Determining parameters for static system

Question

So i have to determine parameters for static system: $y=o1 + o2u$

So, my idea was to pick mesurments for witch $\det[]!=0$ (2 of them as L=1 and R=2)

Parameters :$n=1 u=-2 y=9$ and $n=2 u=1 y=-2$

So i re write my thing as $y=\begin{bmatrix}o1 & o2\end{bmatrix} \begin{bmatrix}1\\u \end{bmatrix}$

So $U=\begin{bmatrix}1 & 1\\-2 &1\end{bmatrix}$

And $Y=\begin{bmatrix}9 & -2 \end{bmatrix}$

And then calulate the $o=(UU^T)^1UY^T$ there is a minus next to that 1.

Is this a sensible approach?

ps Sorry if this makes no sens, i'm really trying to get a grasp on modeling

Answer 1

You would need greater than or equal to 2 to make it more accurate. I guess 2 is OK. Let's say you have $n$ pair of data $\vec{u}$ and $\vec{y}$. Then

$$U=\begin{bmatrix} 1 & u_1\\ 1 & u_2\\ ...&...\\ 1& u_n \end{bmatrix}, U\vec{o}=\vec{y} $$

So $$\vec{o}=(U^TU)^{-1}U^T\vec{y}.$$

The determinant of $U^TU$ is not zero as long as the $u_i$'s are distinct.