A system is observable is the observed outputs uniquely determine any initial state. You determine observability by checking the rank of the observability matrix, A system is observable if and only if \(rank(O_n)=n\)
$$0=\begin{bmatrix}
C \
CA \
CA^2 \
\vdots \
CA^{n-1}
\end{bmatrix}$$
You need a measurement of the lowest derivative state in order to be observable. For instance, you can observe velocity from position measurements, but you can’t observe position measurements from velocity.
[[N4SID]] – find observability matrices for systems
[[SEAMAC]] – uses observable modes
State-Space Estimators – gain matrix can be solved for desired eigenvalues if the system is observable
[[State-Space model with Sensor Bias]] – A system with sensor bias might not be observable
[[Sigma Weighting Matrix]] – slow modes are unobservable as gain increases
[[Orion Navigation System]] – some states are minimally observable
[[State Observers]]
- EasyIntroductionObservability
- bevlyMECH4420Lectureb