State-space filters in fixed-point?
Do a similarity transform on the state-space equation*.
I'm assuming your original system is
$$\begin{matrix}
x_n = A x_{n-1} +  B u_n \\
y_n = C x_n
\end{matrix}$$
Let
$T = \begin{bmatrix} 1 &amp; 0 \\ 0 &amp; 5 \cdot 10^{-8}\end{bmatrix}$ (Note that I arbitrarily chose this by educated eyeball and some messing around -- any $T$ that is invertible will work in theory, so you're free to chose one that makes your problem pretty.)
Then define $\chi_n = T x_n$. The system
$$\begin{matrix}
\chi_n = T^{-1} A T \chi_{n-1} + T^{-1} B u_n \\
y_n = C\,T\,\chi_n
\end{matrix}$$
has exactly the same input-output dynamics as your original system.  The difference is that $T^{-1} A T \simeq \begin{bmatrix}0.98992389 &amp; -0.00584622 \\0.00868056 &amp; 1\end{bmatrix}$ is much better conditioned numerically.  You'll still have the issue that your C matrix is &quot;poorly conditioned&quot;, but that pretty much means that the second element of $\chi$ doesn't have much effect on your final answer.
* &quot;Linear Systems&quot; by Thomas Kailath, pp 53-54, Prentice-Hall, 1980