  Simultaneous localization and mapping (SLAM) using automotive radar sensors
can provide enhanced sensing capabilities for autonomous systems. In SLAM
applications, with a greater requirement for the environment map, information
on the extent of landmarks is vital for precise navigation and path planning.
Although object extent estimation has been successfully applied in target
tracking, its adaption to SLAM remains unaddressed due to the additional
uncertainty of the sensor platform, bias in the odometer reading, as well as
the measurement non-linearity. In this paper, we propose to incorporate the
Bayesian random matrix approach to estimate the extent of landmarks in radar
SLAM. We describe the details for implementation of landmark extent
initialization, prediction and update. To validate the performance of our
proposed approach we compare with the model-free ellipse fitting algorithm with
results showing more consistent extent estimation. We also demonstrate that
exploiting the landmark extent in the state update can improve localization
accuracy.
