Figure 4.

The figures show the uncertainty in the relative position of a vehicle driving 30 $\mathrm{m}$ (blue) and 50 $\mathrm{m}$ (red) ahead. The red and blue dots are the particle clouds, and the black ellipses are the linearized Gaussian uncertainty. Figure (a) shows the relative position in the navigation frame coordinates with a 0.5 $\mathrm{m}$ ($1\sigma$) error in the north and east direction. After rotating this position into the ego vehicle frame using the ego vehicle’s heading angle with an uncertainty of 1${}^{\circ }$ ($1\sigma$) in Figure (b) and 5${}^{\circ }$ ($1\sigma$) in Figure (c), the uncertainty in the relative position is clearly increased.