I'm tracking the state of a robot using an EKF defined by:
$$(x,y,\theta)$$
where $x$ and $y$ are the coordinates in the ground-plane and $\theta$ the heading angle.
I initialized the covariance matrix $P$ to the following values: 
$$P
= 
\begin{bmatrix}
\sigma\_{xx}^2 & 0 & 0 \\
0 & \sigma\_{yy}^2 & 0 \\
0 & 0 & \sigma\_{\theta \theta}^2 \\
\end{bmatrix}
$$
where $\sigma\_{xx}=1$, $\sigma\_{yy}=1$ and $\sigma\_{\theta \theta }=0.1$

In the system i'm using, valid measurements are rearely obtained so the predicted covariance matrix becomes very big.
My question concerns the angle uncertainty, the angle is predicted from angle increments $\Delta\_{theta}$ so, at each time stamp $k$:
$$\theta=\theta+\Delta\_{theta\_{k}}$$
We wrap the value of the obtained angle to make $\theta\in[-\pi,\pi]$.
Does the uncertainty have to be also wrapped to the interval $[-\pi,\pi]$? means that making $\sigma\_{\theta }\in[-\pi,\pi]$?