some factors that are often a subject to experimental estimation rather than system identification. These are, for instance, the efficiency map of the motor, liquid friction coefficient (may be estimated from the step response), motor inertia etc. I do not know which exactly feedback loop you are taking about, but the mechanical torque in electrical machines can be estimated from the current, that is true.