Yes, you can. You can amplify small differences due to an additional gravitational field. Then you can run a model with this disturbance included and optimize t

Yes, you can. You can amplify small differences due to an additional gravitational field. Then you can run a model with this disturbance included and optimize the parameters such that the difference between the observation and model vanishes. This optimization landscape is not convex however and gets more different "valleys" with time and by knowing which valley you are in you gain information there are several caviats. If there is noise in the measurement of the system this flattens the curve meaning it is harder to distinguish which valley of the object you are in. If there is noise in system itself this noise will amplified and more and more valleys become possible with time meaning at some point the system state holds almost no information about the system. However as long as the system runs the thing under measurement should not move as otherwise gets way more difficult and less possible to optimise the difference between the observed and the system behaviour for a certain in parameter under measurement. In general this approach is not advisable as the chaotic system would also need parts build to enormous precision for that not impact the system more than the signal that influences the system. So it usually better to go with a decently straight forward approach as there are different systems which also amplify small differences but are a lot simpler to work with such as the measurement bridge.