With a state-space model of a system
$$\dot{x}=Ax+Bu$$
and an estimator
$$\dot{\hat{x}}=A\hat{x}+Bu+L(y-C\hat{x})$$
Remember that \(u=-Kx\) and \(y=Cx\). These can then be combined into a single state-space representation
$$\begin{bmatrix}
\dot{x} \ \dot{\hat{x}}
\end{bmatrix}=
\begin{bmatrix}
A & -BK \
LC & A-BK-LC
\end{bmatrix}
\begin{bmatrix}
x \ \hat{x}
\end{bmatrix}=[A]_{combined}
\begin{bmatrix}
x \ \hat{x}
\end{bmatrix}$$
Swapping the estimator (L) and (K) gains can sometimes give better performance in the presence of noise and actuator limits
[[OGLI Simulation Program]] – used a mid-course estimator
- bevlyMECH4420Lectureb