| Yes: both observability and parameter identifiability assume knowledge of the model structure; system identification includes methods for choosing a model structure for a black-box system. > This is why I never understood why this analysis was very helpful If a system is not identifiable/observable, there may be multiple values for the parameters/state (respectively) that are consistent with observations; if you try to infer these without checking for identifiability/observability, you may obtain values that are consistent with observations but very different to the true values, which can result in serious errors when you try to do something using them. > it isn't very useful outside of the specific experiment / motion / inputs used There are cases where some parameters cannot be identified regardless of what inputs are provided to the system. For example, when you write down the differential equations governing the system in a particular way, you might see that two parameters (k1 and k2) always appear together as a product (k1 * k2), never independently - so their individual values are not identifiable, though (k1 * k2) is; this could be fixed by re-parametrising, by replacing k1 * k2 by k3. Also, some parameters have very little effect on the behaviour of a system, so are weakly constrained by observations ("sloppiness"), whilst others are more tightly constrained - it can useful to know which are which. |