  This paper presents a new approach to detecting road boundaries based on
sparse radar signals. We model the roadway using a homogeneous model and derive
its conditional predictive model under known radar motion. Using the
conditional predictive model and model radar points using a Dirichlet Process
Mixture Model (DPMM), we employ Mean Field Variational Inference (MFVI) to
derive an unconditional road boundary model distribution. In order to generate
initial candidate solutions for the MFVI, we develop a custom Random Sample and
Consensus (RANSAC) variant to propose unseen model instances as candidate road
boundaries. For each radar point cloud we alternate the MFVI and RANSAC
proposal steps until convergence to generate the best estimate of all candidate
models. We select the candidate model with the minimum lateral distance to the
radar on each side as the estimates of the left and right boundaries. We have
implemented the proposed algorithm in C++. We have tested the algorithm and it
has shown satisfactory results. More specifically, the mean lane boundary
estimation error is not more than 11.0 cm.
